第八章扭量光影初步

8.2 无形式的物质与有形式的物质

8.2 Matter-without-form and matter-with-form

　

         杨富斌写道,

         有人把道家哲学所讲的"无"译为"being-without-form",即"无形式的存在",而把"有"译为"being-with-form",即"有形式的存在",这是颇为传神的.(《怀特海过程哲学研究》,190页.)

　

YANG Fubin wrote:

Someone translates "wu" and "you" in Taoist philosophy into "being-without-form" and "being-with-form"; this is quite vivid. (On Whitehead's Process Philosophy, p. 190.)

　

         道家哲学所讲的"无"的意思是"无形式的物质","有"的意思是"有形式的物质".

The "wu" and "you" in Taoist philosophy means "matter-without-form" and "matter-with-form".

　

          老子在《道德经》的第二章指出:

有无相生.

有形式的物质与无形式的物质互相变成.

　

In Chapter 2 of Tao-te-Ching, Lao-Tzi pointed out:

Matter-with-form and matter-without-form become each other.

　

8.2.1 计算变成实在是物质的形式的转化的过程

8.2.1 Computing-becoming reality is the process of transformation in the form of matter

　

         鲁品越指出:

         事物就是过程—就是在与其他事物的内在联系中(包括人类实践中)不断创造和展现自身存在的过程.

         客体本身并不是孤立的"自我存在物",而是它在各种相互作用情境下的各种表现之总和.

(《深层生成论:自然科学的新哲学意境》,422页.)

LU Pinyue pointed out:

Things are processes - processes of constantly creating and manifesting their existence through their inner connections with other things (including through human praxis).

An object itself is not an isolated "self existent", but the sum total of all kinds of behaviours under various kinds of circumstances of interactions.

(Theory of generation in the depths: a new philosophical vista of natural sciences, p. 422.)

　

         根据怀特海的著作 Process and Reality 第22-23页,存在就是变成(becoming)的过程.

According to pages 22-23 of the book Process and Reality by Whitehead, being is a process of becoming.

　

         迈克斯·泰格马克在他的书《穿越平行宇宙》的第274、271页指出:

         我们生活在一种"关系实在"中,因为我们周围世界的性质并不是来源于它的终极构件的性质,而是来源于这些构件相互之间的数学关系.这样就解决了棘手的"无穷后退问题",在这个问题中,自然界的物体的性质只能由它的构件的性质来解释,而组成构件的性质又需要进一步解释,从而衍生出无穷无尽的问题.

　

On pages 266, 267, and 271 of his book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, Max Tegmark pointed out:

　

We live in a relational reality, in the sense that the properties of the world around us stem not from properties of its ultimate building blocks, but from the mathematical relations between these building blocks. Thus we solve the thorny infinite regress problem where the properties of nature can only be explained from the properties of its parts, which require further explanation, ad infinitum.

　

         行星地球在宇宙中运动着.因此在"无形式的物质"里,"有形式的物质"好像是运动着的数学关系.不仅从无形式的物质到有形式的物质需要计算,从有形式的物质到无形式的物质也需要计算.

The planet Earth is moving in the universe. Hence in "matter-without-form", "matter-with-form" is like the moving mathematical relation. Computing is necessary not only from matter-without-form to matter-with-form, but also from matter-with-form to matter-without-form.

　

         就像河水中映出的月亮,关系相对于其载体在运动着,产生着计算.计算变成实在不是构成的.计算变成实在是"变成"的过程.

As the moon reflected on river water, a relation moves with respect to what bears the relation, generating computing. The computing-becoming reality is not constructive. A computing-becoming reality is a process of "becoming".

　

计算变成实在是物质的形式的转化的过程.      (8.2.1-1)

　

Computing-becoming reality is the process of transformation in the form of matter.      (8.2.1-1)

　

         孙子在《孙子算经》的序中指出:

夫算者,阴阳之父母,群生之元首,万物之祖宗.

　

In the preface of his book Sun-tzu's Book of Computing, Sun-tzu pointed out:

         Computing is father and mother of yin and yang, the beginning of living things, and everything's ancestry.

　

扭量光影是计算变成实在.        (8.2.1-2)

　

The twistor-light-silhouette is computing-becoming reality.        (8.2.1-2)

　

8.2.2 挑选合适的数学,串起神秘的现象

8.2.2 Select the right math to string mysterious phenomena together

　
         扎比内·霍森费尔德在她的书《迷失》中写道:
         有必要以观察为引导.
         物理不是数学,是选择合适的数学.(《迷失》第315页.)
　
In her book Lost in Math: How Beauty Leads Physics Astray, Sabine Hossenfelder wrote:
    Observational guidance is necessary.
    Physics isn't math. It's choosing the right math. (Lost in Math: How Beauty Leads Physics Astray, p. 234.)
　

         要求新理论有一致性—既内在一致,也跟实验一致,跟所有实验都要一致,这才是物理学如此困难的原因.(《迷失》第12页)

It's the requirement that a new theory needs to be consistent, both internally consistent and consistent with experiment—with each and every experiment—that makes it so difficult. (Lost in Math: How Beauty Leads Physics Astray, p.9.)
　
         数据不再不请自来,我们必须知道上哪儿去找数据, ...(《迷失》第49页.)
Data don't come to us anymore—we have to know where to get them, ... (Lost in Math: How Beauty Leads Physics Astray, p. 35.)
　
         有能力适应新证据,才能成为真正的科学家.(《迷失》第55页.)
It is the ability to adapt to new evidence that marks the true scientist. (Lost in Math: How Beauty Leads Physics Astray, p. 39.)
　

挑选合适的数学,串起神秘的现象.      (8.2.2-1)

　

Select the right math to string mysterious phenomena together.      (8.2.2-1)

　

8.3 经由虚处发展

8.3 Developing via where there is feebleness

         王弼(226~249)在评论《道德经》时写道："以无为用".

WANG Bi (226~249), when commenting on Tao-te-Ching, wrote,

         Make use of the void.

经由虚处发展的规律      (8.3-1)

　

The law of developing via where there is feebleness      (8.3-1)

         (8.3-1)所述的生成原则与斯特恩-盖拉赫实验所显示的现象是一致的.

The generative principle stated in (8.3-1) is consistent with the phenomenon shown in the Stern-Gerlach experiment.

         经由虚处发展的例子有莫比乌斯环型反引力、阴影、莫比乌斯环、旋量、扭量、CPT 联合反演.

Examples of developing via where there is feebleness are Möbius-loop-typed antigravitation, shadows, Möbius loops, spinors, twistors, and the combined CPT transformation.

8.3.1 莫比乌斯环

8.3.1 A Möbius loop



从拓扑学上讲,莫比乌斯环的边缘是一个圆周.马克·阿姆斯特朗的著作《基础拓扑学》的第1.5节指出:

注意 Möbius 带的边缘是由一整个圆周构成,所以只需将这个圆周与球面上所开圆洞的边界圆周粘起来便可. ...... 所得到的闭曲面叫作射影平面.

                                                                                     (8.3.1-1)



Topologically, the boundary of a Möbius loop is a circle. Section 1.5 of M. A. Armstrong's book Basic Topology states:

　

The Möbius loop has after all a single circle as boundary, and all that we are asking is that the points of this boundary circle be identified with those of the boundary circle of the hole in the sphere. ... The resulting closed surface is called the projective plane.

                                                                                                           (8.3.1-1)

　

         让一条纸带正面的中点和背面的中点分别代表 +0 和 -0 ,让纸带的两端分别代表 + ¥ 和 - ¥ ;将这条纸带做成没有厚度的拓扑莫比乌斯环,它可以称为射影莫比乌斯环

         从拓扑学和物理学上看,射影莫比乌斯环有很多含义:

1. 从拓扑学上讲,射影莫比乌斯环没有厚度, + ¥ 和 - ¥ 是同一个点.

2. 拓扑射影莫比乌斯环可大可小,没有确定的长度,也没有确定的宽度.

3. 中心的圆周代表零、正与负的复合体.

4. 射影莫比乌斯环有挠率.

5. 最基本的射影莫比乌斯环的内部自旋是 1/2 (这对应着费米子),外部自旋是 1 (这对应着玻色子).

6. 射影莫比乌斯环的"零"分为 +0 和 -0 .

                                                                     (8.3.1-2)

　

Let the middle points of the front side and the reverse side of a strip of paper represent +0 and -0 respectively; let the two ends of the strip represent +¥ and -¥ respectively; make the strip into a topological Möbius loop which has no thickness, and such a Möbius loop can be called a projective Möbius loop.

　

From the perspectives of topology and physics, the projective Möbius loop has many implications.

1. Topologically, the projective Möbius loop has no thickness; + ¥ and - ¥ are the same point.

2. A topological projective Möbius loop can be large or small; there is not a definite length nor a definite width on the projective Möbius loop.

3. The central circle represents the null and a compound of the positive and the negative.

4. A projective Möbius loop has torsion.
5. For a most fundamental projective Möbius loop, the internal spin is 1/2 (This corresponds to a fermion), and the external spin is 1 (This corresponds to a boson).
6. The "zero" on a projective Möbius loop is divided into +0 and -0.
                                                                                                                                   (8.3.1-2)

　

8.3.2 莫比乌斯环型反引力场发动机与扭量空间互为发生器

8.3.2 The Möbius-loop-typed antigravitation engine and twistor space are each other's generators

　

         仅当计算变成实在的惯性系被反引力拖曳时才存在的现象和物理量称为反引力现象和反引力物理量.反引力物理量属于非局域量.产生反引力的计算变成实在可以叫作反引力源.其惯性系被反引力场拖曳的物体可以叫作反引力物体.

Phenomena and physical quantities which exist only when the inertial frame of a computing-becoming reality is being dragged by antigravitation are called the antigravitational phenomena and antigravitational physical quantities. Antigravitational physical quantities are nonlocal quantities. The computing-becoming reality that generates antigravitation can be called the antigravitation source. An object whose inertial frame is dragged by the antigravitational field can be called an antigravitational object.

         根据彭罗斯的著作《通向实在之路》694页和《旋量与时空》第2卷128页,只有扭量空间能既与复数空间兼容又与与广义相对论所需要的四维空间兼容.

According to page 974 of The Road to Reality and page 128 of Spinors and Space-Time, Vol. 2 by Penrose, only twistor space is compatible both with complex space and with the 4-dimensional space required by general relativity.

莫比乌斯环型反引力的生成原理

　

         假设物体B是一个完全对称的宏观物体,它在沿着 x 轴运动,假设 x 轴是一个圆周.

　

         由于洛仑兹收缩效应,物体 B 的正前方和正后方的空间曲率相对较大.鉴于爱因斯坦的旋转圆盘,物体B的短程线将弯曲进入看不见的复数空间：像莫比乌斯环(莫比乌斯环有挠率)那样先离开 x 轴,绕过空间曲率大的区域后再接近 x 轴.当物体 B 沿此弯曲的短程线运动时,又产生了新的空间曲率相对较大的区域,于是短程线要躲开这个区域,因此在到达 x 轴后,它要从 x 轴的另一侧像莫比乌斯环那样绕过空间曲率相对较大的区域.这样,物体 B 的短程线挠曲扭转,变成了一条没有宽度的莫比乌斯环,短程线近似地成为一条圆形的正弦曲线.

　

         莫比乌斯环有挠率.如果物体B周围的空间出现了对称破缺,那么就会出现反引力(即惯性力场的惯性系拖曳效应),这种反引力可以叫做莫比乌斯环型反引力,物体 B 可以叫做反引力场发动机.对称破缺会使反引力定向.

　

        只有扭量空间能既与复数空间兼容又与广义相对论所需要的四维空间兼容.因此物体 B 进入了扭量空间.莫比乌斯环型反引力将闵可夫斯基空间变为扭量空间,从而改变了空间的曲率,这使物体 B 失去了引力质量,并根据等效原理而失去了惯性质量,使闵可夫斯基空间里的有质量粒子变为扭量空间里的无质量粒子.当莫比乌斯环型反引力不够强时,空间处于闵可夫斯基空间与扭量空间的动态平衡之中.

　

         莫比乌斯环型反引力场发动机与扭量空间互为发生器.



         因此莫比乌斯环型反引力场发动机既是扭量空间发生器,又是不可定向空间发生器;它将反引力物体的空间变为扭量空间,并产生不可定向空间曲率.

　

         运动和反引力倾向于避开空间曲率较大处,这是经由虚处的计算变成.

　

         一方面, 洛仑兹收缩效应是运动学效应,不受力的影响.另一方面,我们知道,如果小路在一个狭窄的走廊里延伸,那么小路就不能曲曲弯弯.因此反引力效应具有"非全即无"的性质,依阻力是否足够小而定.

　

         反引力场是耗散结构,产生秩序.

　

         (请参看我的论文《UFO：现象、理论、实验, 附录》和本网站的第二章.)

　

                                                                                                                                                                       (8.3.2-1)

　

The generative principle of Möbius-loop-typed antigravitation

Suppose that Body B is a perfectly symmetrical macroscopic object, which is moving along the x-axis, and suppose that the x-axis is a circle.

　

Because of Lorentz contraction, the space curvatures both in front of and at the back of Body B are comparatively large. In view of Einstein's spinning disc, the geodesic of Body B will be bent, entering invisible complex space: first, like a Möbius loop (the Möbius loop has torsion), it will leave the x-axis, go round the large-curvature area, and then get near the x-axis. When Body B moves along this bent geodesic, a new area where the space curvature is comparatively large forms. Then the geodesic will avoid this area, and hence, when arriving at the x-axis, it will go round the area where the space curvature is comparatively large by way of the other side of the x-axis, like a Möbius loop. Thus the geodesic of Body B is twisting around, becoming a Möbius loop without width, and the geodesic is approximately a circular sinusoid.

　

The Möbius loop has torsion. If symmetry breaking occurs in the space around Body B, then there will be antigravitation (i.e. an inertial-frame-dragging effect of an inertia force field), which can be called Möbius-loop-typed antigravitation, and Body B becomes a Möbius-loop-typed antigravitation engine. Symmetry breaking will give an orientation to the antigravitation.

　

Only twistor space is compatible both with complex space and with the 4-dimensional space required by general relativity. Hence Body B has enter twistor space. Möbius-loop-typed antigravitation changes Minkowski space into twistor space, thereby changing the curvature of space; this makes Body B lose its gravitational mass, and, according to the equivalence principle, lose its inertial mass, turning a massive particle in Minkowski space into a massless particle in twistor space. When Möbius-loop-typed antigravitation is not strong enough, the space is in dynamic equilibrium between Minkowski space and twistor space.

　

The Möbius-loop-typed antigravitation engine and twistor space are each other's generators.

　

Hence a Möbius-loop-typed antigravitation engine is both a twistor-space generator and a non-orientable-space generator; it changes the space of an antigravitational object into twistor space, and it generates non-orientable space curvatures.

　

Motion and antigravitation tend to keep away from where the space curvature is larger, and this is the computing-becoming via where there is feebleness.

　

On the one hand, Lorentz contraction is a kinematical effect and is not affected by forces. On the other hand, if a path stretches in a narrow corridor, then the path cannot run in zigzags. Hence antigravitational effect has the nature of "whole, or none", depending on whether the resistance is small enough.
　
The antigravitational field is a dissipative structure, generating order.
　
(Refer to my paper UFO: Phenomena, Theories and Experiments, Appendix and Chapter 2 of this website.)
                                                                                                                                                                                      (8.3.2-1)

　

鉴于(8.3.1-2),莫比乌斯环型反引力最基本的自旋是 1/2 .      (8.3.2-2)

　

In view of (8.3.1-2)), the most fundamental spin of Möbius-loop-typed antigravitation is 1/2 .      (8.3.2-2)

　

         仅当计算变成实在的惯性系被反引力拖曳时才存在的现象和物理量称为反引力现象和反引力物理量.反引力物理量属于非局域量.产生反引力的计算变成实在可以叫做反引力源.其惯性系被反引力拖曳的计算变成实在可以叫做反引力计算变成实在.

　

The phenomenon and the physical quantity which exists only when the inertial frame of computing-becoming reality is being dragged by antigravitation is called the antigravitational phenomenon and the antigravitational physical quantity. The antigravitational physical quantity is nonlocal quantity. The computing-becoming reality that generates antigravitation can be called the antigravitation source. The computing-becoming reality whose inertial frame is dragged by antigravitation can be called antigravitational computing-becoming reality.

        一方面, 洛仑兹收缩效应是运动学效应,不受力的影响.另一方面,我们知道,如果小路在两个障碍物之间延伸,小路就不能曲曲弯弯了.类似地,如果物体B受到的正方向或负方向的力太大,则沿B的正方向或负方向就不会出现反引力.

On the one hand, Lorentz contraction is a kinematical effect and is not affected by forces. On the other hand, if a path stretches between two obstacles, then the path can not run zigzag. Similarly, if Body B receives too large a force in the front or back direction, then antigravitation in the front or back direction of Body B will not appear.

         关于反引力场发动机,见"反引力场发动机"网站第三章.它是一台莫比乌斯环型反引力场发动机.

For the antigravitation engine, see Chapter 3 of Antigravitation Engine Site. It is a Möbius-loop-typed antigravitation engine.
　

莫比乌斯环型反引力具有"非全即无"的性质,依阻力是否足够小而定:
当 | a_反引力 | > | ∑R | 时, | ∑R | 变为零;

当 | ∑R |≥ | a_反引力 | 时, | a_反引力 | 变为零;

其中 a_反引力是反引力加速度, | ∑R |是不包含a_反引力在内的沿反引力的前方方向的合加速度的绝对值.

(9.2(4)-1a)和(9.2(4)-1b)是一个实际的例子.
                                                                       (8.3.2-3)

　

Möbius-loop-typed antigravitation has the nature of "whole, or none", depending on whether the resistance is small enough:
if | a_{antigravitational} |> | ∑R | , | ∑R | becomes zero;

if | ∑R |≥ | a_{antigravitational} |, a_{antigravitational} becomes zero;

where a_{antigravitational} is antigravitational acceleration; | ∑R | is the absolute value of the resultant acceleration which is along the front direction of the antigravitational acceleration, excluding a_{antigravitational} .

For an actual example, see(9.2(4)-1a) and (9.2(4)-1b).

                                                                                                                                                        (8.3.2-3)

　

         (8.3-1)所述的生成原则与斯特恩-盖拉赫实验所显示的现象是一致的.

The generative principle stated in (8.3-1) is consistent with the phenomenon shown in the Stern-Gerlach experiment.

当 | ∑R |≥ a_反引力时,反引力倾向于避开阻力.         (8.3.2-4)

　

When | ∑R |≥ a_{antigravitational} , antigravitation tends to keep away from resistance.         (8.3.2-4)

　

　

由于具有非全即无的性质,莫比乌斯环型反引力可以像外壳那样护送被拖曳的物体,直到反引力消失.         (8.3.2-5)

　

Having the nature of "whole, or none", Möbius-loop-typed antigravitation is able to serve as a shell escorting the body being dragged until the antigravitation disappeares.         (8.3.2-5)

　

由(8.3.2-3)可以知道,莫比乌斯环型反引力只存在于特定层级和特定方向.莫比乌斯环型反引力突然出现,突然消失.         (8.3.2-6)

　

From (8.3.2-3) one can know that Möbius-loop-typed antigravitation exists only in specific hierarchies and specific directions. Möbius-loop-typed antigravitation appears all at once, and disappears all at once.                                                                                                                                     (8.3.2-6)

　

         这有助于解释下面的事实：布鲁斯·杰农^[1]和他的父亲曾经在他们自己的飞机里飞入了奇怪的云隧道,他写道：

刚一进入云,我们就目睹了一种神秘的景象.天色变得又暗又黑... 没有闪电,只有异常明亮的白色闪光... 云壁是完美的圆形,在慢慢地紧缩.云壁上到处都喷出小云朵, ... 在飞机周围逆时针自转. ... 大约有五秒钟我离奇地感觉到失去了重量,并且感受到一股向前增加的动量. ... 当我向后看时,我倒吸了一口气,吃惊地看见隧道壁瓦解了,形成了一道缓慢地顺时针旋转着的缝隙.

This helps to explain the following fact: Bruce Gernon^[1] and his fatheronce, in their own plane, flew into a strange cloud tunnel. He wrote:

Upon entering the cloud we witnessed an uncanny spectacle. It became dark and black... There were no lightning bolts, only extraordinarily bright white flashes... The walls were perfectly round and slowly constricting. All around the edges were small puffs of clouds... swirling counterclockwise around the airplane. ... For about five seconds I had the strange feeling of weightlessness and an increased forward momentum. When I looked back, I gasped to see the tunnel walls collapse and form a slit that slowly rotated clockwise.

[1] http://www.bermuda-triangle.org/bruce_gernon.html

[1] http://www.bermuda-triangle.org/bruce_gernon.html

　

莫比乌斯环型反引力使反引力物体进入不可定向的射影空间从而进入一种失去内侧和外侧之间的边界的特殊状态.      (8.3.2-7)

　

Möbius-loop-typed antigravitation brings an antigravitational object into nonorientable projective space and hence into a special state of losing the boundary between the inside and the outside.         (8.3.2-7)

　

8.3.3 向虚涨落

8.3.3 Feebleness-oriented fluctuation

　

         请参看汪克林和曹则贤的著作《量子物理若干基本问题》第4页.

Please refer to p. 4 of WANG Kelin and CAO Zexian's book Some Fundamental Problems in Quantum Physics.

　

         薛定谔指出,

凡是既有内部自由度又有外部自由度且两者间存在能量交换的物理系统都会具有颤动现象.(《量子物理若干基本问题》,第004页)                                  (8.3.3-1)

　

Schrӧdinger pointed out that

Any physical system with both internal and external degrees of freedom and energy exchange between the two will have the phenomenon of trembling motion.
(Some Fundamental Problems in Quantum Physics, p. 004)                              (8.3.3-1)

　

         在该书第004页的图1.1.1中,有一列行进中的列车.车厢壁上有一个弹簧,弹簧与列车的速度平行.在弹簧的中点有一个小球.小球在极迅速地来回振动.小球的瞬时速度很大,但大时间尺度上的表观速度是列车的行进速度.

There is a moving train in Fig. 1.1.1 on p. 004 of the above-mentioned book. On the wall of the carriage there is a spring, which is parallel to the speed of the train. In the middle of the spring there is a small ball. The ball is vibrating back and forth very quickly. The instantaneous speed of the ball is very large, but the superficial speed on a large time scale is the speed at which the train is traveling.

　

         上述的颤动可以称为向虚涨落.

The above-mentioned trembling motion can be called feebleness-oriented fluctuation.

　

         根据特里斯坦·尼达姆(Tristan Needham)的书《可视化微分几何和形式：一部五幕数学正剧》,

　

曲率是相邻测地线之间的作用力.如果两条相邻的测地线轨迹穿过一个正曲率的区域,它们就会相互吸引.另外,穿过一个负曲率区域的两条相邻测地线轨迹会相互排斥,并加速分离.在这两种情况下,吸引力和排斥力都是与两条测地线的间隔成比例的,而且这个(局部的)比例"常数"等于曲面在质点所在位置的曲率! 这就是雅克比的发现的本质.测地线偏移方程(即雅克比方程)还有一个完全不一样的名字,称为谐振子方程,在物理学(经典领域和量子领域)中无处不在.由牛顿第二运动定律得到的运动方程与雅克比方程完全相同,只是用弹簧的弹性系数代替了曲面的曲率.砝码以正弦曲线上下振动.
(见特里斯坦·尼达姆(Tristan Needham)的书《可视化微分几何和形式：一部五幕数学正剧》第310、312、313页.)
　
                                                                                                 (8.3.3-2)

　
According to Tristan Needham's book Visual Differential Geometry and Forms: A mathematical drama in five acts,
　

Curvature is a force between neighbouring geodesics. If two neighbouring geodesics pass through a region of positive curvature, they are attracted to each other. On the other hand, neighbouring geodesics travelling through a region of negative curvature are repelled by each other, accelerating apart. In both cases, the force of attraction or repulsion is directly proportional to the separation of the geodesics, and (locally) the proportionality "constant" is equal to the curvature of the surface at the location of the particle! This is essence of Jacobi's discovery. This Equation of Geodesic Deviation also goes by a quite different name—it is the equation of the harmonic oscillator, which is ubiquitous in physics, in both the classical and quantum realms. Newton's Second Law of Motion now yields exactly the same equation of motion as Jacobi's Equation, but with the surface's curvature replaced by the spring's stiffness. The weight oscillates up and down, sinusoidally.
(See Tristan Needham's book Visual Differential Geometry and Forms: A mathematical drama in five acts. pp. 269, 271, 272.)
　
                                                                                                               (8.3.3-2)

　
         彭罗斯关于zig粒子和zag粒子的观点如下.(见《通向实在之路》§ 25.2.)

Penrose's idea of the zig particle and the zag particle is as follows. (See The Road to Reality, § 25.2.)

         狄拉克方程可以写成耦合了这两个二维旋量的方程,每一个都作为另一个的"源"而起作用.从这些方程的形式我们看到,狄拉克电子可以被看做是由两种成分组成的.让我们将其称为 "zig" 粒子和 "zag" 粒子.作为无质量粒子,它们每一个都以光速运动,但更确切地说,我们可以将它们看成是在来回"摇晃".实际上,这就是那种所谓的 zitterbewegung 现象的实在化.电子(和其他自旋1/2的有质量粒子)可以看作是在时空里左旋的无静质量 zig 粒子和右旋的无静质量 zag 粒子之间的振荡,振荡频率本质上就是电子的德布罗意频率.虽然速度的方向在不断地反转,但在电子静止的参照系中,自旋的方向则保持不变. (《通向实在之路》§ 25.2)

The Dirac equation can be written as an equation coupling these two 2-spinors, each acting as a kind of 'source' for the other. From the form of these equations, we see that the Dirac electron can be thought of as being composed of two ingredients. Let us call these the 'zig' particle and the 'zag' particle. Being massless, each of these should be travelling with the speed of light, but we can think of them, rather, as 'jiggling' backwards and forwards. In fact, this is a realization of the phenomenon referred to as "zitterbewegung". The electron (or other massive particle of spin 1/2) can be viewed, in spacetime, as oscillating between a left-handed massless zig particle and a right-handed massless zag particle; the oscillation rate is essentially the de Broglie frequency of the electron. Although the velocity keeps reversing, the spin direction remains constant in the electron's rest-frame. (The Road to Reality. § 25.2)



彭罗斯用电子的 zigzag (之字形运动)图像来解释 Zitterbewegung 颤动.他写道:
"zig 是左旋的, zag 是右旋的.虽然电子的速度的方向在不断地反转,但在电子静止的参照系中,自旋的方向则保持不变.由于电子的晃动,电子的瞬时运动总是测得为光速,尽管电子的总体平均运动小于光速." (《通向实在之路》§ 25.2)

                                                                                                               (8.3.3-3)

　

Penrose explained Zitterbewegung with the zigzag picture of the electron. He wrote:

"The spin is left-handed in the case of the zig and right-handed for the zag. Although the velocity of the electron keeps reversing, the spin direction remains constant in the electron's rest-frame. The electron's instantaneous motion is always measured to be the speed of light, owing to the electrons jiggling motion, even though the overall averaged motion of the election is less than light speed." (The Road to Reality. § 25.2)

                                                                                                                                      (8.3.3-3)

　

8.4 作为复射影的扭量实在

8.4 Twistor reality as complex projection

　

8.4.1 我们利用射影几何学中的对偶性攀登维度阶梯;射影扭量宇宙航行

8.4.1 We use the dualism in projective geometry to climb the dimension ladder; projective twistor astronavigation

　

         托尼·罗宾的书《时空投影》的第7章的标题是"扭量和投影".

The title of Chapter 7 of Tony Robbin's book Shadows of Reality is "Twistors and Projections".

　

         扭量理论是一种射影理论.扭量实在是计算变成实在.

The twistor theory is a kind of projective theory. Twistor reality is computing-becoming reality.

         托尼·罗宾在他的书《时空投影》中指出:

在19世纪,数学家和哲学家们用两种数学模型来探索和理解这种困难的思想：平面国模型(切片模型)和影子模型(投影模型).(3页.)

但是在影子模型中,如果太阳把椅子在一个光滑海滩的表面投下影子,整个椅子就将出现在生活于那个海滩上的任何二维生物面前.的确,在阴影下,各部分之间的长度或角度可能被投影扭曲,但椅子的连续性得以保持,且保持了椅子各部件之间的关系.(3-4页.)

投影图形是整体的,切片图形不是整体的,而平面国的空间模型的不连通性越来越引起困难.即使是时间,也不能这么简单地描述成一系列的切片.(4页.)

我们使用投影方法攀登维度阶梯… (5页.)

         19世纪射影几何的成就是逐渐将射影几何从笛卡尔 x, y 网格中移除,并跟踪当测量值因不同的投影而变化时,在图形中什么是保持不变的.结果,在射影直线或光线的专门的定义中就没有了坐标网格.在事件空间里没有隐含的空间网格,这种前景对于物理学家而言通常是很有吸引力的.(第126页.)

In his book Shadows of Reality, Tony Robbin pointed out:

During the nineteenth century, mathematicians and philosophers explored and comprehended such difficult thoughts by the use of two mathematical models: the Flatland, or slicing, model and the shadow, or projection, model. (Preface.)

But in the shadow model, if the sun were to cast a shadow of the chair on the surface of a smooth beach, then the whole chair would be present to any two-dimensional creatures living on that beach. True, with shadows, the lengths or angles between the parts could be distorted by the projection, but the continuity of the chair is preserved, and with it is preserved the relationship between its parts. (Preface.)

Projected figures are whole, sliced figures are not, and more and more the disconnected quality of the Flatland spatial model presents problems. Even time cannot be so simply described as a series of slices. (Preface.)

We use projection methods to climb the dimension ladder... (Preface.)

The achievement of nineteenth-century projective geometry was to gradually remove projective geometry from the Cartesian x, y grid and to track what remained constant in figures as their measurements changed due to different projections. Consequently, there is no one grid that is the exclusive definition of a projective line, or of a light ray. The prospect of an event space without an underlying grid of space is appealing to physicists in general. (p. 74.)

　

         鉴于彭罗斯的书《通向实在之路》688页,扭量提供了据以表述无质量粒子的可伸缩元素.

In view of page 965 of Penrose's book The Road to Reality, twistors provide the scalable factors in terms of which massless particles are to be expressed.

　

         罗宾在他的著作《时空投影》中指出:
         将直线(特别是拥有距离的弹性标记的直线)等同于点,乃是射影几何学的基本法宝.(第87页.)

         在德沙格(Desargues)定理中, 关于点(顶点)的陈述互换成关于直线(边)的陈述,从而确立了射影几何学中的对偶性的基本特征.一个人能说出关于点的每一件事,都可以用它关于直线的每一件事来代替,反之亦然.(第93页.)

In his book Shadows of Reality, Robbin pointed out:

Equating lines with points, especially lines with elastic markers of distance, is a fundamental gambit of projective geometry. (Shadows of Reality. p. 49.)

In Desargues's theorem a statement about points (vertices) is exchanged for a statement about lines (edges), and this establishes the basic feature of dualism in projective geometry. Everything one can say about a point, one could instead say about a line, and vice versa. (pp.53, 54.)

         时空关系网的单位由射影直线构建.(126页.)

　

The units of space and time are built from projective lines. (Refer to p. 74.)

　

         彭罗斯指出:

         中心观点是认为空间-时间本身是次生的二级观念,是由更为原始的具有量子特性的某种东西建构而来的,这某种东西被称为扭量空间. (《新物理狂想曲》386页.) 为了更为全面透彻地发展理论,让我们回到原初纯自旋网络图像上来.注意,在这一图像里不见踪影的主要之点就是空间位移. ... 原版自旋网络没有距离量度,因为自旋是角动量,只与旋转和角度有关.在该理论中我们或许需要一个与线性动量对应的角色以便能够把平移和实际距离收编进来.(《通向实在之路》,689、690页.)

Penrose pointed out:

The central idea is that space-time itself is to be regarded as a secondary notion, constructed from something more primitive, with quantum aspects to it, referred to as twistor space. (Fashion, Faith, and Fantasy in the New Physics of the Universe. page 336.) To proceed further, let us return to the original pure spin-network picture, noting that the main thing that was missing from it was any reference to spatial displacement ... in the original spin-net-work theory, there is no measure of distance because spin is angular momentum, having to do merely with rotations and angles. We would need a corresponding role for linear momentum in that theory in order to be able to incorporate translational displacements and actual distances. (The Road to Reality. page 967.)

　

罗宾指出:
　
1. 彭罗斯的创造性飞跃,乃是意识到还有另一个几何对象可以模拟光线:射影直线可以容纳光线的所有长度.(《时空投影》第125页.)
　
2. 射影直线完全有可能具有一系列有序的点,但是—类似于光线—它们没有确定的长度.(《时空投影》125、126页)
　
                                                                                                (8.4.1-1)

　

Robbin pointed out:
1. It was Penrose's creative leap to realize that there is another geometric object that can model light rays: the projective line can accommodate all the various lengths of a light ray.

2. Projective lines may have an ordered series of points, but—like light-rays— they do not have a definite length.

                      (Shadows of Reality, p. 74.)                                                            (8.4.1-1)

　

         鉴于(8.4.1-1),

1. 扭量空间是射影空间,因此在扭量空间里没有确定的距离长度,也没有确定的时间长度.一个射影点等同于无限延伸,瞬间等同于永恒.
2. 在扭量空间里没有确定的长度.这是缩地术、射影扭量宇宙航行的物理基础.(参看(8.4.2-2).)

                                                                 (8.4.1-2)

　

In view of (8.4.1-1),

1. Twistor space is a projective space, and hence in twistor space there is neither a definite length of distance nor a definite length of time. A point is equivalent to an infinite extension; an instant is equivalent to eternity.
2. In twistor space there is not a definite length. This is the physics behind ground contracting technique and projective twistor astronavigation. (Refer to (8.4.2-2).)

                                                                                                                                (8.4.1-2)

　

         根据佛教法华经,三世一时(一段短时间里包含过去、现在、未来的全部时间).

According to Buddhist Lotus Sutra, a short while contains all the times of the past, present, and future.

         我们利用射影几何学中的对偶性攀登维度阶梯.

We use the dualism in projective geometry to climb the dimension ladder.
　

8.4.2 扭量空间

8.4.2 Twistor spaces

　

         根据《时空投影》128页和130页,可以知道

　

彭罗斯将光线的射影模型与复数相结合,构造了一种复射影空间,即扭量空间.紧化,就相当于在光线中加一个挠彭曲扭转.平行路径随着它们的推进而挠曲扭转.扭量所代表的路径是通过紧化而封闭的.        (8.4.2-1)



According to Shadows of Reality, pp. 75, 76~77, one can know that

　

Penrose combines the projective model of light rays with complex numbers to build a complex projective space, i.e. the twistor space. Compactification is equivalent to adding a twist to the light rays. Parallel paths twist as they progress. The paths a twistor represents are closed by compactification.                               (8.4.2-1)

　

         紧化需要旋量.一个旋量类似于一条莫比乌斯环.旋量可以用矩阵来表示.一个扭量由两个旋量构成;一个描述光线的角动量(与黎曼球面有关),另一个描述光线的四维动量(与挠曲扭转有关).在一个扭量空间里就好比在一个楼层上.在不同的扭量维度楼层上可以看到完全不同的光影.

　

Compactification requires spinors. A spinor is comparable with a Möbius band. Spinors can be represented by matrices. A twistor consists of two spinors; one describes the angular momentum (related to the Riemann sphere) of a light ray, and the other describes the 4-dimensional momentum (related to the twist) of the light ray. Being in a twistor space is like being on a floor. On different twistor dimensional floors you can see completely different light and silhouettes.

　

         彭罗斯的书《通向实在之路》的图33.11描绘了扭量空间.图中的原点可以被看作是一种光的光源,这种光可以称为 T 光, T 光形成扭量空间 T,包括 T⁺、N、T^-.它们的射影子空间分别是空间 PT⁺、 PN、 PT^- .扭量空间 T 是复四维空间,射影扭量空间 PT 是复射影三维空间.空间 PT里的一条线对应着空间 PN 里的一个黎曼球面.

Fig. 33.11 in Penrose's book The Road to Reality depicted twistor spaces. In the figure, the origin can be regarded as a source of a kind of light which can be called T light, and which forms a twistor space T, including T⁺, N and T^-. They have projective subspaces PT⁺, PN, and PT^- respectively. The twistor space T is a complex four-dimensional space; the projective twistor space PT is a complex projective 3-dimensional space. A line in the space PT corresponds to a Riemann sphere in the space PN.

　

         注意到《通向实在之路》的图33.11里的长方块有厚度,可以知道扭量空间 T 里的一个点对应着扭量空间 PT 里的一条线.

Noting that the rectangular block in Fig. 33.11 in the book The Road to Reality has a thickness, one can know that a point in the twistor space T corresponds to a line in the twistor space PT.

　

         根据《通向实在之路》697页,闵可夫斯基空间 M 是扭量空间 PN 中的复直线,是 PN 的次级结构.

According to The Road to Reality, pp. 977, 978, Minkowski space M is the space of complex lines lying in PN, and is the secondary structure of the twistor space PN.

　

根据《通向实在之路》,
1. 紧化闵可夫斯基空间 M^# 是扭量空间 PN 中的复射影直线,是 PN 的次级结构.

2. 基于(8.3.2-1),莫比乌斯环型反引力使闵可夫斯基空间空间变为紧化闵可夫斯基空间.

3. 紧化闵可夫斯基空间是射影空间.
4. 空间 M^# 是一个带有洛伦兹共形度规的四维实紧流形(《通向实在之路》第690页).
                                                                  (8.4.2-2)

　

According to The Road to Reality,
1. Compactified Minkowski space M^# is the space of complex projective lines lying in PN, and is the secondary structure of the twistor space PN.

2. Based on (8.3.2-1), Möbius-loop-typed antigravitation changes Minkowski space into compactified Minkowski space.

3. Compactified Minkowski space is a projective space.
4. The space M turns out to be a 4-dimensional real compact manifold with a Lorentzian conformal metric (The Road to Reality. p. 969).
                                                                             (8.4.2-2)

　

         由罗宾的书的第7章可以知道,复射影直线被建模成射影平面,卷成一个球,称为黎曼球面.(参看《时空投影》,128页.)

From Chapter 7 of Robbin's book one can know that a complex projective line, modeled as a projective plane, rolls up to be a sphere, called the Riemann sphere. (See Shadows of Reality, p. 75.)

　

根据《通向实在之路》693页,扭量是与时空总体关联的实体.这种总体性有一个好处,那就是我们可以找到一种体系来取代整个时空.         (8.4.2-3)



According to page 973 of The Road to Reality, twistors are seen to be entities that refer globally to the spacetime. This globality has an advantage when we are seeking a formalism intended to replace the spacetime.         (8.4.2-3)

　

　

根据彭罗斯的书《通向实在之路》第687~688页,在扭量理论里,基本的射影关系如下:
1. 在闵可夫斯基空间 M 里的一个点对应着在扭量空间 PN 里的一个黎曼球面,一个黎曼球面是一个天球.

2. 在闵可夫斯基空间 M 里的一条光线对应着在扭量空间 PN 里的一个点.

                                                              (8.4.2-4)

　



According to pages 964~965 of Penrose's book The Road to Reality, in the twistor theory the basic projective relations are as follows:
1. A point in Minkowski space corresponds to a Riemann sphere in the twistor space PN, and a Riemann sphere is a celestial sphere.

2. A ray of starlight in Minkowski space M corresponds to a point in the twistor space PN.

                                                                                                         (8.4.2-4)

　

　

         彭罗斯写道,

洛伦兹四维空间的特殊性在于,这个共形流形可以很自然地解释为复流形(黎曼球面),这是一种在其他任何空间和时间维数下都不会出现的性质.《通向实在之路》第694页.

Penrose wrote:

What is particular about the Lorentzian 4-dimensioinal case, however, is that this conformal manifold can be naturally interpreted as a complex manifold (the Riemann sphere), a property that does not arise in any other number of space and time dimensions. (The Road to Reality. p. 974.)

　

         彭罗斯写道: "我把这些黎曼球面画成拉长了的样子,以折中它们在PT的射影几何下也是射影直线这一事实!"(《通向实在之路》, 图 33.12及其说明])

Penrose wrote, "I have drawn these Riemann spheres very elongated, as a compromise with the fact that they are also projective straight lines in the projective geometry of PT!" (The Road to Reality, Figure 33.12 and its caption.)

　

         彭罗斯指出:
         复 n 维流形可以被看作是实 2n 维流形.我们有各种方法来表述这一概念.本质上说,这里需要的是一种高维下的柯西-黎曼方程.我们可以自由地在关于复流形的两种基本观点之间作出选择.(《通向实在之路》§ 12.9.)
Penrose pointed out:

A "complex n-manifold" can be viewed as being a real 2n-manifold. There are various ways of formulating this notion. Essentially, what is required is a higher-dimensional version of the Cauchy-Riemann equations. We can move freely between the two philosophical standpoints with regard to complex manifolds. (The Road to Reality. § 12.9.)

　

　

         根据彭罗斯的《新物理狂想曲》,第390页,非零扭量 (non-zero twistors) 包括非零模扭量 (non-null twistors) 和零模扭量 (null twistors).

1. 非类光扭量包括

   1) 正扭量( ||Z|| > 0 )即右手扭量,属于空间 T⁺ 或空间 PT⁺ ;

   2) 负扭量( ||Z|| < 0 )即左手扭量,属于空间 T^- 或空间 PT^- .

2. 类光扭量( ||Z|| = 0 )属于空间 N 或空间 PN .

                                                                    (8.4.2-5)

　

According to page 339 of Penrose's book Fashion, Faith, and Fantasy in the New Physics of the Universe, non-zero twistors include non-null twistors and null twistors.

1. Non-null twistors include

   1) positive twistors ( ||Z|| > 0 ), i.e. right-handed twistors, belonging to the space T⁺ or the space PT⁺ ;

   2) negative twistors ( ||Z|| < 0 ), i.e. left-handed twistors, belonging to the space T^- or the space PT^- .

2. Null twistors ( ||Z|| = 0 ) belong to the space N or the space PN.

                                                                                                                     (8.4.2-5)

         彭罗斯在《通向实在之路》695页指出,

只有零模扭量能够与实闵可夫斯基空间 M 中的事件互相关联,这时我们说扭量是类光的.      (8.4.2-6)

On page 975 of his book The Road to Reality, Penrose pointed out:

Only the null twistor can be incident with an event in real Minkowski space M, in which case we say that the twistor is null.      (8.4.2-6)

　

         直接与实闵可夫斯基空间中的事件互相关联的是类光扭量.
It is the light-like twistors that provide the direct link with an event in real Minkowski space M. Hence when a twistor space is incident with an ordinary event, light can be seen.

只有类光扭量能够与实闵可夫斯基空间 M 中的事件互相关联,因此当一个扭量空间与普通空间里的事件互相关联时可以看到光.      (8.4.2-7)

　

Only the light-like twistor can be incident with an event in real Minkowski space M; hence when a twistor space is incident with an event in ordinary space, light can be seen.      (8.4.2-7)

　

　

         根据罗宾的《时空投影》,130页、138页,旋量导致自旋.

According to pages 77 and 81 of Robbin's Shadows of Reality, Spinors lead to spin.



罗宾写道:
粒子中自旋的起源,被看做是几何学的作用.(《时空投影》第138页.)                        (8.4.2-8)

　

　

Robbin worte:
The origin of spin in particles is seen as a function of geometry. (Shadows of Reality. p. 81.)      (8.4.2-8)

　

         彭罗斯指出:

投影扭量空间由三部分构成：PT⁺ 代表右旋无质量粒子; PT^- 代表左旋无质量粒子; PN 代表无自旋粒子.(《新物理狂想曲》,图4.2的说明.)

Penrose pointed out:

Projective twistor space PT is composed of three parts: PT+, representing right-spinning massless particles, PT-, representing left-spinning ones, and PN, representing non-spinning ones. (Fashion, Faith, and Fantasy in the New Physics of the Universe, the caption of Fig. 4.2.)

         彭罗斯描述了"左旋非线性引力子".他指出,左旋的引力子是实际的爱因斯坦非线性真空方程的解,而不是其线性近似解.(《通向实在之路》, § 33.11.)

Penrose described the "left-handed non-linear graviton". He pointed out that a left-handed graviton is a solution of the actual non-linear Einstein vacuum equation, rather than of its linear approximation. (The Road to Reality, § 33.11.)

         由此可以得出结论:

左手螺旋扭量发出左旋扭量光,即 T^- 光;右手螺旋扭量发出右旋扭量光即 T⁺ 光.左旋扭量光对应着收缩,右旋扭量光对应着膨胀.         (8.4.2-9)

　

Hence one can draw a conclusion:

The left-handed-helix twistor emits left-handed twistor-light, i.e. T⁺ light; the right-handed-helix twistor emits right-handed twistor-light, i.e. T^- light. The left-handed twistor-light corresponds to positive curvature and contraction, and the right-handed twistor-light corresponds to negative curvature and expansion.         (8.4.2-9)

　

         基于《通向实在之路》150页可以知道,扭量空间是两个自旋空间,这两个自旋空间具有相反的手征.

Based on page 210 of The Road to Reality, one can know that a twistor space is two spin-spaces which have opposite chirality.

鉴于(8.3.3-3),虽然 T 光是左/右旋分量光,但是在光子的静止参照系中,由于 Zitterbewegung 颤动,光子的自旋的方向保持不变.         (8.4.2-10)

　

In view of (8.3.3-3), though T light is left/right-handed component light, the spin direction of a photon remains constant in the photon's rest-frame due to Zitterbewegung.         (8.4.2-10)

　
         应该注意的是,自旋或螺旋运动与自转运动是不同的.

It should be noted that the spin or helical motion is different from the rotational motion.

　

1. 闵可夫斯基空间里的一个点粒子对应着扭量空间 PN 里的一个黎曼球面,它是宏观量子;这有助于解释宏观量子现象.
2. 一方面,在闵可夫斯基空间 M 里,作为一个点粒子,电子没在自旋;但是另一方面,在扭量空间 PN里,作为一个黎曼球面,电子在自旋.

　

3. 粒子具有自旋.鉴于(8.3.2-1),粒子具有扭量空间.鉴于(8.3.2-5),粒子具有"外壳",这可能就是"量子域墙".

                                                                      (8.4.2-11)

　

1. A point particle in Minkowski space corresponds to a Riemann sphere in the twistor space PN, and the Riemann sphere is a macroscopic quantum; this helps to explain macroscopic quantum phenomena.
2. On the one hand, in Minkowski space M, as a point particle, an electron is not spinning; but on the other hand, in the twistor space PN, as a Riemann sphere, an electron is spinning.

3. A particle has spin. In view of (8.3.2-1), a particle has its twistor space. In view of (8.3.2-5), a particle has its "shell", which might be the quantum "domain walls".

                                                                                                                  (8.4.2-11)

　

8.4.3 不可定向空间

8.4.3 Non-orientable space

　

8.4.3.1 不可定向空间

8.4.3.1 不可定向空间

　

         在拓扑学里,不可定向曲面又称为单侧曲面.射影平面是不可定向曲面.(参看包志强.《点集拓扑与代数拓扑引论.122页.》)莫比乌斯环是一个不可定向曲面.

In topology, a non-orientable surface is also called a one-sided surface. A projective plane is a non-orientable surface. (See BAO Zhiqiang. Introduction to General Topology and Algebraic Topology. p. 122.) A Möbius loop is a non-orientable surface.

　

         托尼·罗宾在他的著作《时空投影》中指出:

　

在射影几何里,平行线在右无穷远点相交,并不排除这些平行线在左无穷远点相交.但是,根据射影几何最基本的公理和定义,平行线只相交一次.因此,正如克莱因所解释的,这两个遥远的点必须是同一点.(97页.)
从拓扑学上讲,射影平面是一个莫比乌斯环,带内缝进一个圆盘,所以这个带就变成了一个封闭的像球面一样的物体;一个人需要绕带两圈才能回到其开始出发的地方,因为这种几何内在地有一种挠曲扭转.(98页.)                                                                                                                                                                                                                                                                         (8.4.3.1-1)

　

In his book Shadows of Reality, Tony Robbin pointed out:

　

In projective geometry, the fact that parallel lines meet at a point infinitely far to the right does not preclude those same parallel lines from meeting at a point infinitely far to the left. But by the most basic axioms and definitions of projective geometry, parallel lines meet only once. Therefore, as Klein explained, these two distant points must be the same point, ...... (page 56.)
Topologically, a projective plane is a Möbius band with a disk sewn in so the band becomes a closed sphere-like object; one needs to go around twice to get back to where one started right side up, because a twist is built into the geometry. (page 57.)

                                                                       (8.4.3.1-1)

　

         马克·阿姆斯特朗的《基础拓扑学.修订版.》的132页指出,

　

包含莫比乌斯环作为子空间的曲面叫做是不可定向的.      (8.4.3.1-2)

　

Page 154 of M. A. Armstrong's book Basic Topology points out:

　

Surfaces which contain a Möbius loop are said to be non-orientable.      (8.4.3.1-2)

　

8.4.3.2 变向曲线球困难说明扭量空间是不可定向空间

8.4.3.2 The googly problem shows that twistor space is non-orientable space

　

         彭罗斯说:

         扭量理论在我们称之为变向曲线球的问题上失败了大约30年,遇到了似乎无法解决的困难.(《新物理狂想曲》第384页.)

Penrose said,

Twistor theory had foundered, for some 30 years, on a seemingly insurmountable difficulty that we referred to as the googly problem. (Fashion, Faith, and Fantasy in the New Physics of the Universe. page p. 334.)

　

         但是有一个基本的困难依然没有解决,这个基本的困难被称为变向曲线球困难.(变向曲线球一词用于板球运动,描述的是在板球运动中以右旋的动作投球给击球手,但球在途中却明显变成了以左旋的作用递送.) (《(《新物理狂想曲》第404~405页.)

But a fundamental problem, referred to as the googly problem, had remained unsolved. (A googly is a term used in the game of cricket to describe a ball bowled with a right-handed spin, but delivered with the apparent action for delivering a left-handed spin.) (Fashion, Faith, and Fantasy in the New Physics of the Universe. page p. 334.)(Fashion, Faith, and Fantasy in the New Physics of the Universe. page p. 351.)

　

变向曲线球困难说明扭量空间是不可定向空间.        (8.4.3.2-1)

　

The googly problem shows that twistor space is non-orientable space.        (8.4.3.2-1)

　

         彭罗斯画出了可以实际想象的单个扭量的"实"图像,即鲁滨逊线汇(《通向实在之路》, § "33.6 作为无质量自旋粒子的扭量的几何", 图33.15.)

Penrose pictured the Robinson congruence, which is a "real" picture of a single twistor which we can actually visualize (The Road to Reality, § "33.6 Geometry of twistors as spinning massless particles", Fig. 33.15.)

         由鲁滨逊线汇可以看出,扭量空间是不可定向空间.

It can be seen from the Robinson congruence that twistor space is non-orientable space.

Penrose pointed out:

Thus a point in spacetime becomes a Riemann sphere in twistor space. We should think of twistor space as the space in terms of which we should describe physics (fig. 6.4). (See The Nature of Space and Time p. 110 and p. 111, Figure 6.4.)
8.4.3.3 扭量空间里的黎曼球面

8.4.3.3 The Riemann sphere in twistor space

彭罗斯写道:
想象位于时空一点的观察者,向着太空观星.

在相对论中一个观察者的天球自然地成为一个黎曼球面.

(《时空本性》第108~109页.)
                                                (8.4.3.3-1)

　

Penrose wrote:
　
Imagine an observer situated at a point in spacetime, out in space looking at the stars.
　
The celestial sphere of an observer, in relativity theory, is naturally a Riemann sphere.
　
(The Nature of Space and Time. pp. 109~110.)
　
                                                                                (8.4.3.3-1)

         彭罗斯指出:

         时空中的一点在扭量空间中变成为一个黎曼球面.我们应该把扭量空间当作按照这种黎曼球面来描述物理的空间(图6.4). (见《时空本性》第109页和第110页图6.4.)

Penrose pointed out:

Thus a point in spacetime becomes a Riemann sphere in twistor space. We should think of twistor space as the space in terms of which we should describe physics (fig. 6.4). (See The Nature of Space and Time p. 110 and p. 111, Figure 6.4.)

         由罗宾的书的第7章可以知道,复射影直线被建模成射影平面,卷成一个球,称为黎曼球面.(参看《时空投影》,128页.)

From Chapter 7 of Robbin's book one can know that a complex projective line, modeled as a projective plane, rolls up to be a sphere, called the Riemann sphere. (See Shadows of Reality, p. 75.)

         在《通向实在之路》的第33.3 节,彭罗斯指出:

         那么准确说什么是共形群呢?严格说来,这个群不是作用在闵可夫斯基空间 M 上的,而是作用在 M 的扩展所谓紧化闵可夫斯基空间 M^# 上的. ... 它在理解扭量几何以及这种几何与物理时空几何的关系方面是一种有用的媒介.

         "紧化闵可夫斯基空间" M^# 正是通过类似的操作由普通闵可夫斯基空间 M 得来的,只是现在邻接的"无穷远元素"被证明是一个处于无穷远的完整的光锥.这个结果空间有着较闵可夫斯基空间本身更大的对称性(即共形群). (第690页.)

         这样,对处于E^2,4 (即伪欧几里得空间)原点的"观察者"来说, M^# 即是天球! (第692页.)

         O(2,4) (即作用在 E^2,4 上的伪正交群)中必存在两个在 M^# 上起着单位元作用的元素,即 O(2,4) 的单位元素本身和 O(2,4) 的负单位元素,后者简单地说就是使每个生成元反向.除了源于这种生成元方向反转的二对一的对应性质, O(2,4)还是共形群.(第692页.)

In § 33.3 of his book The Road to Reality, Penrose pointed:

What exactly is the conformal group? Strictly speaking, this group acts not on Minkowski space M, but on a slight extension of M known as compactified Minkowski space M^#. ... It is a useful intermediar to the understanding of twistor geometry and its relation to physical spacetime geometry. (The Road to Reality. p. 968.)

In a similar way, the "compactified Minkowski space" M^# is obtained from ordinary Minkowski space M by adjoining an "infinite element" which, this time, turns out to be a complete light cone at infinity. the resulting space has a greater symmetry (namely the conformal group) than Minkowski space itself. (The Road to Reality. p. 969.)

... M^# is the "celestial sphere" for some "observer" situated at the origin of a pseudo-Euclidean 6-space E^2,4. (pp. 970~971.)

(O(2,4) is the pseudo-orthogonal group acting on E^2,4.) There are exactly two elements of O(2,4) that act as the identity on M^#, namely the identity element of O(2,4) itself and the negative identity element of O(2,4), the latter simply reversing the direction of each generator. Apart from the two-to-one nature of the correspondence arising from this reversibility of the generator direction, O(2,4) is the conformal group. (p. 971.)



罗宾指出:
观察者总是位于天球光线的中心,因为光线在当前时刻聚集在一个特定的位置上,组成观察者的天图.这些光线,若延续到未来,则构成未来一半的光锥,即观察者的反天图.对于光线本身,这两幅天图被"视为等同",意思是它们被合(即"胶合")在一起 ... 光线穿过光锥的拧点时,它们的位置在光锥的上半部分被反转.紧化,就相当于在光线中加一个扭曲.(《时空投影》第129~130页.)

                                                                                                          (8.4.3.3-2)

Robbin pointed out:
　
The viewer is always in the center of the light from the celestial sphere, because the light rays converge on a specific location at the present moment to compose the viewer's sky map. Those rays, if continued into the future, make up the future half of the light cone, or the viewer's anti-sky map. For the light rays themselves, these two sky maps are "identified", meaning that they are brought or "glued" together, ... As the light rays pass through the pinch point, their positions are reversed in the top half of the light cone. Compactification is equivalent to adding a twist to the light rays (Fig. 7.6). (Shadows of Reality. p. 76.)
                                                                                                                                     (8.4.3.3-2)

　

8.4.4 贴附于莫比乌斯环的黎曼球面：黎曼球面泡

8.4.4 A Riemann sphere attached to a Möbius loop: a Riemann-sphere-bubble

8.4.4.1 莫比乌斯变换;黎曼球面泡

8.4.4.1 Möbius transformations; Riemann-sphere-bubbles

         Needham 的书《复分析：可视化方法》 § 3.5.5 让我们可视化地看到了在黎曼球面上的四种类型的莫比乌斯变换: (a)椭圆型、(b)双曲型、(c)斜驶型、(d)抛物型. Needham 指出,复平面上的四种类型的运动诱导出黎曼球面上的四种类型的运动.

Section 3. V. 5 of Needham's book Visual Complex Analysis lets us visualize four types of Möbius transformation on the Riemann sphere: (a) the elliptic type, (b) the hyperbolic type, (c) the loxodromic type, and (d) the parabolic type. Needham pointed out that four types of motion in the complex plane induce four types of motion on the Riemann sphere.
　
         椭圆型又称为旋转型,双曲型又称为后推(boost)型,斜驶型又称为四螺旋型,抛物型又称为类光旋转型. (见 Tristan Needham. Visual Complex Analysis. 25th Anniversary Edition. p. 173.)
The elliptic type is also called the rotation type; the hyperbolic type is also called the boost type; the loxodromic type is also called the four-screw type; and the parabolic type is also called the null rotation type. (See Tristan Needham. Visual Complex Analysis. 25th Anniversary Edition. p. 173.)
　

         Needham 在他的著作《复分析：可视化方法》的 § 3.5.5中讨论了抛物型莫比乌斯变换.根据这本书的第272页(§ 6.3.7),这种类型的运动只有双曲几何才会有,称为极限旋转.         (8.4.4.1-1)

　

In § 3.5.5 of his book Visual Complex Analysis, Needham discussed the parabolic type of Möbius transformation on the Riemann sphere. According to § 6.3.7 of the book, this kind of motion is peculiar to hyperbolic geometry, called a limit rotation.         (8.4.4.1-1)

　
         Needham 写道:
         如果 S 是空间中的一个"光滑"曲面,即指在其每一点上都有切平面,这样,说一个向量场在各点都切于 S 是有意义的.直观地说,我们可以形象地把一个向量场描绘为流体在 S 上形成的速度场.(《复分析：可视化方法》§ 10.3 闭曲面上的流.)
　
Needham wrote:
If a curved surface S in space is "smooth" in the sense that there exists a tangent plane at each of its points, then it makes sense to speak of a vector field that is everywhere tangent to S. Intuitively, we may picture such a vector field as the velocity of a fluid that is flowing over S. (Visual Complex Analysis. § 10.3 Flows on Closed Surfaces.)
         约翰·惠勒提出了量子泡沫的概念.他写道:

有意思的是,当我后来对引力和广义相对论产生兴趣后,却发现不得不提出所谓"量子泡沫"的概念.这种量子泡沫不仅由无数个不断生灭的粒子组成,而且包括因涨落变成泡沫状的弯曲时空本身.(《约翰·惠勒自传：京子、黑洞和粒子泡沫》,第140页.)
　
         如果我的想法正确,那么足够小区域上的时空不只是有"起伏",不只曲率不规则,而且应当是分形成不断变化的多联通几何.(《约翰·惠勒自传：京子、黑洞和粒子泡沫》,第235页.)
         虫洞只不过是可以发生的这些扭曲的一种简单的表示.涨落会是如此剧烈以至于根本就不存在左和右、前与后之间的区别.日常的长度概念消失了,日常的时间概念也不见了.对于这种状态,我找不出比"量子泡沫"更贴切的名词了.(《约翰惠勒自传：京子、黑洞和量子泡沫》.第236页.

                                                                                                                        (8.4.4.1-2)

John Archibald Wheeler invented the idea of "quantum foam". He wrote:

Paradoxically, when I later became interested in gravitation and general relativity, I found myself forced to invent the idea of "quantum foam", made up not merely of particles popping into and out of existence without limit, but of spacetime itself churned into a lather of distorted geometry. (Geons, Black Holes, and Quantum Foam. pp. 148~149.)
　
If I was right, spacetime in small-enough regions should be not merely "bumpy", not merely erratic in its curvature; it should fractionate into ever-changing, multiply connected geometries. (Geons, Black Holes, and Quantum Foam. p. 246.)
The wormhole would be but one simple manifestation of the distortions that could occur. So great would be the fluctuations that there would literally be no left and right, no before and no after. Ordinary ideas of length would disappear. Ordinary ideas of time would evaporate. I can think of no better name than quantum foam for this state of affairs. (Geons, Black Holes, and Quantum Foam: A Life in Physics. p. 248.)

                                                                                                                            (8.4.4.1-2)

　

1. 黎曼球面是可定向空间.嵌入了一条拓扑莫比乌斯环的黎曼球面称为贴附于莫比乌斯环的黎曼球面.贴附于莫比乌斯环的黎曼球面是不可定向空间.
2. 黎曼球面上的莫比乌斯变换显示出扭量空间里的黎曼球面是一种类似于肥皂泡的流体.

3. 在黎曼球面的北极做一个孔,然后把这个孔用莫比乌斯环封合(请参看(8.3.1-1))和《拓扑学奇趣》第61页),这样的贴附于莫比乌斯环的黎曼球面可以称为黎曼球面泡.黎曼球面泡是不可定向空间,是闭曲面.

4. 鉴于(8.4.2-3)、(8.4.2-4)、(8.4.3.3-1)、(8.4.3.3-2),黎曼球面泡取代整个时空,因此黎曼球面泡的惯性质量是它所对应的万有引力场的惯性质量.

5. 若干黎曼球面泡膨胀、嵌套、碰撞、聚并、融合、破裂,形成新的黎曼球面泡.

6. 黎曼球面泡形成黎曼球面泡沫.由于扭量光影循环,黎曼球面泡沫形成扭量光影泡沫.

7. 双曲几何的共形表示适用于扭量空间,因此适用于黎曼球面泡和黎曼球面泡沫.

8. 扭量光影没有静止质量.

                                                                            (8.4.4.1-3)

　

1. The Riemann sphere is orientable space. A Riemann sphere embedded with a topological Möbius loop is called a Riemann sphere attached to a Möbius loop. A Riemann sphere attached to a Möbius loop is non-orientable space.2. Möbius transformations on the Riemann sphere show that a Riemann sphere in the twistor space is a fluid similar to a soap bubble.

3. Make a hole at the north pole of a Riemann sphere, and then seal the hole with a Möbius loop (See (8.3.1-1) and page 61 of the book 《拓扑学奇趣》); such a Riemann sphere attached to a Möbius loop can be called a Riemann-sphere-bubble. A Riemann-sphere-bubble is a non-orientable space, and is a closed surface.

4. In view of (8.4.2-3), (8.4.2-4), (8.4.3.3-1), and (8.4.3.3-2), a Riemann-sphere-bubble replaces the spacetime globally; hence the inertial mass of a Riemann-sphere-bubble is the inertial mass of the gravitational field of the particle that the Riemann-sphere-bubble corresponds to.

5. Riemann-sphere-bubbles expand, nest, collide, coalesce, merge, and burst, creating new Riemann-sphere-bubbles.

6. Riemann-sphere-bubbles form Riemann-sphere foam. Because of the twistor-light-silhouette cycle, Riemann-sphere foam forms twistor-light-silhouette foam.

7. The conformal representation of hyperbolic geometry applies to twistor space, and hence applies to the Riemann-sphere-bubble and Riemann-sphere foam.

8. The twistor-light-silhouette has not rest mass.

                                                                                                      (8.4.4.1-3)

　

斯特恩·奥登瓦尔德写道:

         星系群体大尺度结构的主要特征是,星系群体似乎被限制在巨大的纤维状结构中,这些纤维状结构如同肥皂泡表面的薄膜那样包围着里面没有星系的巨洞.(《宇宙学是什么》.第155页.)

                                                                                                                          (8.4.4.1-4)



Sten Odenwald wrote:

A dominant feature of the large-scale galaxy population is its seeming confinement into vast filaments surrounding large galaxy-free voids like the film on the surface of soap bubbles. (A Degree in a Book: Cosmology. p. 159.)

                                                                                                         (8.4.4.1-4)

　

         (8.4.4.1-3)有助于解释宇宙的大尺度结构.

(8.4.4.1-3) helps to explain the large-scale structure of the universe.

　

8.4.4.2 作用量单位

8.4.4.2 A unit of action

彭罗斯指出:

我们必须用整个黎曼球面取代原点来改造复二维空间,这样,我们得到的不仅是一个零,而是整个黎曼球面的零值,每个零对应一根纤维,给出丛 B 的零截面.这个过程就是所谓的吹胀复二维空间的原点(代数几何学、复流形理论、弦理论、扭量理论和其他许多领域中的一个很重要的概念).(《通向实在之路》第245~246页).

                                                                                                                                       (8.4.4.2-1)

　

Penrose pointed out:

We must modify the complex two-dimensional space by replacing the origin by a copy of the entire Riemann sphere, so that instead of having just one zero, we have a whole Riemann sphere's worth of zeros, one for each fiber, giving the zero section of the bundle. This procedure is known as blowing up the origin of a complex two-dimensional space (an important idea for algebraic geometry, complex-manifold theory, string theory, twistor theory, and many other areas). (The Road to Reality. p. 338).

                                                                                                                             (8.4.4.2-1)

　

1. 想象在地上有一个黎曼球面.这个球面的影子没有确定的长度,但是有确定的根部.
　
2. 以吹胀一个复二维空间的原点(即吹胀一个黎曼球面)所需要的努力的量值为一个作用量单位;于是该作用量单位对应着上述球面的影子的根部.
　
3. 该作用量单位对应着普朗克常量,并且导致宏观量子现象.
　
                                                                         (8.4.4.2-2)

1. Imagine that there is a Riemann sphere on the ground. The shadow of the sphere has no definite length, but has a definite base.
2. Take the required amount of effort to blow up the origin of a complex two-dimensional space (i.e. to blow up a Riemann sphere) as a unit of action; then this unit of action corresponds to the base of the shadow of the above-mentioned sphere.

3. The said unit of action corresponds to Planck constant, and causes macroscopic quantum phenomena.

                                                                                                                                           (8.4.4.2-2))

         彭罗斯指出,

不存在那种经典的定义明确的关于一个时空矢量是类空、类时还是类光的概念.(《通向实在之路》§ 33.2)        (8.4.4.2-3)

Penrose pointed out that

There is no classically well-defined notion of whether a spacetime vector is spacelike, timelike, or null. (The Road to Reality, § 33.2                                                              (8.4.4.2-3)

　

1. 扭量光是以 h' 为作用量单位的光.
2. 扭量光包括扭量 T⁺ 光、扭量 T^- 光、扭量 N 光、扭量 M^# 光等等.
3. 扭量 N 光的光子是黎曼球面泡.
                                               (8.4.4.2-4)

　

1. Twistor light is light that uses h' as a unit of action.
2. Twistor light includes twistor T⁺ light, twistor T^- light, twistor N light, twistor M^# light, etc.
3. A photon of twistor N light is a Riemann-sphere-bubble.
                                                                       (8.4.4.2-4)

　

8.4.4.3 黎曼球面泡不确定关系

8.4.4.3 Riemann-sphere-bubble uncertainty relations

         黎曼球面泡是事件粒子(见 § 8.6.2).与量子力学的不确定关系相对应,可以建立起黎曼球面泡不确定关系如下:

p x'_cutoff ~ ħ' / 2      (a_反引力 ≠ 0);      (8.4.4.3-1)

E t'_lifespan ~ ħ' / 2      (a_反引力 ≠ 0);      (8.4.4.3-2)

式中 ħ' 是一个作用量单位除以 (2 ) , cutoff 是最小尺度; p 是动量, x'_cutoff 是最短距离的尺度, E 是能量, t'_lifespan 是寿命.关于 ħ' ,见本网站第十一章.

A Riemann-sphere-bubble is an event-particle (See § 8.6.2). Corresponding to the uncertainty relations in quantum mechanics, Riemann-sphere-bubble uncertainty relations can be set up as follows:

p x'_cutoff ~ ħ' / 2      (a_反引力 ≠ 0);      (8.4.4.3-1)

E t'_lifespan ~ ħ' / 2      (a_{antigravitational} ≠ 0);      (8.4.4.3-2)

where ħ' is a unit of action divided by (2 ) , cutoff is the very smallest scale, p the momentum, x'_cutoff the very shortest distance scale, E the energy, and t'_lifespan the lifespan. For ħ' , see Chapter 11 of this website.

         (8.4.4.3-1)和(8.4.4.3-2)可以叫做黎曼球面泡不确定关系.

(8.4.4.3-1) and (8.4.4.3-2) can be called Riemann-sphere-bubble uncertainty relations.

　
由(8.4.4.3-2)可以得到
t'_lifespan ( m v² / 2 ) ~ ħ' / 2
t'_lifespan ( m v² ) ~ ħ'
                                                                                                                       t'_lifespan ~ ħ' / ( m v² )                           (8.4.4.3-3)
From (8.4.4.3-2) one obtains
t'_lifespan ( m v² / 2 ) ~ ħ' / 2
t'_lifespan ( m v² ) ~ ħ'
                                                                                                                       t'_lifespan ~ ħ' / ( m v² )                           (8.4.4.3-3)
另请参看(13-8)
See also (13-8).

扭量光影循环和(8.4.2-6)导致电磁不确定.         (8.4.4.3-4)

　

The twistor-light-silhouette cycle and (8.4.2-6) cause the uncertainty in electromagnetism.         (8.4.4.3-4)

　
　

当 h' >> h ,存在着宏观量子泡沫.      (8.4.4.3-5)

　

When h' >> h , there exists macroscopic quantum foam.      (8.4.4.3-5)

8.4.4.4 量子纠缠与量子测量

8.4.4.4 Quantum entanglement and quantum measurement

　

1. 在闵可夫斯基空间 M 里的一条光线对应着在扭量空间 PN 里的一个点.(见(8.4.2-4)以及《新物理狂想曲》387页图4.1及其说明.)这是量子纠缠的物理基础.
　
2. 根据(8.4.1-1),射影直线没有确定的长度.因此扭量光影处于量子叠印态.
　
                                                                                      (8.4.4.4-1)

　

1. A light ray in Minkowski space M corresponds to a point in the twistor space PN. (See (8.4.2-4) and Fashion, Faith, and Fantasy in the New Physics of the Universe. pp. 337, Fig. 4-1 with its caption.) This is the physics behind quantum entanglement.
　
2. According to (8.4.1-1), projective lines do not have a definite length. Hence the twistor-light-silhouette is in quantum superimposition states.

                                                (8.4.4.4-1)

　

1. 一个黎曼球面泡在 | ∑R |≥ a_反引力处坍缩为一个点.量子运动发生在扭量空间.量子测量发生在闵可夫斯基空间.
　
2. 粒子以扭量光影的形式存在于扭量空间;直到在闵可夫斯基空间里测量时,粒子才以常见的形式存在于闵可夫斯基空间.
　
3. 在测量前我们使用投影模型,在测量时我们使用切片模型.我们使用投影模型来理解波函数,我们使用切片模型来理解测量.
                                                                                                                                                (8.4.4.4-2)

　

1. A Riemann-sphere-bubble collapses into a point at the place where | ∑R |≥ a_{antigravitational} . Quantum motion takes place in twistor space. Quantum measurement takes place in Minkowski space.

　

2. The particles, in the form of twistor-light-silhouettes, exist in twistor spaces; the particles do not exist in Minkowski space in the normal form until measured in Minkowski space.

　

3. Before the measurement we use the projection model; during the measurement we use the slicing model. We use the projection model to comprehend the wave function; we use the slicing model to comprehend the measurement.

                                                                                                                                                     (8.4.4.4-2)

         这意味着物体可以突然出现在远处的一个地方.这有助于说明为什么一些由遥远的发射源发出的宇宙射线具有超过GZK截断的能量.

This means that an object can suddenly appear at a place far away. This helps to explain why some cosmic rays emitted by distant sources have energies above the GZK limit.
　

8.4.4.5 黎曼球面泡上的莫比乌斯变换生成时空的洛伦兹变换,这导致暗能量

8.4.4.5 Möbius transformations on the Riemann-sphere-bubble yield Lorentz transformations of spacetime, which causes dark energy

　

赫尔曼·外尔指出:

力学的基本规律是一种空白的形式,只有当它所包含的力的概念被物理学所填满时,它才能获得具体的内容.(《空间-时间-物质》第53页.)      (8.4.4.5-1)

　

Hermann Weyl pointed out:

The fundamental law of mechanics is a blank form which acquires a concrete content only when the conception of force occurring in it is filled in by physics. (Space-Time-Matter, pp. 66~67.)         (8.4.4.5-1)

　

《数学指南－实用数学手册》在"3.6 微分几何"一节中指出,
基本关系"力 = 曲率"是在数学和物理中最深刻的已知联系.

                                                                 (8.4.4.5-2)

　

In the section of "3.6 Differential geometry", Oxford Users' Guide to Mathematics points out that

The basic relation "force = curvature" is the deepest known connection between mathematics and physics.

                                                                                                                (8.4.4.5-2)

　

         Needham 指出:

         莫比乌斯变换是共形的, ...

         复平面上的每一个莫比乌斯变换都生成时空中唯一的洛伦兹变换.反过来,可以证明每一个洛伦兹变换都对应唯一(不论正负号)的莫比乌斯变换.

(《《可视化微分几何和形式：一部五幕数学正剧》》第80页、第87~88页.)

                                                                                                                                          (8.4.4.5-3)

　

Needham pointed out:

　

Mӧbius transformations are conformal ...

　

Every Mӧbius transformation of a complex plane yields a unique Lorentz transformation of spacetime. Conversely, it can be shown that to every Lorentz transformation there corresponds a unique (up to sign) Mӧbius transformation. (Visual Differential Geometry and Forms: A mathematical drama in five acts, p. 70 and pp. 76~77.)

                                                           (8.4.4.5-3)

　

黎曼球面泡上的莫比乌斯变换生成时空的洛伦兹变换,这导致各种各样的暗能量.         (8.4.4.5-4)

　

Möbius transformations on the Riemann-sphere-bubble yield Lorentz transformations of spacetime, which causes various dark energy.                   (8.4.4.5-4)

         根据彭罗斯和林德勒的描绘(见《Spinors and space-time Vol. 1 旋量与时空第1卷》第9页和第26~28页),可以想象在一个近光速的扭量空间里能看见什么.

         想象一位以接近速度 c 飞行的宇航员正在向着一颗目标星飞行,并且正在观看群星.他的一只眼睛可以作为黎曼球面的北极,天球可以作为黎曼球面.光线从过去走向未来.时间被包含在空间里.随着他的速度增加,所有其他的星星(包括他后面的星星)由于相对论性光行差效应而越来越拥挤到该目标星的周围,群星渐渐融合成他眼前的一幅模糊的合一的全景图像.
         对于这位宇航员而言,在他前面是一幅过去、现在、未来的全景图像,时间的一个个瞬间变成空间的一张张切片;这可以称作光行差全景图.一个球面波的子波分属于过去、现在、未来.

                                                                                                                                   (8.4.4.5-5)

According to what Penrose and Rindler depicted (See Spinors and Space-Time, Vol. 1, pp. 9, 26~28), one can imagine what one can see in a twistor space which travels at a speed closed to the speed of light.

Imagine an astronaut, who travels at a speed closed to c toward a target star, looking at the stars. One of his eyes can serve as the north pole of the Riemann sphere, and the celestial sphere can serve as the Riemann sphere. Light rays extend from past to future. Time is contained in space. Because of the effect of relativistic aberration of light, all other stars (including stars behind him) crowd more and more around the target star as his speed increases; stars gradually merge into a blurry panoramic image of oneness before his eyes.

　

For this astronaut, what ahead of him is a panoramic image in the past, present, and future; moment upon moment of time becomes slice upon slice of space; and this can be called a light-aberration panorama. The wavelets of a spherical wave belong to the past, the present, and the future respectively.

　

                                                                                                                                       (8.4.4.5-5)

这是在黎曼球面泡上的后推(boost)型莫比乌斯变换.(参看《可视化微分几何和形式：一部五幕数学正剧》第90页.)

This is the Möbius transformation of the boost type on the Riemann-sphere-bubble. (Refer to Visual Differential Geometry and Forms: A mathematical drama in five acts. p. 78.)

Needham 写道:

图 36b 则画出了相当于复平面中以原点为中心的膨胀 z → ρz 在黎曼球面上诱导出的变换,这里 ρ > 1. 若 ρ < 1, 则有复平面上的压缩,而黎曼球面上的点则向南而不是向北运动.(《复分析:可视化方法.》第133页.)                                             (8.4.4.5-6)

　

Needham wrote:

With ρ > 1, figure [3.26b] illustrates the induced transformation of the Riemann sphere corresponding to the origin-centred expansion of the complex plane, z → ρz. If ρ < 1 then we have a contraction of the complex plane, and points on the Riemann sphere move due South instead of due North. (Visual Complex Analysis. 25th Anniversary Edition. p. 174.)

                                                                                                                           (8.4.4.5-6)

　

Needham 指出:

直观地说,我们可以形象地把一个向量场描绘为流体在光滑曲面上形成的速度场.
(《复分析:可视化方法.》第408页.)                                             (8.4.4.5-7)

　

Needham pointed out:

Intuitively, we may picture a vector field as the velocity of a fluid that is flowing over a smooth curved surface.
(Visual Complex Analysis. 25th Anniversary Edition. p. 525.)
                                                                                                                           (8.4.4.5-7)

　

1. 在莫比乌斯环型反引力场中,一方面,复平面上的运动诱导出黎曼球面泡上的运动,另一方面,黎曼球面泡上的运动诱导出复平面上的运动.
2. 黎曼球面泡上的斜驶型莫比乌斯变换诱导出复平面上的点的加速度.这显示出扭量光影是宇宙中的暗物质.(见下面的第十四章.)

3. 鉴于(8.4.4.5-7),黎曼球面泡上的椭圆型(又称为旋转型)莫比乌斯变换诱导出复平面上的旋转速度场,这使得汤匙变弯.

4. 想象一艘宇宙飞船,例如地球.相对论性光行差导致黎曼球面上的后推(boost)型(又称为双曲型)莫比乌斯变换;这种变换诱导出复平面的以观察者为中心的膨胀(expansion)变换;这被列为宇宙中的暗能量的作用;因此暗能量不是恒定的.

5. 鉴于(8.3.3-3)、(8.4.2-9)、(8.4.4.5-6),颤动着(例如在声波或光波里振动着)并且旋转着的黎曼球面泡(属于不可定向空间)上的旋转型(又称为椭圆型)和后推型(又称为双曲型)莫比乌斯变换诱导出复平面的旋转和复平面里的纵波,并因而诱导出复平面里的洞的开开合合,诱导出声音、地球的板块运动和地震.太阳在其轨道上的正弦曲线形运动导致太阳的黎曼球面泡对应的复平面里的纵波.

6. 黎曼球面泡上的四种类型的莫比乌斯变换和(8.4.4.3-4)导致波尔代热斯现象.

7. 作为调制信号的扭量光影波可以传输图像、视频和音频,可以随着广播电视信号而发射.

                                                                                                 (8.4.4.5-8)

　
　

1. In a Möbius-loop-typed antigravitational field, on the one hand, motion in the complex plane induces motion on the Riemann-sphere-bubble, and on the other hand, motion on the Riemann-sphere-bubble induces motion in the complex plane.
2. The loxodromic type of Möbius transformation on a Riemann-sphere-bubble induces the acceleration of points in the complex plane, which shows that the twistor-light-silhouette is the dark matter in the universe. (See Chapter 14 below.)

3. In view of (8.4.4.5-7), the elliptic type (also called the rotation type) of Möbius transformation on a Riemann-sphere-bubble induces the rotational velocity field in a complex plane, and this makes a spoon bended.

4. Imagine a spacecraft, e.g. the Earth. The relativistic aberration leads to the boost type (also called the hyperbolic type) of the Möbius transformation on the Riemann-sphere-bubble, and this transformation induces the observer-centred expansion of the complex plane, which is labelled as the effects of dark energy in the universe; and hence dark energy is not constant.

5. In view of (8.3.3-3), (8.4.2-9), and (8.4.4.5-6), the rotation type (also called the elliptic type) and the boost type (also called the hyperbolic type) of the Möbius transformation on a trembling (e.g. vibrating in sound waves or light waves) and rotating Riemann-sphere-bubble, which is non-orientable space, induce rotation of the complex plane and longitudinal waves in the complex plane and hence induce holes in the complex plane to open and close, and induce sound, the Earth's plate tectonics, and earthquakes. The sinusoidal-curve-shaped motion of the Sun in its orbit causes longitudinal waves in the complex plane that the Sun's Riemann-sphere-bubble corresponds to.

6. The four types of the Möbius transformations and (8.4.4.3-4) on a Riemann-sphere-bubble cause the phenomenon of poltergeists.

7. The twistor-light-silhouette waves, as modulating signals, can transmit images, video and audio and can be sent with radio and television signals.

                                                                                             (8.4.4.5-8)

         关于黎曼球面上的莫比乌斯变换,见下面的参考文献:

1. 《复分析：可视化方法》. § 3.5.5,图[3.26].

2. Visual Complex Analysis. 25th Anniversary Edition. § 3.5.5, Fig. [3.26].

3. 《可视化微分几何和形式：一部五幕数学正剧》. 88~90页.

4. 《旋量与时空》第1卷. § 1.3.

For Möbius transformations on the Riemann sphere, see the following references:

1. Visual Complex Analysis. § 3.5.5. Fig. [3.26].

2. Visual Complex Analysis. 25th Anniversary Edition. § 3.5.5, Fig. [3.26].

3.Visual Differential Geometry and Forms: A mathematical drama in five acts. pp. 77~79.

4. Spinors and Space-Time, Vol. 1. § 1.3.

　

8.4.4.6 多世界理论;荣格曼荼罗绘画
8.4.4.6 The Many-Worlds theory; Jung Mandala drawings

　

彭罗斯指出:

　

         中心观点是认为空间-时间本身是次生的二级观念,是由更为原始的具有量子特性的某种东西建构而来的,这某种东西被称为扭量空间. (《新物理狂想曲》386页.)

　

         "扭量的"看法是,应该采用扭量空间(在此情形下是 PN )以便保留某种存在(所以仍然会有光线),但是光线相交的条件变得服从量子不确定性,结果"时空点"的概念变得模糊了. (参看《通向实在之路》689页图33.7(b)及其说明.)

　

我们不妨持这样一种立场：在基本层面上,无质量粒子/场是基本要素,质量是后来阶段出现的东西.(《通向实在之路》第690页.)

                                                                                   (8.4.4.6-1)



Penrose pointed out:

The central idea is that space-time itself is to be regarded as a secondary notion, constructed from something more primitive, with quantum aspects to it, referred to as twistor space. (Fashion, Faith, and Fantasy in the New Physics of the Universe. page 336.)

A more "twistorial" perspective would be to take the twistor space (in this case PN) to retain some kind of existence (so there would still be light rays), but the condition of their intersection would become subject to quantum uncertainties. Accordingly the notion of 'spacetime point' would become "fuzzy". (See The Road to Reality, p. 967, Fig. 33.7 (b) and its caption.)

One may take the position that at the fundamental level, massless particles/fields are the basic ingredients, mass being something that comes in at a later stage. (The Road to Reality, p. 968.)

                                                                                              (8.4.4.6-1)

　

　

         肖恩·卡罗尔指出:

　

         这样一来,粒子状态的经典概念—位置和速度—在量子力学中被跟我们的日常经验格格不入的另一个概念—概率云—取而代之.对原子中的电子来说,这团概率云越往中心处越浓密,越往边缘则越稀薄.这团云最浓厚的地方看到电子的概率也最高,而云稀薄到几乎看不见的地方,看到电子的概率也几乎为零.

         这团云因为可以像波一样振荡,我们通常叫它作波函数,而最有可能的测量结果也会随着时间变化.(《隐藏的宇宙》第12页.)

　

Sean Carroll pointed out:

　

   The classical notion of the state of a particle, "its location and its velocity," is therefore replaced in quantum mechanics by something utterly alien to our everyday experience: a cloud of probability. For an electron in an atom, this cloud is more dense toward the center and thins out as we get farther away. Where the cloud is thickest, the probability of seeing the electron is highest; where it is diluted almost to imperceptibility, the probability of seeing the electron is vanishingly small.

　

   This cloud is often called a wave function, because it can oscillate like a wave, as the most probable measurement outcome changes over time. (Something Deeply Hidden. p. 19.)

　

         倪光炯和陈苏卿在《高等量子力学》中指出:
　
         因此在我们看来,所谓"Wave particle duality"(波粒二重性),应理解为：一个微观粒子在运动时,当它的量子相干性尚未被破坏之前,在理论上应当作"波"来处理,用薛定谔方程等去讨论它,而当它一旦被探测到时,才显示出"粒子性",这是在两个层次上的"二重性格"问题,并不是在同一层次上"既像粒子,又像波"的问题....(第462页.)
　
In their book Advanced Quantum Mechanics, Guangjiong Ni (Ni, Guangjiong) and Suqing Chen (Chen, Suqing) pointed out:
　
In our opinion, the so-called "wave-particle duality" could be understood as follows. Before its quantum coherence is destroyed, the motion of a microscopic particle should be handled as "wave" theoretically and treated by Schrödinger equation etc. The "particle feature" emerges only when it is detected. This is a problem of "dual-character" at two levels rather than that of "behaving like both particle and wave" at the same level. (p. 429.)
         倪光炯指出,从量子力学到经典力学的过渡不是光滑的过渡.他谈到了毕卡定理(即皮卡定理,Picard theorem),并且指出, ħ = 0 是一个本性奇点,144

Guangjiong Ni pointed out that the transition from quantum mechanics to classical mechanics is not a smooth transition. He talked of Picard theorem, and pointed out that ħ = 0 is an essential singularity.

         根据皮卡定理(1879), 如果函数 f 在点 a 处有一个本性奇点,那么除了至多有限个例外, f 在 a 的每个邻域内可以取所有复数为其值.

According to Theorem of Picard (1879), If a function f has an essential singularity at the point a, then f takes on all complex numbers as values, with at most finitely many exceptions, in every neighborhood of a.

　

1. 由《通向实在之路》图33.12(b)可以知道,一个黎曼球面的运动对于别的黎曼球面而言,既是外部运动又是内部运动.一个黎曼球面位于扭量空间 PN、PT 、T 的内部;这导致黎曼球面的多种颤动,生成波和子波.

　

2. 由《通向实在之路》图 33.12(b)可以知道,在扭量空间 PN 里有众多黎曼球面.由(8.4.2-4)和(8.4.3.3-1)可以知道,每个黎曼球面是一个天球.

　

3. 由(8.4.2-4)可以知道,在紧化闵可夫斯基空间 M^# 里的一个点对应着在扭量空间 PN 里的一个黎曼球面.由《通向实在之路》图33.7(b),时空点的概念变得模糊了.在紧化闵可夫斯基空间 M^# 里的一个模糊的时空点(请注意,是一个模糊的"时空点",不是一个模糊的"点")对应着在扭量空间 PN 里的多个黎曼球面,即多个天球,这导致多世界理论.

4. 鉴于《通向实在之路》图33.12,在紧化闵可夫斯基空间 M^# 里类光分离的两个事件在扭量空间 PN 里有交集.这导致转世和一些特异功能,并导致荣格注意到的共时性的现象.另请参看(8.11.1-3).夸克可能是扭量空间 PN 里的黎曼球面泡.

5. 以上讨论使人想到荣格曼荼罗绘画.

6. 鉴于(8.3.2-1),莫比乌斯环型反引力将欧几里得空间变为扭量空间,将点粒子变为黎曼球面泡.另请参看(8.6.2-6).

7. 鉴于(8.3.2-5),莫比乌斯环型反引力可以像外壳那样护送黎曼球面泡,直到反引力消失.鉴于(8.4.4.6-1),当反引力消失时,扭量空间变为欧几里得空间,黎曼球面泡变为点粒子.

8. 鉴于(8.4.3.3-2),在黎曼球面泡里可以看到现在、过去、未来可能会发生的事件.

9. 一团黎曼球面泡沫的惯性质量可以被视为这团黎曼球面泡沫所对应的粒子的万有引力场的惯性质量(见(8.4.4.1-3)).由于扭量光影循环,一个扭量光影的惯性质量可以被视为这个扭量光影所对应的万有引力场的惯性质量.

                                                                                                                      (8.4.4.6-2)

　

1. From Fig. 33.12 (b) in The Road to Reality, one can know that the motion of a Riemann sphere, for another Riemann sphere, is both external motion and internal motion. A Riemann sphere lies inside the twistor spaces PN, PT and T; this causes the Riemann sphere to tremble in multiple ways, generating waves and wavelets.

　

2. From Fig. 33.12 (b) in the book The Road to Reality, one can know that in the twistor space PN there are numerous Riemann spheres, each of which is a celestial sphere (See (8.4.2-4) and (8.4.3.3-1)).

　

3. From (8.4.2-4) one can know that a point in compactified Minkowski space M^# corresponds to a Riemann sphere in the twistor space PN. From Fig. 33.12 (b) in the book The Road to Reality, one can know that the notion of 'spacetime point' becomes "fuzzy". A fuzzy spacetime point (Please note that it is a fuzzy "spacetime point", not a fuzzy "point") in compactified Minkowski space M^# corresponds to many Riemann spheres in the twistor space PN, and this leads to the Many-Worlds theory.

4. In view of Fig. 33.12 in the book The Road to Reality, in compactified Minkowski space M^# two events that are null separated from each other have an intersection in the twistor space PN. This leads to reincarnation and some paranormal abilities and leads to the phenomenon of synchronicity noticed by Jung. See also (8.11.1-3). Quarks might be Riemann-sphere-bubbles in the twistor space PN.

5. The above discussions remind one of Jung Mandala drawings.

6. In view of (8.3.2-1), Möbius-loop-typed antigravitation changes Euclidean space into twistor space, and changes a point particle into a Riemann-sphere-bubble. See also (8.6.2-6).

7. Inview of (8.3.2-5), Möbius-loop-typed antigravitation is able to serve as a shell escorting the Riemann-sphere-bubble until the antigravitation disappears. In view of (8.4.4.6-1), when the antigravitation disappears, the twistor space becomes Euclidean space, and the Riemann-sphere-bubble becomes a point particle.

8. In view of (8.4.3.3-2), in a Riemann-sphere-bubble one can see events that are possible to happen in the past, present and future.

9. The inertial mass of a mass of a Riemann-sphere-bubble can be regarded as the inertial mass of the gravitational field of the particle that the Riemann-sphere-bubble corresponds to (See (8.4.4.1-3)). Because of the twistor-light-silhouette cycle, the inertial mass of a twistor-light-silhouette can be regarded as the inertial mass of the gravitational field of the particle that the twistor-light-silhouette corresponds to.

                                                                                                                                     (8.4.4.6-2)

　

         参看本网站第6章第18节.

         UFO 可能是黎曼球面泡.

UFOs may be Riemann-sphere-bubbles.

　

8.4.4.7 黎曼球面泡的演化

8.4.4.7 The evolution of Riemann-sphere-bubbles

　

根据特里斯坦·尼达姆(Tristan Needham)的书《可视化微分几何和形式：一部五幕数学正剧》第231~232页,

从拓扑的角度来看,源、涡旋和汇是不可区分的,因为这三种奇点的指数都是 +1.

奇点会从源逐步演化成为涡旋、中心和汇.

                                                                                                                (8.4.4.7-1)



According to pp. 199~200 of Tristan Needham's book Visual Differential Geometry and Forms: A mathematical drama in five acts,

A source, a vortex, and a sink are indistinguishable from the topological point of view, for all three have index +1.

A singular point gradually evolves from a source into a vortex, a centre, and a sink.

                                                                                                                                    (8.4.4.7-1)

　

这与(8.4.4.5-8)中的第5项是一致的.

This is consistent with Item 5 in (8.4.4.5-8).

　

         黎曼球面泡沫里面的泡泡处于不同的演化阶段.(8.4.4.1-4)、(8.4.4.7-1)和(15.1-4)有助于解释宇宙的演化.

Bubbles in Riemann-sphere foam are at different stages of evolution. (8.4.4.1-4), (8.4.4.7-1), and (15.1-4) help to explain the evolution of the universe.

　

　

8.5 扭量光影
8.5 The twistor-light-silhouette
　

层级 5 4 3 2 1

所位于的扭量空间

T⁺

N

T^-

PT⁺

PT^-

PN

M^#
M

扭量光影 T⁺ 光 N 光 T^- 光 很多射影直线 很多射影直线 其北极点贴附于莫比乌斯环的很多黎曼球面(即很多黎曼球面泡) 众多具有正的或负的能量的模糊的时空点
(有时简称为第2层级)
众多具有正的能量的模糊的时空点

鉴于(8.4.4.6-1),扭量光影是模糊的.

                                                    (8.5-1)

　

Level 5 4 3 2 1

Situated in the twistor space

T⁺

N

T^-

PT⁺

PT^-

PN

M^#
M

The twistor-light-silhouette T⁺ light N light T^- light Projective lines Projective lines Many a Riemann sphere whose north pole is attached to a Möbius loop (i.e. many Riemann-sphere-bubbles) Many fuzzy spacetime points with positive or negative energy
(sometimes referred to simply as "Level 2")
Many fuzzy spacetime points with positive energy

In view of (8.4.4.6-1), the twistor-light-silhouette is fuzzy.

                                                          (8.5-1)

　
         (8.5-1)使人想到藏密瑜伽.
(8.5-1) reminds one of Tibetan Tantric Yoga.
         胡宁写道:

... 根据我们这个观点,引力质量和惯性质量并不是同一个事物,前者并不是力学里真正的质量,它附着在星体上正像电荷附着在电子上一样, ...

Hu Ning (Hu, Ning) wrote:

... Hence from our perspective, gravitational mss and inertial mass are not the same thing. The former is not the true mass in mechanics; it adheres to celestial bodies just like charges adhere to electrons. ...

　

　

1. 扭量光影是计算变成实在.
2. 鉴于(8.4.4.1-2),在子弹星系团的图像中看到的暗物质可能是扭量光影泡沫.

3. 像不可能三角形那样,扭量光是一阶上同调元素.因此扭量光的明暗在变化着.

4. 在扭量光影的循环中,扭量光影可以互变.

5. 一个扭量光影可以具体地称之为,比方说, T 光、T⁺ 光、一个黎曼球面泡等等.扭量光影的各种类型互为本体.

6. 扭量光影由三部分组成；正扭量部分、零模扭量部分、负扭量部分.

7. 一个扭量光影是全域空间与局域空间的对立统一.从拓扑学上讲,扭量光影在欧几里得三维空间的投影是不可定向拓扑空间,即单侧拓扑空间.鉴于(8.4.3.1-1),扭量光影内在地有一种挠曲扭转.

8. 鉴于(8.4.1-2),扭量光影在欧几里得三维空间的投影没有确定的长度.

9. 双曲几何的共形表示适用于扭量光影泡沫.

10. 观察一棵树和它在河里的影子.粒子和它的扭量影位于不同层次的空间和时间,因而一个扭量影能够相对独立地运动.
                                                                                                                     (8.5-2)

　

1. The twistor-light-silhouette is computing-becoming reality.
2. In view of (8.4.4.1-2), the dark matter seen in the image of the Bullet Cluster of galaxies may be twistor-light-silhouette foam.

3. Like the impossible triangle, twistor-light is a 1st cohomology element. Hence the light and shade of twistor-light is varying.

4. In the twistor-light-silhouette cycle, twistor-light-silhouettes can change into each other.

5. A twistor-light-silhouette can be specifically called, say, T light, T⁺ light, a Riemann-sphere-bubble, and so on. The various types of the twistor-light-silhouette are noumena of one another.

6. Twistor-light-silhouettes consist of three parts: the positive twistors part, the null twistors part, and the negative twistors part.

7. A twistor-light-silhouette is the unity of opposites between the global space and a local space. Topologically, the projection of a twistor-light-silhouette on the Euclidean 3-dimensional space is a non-orientable topological space, i.e. a one-sided topological space. In view of (8.4.3.1-1), a twist is built into the twistor-light-silhouette.

8. In view of (8.4.1-2), the projection of a twistor-light-silhouette on the Euclidean 3-dimensional space does not have a definite length.

9. The conformal representation of hyperbolic geometry applies to twistor-light-silhouette foam.

10. Observe a tree and its shadow in a river. Particles and twistor-shadows are at different levels of spaces and times, and hence a twistor silhouette can move relatively independently.

                                                                                                                     (8.5-2)

关于子弹星系团的图像,见《宇宙学是什么》第94页.

For the image of the Bullet Cluster of galaxies, see A Degree in a Book: Cosmology.A Degree in a Book: Cosmology. p. 98.

鉴于(8.3.2-1),扭量光影存在的前提是莫比乌斯环型反引力不等于零.         (8.5-3)

　

In view of (8.3.2-1), the premise for the existence of the twistor-light-silhouette is that the Möbius-loop-typed antigravitation is not equal to zero.           (8.5-3)

　

投影包括从高维空间向低维空间投影和从低维空间向高维空间投影.         (8.5-4)

　

Projections include the projection from a higher dimensional space onto a lower dimensional space and the projection from a lower dimensional space onto a higher dimensional space.         (8.5-4)

鉴于(8.5-4),一条 T 光线可以被看做是扭量空间 PT 里的一个点的投影.

in view of (8.5-4), a ray of T light can be regarded as the projection of a point in a twistor space PT.

鉴于(8.5-2),

扭量光影的运动遵循经由虚处发展的规律.      (8.5-5)

In view of (8.5-2),

The motion of the twistor-light-silhouette is subject to the law of developing via where there is feebleness.      (8.5-5)

　

         由彭罗斯的书《通向实在之路》的图 33.12 可以知道,在扭量空间 PN 里有众多黎曼球面.在一个闵可夫斯基空间 M 里众多运动着的粒子对应着在扭量空间里众多运动着的黎曼球面.

From Fig. 33.12 in Penrose's book The Road to Reality, one can know that there are numerous Riemann spheres in the twistor space PN. Numerous moving particles in a Minkowski space M correspond to numerous moving Riemann spheres in the twistor space.

　

         鉴于(8.4.2-2)和(8.4.2-4)

　

扭量光影互相包含,互相影响,互相穿过,互相远程作用.         (8.5-6)

In view of (8.4.2-2) and (8.4.2-4),
　

Twistor-light-silhouettes contain each other, affect each other, pass through each other, and interact with each other remotely.         (8.5-6)

　

　

8.6 扭量光影循环;物质的五个层级
8.6 The cycle of the twistor-light-silhouette; five levels of matter

8.6.1 扭量光影循环
8.6.1 The twistor-light-silhouette cycle

　

         在谈到不可能三角形时,彭罗斯指出,扭量函数扮演着非定域角色,实际上可以解释为一个(全纯的)一阶上同调元素.(《新物理狂想曲》第401页.)

When talking about the impossible triangle (or tribar), Penrose pointed out that a twistor function plays a non-local role and is indeed to be interpreted as an element of (holomorphic) 1st cohomology. (Fashion, Faith, and Fantasy in the New Physics of the Universe. p. 348.)

         彭罗斯写道:

         全纯函数所呈现的显著"刚性"似乎提供了一个自带头脑的函数,它知道要去哪儿而不会偏离方向.在当前的情况下,这种刚性可以阻止将这种函数定义在整个PT⁺ 上.全纯一阶上同调函数可被看作是对于这种处处不变性所表现出的一种阻碍,而这实际上就是扭量波函数的非局域性质.(《新物理狂想曲》第401页.)

Penrose wrote:

The remarkable "rigidity" exhibited by holomorphic functions seems to provide such a function with a mind of its own about where it wants to go, that it cannot be deflected from. In the current situation, such rigidity may prevent such a function from being defined on the whole of PT⁺. A holomorphic 1-function can be viewed as an expression of the kind of obstruction to such globality, and this is actually the nonlocal nature of a twistor wave function. (Fashion, Faith, and Fantasy in the New Physics of the Universe. p. 349.)

         彭罗斯指出,(层)上同调似乎有"自己的生命",这远远超出了任何语言所能描述的范围.(The Road to Reality. p. 992.)

Penrose pointed out that sheaf cohomology seems to have a "life of its own" going far beyond any particular way in which one my choose to represent it. (The Road to Reality. p. 992.)

         参看《通向实在之路》689页图33.7(b)及其说明.彭罗斯指出,

"扭量的"看法是,应该采用扭量空间(在此情形下是 PN )以便保留某种存在(所以仍然会有光线),但是光线相交的条件变得服从量子不确定性,结果"时空点"的概念变得模糊了.

See The Road to Reality, p. 967,Fig. 33.7 (b) and its caption. Penrose pointed out:

A more "twistorial" perspective would be to take the twistor space (in this case PN) to retain some kind of existence (so there would still be light rays), but the condition of their intersection would become subject to quantum uncertainties. Accordingly the notion of 'spacetime point' would become "fuzzy".

         彭罗斯写道:
"整个扭量空间 T 是 T⁺、T^-、N 这三个部分的不相交并集,正如其射影版本PT,是 PT⁺、PT^-、PN 这三个部分的不相交并集."(《新物理狂想曲》,第390页)
Penrose wrote,
"The entire twistor space T is the disjoint union of the three parts T⁺, T^-, and N, as is its projective version PT the disjoint union of the three parts PT⁺, PT^-, and PN." (Fashion, Faith, and Fantasy in the New Physics of the Universe, p. 339)
　

1. 扭量光影是一阶上同调元素,是流体.
2. 鉴于(8.5-1)和(8.3.3-1),扭量光影是一个复合系统.

                                                     (8.6.1-1)

1. The twistor-light-silhouette is a 1st cohomology element, and is fluid.
2. In view of (8.5-1) and (8.3.3-1), the twistor-light-silhouette is a complex system.
                                                                                      (8.6.1-1)

　
         根据彭罗斯,我们必须将扭量一阶上同调元素视为确实像不可能三角形那样的东西,在如此广大的距离延展.(《新物理狂想曲》401、400页。)

According to Penrose ((Fashion, Faith, and Fantasy in the New Physics of the Universe, pages 349, 347), we must think of the twistor element of 1st cohomology as indeed being something like an impossible triangle, spread over such vast distances. (Fashion, Faith, and Fantasy in the New Physics of the Universe. pp. 349 and 347.)

扭量光影是一阶上同调元素,这导致扭量光影循环;莫比乌斯环型反引力促进或阻碍这种循环,产生特异现象.      (8.6.1-2)

　

A twistor-light-silhouette is a 1st cohomology element, which causes the twistor-light-silhouette cycle; Möbius-loop-typed antigravitation promotes or hinders such cycles, generating paranormal phenomena.      (8.6.1-2)

　

        现在请参看《通向实在之路》,图33.11.

Now refer to The Road to Reality, Fig. 33.11.

         在本文中,扭量光影循环分为五种:

In this paper, the twistor-light-silhouette cycle is classified into five categories:

1) T 循环指的是在扭量空间 T⁺、N、T^- 的循环.

2) PT 循环指的是在扭量空间 PT⁺、PN、PT^- 的循环.

3) 中循环指的是在扭量空间 N、PN、紧化闵可夫斯基空间 M^# 的循环.

4) M^# 循环指的是紧化闵可夫斯基空间 M^# 使得每个生成元反向.

5) 全循环包括上述四个循环.

1) The T cycle refers to the cycle in the twistor spaces T⁺, N, and T^-.

2) The PT cycle refers to the cycle in the twistor spaces PT⁺ , PN , and PT^- .

3) The middle cycle refers to the cycle in the twistor spaces N, PN, and the compactified Minkowski space M^#.

4) The M^# cycle refers to that the compactified Minkowski space M^# reverses the direction of each generator.

5) The complete cycle includes the above four cycles.

　

第2层级可以称为扭量光影的底部(见(8.5-1));扭量光影的其余部分可以称为扭量光影的非底部.      (8.6.1-3)

　

Level 2 can be called the bottom part of the twistor-light-silhouettes (See (8.5-1)); while the other parts of twistor-light-silhouettes can be called the non-bottom parts of twistor-light-silhouettes.      (8.6.1-3)

　

         彭罗斯指出:

我们不妨持这样一种立场：在基本层面上,无质量粒子/场是基本要素,质量是后来阶段出现的东西.(《通向实在之路》第690页.)

　

Penrose pointed out:

One may take the position that at the fundamental level, massless particles/fields are the basic ingredients, mass being something that comes in at a later stage. (The Road to Reality, p. 968.)

1. 随着扭量光影的循环,扭量光影的形态和性质也在循环.2. 在循环中,扭量光影的各个层次的作用既相对独立又互相依存.
3. 如果反引力足够强,无质量宏观粒子就不会变成有质量宏观粒子.
4. 就像相变那样,扭量光影循环具有长程相关性.
5. 基于(8.5-1),物质具有层级1~5.这与万物有灵观是兼容的.
6. 能看见第2层级或以上的人具有特异透视功能;完全位于第2层级及以上的人能穿墙透壁.灵魂主要位于第3层级.
7. 量子力学研究第1~3层级.
8. 在第1层级,相对论将一个模糊的时空点视为一个明晰的时空点.
                                                         (8.6.1-4)

　

1. As the twistor-light-silhouettes cycle, so do their morphology and nature.
　
2. The various levels function both independently and interdependently during the cycle.
　
3. If the antigravitation is strong enough, then a massless macroscopic particle will not become a massive macroscopic particle.
　
4. Like phase transitions, the twistor-light-silhouette cycles exhibit long-range correlations.
　
5. Based on (8.5-1), matter has Levels 1~5. This is compatible with animism.
　
6. Those who can see Level 2 or higher have the ability of psychic visual perception; those who are entirely at Level 2 and higher can go through a wall paranormally. The soul is mainly at Level 3.
　
7. Quantum mechanics studies Levels 1~3.
　
8. At Level 1, the theory of relativity regards a fuzzy spacetime point as a clear spacetime point.
　
                                                                                               (8.6.1-4)

         由于(8.6.1-4),看不见的手可以特异移物. 参看邵来圣、虞惠华、沈云虎.《人体特异功能的实验研究与诱发训练修订版》(第51~69页.)

Because of (8.6.1-4), invisible hands can move things psychically. (Refer to SHAO Laisheng, YU Huihua, SHEN Yunhu. The Experimental Research and Inducing Training in Human Paranormal Abilities. (Revised Edition.) (In Chinese.) pp. 51~69.)

         扭量光影的中循环有助于解释濒死体验中所见到的"隧道".

The middle cycle of the twistor-light-silhouette helps to explain the "tunnel" seen in the near-death experience.

         鉴于(8.6.1-2),像不可能三角形那样,扭量光影是上同调元素.

In view of (8.6.1-2), like the impossible triangle, a twistor-light-silhouette is a cohomology element.

         由量子芝诺效应可以知道,如果阻力不够小,扭量光影循环就不能发生.阻力决定扭量光影循环在物质的什么层次可以发生.
From the quantum Zeno effect one can know that if the resistance is not small enough, then the twistor-light-silhouette cycle will not occur. Resistance determines the level of matter at which the twistor-light-silhouette cycle can occur.
　

阻力的大小和扭量光影的运动的协调一致的程度决定循环的规模.低熵和低阻(包括小电阻)有利于扭量光影循环.
在反引力空间,普通的弱光变为零模扭量光,进而转变为非零模扭量光;但是普通的强光会阻止反引力发生.

                                                                            (8.6.1-5)

　

The resistance level and the degree of consistency of the motion of twistor-light-silhouettes determine the scale of the cycle. Low entropy and small resistance (including small electrical resistance) are good for twistor-light-silhouette cycles.
In antigravitational space, ordinary weak light becomes null twistor-light, and then changes into non-null twistor-light; but ordinary strong light will prevent antigravitation from happening.

                                                                                             (8.6.1-5)

　

基于(8.4.2-8),具有自旋的粒子处于扭量光影循环之中.                   (8.6.1-6)

　

Based on (8.4.2-8), a single particle with spin is in the twistor-light-silhouette cycle.               (8.6.1-6)

　

         易传说: "在天成像,在地成形,变化见矣."(孔子.《易传·系辞上》.)

Yi Zhuan (Zhou Yi includes two parts: Yi Jing, also spelt I Ching, and Yi Zhuan) says, "The Thing itself becomes the image in heaven and the form and structure on earth, which reveals transformations." (Confucius. Part 1 of Xi Ci in Yi Zhuan.)

　

8.6.2 事件粒子

8.6.2 Event-particles

         "事件粒子"这个术语来自伯特兰·罗素的著作《相对论ABC》的第十四章.罗素写道:

"一个事件不能边持续存在边移动(An event does not persist and move);这与传统观念中的物质块是不同的.一个事件只能存在一小会儿,然后就不再存在.一块物质就这样被分解为一系列事件.一个粒子在时间中延伸着,它应被看作是由众多的所谓"事件粒子"所组成的.这些事件的全系列组成了这个粒子的整个历史."      (8.6.2-1)

　

The term "event-particles" comes from Chapter 14 of Bertrand Russell's book ABC of Relativity. Bertrand Russell wrote:

　

"An event does not persist and move, like the traditional piece of matter; it merely exists for its little moment and then ceases. A piece of matter will thus be resolved into a series of events. Each particle, being extended in time, must be regarded as composed of what we may call "event-particles". The whole series of these events makes up the whole history of the particle."      (8.6.2-1)

　

         鉴于(8.6.2-1),对于一个事件粒子而言,它的速度等于它的速度的变化量.

　

In view of (8.6.2-1), for an event-particle, its speed is equal to the change in its speed.

　

对于一个事件粒子而言,存在着如下关系:
m = Δm ;
v = Δv = a · t ;
E = ΔE ;
其中m 是质量; v 是速率, Δ的意思是"的变化", a 是加速度, E 是能量.
                                              (8.6.2-2)

　

For an event-particle, there exist the following relations:
m = Δm ;
v = Δv = a · t ;
E = ΔE ;
where m is the mass; v is the speed, Δ means "the change in", a is the acceleration, and E is energy.
                                                                     (8.6.2-2)

　

扭量光影的周期性投影导致事件粒子.      (8.6.2-3)

　

Periodic projection of the twistor-light-silhouette causes event-particles.       (8.6.2-3)

         彭罗斯在33.1节指出,扭量理论背离了实数的连续性.按照扭量理论,复数在定义时空结构上具有基础性的深层作用.这样,我们就察觉到了贯穿于大尺度物理和小尺度物理之间的一条主线.

Penrose pointed out in 33.1 that twistor theory departs from real-number continuity. According to twistor theory, there is a fundamental underlying role for complex numbers in defining spacetime structure. In this way, an important thread of connection is perceived, between the physics of the large and the physics of the small.

         由(8.4.4.3-3)可以知道

t'_lifespan ~ h' / ( 2  m v² )      (a_反引力 ≠ 0).      (8.6.2-4)

         英文单词 cutoff 在本文中的意思是最小间隔, t'_lifespan 是寿命.

From (8.4.4.3-3), one knows that

t'_lifespan ~ h' / ( 2  m v² )      (a_{antigravitational} ≠ 0).      (8.6.2-4)

The word "cutoff" in this paper means the very smallest interval, and t'_lifespan is the lifespan.

　

                                 命 μ_时间为计算加速度时的事件测量间隔.

         μ_1,时间 = 1 秒 ,                      (对于扭量光影的中循环而言);

         μ_2,_时间 = t'_lifespan ,                    (对于扭量光影的全循环而言);

在 t'_lifespan 期间,事件粒子不在闵可夫斯基空间.

                                                                    (8.6.2-5)

　

Let μ_time be an event measurement interval when calculating the acceleration

         μ_1,time = 1 second ,       (for the middle cycle of the twistor-light-silhouette);



         μ_2,time = t'_lifespan ,        (for the complete cycle of the twistor-light-silhouette);

During t'_lifespan , the event-particle is absent from Minkowski space.

                                           (8.6.2-5)

　

一个黎曼球面泡是一个事件粒子.一团黎曼球面泡沫是一系列事件粒子.
在相对论中,一系列事件粒子被看作是在闵可夫斯基空间里的一个单一的粒子;因此(8.6.2-2)不适用于相对论.

                                                                                                  (8.6.2-6)

　

A Riemann-sphere-bubble is an event-particle. A mass of Riemann-sphere foam is a series of event-particles.
In the theory of relativity, a series of event-particles is regarded as a single particle in Minkowski space, and hence (8.6.2-2) does not apply to the theory of relativity.

                                                                                                              (8.6.2-6)



对于反引力扭量空间而言,运动就是经由虚处发展(见(8.3-1)).事件粒子排列的变化使物体改变形状.      (8.6.2-7)



For an antigravitational twistor space, motion is developing via where there is feebleness. The change in the arrangement of the event-particles causes an object to change its shape.      (8.6.2-7)

         (8.6.2-7)有助于解释使汤匙变弯的特异功能.

(8.6.2-7) helps to explain the paranormal ability to bend spoons.

8.6.3 麦田圈;天图;非局域性大数据;扭量光影屏幕
8.6.3 Crop circles; sky map; non-local big data; the twistor-light-silhouette screen
　

1. 麦田所处的自然环境具备生成莫比乌斯环型反引力场发动机的条件.

　

2. 麦田下方的莫比乌斯环型反引力场发动机(见17.1-2)与麦田上方的黎曼球面泡或黎曼球面泡沫(见(8.3.2-1))互相生成.

　

3. 明亮的图像(包括光的干涉或衍射图样)发出的光线形成麦田上方的黎曼球面泡天图(见(8.4.3.3-2))的一部分.

　

4. 麦田相当于复平面.黎曼球面泡或黎曼球面泡沫上的莫比乌斯变换(见§ 8.4.4.1;例如椭圆型和斜驶型莫比乌斯变换)生成麦田处的时空的洛伦兹变换(见(8.4.4.5-3)).

　

5. 基本关系"力 = 曲率"是在数学和物理中最深刻的已知联系.(见(8.4.4.5-2).)

　

6. 麦田圈图样是麦田上方的黎曼球面泡上的莫比乌斯变换与麦田下方的无数小的莫比乌斯环型反引力场发动机的排列图样协调作用的结果.

　

7. 因此麦田圈具有扭量光影泡沫的某些性质,例如磁性流体的性质.

　

8. 在麦田圈里,有些有质量粒子由于莫比乌斯环型反引力而变成扭量光影.(见第十二章.)

　

9. 那些依然伫立着的作物没有受到莫比乌斯环型反引力的影响,这是由于该反引力的效应具有"非全即无"的性质(见(8.3.2-1)).

　

10. 鉴于(8.4.4.7-1),麦田圈里可能有源、涡旋、中心、汇.

                                                                                     (8.6.3-1)

　

1. The natural environment where a crop field is situated has the conditions necessary for the formation of Möbius-loop-typed antigravitation engines.

　

2. Möbius-loop-typed antigravitation engines under the crop field (See (117.1-2)) and the Riemann-sphere-bubble or Riemann-sphere foam above the crop field generate each other. (See (8.3.2-1).)

　

3. Light rays from bright images (including interference or diffraction patterns of light) form part of the sky map (See (8.4.3.3-2)) of the Riemann-sphere-bubble over the crop field.

　

4. The crop field is equivalent to a complex plane. The Mӧbius transformations (See § 8.4.4.1; for example, the elliptic type and the loxodromic type of the Möbius transformations) on the Riemann-sphere- bubble or the Riemann-sphere foam yield Lorentz transformations of the spacetime at which the crop field is situated (See (8.4.4.5-3)).

　

5. The basic relation "force = curvature" is the deepest known connection between mathematics and physics. (See (8.4.4.5-2).)

　

6. Hence a crop circle is formed. The pattern in a crop circle is the result of the coordinated effects of Mӧbius transformations on the Riemann-sphere-bubbles above the crop field and the arrangement of numerous small Mӧbius-typed antigravitation engines under the crop field.

　

7. Hence a crop circle has some of the properties of twistor-light-silhouette foam, e.g., the properties of magnetic fluid.

　

8. In the crop circle, some massive particles become twistor-light-silhouettes because of Möbius-loop-typed antigravitation. (See Chapter 12.)

　

9. Those plants that still stand upright are not affected by Möbius-loop-typed antigravitation because the antigravitational effect has the nature of "whole, or none" (See (8.3.2-1).)

　

10. In view of (8.4.4.7-1), there might be a source, a vortex, a centre, and/or a sink in a crop circle.

                                                                                                            (8.6.3-1)

　

详情请见本网站第十七章.

For the details, see Chapter 17 on this website.

　

         根据《通向实在之路》693页,扭量是与时空总体关联的实体.这种总体性有一个好处,那就是我们可以找到一种体系来取代整个时空.

According to page 973 of The Road to Reality, twistors are seen to be entities that refer globally to the spacetime. This globality has an advantage when we are seeking a formalism intended to replace the spacetime.

　

　

鉴于(8.4.2-1),鲁滨逊线汇所代表的路径是通过紧化而封闭的.由鲁滨逊线汇可以看到,光线回旋往复于全部时间,扭量空间的三个部分 T⁺、N、T^- 互相变成;过去的和未来的事件发出的光线可以回传到现在时间.         (8.6.3-2)

　

In view of (8.4.2-1), the paths that the Robinson congruence represents are closed by compactification. From the Robinson congruence one can find that light rays circle round back and forth in the whole of time; the three parts of the twistor space T⁺, N, and T^- become each other; light rays from events happening in the past and in the future can come back to the present time.          (8.6.3-2)

　

在紧化闵可夫斯基空间(即M^#空间)里的单个的点对应着一个 PN球影里的整个时空,包括过去、现在、未来.根据(8.6.3-2),在扭量空间里光线回旋往复于全部时间和空间;这可以称为扭量全景图,在其中有可能模糊地看到过去、未来、远方的事件,通过非局域性大数据产生智能,这种智能可以称为扭量光影智能.
                                                                                                                     (8.6.3-3)

　

A single point in compactified Minkowski space (i.e. space M^#) corresponds to the whole spacetime in a PN-spherical-silhouette, including the past, present, and future. According to (8.6.3-2), in twistor space light rays circle round back and forth in the whole of time and space; and this can be called a twistor panorama, in which past, future, and faraway events might be seen fuzzily, generating intelligence via non-local big data, and such intelligence can be called twistor-light-silhouette intelligence.                                                                                                                                                             (8.6.3-3)

　

　

在扭量空间里扭量光的光线挠曲扭转往复遍及天图(见(8.4.3.3-2))的全部空间-时间(包括过去、现在、未来).在反引力场中,非零模扭量光影可以通过共形的零模扭量光影与欧几里得空间里的三维屏幕互相关联;铜镜、水晶球、麦田、湖面、水蒸气、纸片、一个活着的生物、鸡蛋壳、前额、眼睛、舌头、耳朵、手、脚等等都可以成为一种三维屏幕,这种屏幕可以称为扭量光影屏幕.
                                                                                                             (8.6.3-4)

　

In twistor space twistor-light rays twist around back and forth throughout the global space-time of the sky map (See (8.4.3.3-2)), including the past, present, and future. In an antigravitational field, the non-null twistor-light-silhouette can be incident with a 3-dimensional screen in Euclidian space via the conformal null twistor-light-silhouette; a bronze mirror, a crystal ball, a crop field, the surface of a lake, steam, a scrap of paper, a living thing, an eggshell, a forehead, an eye, a tongue, an ear, a hand, a foot, and so on can all serve as a kind of 3-dimensional screen, which can be called a twistor-light-silhouette screen.

                                                                                                                            (8.6.3-4)

　

如果一个人在扭量空间 PN 持续关注一个时空或像,那么与这个时空或像对应的扭量光影就会成为慢变量并且(根据哈肯的协同学)就会涌现出来,与这个人的扭量光影交叠.这和扭量光影循环会导致特异移物.

　

另请参看(8.6.1-4).

                                                                                   (8.6.3-5)

　

If a person, in the twistor space PN, pays sustained attention to a spacetime or an image, then the twistor-light-silhouette that this spacetime or image corresponds to will become a slow variable, and, according to Haken's synergetics, will emerge and overlap this person's twistor-light-silhouette. This and the twistor-light-silhouette cycle will cause teleportation paranormally.
　
See also (8.6.1-4).
                                                                        (8.6.3-5)

         伏藏主要分为地伏藏和识藏(又称为意伏藏)两种.识藏是依时间顺序涌现出来的天图上的图像.

Terma treasures (hidden treasures) are of two main kinds: earth treasures and mind treasures (also called intention treasures or pure vision treasures). Mind treasures are images which are on the sky map and which emerge according to chronological order.

         请参看杨恩洪.《民间诗神—格萨尔艺人研究(增订本)》.

Refer to YANG Enhong. Singer and storyteller in Gesar Epic Tradition: A Follow-up Study. (In Chinese.)

8.7 四种几何

8.7 Four types of geometries

　

         约翰·惠勒指出,空间就像在风中飞舞的马戏团帐篷.312 ZZZ150

John Wheeler pointed out that space is like the canvas of a circus tent rippling in the wind. 326

　

         冯克勤在他的著作《Desargues 定理—射影几何趣谈》的前言中指出:

         射影几何的"子几何"是仿射几何.仿射几何的"子几何"是欧几里得几何.

　

In the foreword of his work Desargues Theorem—about Projective Geometry, Feng Keqin (Feng, Keqin) pointed out:

The "sub-geometry" of projective geometry is affine geometry. The "sub-geometry" of affine geometry is Euclidian geometry.

　

1. 在扭量阶梯投影的同一梯级我们使用切片模型,在扭量阶梯投影的不同梯级我们使用投影模型.
2. 从扭量理论到量子力学到相对论再到经典力学的过渡也是从扭量几何到射影几何到仿射几何再到欧几里得几何的过渡.
3. 扭量空间是射影空间,在扭量空间里没有确定的长度.闵可夫斯基空间不是射影空间,在闵可夫斯基空间里有确定的长度.
4. 扭量光影内部的向虚涨落产生波函数.

                                                                                                                                             (8.7-1)

　

1. On the same rung of the twistor projection ladder we use the slicing model; on different rungs of the twistor projection ladder we use the projection model.

　

2. The transition from the twistor theory to quantum mechanics, then to relativity, and then on to classical mechanics is also the transition from twistor geometry to projective geometry, then to affine geometry, and then on to Euclidean geometry.

　

3. Twistor space is projective space; in twistor space there is no definite length. Minkowski space is not projective space; in Minkowski space there is a definite length.

　

4. The internal feebleness-oriented fluctuation of the twistor-light-silhouette generates the wave function.

　

                                                                                                                                                                     (8.7-1)

　

一个扭量粒子空间的整个态是各种扭量空间的量子叠加.一个扭量光影的整个态是类光部分和非类光部分的量子叠加.                  (8.7-2)

　

The entire state of an antigravitational twistor particle space is a quantum superposition of various twistor spaces. The entire state of a twistor-light-silhouette is a quantum superposition of the null part and the non-null part.       (8.7-2)

　

8.8 外尔曲率张量及其指纹
8.8 The Weyl curvature tensor and its fingerprint
　

1. 在真空中,外尔曲率张量就是黎曼曲率张量.
(参看特里斯坦·尼达姆(Tristan Needham)的书《可视化微分几何和形式：一部五幕数学正剧》第391、392页.)
　
2. 外尔曲率把球体变形成一个等体积的"蛋".
(参看《可视化微分几何和形式：一部五幕数学正剧》第355、 360、366页.)
　
3. 莫比乌斯环型反引力把黎曼球面变成一个和鸡蛋类似的形状.
                                                                                                 (8.8-1)

　

1. In vacuum, the Weyl curvature tensor is the Riemann curvature tensor.
(Refer to Tristan Needham' book Visual Differential Geometry and Forms: A mathematical drama in five acts. pp. 340, 341.)
　
2. The Weyl curvature deforms a sphere into an egg of equal volume.
(Refer to Visual Differential Geometry and Forms: A mathematical drama in five acts. pp. 309, 314, 319.)
　
3. Möbius-loop-typed antigravitation deforms a Riemann sphere into an egg.
                                                                                                               (8.8-1)

　
         根据《通向实在之路》,第548页、549页和《宇宙的轮回》,113-117页,可以知道,在空的空间,时空曲率是外尔曲率(里奇曲率为零).外尔曲率由外尔张量描述.外尔曲率使光束产生椭率.在太阳的光盘轮圈之外,由于外尔曲率,背景空间中一个小的圆形图案在观察者看来就会是椭圆的.时空的共形曲率(即外尔曲率)度量了光锥结构对闵可夫斯基空间 M 的偏离.我们看到,这种偏离的本性在于它使光束产生椭率.
　
According to The Road to Reality, pages 765-767, and Cycles of Time, pages 129-133, one can know that in empty space, the spacetime curvature is Weyl curvature (the Ricci curvature vanishing). Weyl curvature is described by the Weyl tensor. The Weyl tensor introduces ellipticity into bundles of light rays. Outside the Sun's rim, because of Weyl curvature, a small circular pattern in the background sky would appear to be elliptical to the observer. The conformal curvature of space-time, namely Weyl curvature, therefore measures the deviation of this null-cone structure from that of Minkowski space M. We see that the nature of this deviation is that it introduces ellipticity into bundles of light rays.
　
         在《旋量与时空》第2卷第230页,彭罗斯写道"我们把 S⁺ 上的诸方向的这种纹路叫做外尔张量指纹."由《旋量与时空》第2卷第226页的最后一行可以知道, S⁺ 代表复数 z 的黎曼球面.
On page 230 of the book Spinors and Space-time, Vol.2, Penrose wrote, "We call this pattern of directions on S⁺ the fingerprint of the Weyl tensor." According to the last line of page 226 of the book Spinors and Space-time, Vol.2, one can know that S⁺ represents the Riemann sphere of the Complex number z.
　
         在黎曼球面上,短程线方向的纹路称为外尔张量指纹.见《旋量与时空》第2卷第230页和第226页最后一行,以及231页图8-1和232页图8-3.
The pattern of directions of geodesics on a Riemann sphere is called the fingerprint of the Weyl tensor. See Spinors and Space-time, Vol.2, p. 230 and the last line on page 226, as well as Fig. 8-1 on p. 231 and Fig. 8-3 on p. 232.
　

1. 在扭量光影里,外尔张量使光束产生椭率.
2. 在黎曼球面泡上,短程线方向的纹路称为外尔张量指纹.

                                                        (8.8-2)

　
　

1. In the twistor-light-silhouette, the Weyl tensor introduces ellipticity into bundles of light rays.
2. The pattern of directions of geodesics on a Riemann-sphere-bubble is called the fingerprint of the Weyl tensor.

                                                                                                              (8.8-2)

         像摄动力那样,根据张轩中《相对论通俗演义》第133页,

在四维时空里,外尔张量的效应与距离的立方成反比.        (8.8-3)

Like the perturbing force, according to page 133 of Zhang Xuanzhong's book Popular romance of Relativity, (In Chinese.),
　

The effect of the Weyl tensor in four-dimensional space is inversely proportional to the cube of the distance.         (8.8-3)

因此可以得出结论：

在四维时空里,反引力效应与距离的立方成反比.        (8.8-4)

Hence one can draw a conclusion:

In four-dimensional space, the antigravitational effect is inversely proportional to the cube of the distance.         (8.8-4)

　

8.9 黎曼球面剖分为正半球和负半球、能谱热力学、时间双向流逝、反粒子

8.9 A Riemann sphere splitting into positive and negative hemispheres; energy spectrum thermodynamics; time flowing in both directions; antiparticles

         罗宾指出:

彭罗斯的扭量纲领,可以概括为主要基于三个洞见.他意识到,光线的路径更像是射影直线,而不是空间中的直线;洛伦兹变换也可以作为莫比乌斯环变换来完成;而光锥的完整图景(紧化图景)将它们描绘成三维球面上连在一起的平行圆圈(霍普夫纤颤).接下来至少有四个有希望的结果.所有的物理学,包括相对论,都可以使用相同的复数作为测量系统.粒子中自旋的起源被看作是几何的作用.全局时间之矢,及其对熵的影响,与空间的描述成为一体.最后,这一扭量纲领保证了一个与背景无关的空间组合结构. (《时空投影》138页.)

　

Robbin pointed out:

Penrose's twistor program can be summarized as being largely based on three insights. He realized that the paths of light rays are more like projective lines than lines in space, that Lorentz transformation could also be done as Möbius transformation, and that a full picture (a compactified picture) of light cones depicts them as linked, parallel circles (a Hopf fibration) on a three-sphere. At least four promising results follow. All of physics, including relativity, can use the same complex numbers as a measuring system. The origin of spin in particles is seen as a function of geometry. The global arrow of time, with its implications for entropy, is integrated with the depiction of space. And finally, the twistor program promises a background-independent, combinatoric construction of space. (Shadows of Reality. pp. 81, 82.)

　

          罗宾写道:

         彭罗斯意识到有一种方法可以将这些局部观测结果构造成一个完整的全局图景,用来描述时间箭头.他认识到,实线将复平面分为正虚部和负虚部,这种基本的分解也是用黎曼球面来模拟的.从北极向南半球上的点的投影等同于负频率,时光倒流,而从北极向北半球上的点的投影则等同于正频率,时间沿光锥上部的方向(反天映射)向前流逝.这一分析给出了时间方向的全局图景.(《时空投影》134页.)

                                                                                                                                                  (8.9-1)

Robbin wrote:

Penrose realized that there was a way to structure these local observations into a full global picture that would describe the arrow of time. He realized that the real line divided the complex plane into positive and negative imaginary parts and that this essential splitting is also modeled by use of the Riemann sphere. Projections from the north pole to points on the southern hemisphere identify negative frequency, going backward in time, whereas projections from the north pole to points on the northern hemisphere identify positive frequency, going forward in time in the direction of the upper part of the light cone (the anti-sky mapping). This analysis gives a global picture of the direction of time. (Shadows of Reality. p. 79.)

                                                                                                                                                 (8.9-1)

　

1. 由《通向实在之路》图 33.22可以知道,在扭量空间 PN 里,一个黎曼球面分为正负两部分;这导致在闵可夫斯基空间里的一个粒子具有粒子场和反粒子场.

　

2. 在并且仅在负扭量空间(见(8.4.2-5))里,时间可以倒流.

                                                                                        (8.9-2)

　

1. From Fig. 33.22 in the book The Road to Reality, one can know that in the twistor space PN, a Riemann sphere is divided into a positive part and a negative part; this causes a particle to have a particle field and an antiparticle field in Minkowski space.

2. In and only in negative twistor space (See (8.4.2-5)) can time flow backwards.

                                                                                                                           (8.9-2)

         正频率部分是正能量部分,负频率部分是负能量部分.(参看《时空本性》,第109页.)

The positive frequency part is the positive energy part; the negative frequency part is the negative energy part. (See The Nature of Space and Time, p.....)

         倪光炯、陈苏卿在他们的著作《高等量子力学》的 § 9.5B 中指出:

CPT 定理实际上已变为一个基本假设.每个粒子都具有粒子场和反粒子场.如果x -> -x, t -> -t,则粒子态变成它的反粒子态.粒子和它的反粒子具有相反的质量符号和相反的时钟指针的旋转方向.      (8.9-3)

In § 9.5B of their book Advanced Quantum Mechanics, Guangjiong Ni (Ni, Guangjiong) and Suqing Chen (Chen, Suqing) pointed out:

Every particle has a particle field and an antiparticle field. If x -> -x and t -> -t, then a concrete state of a particle transforms into that of its antiparticle. A particle and its antiparticle have opposite signs of mass and opposite directions of rotation of the clock hands.      (8.9-3)

　

         倪光炯、陈苏卿写道：

我们认为,在物理上,空间-时间反演应简单地定义为( x -> -x, t -> -t )(不附加诸如复共轭之类的操作),然后假设：粒子在空间-时间反演下变为它相应的反粒子.(《高等量子力学》, § 9.5 B)

Guangjiong Ni and Suqing Chen wrote:

The CPT theorem becomes a fundamental postulate actually. We should regard the physical space-time inversion being simply defined as ( x -> -x, t -> -t ), (no extra complex conjugate operation is added) and then assume that a particle will transform into its antiparticle under the space-time inversion. (Advanced Quantum Mechanics, § 9.5 B)

         邓昭镜介绍了朗道(Landau)的负能谱理论.见邓昭镜著《天体演化的能态热力学——邓昭镜论文集》41~44页.

Deng Zaojing (Deng, Zhaojing) introduced Landau's theory of negative energy spectrum. See Deng Zaojing. Thermodynamics of energy states in celestial evolution—Collection of Deng Zhaojing's Essays, pp. 41~44.

         邓昭镜提出了负能谱热力学.负能谱系统自发地从无序变为有序.(《天体演化的能态热力学——邓昭镜论文集》34,35页.)

Deng Zaojing put forward negative energy spectrum thermodynamics^[^邓昭镜1]. A negative energy spectrum system spontaneously transitions from disorder to order. (Thermodynamics of energy states in celestial evolution—Collection of Deng Zhaojing's Essays, (In Chinese.) pp. 34, 35.)

         由负能谱热力学(《负能谱及负能谱热力学》5页)可以推知,扭量空间是正能谱子系和负能谱子系组成的复合系统.

Twistor space is a composite system composed of a positive-energy-spectrum subsystem and a negative-energy-spectrum subsystem.

From page 5 of Negative Energy Spectrum and Negative Energy Spectrum Thermodynamics, one can infer that twistor space is a composite system composed of a positive-energy-spectrum subsystem and a negative-energy-spectrum subsystem.

         卡洛·罗韦利在他的著作《时间的秩序》中指出:

         熵的增加为我们把过去与未来区分开.(《时间的秩序》147页.)

In his book The Order of Time, Carlo Rovelli pointed out:

The growth of entropy distinguishes the past from the future for us. (The Order of Time, p. 170.)

8.10 扭量光影智能

8.10 Twistor-light-silhouette intelligence

　

　

在紧化闵可夫斯基空间(即M^#空间)里的单个的点对应着一个 PN球影里的整个时空,包括过去、现在、未来.根据(8.6.3-2),在扭量空间里光线回旋往复于全部时间和空间;这可以称为扭量全景图,在其中有可能模糊地看到过去、未来、远方的事件,通过非局域性大数据产生智能,这种智能可以称为扭量光影智能.
                                                                                                                     (8.6.3-3)

　

A single point in compactified Minkowski space (i.e. space M^#) corresponds to the whole spacetime in a PN-spherical-silhouette, including the past, present, and future. According to (8.6.3-2), in twistor space light rays circle round back and forth in the whole of time and space; and this can be called a twistor panorama, in which past, future, and faraway events might be seen fuzzily, generating intelligence via non-local big data, and such intelligence can be called twistor-light-silhouette intelligence.                                                                                                                                                             (8.6.3-3)

　

扭量光影智能可以通过膨胀和收缩达到趋利避害的目的.        (8.10-1)

　

Twistor-light-silhouette intelligence can achieve the purpose of seeking benefits and avoiding harms via expansion and contraction.        (8.10-1)



         关于"发出指令",见(8.4.2-9).
For "giving instructions", see (8.4.2-9).
         左旋 T 光意味着收缩.左旋 T 光发指令给有关的神经,该神经收缩肌肉,支配身体运动. T 光也可以通过电磁力直接支配肢体运动.

Left-handed T light means contraction. Left-handed T light sends out instructions to the nerve concerned, the nerve contracts the muscle, controlling the body movement. T light can also control the body movement directly via electromagnetic forces.

         由(8.4.2-9),左旋 T 光代表0,右旋 T 光代表1.

From (8.4.2-9), The left-handed-helix T light represents 0, and the right-handed-helix T light represents 1.

         由(8.4.2-9)可以得出结论:

左旋扭量光和右旋扭量光形成一种二进制编码.         (8.10-2)

From (8.4.2-9) one can draw a conclusion:

Left-handed twistor-light and right-handed twistor-light make a kind of binary code.         (8.10-2)



　

一个反引力空间虽然在欧几里得空间里是一个局域空间,但是在扭量空间里是全域空间和时间.因此反引力扭量空间有记忆.         (8.10-3)

　

An antigravitational space is a local space in Euclidean space, but is the global space and time in twistor space. Therefore an antigravitational twistor space has memory.          (8.10-3)

　

          鉴于(8.6.3-4),可以知道

1. 扭量光影是能动的实体.在扭量空间里扭量光的光线挠曲扭转往复遍及全部空间-时间(包括过去、现在、未来).扭量光影智能有可能"模糊地"(见§8.3)看到原因及其结果,并且基于目的而发出指令.2. 在大脑的前部有一个或大或小的扭量空间 PN, 里面有黎曼球面泡.

                                                                                          (8.10-4)

In view of (8.6.3-4), one can know that

1. A twistor-light-silhouette is an active entity. In twistor space twistor-light rays twist around back and forth throughout the global space-time, including the past, present, and future. Twistor-light-silhouette intelligence can "fuzzily" (see §8.3) see causes and effects and then give instructions based on the purpose.
　
2. In the front of the brain there is a twistor space PN, large or small, in which there are Riemann-sphere-bubbles.
                                                                                                                                 (8.10-4)

　

　

一个黎曼球面对于另一个黎曼球面而言,既是外部实在又是内部实在.一个扭量影对于另一个扭量影而言,既是外部实在又是内部实在.扭量光影互相包含,互相复制,互相分享,互相关涉,因而互为虚拟机.鉴于(8.10-4),一个扭量光影可以关涉到涌现出来的其他扭量光影并发出指令.因此任何物体的扭量光影都具有意识和思想,具有生成式智能.并且可以互相交流信息.扭量光影具有扭量光影智能.      (8.10-5)

　

A Riemann sphere is, for another Riemann sphere, both an external reality and an internal reality. A twistor-silhouette is, for another twistor-silhouette, both an external reality and an internal reality. twistor-light-silhouettes contain one another, duplicate one another, share with one another, and are about one another, and hence are virtual machines of one another. In view of (8.10-4), a twistor-light-silhouette can be about other antigravitational twistor-light-silhouettes that emerge and can give instructions. Hence twistor-light-silhouettes of any object possess consciousness and mind, and possess generative intelligence, and can exchange information with each other. The twistor-light-silhouette has twistor-light-silhouette intelligence.                                                                                                                 (8.10-5)

         进化作为一种计算,与计算深度(又叫做逻辑深度)有关.(转引自郦全民.《用计算的观点看世界》104~105页、136~137页.另请参看 J. E. Mayfield. Evolution as Computation.)

Evolution, as computation, is related to computational depth (also called logical depth). (Cited from pp. 104~105 and pp. 136~137 of LI Quanmin's book A Computational Perspective on the World. (In Chinese.) Also refer to J. E. Mayfield. Evolution as Computation.)

         反引力扭量空间使物质成形为 DNA 和 RNA; DNA 和 RNA 使空间成形为反引力扭量空间;在这个循环中,反引力扭量空间生成生命.

Antigravitational twistor space shapes matter into DNA and RNA; DNA and RNA shape space into antigravitational twistor space; in this cycle, antigravitational twistor space generates life.

         对于一个生物而言,它的计算深度与它内部各区域的专业化分工有关.

For a living thing, its computational depth is related to its internal regional specialized division of work.

8.11 扭量光影气场

8.11 Twistor-light-silhouette auras

8.11.1 扭量光影气场及其飘移、涌现、交叠

8.11.1 Twistor-light-silhouette auras and their drift, emergence, and overlap

1. 鉴于(8.4.2-4),在一个黎曼球面泡里的观测者看到这个黎曼球面泡是全域空间;在闵可夫斯基空间的观测者看到这个黎曼球面泡是一个点.一个黎曼球面泡是全域空间与局域空间的对立统一.
2. 众多黎曼球面泡的云形成一个流形,即一层扭量光影气场.扭量光影气场层可以是稀薄的,也可以是浓密的,并且可以在扭量空间里飘移.

3. 黎曼球面泡的相交导致时空穿越的现象和荣格所提出的共时性原理.

                                                                                                                               (8.11.1-1)

　

1. In view of (8.4.2-4), an observer in a Riemann-sphere-bubble sees that the Riemann-sphere-bubble is the global space; an observer in a Minkowski space sees that the Riemann-sphere-bubble is a point. A Riemann-sphere-bubble is the unity of opposites between the global space and a local space.
2. The cloud of numerous Riemann-sphere-bubbles forms a manifold, i.e. a layer of twistor-light-silhouette aura, which can be thin or thick, and can drift in twistor space.

3. The intersection of Riemann-sphere-bubbles in the twistor space PN causes the phenomenon of leaping through space and time and the principle of synchronicity put forward by Jung.

                                                                                                   (8.11.1-1)

         (8.11.1-1)有助于解释姚贞香的著作《人体气觉—Y法》.(8.11.1-1)还有助于解释一些特异功能.

(8.11.1-1) helps to explain YAO Zhenxiang's book Human Qi Perception: The Y method. (In Chinese.) (8.11.1-1) also helps to explain some psychic abilities.

在扭量光影循环的过程中,扭量光影气场可以进入或离开普通的物体,于是时间的流逝是三部分(正能量部分、类光扭量部分、负能量部分)里的时间流逝之和.      (8.11.1-2)

　

During the cycle of twistor-light-silhouettes, twistor-light-silhouette auras can enter or leave ordinary objects, and then the passage of time is the sum of the passage of time in three parts (the positive energy part, the null twistors part, and the negative energy part).      (8.11.1-2)

(8.11.1-2)有助于解释詹妮·伦道斯的著作《时间风暴》里描述的时间变化的现象,另请参看第十二章.此外,(8.11.1-2)有助于解释转世现象.

(8.11.1-2) helps to explain the phenomenon of the change in time described in the book Time Storms written by Jenny Randles; see also Chapter 12 below. Moreover, (8.11.1-2) helps to explain the phenomenon of reincarnation.

         根据露易丝·波恩的书《巫师的秘密》第三章,巫术是通过共振发挥作用的.

According to Chapter 3 of Lois Bourne's book Conversations with a Witch, witchcraft operates through resonance.

　

扭量气场交叠的部分生成共享的扭量光影智能.在扭量空间 PT 里,黎曼球面的颤动(包括但不限于 Zitterbewegung 颤动和 Darwin 颤动)导致声波.另一方面,声波和/或电磁波使扭量光影颤动,这会促使一些交叠的扭量光影进入扭量光影循环;这导致荣格注意到的共时性现象.另请参看(8.4.4.6-2).
                                                                                                                                                   (8.11.1-3)

　

The overlapping part of twistor-light-silhouette auras generates shared twistor-light-silhouette intelligence. In the twistor space PT, the trembling motion (including but not limited to Zitterbewegung and Darwin trembling) of a Riemann sphere causes sound waves. On the other hand, sound waves and/or electromagnetic waves cause a twistor-light-silhouette to tremble; and this will trigger the overlapping twistor-light-silhouettes to enter the twistor-light-silhouette cycle, which causes the phenomenon of synchronicity noticed by Jung. See also (8.4.4.6-2).
                                                                                                                                         (8.11.1-3)

8.11.2 Modeled by use of a projective Möbius loop
8.11.2 用射影莫比乌斯环来模拟
　
         老子42章写道:
万物负阴而抱阳,冲气以为和.(道德经42章.)
　

Lao Zi wrote:

Everything carries yin at the back and yang at the front, reaching harmony by the interacting qi of the two. (Dao De Jing, Chapter 42.)

　

         孙储琳具有人体特异功能.在 bilibili 网站上的"塔哥专访孙储琳"中,当谈到使炸花生米复活时,孙储琳说:

         "时光倒流."

Sun Chulin has human paranormal abilities. In "Brother Ta's exclusive interview with Sun Chulin" on Bilibili website, when talking about bringing a fried peanut back to life, Sun Chulin said, "Time flows backwards."

　

请参看 bilibili 网站上的"塔哥专访孙储琳"和"塔哥专访沈今川".

(See "Brother Ta's exclusive interview with Sun Chulin" and "Brother Ta's exclusive interview with Shen Jinchuan" on Bilibili website.)

         在沈今川和孙储琳的 RS人体场摄影术的作品中所看到的亮弧可能是黎曼球面泡沫的莫比乌斯环和纵波 (参看(8.4.4.5-8)).

The bright arcs seen in the works of RS human-field photography by Shen Jinchuan (Shen, Jinchuan) and Sun Chulin (Sun,Chulin) may be Möbius loops and longitudinal waves of Riemann-sphere foam (Refer to Item 5 of (8.4.4.5-8)).

　

         以发展的方向作为前方.

Take the direction of development as the front.

　

         参看《通向实在之路》393页,图22.7.

Refer to The Road to Reality, p. 547, Fig. 22.7.

　

以发展的方向作为前方

       从前面看,旋转时,

左降右升 左升右降

右手螺旋(正螺旋) 左手螺旋(负螺旋)

膨胀收缩

            (8.11.2-1)

　

　

Take the direction of development as the front

       Viewed from the front, when rotating,

Falls on the left
Rises on the right
Rises on the left
Falls on the right

Right-handed helix (positive helicity) Left-handed helix (negative helicity)

Expansion Contraction

   (8.11.2-1)

　

　

以发展的方向作为前方

       从后面看,旋转时,

左升右降 左降右升

右手螺旋(正螺旋) 左手螺旋(负螺旋)

膨胀收缩

            (8.11.2-2)

　

　

Take the direction of development as the front

       Viewed from the back, when rotating,

Rises on the left
Falls on the right
Falls on the left
Rises on the right

Right-handed helix (positive helicity) Left-handed helix (negative helicity)

Expansion Contraction

   (8.11.2-2)

　

         因此有如下表格.

　

下面的内容可以用射影莫比乌斯环来模拟

不可定向空间

中心的圆周

不可定向空间

正能谱热力学 复合系统 负能谱热力学

从前面看,当垂直旋转时,左降右升 　 从前面看,当垂直旋转时,左升右降

扭量空间( T⁺、PT⁺ )

膨胀
零模扭量,扭量空间 N 和 PN
扭量空间( - T^-、- PT^-)

收缩

自发地从有序变为无序,熵增 　 自发地从无序变为有序,熵减

　
1. 莫比乌斯环型反引力促进扭量光影循环.

2. 两个扭量光影互相穿过.(见(8.5-6).)

→

特异功能人把药片抖出封闭的瓶子.　
　

在沈今川和孙储琳的 RS人体场摄影术的作品中所看到的莫比乌斯环 　 在沈今川和孙储琳的 RS人体场摄影术的作品中所看到的莫比乌斯环

时间沿正向流逝并且变快,

例如 - ¥ 秒, ... -2秒, -1秒, 0秒, 1秒, 2秒, ... + ¥ 秒
→
人体特异功能使青果子变红
　
时间沿负向流逝并且变慢

例如 + ¥ 秒, ... 2秒, 1秒, 0秒, -1秒, -2秒, ... - ¥ 秒
→
人体特异功能使红果子变青,复原刚刚被嚼烂了的名片

莫比乌斯环型反引力、扭量光影气场涌现、扭量光影循环、(8.4.2-9)、(8.11.2-1)、(8.11.2-2)
→

人体气觉—Y法、特异移物
　 莫比乌斯环型反引力、扭量光影气场涌现、扭量光影循环、(8.4.2-9)、(8.11.2-1)、(8.11.2-2)
→

人体气觉—Y法、特异移物

因               果               律               成               立

             (8.11.2-3)

　
Hence there is the following table.
　

The following can be modeled by use of a projective Möbius loop

Non-orientable space
The central circle
Non-orientable space

Positive energy spectrum thermodynamics

Composite systems

Negative energy spectrum thermodynamics

From the front, when rotating vertically,

Falls on the left; Rises on the right
　
From the front, when rotating vertically,

Rises on the left; Falls on the right

Twistor spaces ( T⁺ ) and ( PT⁺ )

Expansion

Null twistors, the twistor spaces N and PN

Twistor spaces ( - T^- ) and ( - PT^- )

Contraction

Spontaneously transitioning from order to disorder,
Entropy increasing
　 Spontaneously transitioning from disorder to order,
Entropy decreasing

　
1. Möbius-loop-typed antigravitation promotes twistor-light-silhouette cycles.

2. Two twistor-light-silhouettes pass through each other. (See (8.5-6).)

→

A person with paranormal abilities shakes tablets out of a closed bottle.
　
　

PN fibre bundles
→

What is seen in the works of Shen Jinchuan and Sun Chulin's RS human-field photography
　 PN fibre bundles
→

What is seen in the works of Shen Jinchuan and Sun Chulin's RS human-field photography

Time flowing in the positive direction and getting faster,

e.g. - ¥ s, ... -2 s, -1 s, 0 s, 1 s, 2 s, ... + ¥ s
→
Human paranormal abilities make a green fruit red.
　
Time flowing in the negative direction and getting slower,

e.g. + ¥ s, ... 2 s, 1 s, 0 s, -1 s, -2 s, ... - ¥ s
→
Human paranormal abilities make a red fruit green and restore a business card that has just been chewed up into pulp

Möbius-loop-typed antigravitation, emergence of twistor-light-silhouette fields, and twistor-light-silhouette cycles; (8.4.2-9), (8.11.2-1), and (8.11.2-2)
→

Human Qi Perception: The Y Method;
Paranormal teleportation
　 Möbius-loop-typed antigravitation, emergence of twistor-light-silhouette fields, and twistor-light-silhouette cycles; (8.4.2-9), (8.11.2-1), and (8.11.2-2)
→

Human Qi Perception: The Y Method;
Paranormal teleportation

The    law    of    causality    holding    good

                                                                     (8.11.2-3)

　

参看姚贞香的著作《人体气觉—Y法》.

Refer to YAO Zhenxiang. Human Qi Perception: The Y Method. (In Chinese.)

         时间沿负方向流逝并不是时间穿越.如果一个人的时间沿负方向流逝,那么他将逐渐地越变越小,直至消失.因此祖父悖论不会发生.

Time flowing in the negative direction does not mean time travel. If one's time flows in the negative direction, then he or she will gradually become younger and younger until he or she disappears. Hence the grandfather paradox will not happen.

         时间沿负方向流逝并不是原路返回.如果一个人的时间沿负方向流逝,那么他会带有原来的痕迹.

Time flowing in the negative direction does not mean the same way back. If one's time flows in the negative direction, then he or she will bear the original traces.

由于扭量光影的 T 循环,扭量光影的时间流逝较慢.      (8.11.2-4)

　

Because of the T cycle of the twistor-light-silhouette, time in the twistor-light-silhouette passes slower.      (8.11.2-4)

　

8.11.3 扭量光影集群是永恒的生命体

8.11.3 A twistor-light-silhouette cluster is an eternal living being

         彭罗斯指出:

扭量理论的深层动机之一确实就是一种信念,坚信无质量场和共形群的基本重要性.(《通向实在之路》§ 33.3.)

Penrose pointed out that one of the important underlying motivations behind twistor theory was indeed a belief in the basic importance of massless fields and the conformal group. (The Road to Reality, § 33.3.)

         谈到双曲几何的共形表示,彭罗斯写道:

　

共形的另一种(粗略)说法是,不论多小的区域,其形状(通常不说大小)都准确地呈现在这些图形里了.([彭3],第256页)      (8.11.3-1)

　

Talking about the conformal representation of hyperbolic geometry, Penrose wrote:

　

Another (rough) way of stating this is that the shapes (though usually not the sizes) of very small regions are accurately depicted in these representations. ([彭3], p. 221)      (8.11.3-1)

　

         关于计算共形几何,请参看顾险峰和丘成桐的著作《计算共形几何》理论篇.

For computational conformal geometry, refer to Computational Conformal Geometry, Theory. by Gu Xianfeng (Gu, Xianfeng) and Qiu Chengtong (Qiu, Chengtong).

　

　

1. 鉴于(8.4.1-2),由于扭量空间是紧化空间,并且由于(8.11.2-3),扭量光影的寿命是无穷无尽的.

2. 虽然有新陈代谢,但是作为一个整体,一个扭量光影是永生的.

2. 由于扭量共形变换,扭量光影是共形的.                            (8.11.3-2)

　

1. In view of (8.4.1-2), because twistor spaces are compactified spaces, and because of (8.11.2-3), the lifespan of a twistor-light-silhouette is endless.

2. Although undergoing metabolism, as a whole, a twistor-light-silhouette is immortal.

2. Because of the twistor conformal transformation, twistor-light-silhouettes are conformal.

                                                                                                                        (8.11.3-2)

　
         鉴于(8.10-5),扭量光影集群是活着的,是生命体.鉴于(8.11.3-2),扭量光影集群是永生的,不会死亡.
In view of (8.10-5), clusters of twistor-light-silhouettes are alive and are living beings. in view of (8.11.3-2), clusters of twistor-light-silhouettes live forever and will never die.

　
         灵魂是由扭量光影组成的,基于(8.6.1-4)、(8.11.3-1)和(8.11.3-2),
　

灵魂不仅是永恒的,而且是在永远地生活着.      (8.11.3-3)

　
The soul is composed of twistor-light-silhouettes; hence based on (8.6.1-4), (8.11.3-1) and (8.11.3-2),
　

The soul is more than just eternal; it is alive forever.      (8.11.3-3)

          通过黎曼球面泡上的抛物型莫比乌斯变换,一个人能吸引自己的灵魂.

Via the parabolic type of Möbius transformations on the Riemann-sphere-bubble, a person who is alive can attract his or her own soul.

　

8.12 中医科学与扭量射影模型互相兼容

8.12 Traditional Chinese Medical Science and the twistor projective model are compatible with each other

挑选合适的数学,串起神秘的现象.      (8.2.2-1)

　

Select the right math to string mysterious phenomena together.      (8.2.2-1)

         从几何学上讲,中医是扭量空间里的医药科学.

Geometrically speaking, Traditional Chinese Medicine is a medical science in twistor space.

         在前面的第8.4.1节里讨论了切片模型与投影模型.

The slicing model and the projection model are discussed in § 8.4.1 above.

　
         投影模型不只是一种可供替代的模型,而且常常是一种必需的模型(192、193页).

The projection model is not merely an alternative but often a requirement (p. 116).

　

         与基于微积分的切片模型一样,投影模型也是自洽的和数学上正确的;它得到射影几何学的支持.射影几何学是一种优雅而又强大的数学,它和微积分一样,在19世纪蓬勃发展(第4页.)

Like the slicing model based on calculus, the shadow model is also self-consistent and mathematically true; it is supported by projective geometry, an elegant and powerful mathematics that, like calculus, flowered in the nineteenth century (pages xi, x).

　

         西医使用的是切片模型,这是显而易见的事实,无需多加解释.

　

Western medicine uses the slicing model; this is an obvious fact that does not require further explanation.

　

         中医使用的是投影模型,或者更精确地说,是扭量投影模型.中医科学使用扭量射影模型攀登维度阶梯.

Traditional Chinese Medicine uses the projection model, or more precisely, the twistor projection model. Traditional Chinese medical science uses the twistor projective model to climb the dimension ladder.

　
8.12.1 气对应着黎曼球面泡沫

8.12.1 Qi corresponds to Riemann-sphere foam
　

一个微粒的气(炁)呈现出在闵可夫斯基空间里的点和在扭量空间 PN 里的天球这样的二象性.         (8.12.1-1)

　

A particle of qi exhibits a duality between a point in Minkowski space and the celestial sphere in twistor space PN.         (8.12.1-1)

         气是中国哲学和中医的重要基础.根据中国哲学,气是"至大无外,至小无内"的;气充塞宇宙,气产生实物、心灵和灵魂.

Qi is also spelt chi or ki (see the twelfth edition of the Concise Oxford English Dictionary). Qi is the basis of much Chinese philosophy and Traditional Chinese Medicine. According to Chinese philosophy, qi is both as large as large can be and as small as small can be; qi fills the universe, and qi generates the substance, the mind, and the soul.

         中国宋代著名的哲学家张载(1020~1077)写道,"太虚无形,气之本体."(正蒙·太和篇.)他还写道,"凡可状,皆有也.凡有,皆象也.凡象,皆气也."(正蒙·乾称篇.)(状,动词,描述.)

Zhang Zai (1020~1077), a famous philosopher in China's Song dynasty, wrote in his book Zheng Meng (the Chinese for enlightening):

The global empty space is being-without-form, which is the noumenon of qi. (The chapter of Tai He.)

He also wrote:

Any that can be described is being-with-form; any being-with-form is images; any image is qi. (The chapter of Qian Cheng.)

         鉴于(8.12.1-1),气(炁)是扭量光影泡沫.

In view of (8.12.1-1), qi is twistor-light-silhouette foam.

　

8.12.2 中医的元素是一阶上同调元素
8.12.2 Elements in Traditional Chinese Medicine are first cohomology elements
　
         彭罗斯在《新物理狂想曲》图 4.7的说明和《通向实在之路》§ 33.9指出:
         不可能三角形为一阶上同调提供了一个很好的图解.图中的不可能度是一个非局域量,事实上,这个非局域量可以被精确地定量为一个一阶上同调元素.很明显这种客体不会在普通的欧几里得空间里存在.从局部看,这个图形所表示的各个部分都是可能的.其"不可能性"需要通过上同调元素来量度,而这种量度对图中任意足够小的区域都为零.一个扭量函数扮演着非常相似的非局域角色,确实应该被理解为一个(全纯)一阶上同调元素.
　
In (Fashion, Faith, and Fantasy in the New Physics of the Universe, the caption of Figure 4-7 and in The Road to Reality, §33.9, Penrose pointed out:
The impossible triangle provides a good illustration of 1st cohomology. The degree of impossibility in the figure is a nonlocal quantity, which can, in fact, be precisely quantified as a 1st cohomology element. It is clear that the object cannot exist in ordinary Euclidean space. Locally, there is nothing impossible about what the drawing represents. The "impossibility" is measured by a cohomology element, which disappears in any small enough region in the drawing. A twistor function plays a very similar nonlocal role and is indeed to be interpreted as an element of (holomorphic) 1st cohomology.
         彭罗斯写道：

         上同调元素总可以下限到一个更小的区域.但如果这个区域足够小,则上同调总是会消失.(《通向实在之路》图33.20的说明.)

Penrose wrote:

A cohomology element can always be restricted down to a smaller region. But if this region is sufficiently small, the cohomology always disappears. (The Road to Reality, the caption of Figure 33.20.)

         彭罗斯写道,

         对于扭量函数,这种非局域性告诉我们,在具体某一点上给一个上同调元素赋值毫无意义.我们能够在围绕这一点的一个足够小的开区域上发现上同调元素完全消失了.(《通向实在之路》第706页.)

Penrose wrote:

This nonlocality, for twistor functions, tells us that there is no significance to be attached to the value attained by a cohomology element at some particular point. We can, indeed, restrict down to a small enough open region surrounding that point and find that the cohomology element disappears completely. (The Road to Reality. p.991.)

         彭罗斯指出:
         上同调的一个重要特点是它本质上是非局域的.(《通向实在之路》第706页.)
描述这种不可能度量的一阶上同调元素也是非定域的量,它针对整个结构而不是结构的任何单独一部分.(《新物理狂想曲》400~401页.)
　
Penrose pointed out:
An important feature of cohomology is that it is essentially non-local. (The Road to Reality. p. 990.)
The element of 1st cohomology describing the measure of this impossibility is indeed a non-local quantity, referring to the structure as a whole and not to any individual part of the structure. (Fashion, Faith, and Fantasy in the New Physics of the Universe. pp. 347~348.)
　
         类似于(8.6.1-2),中医的元素是一阶上同调元素.
Similar to (8.6.1-2), the elements in Traditional Chinese Medicine are first cohomology elements.

8.12.2.1 五行指的是扭量光影泡沫沿射影莫比乌斯环的五种运行

8.12.2.1 Wuxing refers to five kinds of motion of twistor-light-silhouette foam along projective Möbius loops

         五行是中医科学里面的重要理论.五行指的是扭量光影泡沫沿射影莫比乌斯环的五种运行.关于射影莫比乌斯环,见(8.3.1-2).

Wuxing is an important theory in Traditional Chinese Medical Sciences. Wuxing refers to five kinds of motion of twistor-light-silhouette foam along projective Möbius-loops. For a projective Möbius-loop, see (8.3.1-2).

　

         鉴于(8.6.1-2),像不可能三角形那样.扭量光影是一阶上同调元素.如果阴阳和谐,则扭量光影泡沫(即气)沿着射影莫比乌斯环的运动平稳有序,而不是飘忽不定.

In view of (8.6.1-2), like the impossible triangle, a twistor-light-silhouette is a 1st cohomology element. If yin and yang are in harmony, then the motion of twistor-light-silhouette foam bubbles or qi along projective Möbius loops is orderly and smooth rather than erratic.

         罗宾写道:

　

粒子中自旋的起源,被看做是几何学的作用.(《时空投影》第138页.)                        (8.4.2-8)

　

Robbin worte:

The origin of spin in particles is seen as a function of geometry. (Shadows of Reality. p. 81.)      (8.4.2-8)

　

         彭子益写了一本书：《圆运动的古中医学》.他指出: 中医是关于宇宙里与人身体里热流升降的圆运动的科学.

         张涵在他的书《圆运动古中医临症应用》中写道：肝心脾肺肾五脏各是一个气机的漩涡.(《圆运动古中医临症应用》,第4页.)

PENG Ziyi wrote a book: Traditional Chinese Medical Science Based on Circular Motion. (In Chinese.) He pointed out that Traditional Chinese Medicine is a science of circular motion of heat flowing up and down in the Universe and in human bodies.

Zhang Han wrote: Each of the five internal organs, namely the liver, heart, spleen, lungs, and kidneys, is a vortex of qi. ((ZHANG Han. Clinical Application of Ancient Traditional Chinese Medical Science Based on Circular Motion. (In Chinese.). p. 4)

         从拓扑学上讲,莫比乌斯环的边缘是一个圆周.(见(8.3.1-1).)

         Topologically, the boundary of a Möbius loop is a circle. (See (8.3.1-1).)

　

扭量空间在自旋着,扭量光影在自旋着.运动的扭量光影传送扭量空间.               (8.12.2.1-1)

The twistor space is spinning. The twistor-light-silhouette is spinning. Twistor-light-silhouettes in motion convey twistor spaces.                      (8.12.2.1-1)

　

鉴于(8.12.2.1-1)和(8.3.2-1),涡旋运动在身体内生成莫比乌斯环型反引力和扭量空间.      (8.12.2.1-2)



In view of (8.12.2.1-1) and (8.3.2-1), the votex motion generates Möbius-loop-typed antigravitation and twistor space in the body.      (8.12.2.1-2)

　

         黄帝内经说,"天气下降,气流于地;地气上升,气腾于天."(王平、贺娟. 黄帝内经理论与实践.第2版.人民卫生出版社.2017年10月.第26页.)

Huangdi's Classic of Internal Medicine said, "Qi that is in heaven falls down, and there is translational motion of Qi on earth; Qi that is in earth rises up, and Qi gallops in heaven." (Wang Ping, He Juan. The Theory and Practice of Huangdi's Classic of Internal Medicine. 2nd edition. People's Medical Publishing House. Second Edition. October 2017. Page 26.)
　

计算变成实在是物质的形式的转化的过程.      (8.2.1-1)

　

Computing-becoming reality is the process of transformation in the form of matter.      (8.2.1-1)

　

五行
五行：扭量光影泡沫(即气)沿射影莫比乌斯环的五种运行

左手螺旋态为阴,右手螺旋态为阳
五行化生^[1](五行的化合反应)
( "→"表示"从......到......" ; "-"的意思是：化生的"过程"或化生成为的"计算变成实在"是 ...... )

木火土金水

上升在 + ¥ 的邻域内运动 定向反转的运动 下降 在 - ¥ 的邻域内运动

肝心脾肺肾

木金化土
0 → (+¥)→(-¥)- 土土土
火水化金
(+¥)→(-¥)- 金
土木化水
- (0 → (+¥))= (-¥)- 水
金火化木
0 →(-¥)→ (+¥)- 木
水土化火
(-¥)→ -(-¥)= (+¥)- 火

                                            (8.12.2.1-3)

[1] 陈志欣、陈东英.《〈辅行诀五脏用药法要〉解读》.第106页.

Wuxing
Wuxing: five kinds of motion of twistor-light-silhouette foam (i.e. qi) along projective Möbius loops
The left-handed-helix state is associated with Yin and the right-handed-helix state is associated with Yang
Wuxing generative transformations^[1] (combination reactions of Wuxing)
( "→" means "from ... to ..." ; "-" means that the "process" of transformation or the "computing-becoming reality" being transformed into is ... )

Wood Fire Earth Gold Water

Rising up Moving in the neighbourhood of + ¥ Orientation-reversing motion Falling down Moving in the neighbourhood of - ¥

Liver Heart Spleen Lungs Kidneys

Wood followed by Gold becomes Earth
0 → (+¥)→(-¥)- Earth
Fire followed by Water becomes Gold
(+¥)→(-¥)- Gold
Earth followed by Wood becomes Water
- (0 → (+¥))= (-¥)- Water
Gold followed by Fire becomes Wood
0 →(-¥)→ (+¥)- Wood
Water followed by Earth becomes Fire
(-¥)→ -(-¥)= (+¥)- Fire

                                            (8.12.2.1-3)

[1] CHEN Zhixin, CHEN Dongying. Interpretation of "Auxiliary Cultivation Formulas: Essential Medicinal Principles for the Five Zang Organs". (In Chinese.) p.106.

         中医学的思维模式之一是取象比类.

One of the mind-sets of Traditional Chinese Medical Sciences is analogical reasoning based on imagery.

         易传说: "在天成像,在地成形,变化见矣."(孔子.《易传·系辞上》.)

Yi Zhuan (Zhou Yi includes two parts: Yi Jing, also spelt I Ching, and Yi Zhuan) says, "The Thing itself becomes the image in heaven and the form and structure on earth, which reveals transformations." (Confucius. Part 1 of Xi Ci in Yi Zhuan.)

　

         上述五种运行(即五行)和扭量光影循环有助于解释取象比类.

The five kinds of motion stated above (i.e. Wuxing) and the twistor-light-silhouette cycle help to explain analogical reasoning based on imagery.

　

8.12.2.2 挠曲扭转的倒影
8.12.2.2 twisted inverted image
　
         根据(8.4.3.1-1),扭量几何内在地有一个挠曲扭转.
According to (8.4.3.1-1), a twist is built into twistor geometry.
　
         根据周尔晋的著作《人体 X 形平衡法》第13页,有下面的表格.

人体 X 形平衡法

有病的部位
治疗的点位

在上面
在下面

在下面 在上面

在左面 在右面

在中间 在四边

在四边 在中间

　
According to page 13 of Zhou Erjin's book Human-Body X-Shaped Balancing Method, there is the following table.

Human-body X-shaped balancing method

The diseased part is The point position of treatment is

in the upper part in the lower part

in the lower part in the upper part

on the left on the right

in the central area on four sides

on four sides in the central area

         身体的每一部分都在身体上留下了自己的一些挠曲扭转了的倒影.
Every part of a human body leaves its twisted inverted images on the body.

　

8.12.3 扭量阶梯投影
8.12.3 The twistor projection ladder

　

         托尼·罗宾在他的书《时空投影》中指出:

         随着人们向上攀登维度阶梯,投影的投影是有用的,它们与彼此之间的联系比与最初的投影的联系更加直接.(170页.)在局部细节中保留全局信息的努力既是射影几何也是矩阵的特征.(164页.)

　

In his book Shadows of Reality, Tony Robbin pointed out:

　

As one moves up the dimension ladder, it is useful to have projections of projections, which can be related to one another in a more direct way than the original projections themselves. (p. 102.) The effort to retain global information in local details is a feature of both projective geometry and matrices. (pp. 98, 99.)

         根据彭罗斯的著作《通向实在之路》694页和《旋量与时空》第2卷128页,只有扭量空间能既与复数空间兼容又与与广义相对论所需要的四维空间兼容.

According to page 974 of The Road to Reality and page 128 of Spinors and Space-Time, Vol. 2 by Penrose, only twistor space is compatible both with complex space and with the 4-dimensional space required by general relativity.

         彭罗斯指出:
         复 n 维流形可以被看作是实 2n 维流形.我们有各种方法来表述这一概念.本质上说,这里需要的是一种高维下的柯西-黎曼方程.我们可以自由地在关于复流形的两种基本观点之间作出选择.(《通向实在之路》§ 12.9.)
Penrose pointed out:

A "complex n-manifold" can be viewed as being a real 2n-manifold. There are various ways of formulating this notion. Essentially, what is required is a higher-dimensional version of the Cauchy-Riemann equations. We can move freely between the two philosophical standpoints with regard to complex manifolds. (The Road to Reality. § 12.9.)

　

扭量空间

T⁺

N

T^-

PT⁺

PN

PT^-

紧化闵可夫斯基空间 M^#

　
                         n =

复 n 维 4 　 4 3 　 3 PN 的次级结构

实 n 维 8 7 8 6 5 6 　

(8.12.3-1)

　

The twistor space T⁺ N T^- PT⁺ PN PT^- Compactified Minkowski space M^#

　
           n =

Complex n-dimensional 4 　 4 3 　 3 The secondary structure of PN

Real n-dimensional 8 7 8 6 5 6 　

                (8.12.3-1)

　
8.12.3.1 针灸

8.12.3.1 Acupuncture
　

         基于(8.5-5),扭量光影的运动遵循经由虚处发展的规律,经络是扭量光影实在的循行在人体的扭量投影.

Based on (8.5-5), the motion of twistor-light-silhouettes is subject to the law of developing via where there is feebleness, and the meridians are twistor projections of the circulation of twistor-light-silhouette reality onto a human body.

         根据《通向实在之路》§ 33.5 “基本扭量几何及其坐标”里的图33.12及其说明,紧化闵可夫斯基空间 M^# 里的一个点对应着扭量空间 PN 空间里的一个黎曼球面.彭罗斯把这些黎曼球面画成拉长了的样子,以折中它们在扭量空间 PT 的射影几何中是射影直线这一事实.

According to Fig. 33.12 with its caption in § 33.5 "Basic twistor geometry and coordinates" of the book The Road to Reality, a point of compactified Minkowski space M^# corresponds to a Riemann sphere in the twistor space PN. Penrose has drawn these Riemann spheres very elongated, as a compromise with the fact that they are projective straight lines in the projective geometry of PT!.

         鉴于(8.4.4.6-2),有下面的表格:

　

扭                量                光                影

在扭量空间 PT 在扭量空间 PN 在紧化闵可夫斯基空间 M^# 在闵可夫斯基空间 M

互相关联的射影直线 众多黎曼球面泡(多世界) 众多具有正的或负的能量的模糊的时空点 　

凹凸不平的人体的经脉 中医所讲的脏腑 与中医所讲的一个脏腑相对应的众多针灸穴位 　

                                               (8.12.3.1-1)

In view of (8.4.4.6-2), there is the following table:

T   W   I   S   T   O   R   -   L   I   G   H   T   -   S   I   L   H   O   U   E   T   T   E   S

In twistor space PT

In twistor space PN

In compactified Minkowski space M^#
In Minkowski space M

Interrelated projective straight lines

Many Riemann-sphere-bubbles
(Many worlds)

Many fuzzy spacetime points with positive or negative energy
　

The meridians of the uneven human body

Internal organ described in Traditional Chinese Medicine

Acupuncture points corresponding to an internal organ described in Traditional Chinese Medicine

                                                       (8.12.3.1-1)

         (8.11.2-2)与针刺疗法中的捻转补泻法是一致的：一般来说,进针时右旋捻针为补,左旋捻针为泻.

(8.11.2-2) is consistent with the following method of acupuncture manipulation: generally speaking, while you push in the needle, if you twist the needle right-handedly, it means an reinforcing therapy, and if you twist the needle left-handedly, it means a reducing therapy.

         值得注意的是,有些特异功能人能直接看到人体内的经脉;换言之,他们能直接看到扭量投影模型.

It is worth noting that some people with paranormal abilities can directly see the meridians in the human body; in other words, they can directly see the twistor projection model.

         由(8.7-2)可以知道,

一个脏腑的整个态是脏腑、穴位、经脉的量子叠加,是类光部分和非类光部分的量子叠加.      (8.12.3.1-2)

　

From (8.7-2), one can know that

　

The entire state of a viscus is a quantum superposition of the viscus, acupuncture points, and the meridians, and is a quantum superposition of the null part and the non-null part.       (8.12.3.1-2)

8.12.3.2 阴阳八卦：光线和复四维扭量空间 T

8.12.3.2 Yin, yang and eight trigrams: light rays and the complex four-dimensional Twistor space T

         扭量空间 T 是复四维空间.

The twistor space T is complex four-dimensional space.

         彭罗斯指出:

         六维空间PT实际上可以理解为具有3个复数维的复空间.(《通向实在之路》688页.)

　

Penrose pointed out:

A six-dimensional space PT actually can be interpreted as a complex space—of three complex dimensions. (The Road to Reality. p.965.)

         八卦实际上可以理解为实八维空间,或复四维空间.

Eight trigrams actually can interpreted as a real eight-dimensional space, or a complex four-dimensional space.

         扭量光线相交形成事件、扭量空间、像.

The intersection of twistor-light rays forms an event, a twistor space, and an image.

         阴爻(即 - - )和阳爻(即 — )构成易经的八卦.中文字"爻"的字形看起来像两条相交光线的量子叠印态(请与《通向实在之路》图33.7(b)相比对).

Yin yao, a line of two dashes (i.e. - - ), and yang yao, a whole line (i.e. — ) form the eight trigrams in Yi Jing, also spelt I Ching (Book of Changes). The character pattern of the Chinese character yao (in the phrases yin yao and yang yao) is two oblique crosses one over the other, and the pattern looks like a quantum-superimposition state of two intersecting light rays (Compare this with Fig. 33.7(b) in the book The Road to reality).
        根据中医科学,中医与易经有同一来源.

According to Traditional Chinese Medical Sciences, Traditional Chinese Medicine and I Ching have the same source.

         中医和易经的同一来源是实八维计算变成实在.

The same source of Traditional Chinese Medicine and I Ching is real eight-dimensional computing-becoming reality.
　
8.12.3.3 三阴三阳构成复三维空间

8.12.3.3 Three yin and three yang form complex three-dimensional space

         彭罗斯指出:

一般而言,如果我们考虑几何问题,那么有用的是射影扭量空间 PT,而如果我们关心的是扭量的代数问题,那么空间 T 是适宜的.(《新物理狂想曲》,389页.)

Penrose pointed out:

Generally speaking, it is the projective twistor space PT that is useful to us if we are thinking of geometrical matters, whereas the space T is appropriate if we are concerned with the algebra of twistors. (Fashion, Faith, and Fantasy in the New Physics of the Universe. pp. 338, 339.)

         投影扭量空间 PT 是复三维空间.

The projective twistor space PT is a complex 3-dimensional space.

         阴爻对应着一个复数的虚部,阳爻对应着一个复数的实部.

Yin yao corresponds to the imaginary part of a complex number, while yang yao corresponds to the real part of a complex number.

         王平、贺娟指出:

         在《黄帝内经》里有三阴三阳模式.(《黄帝内经理论与实践.第2版》29页.)

Wang Ping and He Juan pointed out:

In Huangdi's Classic of Internal Medicine, there is a model of three yin and three yang. (The Theory and Practice of Huangdi's Classic of Internal Medicine. 2nd edition.)

　

         三阴三阳构成复三维空间.

Three yin and three yang constitute a complex 3-dimensional space.

　

8.12.3.4 子午流注：扭量光影之间的远程相互作用

8.12.3.4 : The ebb and flow of qi in the meridians: remote interactions between twistor-light-silhouettes

　

         鉴于(8.5-6),扭量光影之间的远程相互作用导致经络的子午流注.

In view of (8.5-6), remote interactions between twistor-light-silhouettes cause the ebb and flow of the meridians.

　
8.12.3.5 天人合一：扭量光影泡沫互相影响

8.12.3.5 Oneness of heaven and man: twistor-light-silhouette foam bubbles interact with one another

          鉴于(8.5-6),扭量光影泡沫互相影响,这与中医理论里的天人合一的思想是一致的.

In view of (8.5-6), twistor-light-silhouette foam bubbles interact with one another.This is consistent with the thought of "oneness of heaven and man" in the theory of Traditional Chinese Medicine.

　

8.12.4 振动

8.12.4 Vibration

　

8.12.4.1 五音疗法和五色疗法：向虚涨落

8.12.4.1 The pentatonic therapy and the five-color therapy: feebleness-oriented fluctuation

　

         在中医里有五音疗法和五色疗法.鉴于(8.4.4.5-8),特定的音调和特定颜色的光都能震动特定的扭量光影泡沫,使其松散开,从而易于离开或进入人体.(请参看《人体气觉—Y法》第41页.)

In Traditional Chinese Medicine there are the pentatonic therapy and the five-color therapy. In view of (8.4.4.5-8), both a specific tone and a specific color of light can vibrate specific twistor-light-silhouette foam, loosening the bubbles so that they are easy to leave or enter a human body. (See YAO Zhenxiang. Human Qi Perception: The Y Method. (In Chinese.) p. 41.)

　

8.12.4.2 振腹推拿疗法

8.12.4.2 The abdominal vibration massage therapy

　

         振腹推拿疗法的物理原理之一是(8.4.4.5-8)里面的第5项.

One of the physical principles behind the abdominal vibration massage therapy is Item 5 in (8.4.4.5-8).

　

         关于振腹推拿疗法,参看付国兵、戴晓晖主编《振腹推拿》.

For the abdominal vibration massage therapy, see Abdominal Vibration Massage by FU Guobing and DAI Xiaohui (Chief compilers). (In Chinese.)

　

　

参考文献

References

M. A. Armstrong. Basic Topology. Springer Science+Business Media New York. 1983.

马克·阿姆斯特朗著.孙以丰译.《基础拓扑学》修订版. 北京: 人民邮电出版社. 2019年11月第2版.

伏·巴尔佳斯基伏·叶弗来莫维契著. 裘光明译. 《拓扑学奇趣》.湖南教育出版社.2007年10月.

包志强.《点集拓扑与代数拓扑引论》.北京大学出版社.2013年9月.

Bao, Zhiqiang. Introduction to General Topology and Algebraic Topology. Peking University Press. September, 2013. (In Chinese.)

Confucius. Part 1 of Xi Ci in Yi Zhuan.

　

肖恩·卡罗尔.《隐藏的宇宙》.舍其译. 长沙:湖南科学技术出版社,2021.7.

Sean Carroll. Something Deeply Hidden. DUTTON. 2020.

　

陈志欣、陈东英.《〈辅行诀五脏用药法要〉解读》. 北京.中国中医药出版社.2023年9月.

CHEN Zhixin, CHEN Dongying. Interpretation of "Auxiliary Cultivation Formulas: Essential Medicinal Principles for the Five Zang Organs". Beijing: China Press of Traditional Chinese Medicine. September, 2023. (In Chinese.)

　

邓昭镜.《天体演化的能态热力学——邓昭镜论文集》.南京大学出版社.2015年9月.

Deng, Zhaojing. Thermodynamics of energy states in celestial evolution—Collection of Li Ming's Essays. Nanjing University Press. Sept., 2015. (In Chinese.)

　

邓昭镜,陈华林,陈洪,熊祖洪.《负能谱及负能谱热力学》.西南师范大学出版社.2007年4月.

Deng, Zhaojing; Chen, Hualin; Chen, Hong; Xiong, Zuhong. Negative Energy Spectrum and Negative Energy Spectrum Thermodynamics. Southwest Normal University Press. Apr., 2007. (In Chinese.)

丹尼尔·丹尼特. 《心灵种种》. 上海科学技术出版社. 2012.12. 第2版.

Daniel Dennett. Kinds of Minds. Basic Books. 1996.

付国兵、戴晓晖主编. 《振腹推拿》. 第2版. 北京: 中国科学技术出版社. 2017.10.

FU Guobing and DAI Xiaohui (Chief compilers). Abdominal Vibration Massage. 2nd edition. Beijing: China Science And Technology Press. October 2017. (In Chinese.)

顾险峰,丘成桐.《计算共形几何》(理论篇).高等教育出版社.2020年5月.

Gu, Xianfeng; Qiu, Chengtong. Computational Conformal Geometry, Theory. Higher Education Pres Limited Company and International Press of Boston, Inc. 2020.

史蒂芬·霍金、罗杰·彭罗斯.《时空本性》.第2版.杜欣欣、吴忠超译.长沙：湖南科学技术出版社,2007年4月.

Stephen Hawking and Roger Penrose. The Nature of Space and Time. Princeton University Press,1996.

David Hestenes. The Zitterbewegung Interpretation of Quantum Mechanics. Foundations of Physics, Vol. 20, No. 10, (1990), 1213~1232

David Hestenes. The Zitterbewegung Interpretation of Quantum Mechanics. Foundations of Physics, Vol. 20, No. 10, (1990), 1213~1232

[德] 扎比内·霍森费尔德.《迷失》.舍其译.湖南科学技术出版社.2022年9月.

Sabine Hossenfelder. Lost in Math: How Beauty Leads Physics Astray. Paperback. Basics Books. New York. 2018.

郦全民.用计算的观点看世界.广西师范大学出版社. 2016年10月.

Li, Quanmin. A Computational Perspective on the World. Guangxi Normal University Press. Oct. 2016. (In Chinese.)

林书煌、刘惠宜主编. 《人体特异现象的实验与探索》. 北京:中国国际广播出版社.1997. ISBN 7-5078-1605-2.

LIN Shuhuang, LIU Huiyi. (Chief compiler.) Experiments and researches in human paranormal abilities. (In Chinese.)

Beijing: China Radio International Press. 1997. Print. ISBN 7-5078-1605-2.

鲁品越.《深层生成论:自然科学的新哲学意境》. 人民出版社. 2011年3月.

Lu, Pinyue. Theory of generation in the depths: a new philosophical vista of natural sciences. People's Publishing House. Mar. 2011. (In Chinese.)
吕志纯.《量子力学基础》.东北大学出版社.2015年11月.

Lü, Zhichun. Foundation of Quantum Mechanics. Northeastern University Press. Nov. 2015. (In Chinese.)

倪光炯、陈苏卿.高等量子力学(第二版).上海.复旦大学出版社.2005年8月第二版.ISBN 7-309-03836-3. 9.5B节和9.5C节.

倪光炯.学习量子力学五十年— i 与 I 之谜.见:量子力学朝花夕拾.王文正、柯善哲、刘全慧主编.北京:科学出版社,2004. 第144页.

NI Guangjiong. "Fifty Years of Studying Quantum Mechanics" see Flowers of Quantum Mechanics Blooming in the Morning and Viewed in the Sunset — (Teaching and Learning). Chief compilers: WANG Wenzheng, KE Shanzhe, LIU Quanhui. Beijing: Science Press, 2004. p. 144. (In Chinese.)

Tristan Needham. 复分析:可视化方法.齐民友,译.人民邮电出版社.2009年. ISBN 978-7-115-20883-5.第133、134页.

Tristan Needham. Visual Complex Analysis. Oxford University Press. 1997. ISBN 0198534469.

Tristan Needham. Visual Complex Analysis. 25th Anniversary Edition. Oxford University Press. 2023.

特里斯坦·尼达姆(Tristan Needham)著;刘伟安译.《可视化微分几何和形式：一部五幕数学正剧》.北京：人民邮电出版社,2024.1 (2024.3重印).

Tristan Needham. Visual Differential Geometry and Forms: A mathematical drama in five acts. Paperback. Princeton University press, Princeton and Oxford. 2021.

Ni, Guangjiong and Chen, Suqing. Advanced Quantum Mechanics. Rinton Press. 2002. Sections 9.5B and 9.5C.

Guang-jiong Ni, Hong Guan. Einstein-Podolsky-Rosen Paradox and Antiparticle

http://cds.cern.ch/record/376760/files/9901046.pdf

J. E. Mayfield. Evolution as Computation. http://www.public.iastate.edu/~jemayf/evolution%20as%20computation.pdf

J. E. Mayfield. Evolution as Computation. http://www.public.iastate.edu/~jemayf/evolution%20as%20computation.pdf

斯特恩·奥登瓦尔德.《宇宙学是什么》.朱桔译.中信出版集团股份有限公司.2021年10月.

Sten Odenwald. A Degree in a Book: Cosmology. Sirius Publishing, a division of Arcturus Publishing Limited. London. 2019.

彭子益.圆运动的古中医学.李可主校.[M].中国中医药出版社,2007.ISBN 978-7-80231-207-4.

彭子益 PENG Ziyi. Ancient Traditional Chinese Medical Science Based on Circular Motion. Chief proofreader: Li Ke. Beijing: China Press of Traditional Chinese Medicine, 2007. Print. ISBN 978-7-80231-207-4. (In Chinese.)

R. Penrose & W. Rindler. 《Spinors and space-time Vol. 1 旋量与时空第1卷》.北京：世界图书出版公司北京公司.2008年12月.

Penrose, R. and Rindler, W. (1984). Spinors and Space-Time, Vol. 1. Cambridge University Press, Cambridge.

R. Penrose & W. Rindler. 《Spinors and space-time Vol. 2 旋量与时空第2卷》.北京：世界图书出版公司北京公司.2009年1月.

Penrose, R. and Rindler, W. (1986). Spinors and Space-Time, Vol. 2: Spinor and Twistor Methods in Space-Time Geometry. Cambridge University Press, Cambridge.

罗杰·彭罗斯.《通向实在之路——宇宙法则的完全指南》.王文浩译.长沙:湖南科学技术出版社.2013年11月.

Roger Penrose. The Road to Reality: A Complete Guide to the Laws of the Universe. Copyright 2004. First Vintage Books edition, January 2007.

罗杰·彭罗斯.Cycles of Time. (《宇宙的轮回》.) 李泳译.长沙:湖南科学技术出版社.2014年1月.

Roger Penrose. Cycles of Time. Vintage Books. May, 2012.

罗杰·彭罗斯. 新物理狂想曲.李泳译.长沙:湖南科学技术出版社.2021年2月.

Fashion, Faith, and Fantasy in the New Physics of the Universe. Princeton University Press. 2016.

卡洛·罗韦利.时间的秩序.湖南科学技术出版社.2019.

Carlo Rovelli. The Order of Time. Penguin Books. 2019.

托尼·罗宾.《时空投影:第四维在科学和现代艺术中的表达》.潘可慧,潘涛译. 潘涛校. 北京. 新星出版社. 2020年10月.

Tony Robbin. Shadows of Reality: the fourth dimension in relativity, cubism, and modern thought. Yale University Press. New Haven & London. 2006.

伯特兰·罗素.《相对论ABC》.李宁译. 南京: 译林出版社.2016年.

Bertrand Russell. ABC of Relativity. 2009. The Bertrand Russell Foundation Ltd.

M. Scheutz. Computationalism: New Directions. Edited by Matthias Scheutz. A Bradford book. The MIT Press. 2002.

M. Scheutz. Computationalism: New Directions. Edited by Matthias Scheutz. A Bradford book. The MIT Press. 2002.

邵来圣,虞惠华,沈云虎.《人体特异功能的实验研究与诱发训练修订版》.复旦大学出版社. 2008年11月.

Shao, Laisheng; Yu, Huihua; Shen, Yunhu. The Experimental Research and Inducing Training in Human Paranormal Abilities. (Revised Edition.) Fudan University Press. Nov, 2008. (In Chinese.)

孙子.《孙子算经》.见:《算经十书》. 钱宝琮点校. 北京. 中华书局. 2021年1月.

Sun-tzu. Sun-tzu's Book of Computing. Included in Ten Classics of Computing. Proofread by Qian Baocong. Zhong Hua Book Company. Jan. 2021. (In Chinese.)

　

迈克斯·泰格马克.穿越平行宇宙.汪婕舒,译.浙江人民出版社.2017年6月

Max Tegmark. Our Mathematical Universe: My Quest for the Ultimate Nature of Reality. First Vintage Books edition, February 2015.

Alfred North Whitehead. Process and Reality. Corrected Edition. Edited by David Ray Griffin and Donald W. New York: The Free Press, 1978.

汪克林,曹则贤. 量子物理若干基本问题.中国科学技术大学出版社.2019年9月.

Wang, Kelin and Cao, Zexian. Some Fundamental Problems in Quantum Physics. University of Science and Technology of China Press. Sep. 2019.

John Archibald Wheeler with Kenneth Ford. Geons, Black Holes, and Quantum Foam: A Life in Physics. Norton paperback 2000.

约翰·阿奇博尔德·惠勒、肯尼斯·福特.《约翰惠勒自传：京子、黑洞和量子泡沫》.王文浩译.湖南科学技术出版社.2018年5月.

杨富斌, (美) 杰伊·麦克丹尼尔(Jay McDaniel)著.怀特海过程哲学研究.中国人民大学出版社.2018年5月.

Yang, Fubin, Jay McDaniel. On Whitehead's Process Philosophy. China Renmin University Press. May, 1978. page 190. (In Chinese.)

姚贞香.《人体气觉—Y法》.北京:华夏出版社,1989年.

YAO Zhenxiang. Human Qi Perception: The Y method. Beijing: Huaxia Publishing House, 1989. (In Chinese.)

詹妮·伦道斯. 时间风暴. 于海生,译.长春:吉林摄影出版社,2002.

Jenny Randles. Time Storms: Amazing Evidence for Time Warps, Space Rifts and Time Travel. New York: Piatkus/Berkley, 2001, 2002.

杨恩洪.《民间诗神—格萨尔艺人研究(增订本)》.中国社会科学出版社.2017年7月.

YANG Enhong. Singer and storyteller in Gesar Epic Tradition: A Follow-up Study. China Social Sciences Press. July, 2017. (In Chinese.)

张涵.《圆运动古中医临症应用》.中国医药科技出版社.北京.2010年10月.

ZHANG Han. Clinical Application of Ancient Traditional Chinese Medical Science Based on Circular Motion. Beijing: Medical science and technology press of China. Beijing. October, 2010. (In Chinese.)

张旭.反引力场发动机. https://www.twistor-light-silhouette.com

Zhang, Xu. Antigravitation Engine Site. Web. https://www.twistor-light-silhouette.com

张旭. 《UFO：现象、理论、实验》.1990年8月. 发表于《天·地·人科学文化纵横集》.吴之静主编.北京:科学普及出版社,1992 年9月. 第90~113页.

ZHANG Xu. UFO: Phenomena, theories and experiments. August, 1990. This article is published in Heaven, Earth and Man - Across Science And Culture. Chief compiler: WU Zhijing. Beijing: Popular Science Publishing House, September, 1992. Print. Pages 90~113. (In Chinese.)

张轩中.《相对论通俗演义》.广西桂林：广西师范大学出版社. 2008年6月.

ZHANG Xuanzhong. Popular romance of Relativity. Guilin, Guangxi, China: Guangxi Normal University Press. June, 2008. (In Chinese.)

张永德.量子菜根谭:量子理论专题分析.北京:清华大学出版社,2016年11月第3版.

Zhang, Yongde. Talks on the "Roots of Vegetables" in the Quantum Theory: Thematic Analyses on the Modern Quantum Theory. Third edition. Beijing: Tsinghua University Press, Nov., 2016. (In Chinese.)

Teubner-Taschenbuch der Mathematik (德)蔡德勒（E. (Zeidler)等编;李文林等译.《数学指南－实用数学手册》北京:科学出版社,2012.第862页.

E. Zeidler with W. Hackbusch and H.R. Schwarz. Oxford Users' Guide to Mathematics.

周尔晋.《人体 X 形平衡法》.合肥工业大学出版社.2002年11月.
Zhou, Erjin's book Human-Body X-Shaped Balancing Method. Hefei University of Technology Press. Nov. 2002. (In Chinese.)
　
朱良志.《南画十六观》北京大学出版社.2013年7月.
ZHU Liangzhi. Sixteen Views on Chinese Literati Paintings. Peking University Press. July, 2013. (In Chinese.)
　
朱良志,《中国美学十五讲》北京大学出版社. 2006年4月.
ZHU Liangzhi. Fifteen Lectures on Chinese Aesthetics. Peking University Press. April, 2006. (In Chinese.)

层级	5			4		3	2	1
所位于的扭量空间	T⁺	N	T^-	PT⁺	PT^-	PN	M^#	M
扭量光影	T⁺ 光	N 光	T^- 光	很多射影直线	很多射影直线	其北极点贴附于莫比乌斯环的很多黎曼球面(即很多黎曼球面泡)	众多具有正的或负的能量的模糊的时空点 (有时简称为第2层级)	众多具有正的能量的模糊的时空点
鉴于(8.4.4.6-1),扭量光影是模糊的.
(8.5-1)

Level	5			4		3	2	1
Situated in the twistor space	T⁺	N	T^-	PT⁺	PT^-	PN	M^#	M
The twistor-light-silhouette	T⁺ light	N light	T^- light	Projective lines	Projective lines	Many a Riemann sphere whose north pole is attached to a Möbius loop (i.e. many Riemann-sphere-bubbles)	Many fuzzy spacetime points with positive or negative energy (sometimes referred to simply as "Level 2")	Many fuzzy spacetime points with positive energy
In view of (8.4.4.6-1), the twistor-light-silhouette is fuzzy.
(8.5-1)

以发展的方向作为前方
从前面看,旋转时,
左降右升	左升右降
右手螺旋(正螺旋)	左手螺旋(负螺旋)
膨胀	收缩
(8.11.2-1)

Take the direction of development as the front
Viewed from the front, when rotating,
Falls on the left Rises on the right	Rises on the left Falls on the right
Right-handed helix (positive helicity)	Left-handed helix (negative helicity)
Expansion	Contraction
(8.11.2-1)

以发展的方向作为前方
从后面看,旋转时,
左升右降	左降右升
右手螺旋(正螺旋)	左手螺旋(负螺旋)
膨胀	收缩
(8.11.2-2)

Take the direction of development as the front
Viewed from the back, when rotating,
Rises on the left Falls on the right	Falls on the left Rises on the right
Right-handed helix (positive helicity)	Left-handed helix (negative helicity)
Expansion	Contraction
(8.11.2-2)

下面的内容可以用射影莫比乌斯环来模拟
不可定向空间	中心的圆周	不可定向空间
正能谱热力学	复合系统	负能谱热力学
从前面看,当垂直旋转时,左降右升		从前面看,当垂直旋转时,左升右降
扭量空间( T⁺、PT⁺ ) 膨胀	零模扭量,扭量空间 N 和 PN	扭量空间( - T^-、- PT^-) 收缩
自发地从有序变为无序,熵增		自发地从无序变为有序,熵减
	1. 莫比乌斯环型反引力促进扭量光影循环. 2. 两个扭量光影互相穿过.(见(8.5-6).) → 特异功能人把药片抖出封闭的瓶子.
在沈今川和孙储琳的 RS人体场摄影术的作品中所看到的莫比乌斯环		在沈今川和孙储琳的 RS人体场摄影术的作品中所看到的莫比乌斯环
时间沿正向流逝并且变快, 例如 - ¥ 秒, ... -2秒, -1秒, 0秒, 1秒, 2秒, ... + ¥ 秒 → 人体特异功能使青果子变红		时间沿负向流逝并且变慢例如 + ¥ 秒, ... 2秒, 1秒, 0秒, -1秒, -2秒, ... - ¥ 秒 → 人体特异功能使红果子变青,复原刚刚被嚼烂了的名片
莫比乌斯环型反引力、扭量光影气场涌现、扭量光影循环、(8.4.2-9)、(8.11.2-1)、(8.11.2-2) → 人体气觉—Y法、特异移物		莫比乌斯环型反引力、扭量光影气场涌现、扭量光影循环、(8.4.2-9)、(8.11.2-1)、(8.11.2-2) → 人体气觉—Y法、特异移物
因果律成立
(8.11.2-3)

The following can be modeled by use of a projective Möbius loop
Non-orientable space	The central circle	Non-orientable space
Positive energy spectrum thermodynamics	Composite systems	Negative energy spectrum thermodynamics
From the front, when rotating vertically, Falls on the left; Rises on the right		From the front, when rotating vertically, Rises on the left; Falls on the right
Twistor spaces ( T⁺ ) and ( PT⁺ ) Expansion	Null twistors, the twistor spaces N and PN	Twistor spaces ( - T^- ) and ( - PT^- ) Contraction
Spontaneously transitioning from order to disorder, Entropy increasing		Spontaneously transitioning from disorder to order, Entropy decreasing
	1. Möbius-loop-typed antigravitation promotes twistor-light-silhouette cycles. 2. Two twistor-light-silhouettes pass through each other. (See (8.5-6).) → A person with paranormal abilities shakes tablets out of a closed bottle.
PN fibre bundles → What is seen in the works of Shen Jinchuan and Sun Chulin's RS human-field photography		PN fibre bundles → What is seen in the works of Shen Jinchuan and Sun Chulin's RS human-field photography
Time flowing in the positive direction and getting faster, e.g. - ¥ s, ... -2 s, -1 s, 0 s, 1 s, 2 s, ... + ¥ s → Human paranormal abilities make a green fruit red.		Time flowing in the negative direction and getting slower, e.g. + ¥ s, ... 2 s, 1 s, 0 s, -1 s, -2 s, ... - ¥ s → Human paranormal abilities make a red fruit green and restore a business card that has just been chewed up into pulp
Möbius-loop-typed antigravitation, emergence of twistor-light-silhouette fields, and twistor-light-silhouette cycles; (8.4.2-9), (8.11.2-1), and (8.11.2-2) → Human Qi Perception: The Y *Method; Paranormal teleportation*		Möbius-loop-typed antigravitation, emergence of twistor-light-silhouette fields, and twistor-light-silhouette cycles; (8.4.2-9), (8.11.2-1), and (8.11.2-2) → Human Qi Perception: The Y Method; Paranormal teleportation
The law of causality holding good
(8.11.2-3)

五行五行：扭量光影泡沫(即气)沿射影莫比乌斯环的五种运行左手螺旋态为阴,右手螺旋态为阳五行化生^[1](五行的化合反应) ( "→"表示"从......到......" ; "-"的意思是：化生的"过程"或化生成为的"计算变成实在"是 ...... )
木	火	土	金	水
上升	在 + ¥ 的邻域内运动	定向反转的运动	下降	在 - ¥ 的邻域内运动
肝	心	脾	肺	肾
木金化土 0 → (+¥)→(-¥)- 土土土	火水化金 (+¥)→(-¥)- 金	土木化水 - (0 → (+¥))= (-¥)- 水	金火化木 0 →(-¥)→ (+¥)- 木	水土化火 (-¥)→ -(-¥)= (+¥)- 火
(8.12.2.1-3)

Wuxing Wuxing: five kinds of motion of twistor-light-silhouette foam (i.e. qi) along projective Möbius loops The left-handed-helix state is associated with Yin and the right-handed-helix state is associated with Yang Wuxing generative transformations^[1] (combination reactions of Wuxing) ( "→" means "from ... to ..." ; "-" means that the "process" of transformation or the "computing-becoming reality" being transformed into is ... )
Wood	Fire	Earth	Gold	Water
Rising up	Moving in the neighbourhood of + ¥	Orientation-reversing motion	Falling down	Moving in the neighbourhood of - ¥
Liver	Heart	Spleen	Lungs	Kidneys
Wood followed by Gold becomes Earth 0 → (+¥)→(-¥)- Earth	Fire followed by Water becomes Gold (+¥)→(-¥)- Gold	Earth followed by Wood becomes Water - (0 → (+¥))= (-¥)- Water	Gold followed by Fire becomes Wood 0 →(-¥)→ (+¥)- Wood	Water followed by Earth becomes Fire (-¥)→ -(-¥)= (+¥)- Fire
(8.12.2.1-3)

人体 X 形平衡法
有病的部位	治疗的点位
在上面	在下面
在下面	在上面
在左面	在右面
在中间	在四边
在四边	在中间

Human-body X-shaped balancing method
The diseased part is	The point position of treatment is
in the upper part	in the lower part
in the lower part	in the upper part
on the left	on the right
in the central area	on four sides
on four sides	in the central area

扭量空间	T⁺	N	T^-	PT⁺	PN	PT^-	紧化闵可夫斯基空间 M^#
	n =
复 n 维	4		4	3		3	PN 的次级结构
实 n 维	8	7	8	6	5	6
(8.12.3-1)

The twistor space	T⁺	N	T^-	PT⁺	PN	PT^-	Compactified Minkowski space M^#
	n =
Complex n-dimensional	4		4	3		3	The secondary structure of PN
Real n-dimensional	8	7	8	6	5	6
(8.12.3-1)

扭量光影
在扭量空间 PT	在扭量空间 PN	在紧化闵可夫斯基空间 M^#	在闵可夫斯基空间 M
互相关联的射影直线	众多黎曼球面泡(多世界)	众多具有正的或负的能量的模糊的时空点
凹凸不平的人体的经脉	中医所讲的脏腑	与中医所讲的一个脏腑相对应的众多针灸穴位
(8.12.3.1-1)

T W I S T O R - L I G H T - S I L H O U E T T E S
In twistor space PT	In twistor space PN	In compactified Minkowski space M^#	In Minkowski space M
Interrelated projective straight lines	Many Riemann-sphere-bubbles (Many worlds)	Many fuzzy spacetime points with positive or negative energy
The meridians of the uneven human body	Internal organ described in Traditional Chinese Medicine	Acupuncture points corresponding to an internal organ described in Traditional Chinese Medicine
(8.12.3.1-1)