第十一章 吹胀原点：宏观量子的作用量单位
Chapter 11 Blowing up the origin: the unit of action of a macroscopic quantum
|
1. 鉴于(8.11.1-1),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. 一个宏观量子(例如一个黑洞的奇点)的作用量单位是这个宏观量子所对应的黎曼球面泡的作用量单位. (11-1) |
|
In view of (8.11.1-1), 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 unit of action of a macroscopic quantum (e.g. the singularity of a black hole) is the unit of action of the Riemann-sphere-bubble that the said macroscopic quantum corresponds to. (11-1) |
11.1 杨步恩的工作
11.1 YANG Buen's work
杨步恩[1]指出,在行星系统中, η 常数的作用相当于原子理论的普朗克常数ħ , 扮演基本作用量的角色,并且有如下方程:
c / v = λ n n = 1, 2, 3 ... ,
η = λ G M / c , (11.1-1)
其中 v 是行星轨道平均速率, M 是太阳质量.
YANG Buen[1] pointed out that in the planet system, the function of the constant η , which plays the role of the elementary action, corresponds to the function of Planck constant ħ in the atomic theory, and that there are the following equations:
c / v = λ n n = 1, 2, 3 ... ,
η = λ G M / c , (11.1-1)
where v is the average orbital speed of the planet, and M is the mass of the Sun.
以天文单位表达的行星轨道半长径分布公式是
a = 10-8 λ2 n2 ≈ 0.044 n2 AU n = 1, 2, ... .
The formular for the distribution of semi-major axes of planetary orbits expressed in astronomical units (AU) is
a = 10-8 λ2 n2 ≈ 0.044 n2 AU n = 1, 2, ... .
[1] 见杨步恩著《行星卫星量子理论导引》.第1版.大连理工大学出版社.大连.1996年6月. 24 ~ 29页.
和第24页.
[1] See YANG Buen. A Guide to the Quantum Theory for Planets and Satellites. 1st ed., Dalian University of Technology Press, Dalian, China, June, 1996, pp. 24 ~ 29. (In Chinese.)
11.2 手推飞碟"吹胀" 黎曼球面泡
11.2 A hand-push flying saucer "blows up" the Riemann-sphere-bubble
在扭量理论里,一个基本的射影关系是在一个闵可夫斯基空间 M 里面每一个可以观看星空的点都对应着扭量空间 PN 里的一个黎曼球面.
in the twistor theory, a basic projective relation is that every point for a viewer to look at the starry sky in a Minkowski space corresponds to a Riemann sphere in the twistor space PN.
彭罗斯在《通向实在之路》§ 33.6 "作为无质量自旋粒子的扭量子的几何"中指出,
| 扭量空间PT里的光子的螺旋度的大小是 ħ ,空间的额外维源自光子能量.这种描述对其他具有非零自旋 1/2nħ 的无质量粒子也是成立的.螺旋度是扭量模的一半. (11.2-1) |
In § 33.6 "Geometry of twistors as spinning massless particles" of his book The Road to Reality, Penrose pointed out that
|
The magnitude of the helicity of the photon in twistor space PT is just ħ, and the extra dimension of the space comes from the energy of the photon. This description holds also for any other massless particle with nonzero spin 1/2nħ. Helicity is half the twistor norm. (11.2-1) |
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页.)
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).
在本网站里,反引力指的是莫比乌斯环型反引力,即扭量光影的旋转产生的惯性系拖曳效应.
On this website, antigravitation refers to Möbius-loop-typed antigravitation, i.e. inertial-frame-dragging effects generated by the rotation of twistor-light-silhouettes.
|
以下将从反抗万有引力做功和反抗静电力做功两方面来综合考虑,这在某种程度上有些类似于负反馈. (11.2-2) |
| Two aspects, the work opposing gravitation and the work opposing electrostatic force, will be synthesized, which is, to some degree, similar to the negative feedback. (11.2-2) |
彭罗斯在他的著作《通向实在之路——宇宙法则的完全指南》[1]的第33.2节指出,根据扭量的观点,单个的点由黎曼球面来代表.
In Section 33.2 of his book The Road to Reality: A Complete Guide to the Laws of the Universe[1], Penrose pointed out that according to the "twistorial" perspective, a single point is represented by a Riemann sphere.
旋量是随它们推进而旋转的矢量.(托尼·罗宾.《时空投影》[2],第130页.)
Spinors are vectors that rotate as they progress. (Tony Robbin. Shadows of Reality[2], p. 77.)
|
在膨胀阶段中,气泡上部以等于气泡半径变化率的速度运动,底部与喷孔接触并保持静止. (《水中气泡学引论》[3]第23页.) (11.2-3) |
|
During the expansion phase, the upper part of the bubble moves at a speed equal to the rate of the change in the bubble radius, while the bottom contacts the nozzle and remains stationary. (Introduction to the Analysis of Underwater Bubbles Movement[3]. p. 23) (11.2-3) |
参考文献
References
[1] 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.
[1] Roger Penrose. The Road to Reality: A Complete Guide to the Laws of the Universe. Copyright 2004. First Vintage Books edition, January 2007.
[2] 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.
[3] Tony Robbin. Shadows of Reality: the fourth dimension in relativity, cubism, and modern thought. Yale University Press. New Haven & London. 2006.
[3] 王涌 苑志江 蒋晓刚 郑智林.《水中气泡学引论》.上海交通大学出版社.2023年5月.
[3] WANG Yong, YUAN Zhijiang, JIANG Xiaogang, ZHENG Zhilin. Introduction to the Analysis of Underwater Bubbles Movement. Shanghai Jiao Tong University Press. May, 2023. (In Chinese.)
(1)
一个旋量就像一种叫做"手推飞碟"的玩具.
(1)
A spinor is like a toy called "hand-push flying saucer".
反引力就像气球打气筒里面的空气流.黎曼球面泡就像气球.反引力反抗时空曲率 或万有引力场做功,吹胀黎曼球面泡,就好像打气筒用一个力克服阻力做功,吹胀气球.在万有引力场里等效原理成立.
The antigravitation current is like the air current in a balloon inflator. A Riemann-sphere-bubble is like a balloon. Opposing spacetime curvature or a gravitational field antigravitation does work, blowing up a Riemann-sphere-bubble, just as an inflator applies a force overcoming resistance and does work, blowing up a balloon. The equivalence principle holds in the gravitational field.
物体和它的黎曼球面泡之间的万有引力是
F = G m mRSB / r2 , (11.2(1)-1)
式中 m 是物体的质量, mRSB是物体的黎曼球面泡的质量; r 既是产生反引力的物体(可以看作是点质量)与它的黎曼球面泡的中心之间的距离,又是黎曼球面泡的半径,也就是说, r 既是与观测者相对静止的气球打气筒的前端与它刚刚吹起来的气球的中心之间的距离,又是这个气球的半径.
The gravitation between a body and its Riemann-sphere-bubble is
F = G m mRSB / r2 , (11.2(1)-1)
where m is the mass of the body, mRSB is the mass of the Riemann-sphere-bubble of the body; r is the distance between the body (which can be considered as a point mass), generating antigravitation, and the centre of its Riemann-sphere-bubble, and r is also the radius of the Riemann-sphere-bubble; that is, r is the distance between the front end of the balloon inflator (which is at rest with respect to the observer) and the centre of the balloon that the inflator has just blows up, and r is also the radius of the balloon.
反引力反抗万有引力所做的功 W 是
W = (G m mRSB / r2) r. (11.2(1)-2)
Opposing gravitation, the work W done by antigravitation is
W = (G m mRSB / r2) r. (11.2(1)-2)
根据观测,
| 暗能量构成宇宙的72.1%(精确度在1.5%以内),暗物质构成宇宙的23.3%(精确度在1.3%以内)[1]. (11.2(1)-3) |
According to observation,
| dark energy makes up 72.1% (to within 1.5%) of the universe and dark matter makes up 23.3% (to within 1.3%) of the universe[1]. (11.2(1)-3) |
扎比内·霍森费尔德在她的书《迷失》的第268页指出, 暗物质的丰度的测量值是 23%.[2]
On page 201 of her book Lost in Math: How Beauty Leads Physics Astray, Sabine Hossenfelder pointed out that the measured value of the abundance for dark matter is 23 percent.[2]
基于(11.2(1)-3)和(11.2-2),可以假定在宇宙里所做的功里, 72.1%的功是暗能量做的功; 23.45%的功用来吹起黎曼球面泡, 4.45%的功是通常意义上的物质在相互作用中所做的功.
Based on (11.2(1)-3) and (11.2-2), one can assume that among the work done in the universe, 72.1% of the work is done by dark energy; 23.45% of the work is done blowing up Riemann-sphere-bubbles, and 4.45% of the work is done by the interaction of matter in the usual sense.
用 h' 表示 W 与反引力做功的时间 t 的乘积,也就是说,
| 用 h' 表示黎曼球面泡在空间和时间中的规模. (11.2(1)-4) |
于是基于(11.2(1)-3),可以得出如下结论:
| h' = 0.234 5 W t . (11.2(1)-5) |
Let h' denote the product of W and the time t during which antigravitation does work; that is,
| Let h' denote the magnitude of the Riemann-sphere-bubble in space and time. (11.2(1)-4) |
Then based on (11.2(1)-3), one can draw a conclusion:
| h' = 0.234 5 W t . (11.2(1)-5) |
因为 W = f r ; f = (G m mRSB / r2); 所以
h' = 0.234 5 (G m mRSB / r2) r t. (11.2(1)-6)
Since W = f r ; f = (G m mRSB / r2), one finds
h' = 0.234 5 (G m mRSB / r2) r t. (11.2(1)-6)
The prime symbol stands for "antigravitational"; the same applies below.
将(10.2-2)代入(11.2(1)-6)得到
h' = 0.234 5 ((G m m v2 / c2) / r2) r t;
h' = 0.2345 (G m2 v2 / c2) (t / r);
Substituting (10.2-2) into (11.2(1)-6), one finds
h' = 0.234 5 ((G m m v2 / c2) / r2) r t;
h' = 0.2345 (G m2 v2 / c2) (t / r);
根据(11.2-3)和(8.6.2-2), r / t = v, 所以上式变成
h' = 0.2345 (G m2 v2 / c2) (1 / v),
h' = 0.2345 G m2 v / c2, (11.2(1)-7)
式中 v 是来自"打气筒"的引物的速率.这与一种称为"泡泡棒"的玩具的情况类似,泡泡棒的大小和速率与制造出的泡泡的大小有关.
According to (11.2-3) and (8.6.2-2), r / t = v ; hence the above equation becomes
h' = 0.2345 (G m2 v2 / c2) (1 / v);
h' = 0.2345 G m2 v / c2; (11.2(1)-7)
where v is the the speed of the GFM coming from the "balloon inflator". This is similar to the case of a toy called "bubble wand", whose size and speed are related to the size of the bubbles it makes.
由以上叙述可以知道, h' 是黎曼球面泡的规模,也是气球打气筒做功的作用量,即黎曼球面泡作用量.它对应着普朗克常量.因为 h' 有角动量的量纲,所以 h' 又是 黎曼球面泡的最小自旋角动量.这使人想起一种称为"手推飞碟"的玩具以及鲁滨逊线汇(见 § 8.4.3.2).
It can be
known from the above statement that h' is the size of the
Riemann-sphere-bubble, and is also the quantum of action of the work done by the
balloon inflator, i.e. the Riemann-sphere-bubble quantum of
action,
which corresponds to Planck constant. Since
h' has
the
dimensions of
angular momentum, h' is also the least angular momentum of spin of the
Riemann-sphere-bubble. This
reminds one of a toy called "hand-push flying saucer" and
the Robinson congruence (See
§
8.4.3.2).
h' =
0.2345 G m2 v / c2;
(11.2(1)-8)
式中
h' 是黎曼球面泡作用量.
Hence
h' =
0.2345 G m2 v / c2;
(11.2(1)-8)
where
h'
is the Riemann-sphere-bubble quantum of action.
参考文献 References [1] National Aeronautics and Space
Administration.
Wilkinson Microwave Anisotropy Probe.
http://map.gsfc.nasa.gov/ [1] National Aeronautics and Space
Administration.
Wilkinson Microwave Anisotropy Probe.
http://map.gsfc.nasa.gov/
[2] [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.
[2] Sabine
Hossenfelder.
Lost in
Math: How
Beauty Leads
Physics
Astray.
Paperback.
Basics
Books. New
York. 2018.
(2)
(2)
现在假设反引力要吹胀一个氢原子的 黎曼球面泡.将氢原子中质子与电子之间静电力与万有引力的比值记为r电/引,则根据库仑定律和牛顿万有引力定律,
r电/引 = e2 / ( 4 ε0 G mp me ). (11.2(2)-1)
Now antigravitation is to blow up a Riemann-sphere-bubble of a hydrogen atom. Let rel/gr denote the ratio of the electrostatic to the gravitational forces between a proton and an electron in a hydrogen atom; then according to Coulomb's law and Newton's law of universal gravitation,
rel/gr = e2 / ( 4 ε0 G mp me ). (11.2(2)-1)
由(11.2(1)-8),作用量h' 将会是
h' = 0.234 5 ( r电/引 G ) mp2 v / c2. (11.2(2)-2)
Similar to (11.2(1)-8), the quantum of action h'el would be
h' = 0.234 5 ( rel/gr G ) mp2 v / c2. (11.2(2)-2)
根据量子力学,
| 自由粒子的 Zitterbewegung 颤动的瞬时速率是±c . (11.2(2)-3) |
According to quantum mechanics,
| The instantaneous speed of Zitterbewegung of the free particle is ±c . (11.2(2)-3) |
将v = c 代入(11.2(2)-2),得到
Substituting v = c into (11.2(2)-2), one gets
h' = 0.234 5 ( r电/引 G ) mp2 / c. (11.2(2)-4)
h' = 0.234 5 ( rel/gr G ) mp2 / c. (11.2(2)-4)
将(11.2(2)-1)代入(11.2(2)-4),得到h' = 3.313 55 × 10-34 J · s.计算得知
h' / h = 0.500 077, (11.2(2)-5)
式中 h 是普朗克常量.
Substitution of (11.2(2)-1) into (11.2(2)-4) yields h' = 3.313 55 × 10-34 J · s, and calculation shows that
h' / h = 0.500 077, (11.2(2)-5)
where h is Planck's constant.
因此可以推断出在上述条件下有关系式
h' / h = 0.5. (11.2(2)-6)
Hence one can infer that under the above condition there is the relation
h' / h = 0.5. (11.2(2)-6)
(3)
(基于待定系数法)
(3)
(Based on the method of undetermined coefficients)
根据(11.2(1)-8),设
h' = b G m2 v / c2, (11.2(3)-1)
According to (11.2(1)-8), suppose that
h' = b G m2 v / c2, (11.2(3)-1)
式中b是比例常数,于是根据(11.2(2)-4),有方程
h' = b ( r电/引 G ) mp2 / c . (11.2(3)-2)
where b is a proportionality constant, then according to (11.2(2)-4), there is the equation
h' = b ( rel/gr G ) mp2 / c . (11.2(3)-2)
将(11.2(2)-6)代入上式得到
h / 2 = b ( r电/引 G ) mp2 / c ; (11.2(3)-3)
b = c h / ( 2 r电/引 G mp2 ). (11.2(3)-4)
Substitution of (11.2(2)-6) into the above equation yields
h / 2 = b ( rel/gr G ) mp2 / c ; (11.2(3)-3)
b = c h / ( 2 rel/gr G mp2 ). (11.2(3)-4)
将(11.2(2)-1)代入上式得到
b = 2 c ε0 h me / ( e2 mp ) = ( / α ) · ( me / mp ), (11.2(3)-5)
式中 α 是精细结构常数, α = e2 / ( 2 ε0 h c ),也就是 ( 1 / α ) = 2 c ε0 h / e2.
Substitution of (11.2(2)-1) into the above equation yields
b = 2 c ε0 h me / ( e2 mp ) = ( / α ) · ( me / mp ), (11.2(3)-5)
where α is the fine-structure constant, and α = e2 / ( 2 ε0 h c ), i.e. ( 1 / α ) = 2 c ε0 h / e2.
将相关的基本物理常数(采用2006年国际CODATA推荐值)代入上式得到
b ≈ 0.234 464 . (11.2(3)-6)
Substitution of the relevant fundamental physical constants, which take the 2006 CODATA internationally recommended values, into the above equation gives
b ≈ 0.234 464 . (11.2(3)-6)
由(11.2(3)-1)、(11.2(3)-5)和(11.2(3)-6)得到
|
h' = b G m2 v / c2 , 式中 h' 是黎曼球面泡作用量单位, b 是无量纲的常数, b = 2 c ε0 h me / ( e2 mp ) = ( / α ) · ( me / mp ) ≈ 0.234 464 ; m 是产生反引力的物质的质量; v 是是产生反引力的物质的速率;其余是基本物理常量. (11.2(3)-7) |
From (11.2(3)-1), (11.2(3)-5) and (11.2(3)-6), one obtains
|
h' = b G m2 v / c2 , where h' is the twistor-light-silhouette unit of action; b is a dimensionless constant, and b = 2 c ε0 h me / ( e2 mp ) = ( / α ) · ( me / mp ) ≈ 0.234 464 ; m is the mass of the matter that generates antigravitation; v is the speed of the matter that generates antigravitation; and the others are fundamental physical constants. (11.2(3)-7) |
(11.2(3)-7)是黎曼球面泡作用量单位方程.
(11.2(3)-7) is the equation of the twistor-light-silhouettes unit of action.
根据(8.4.4.2-2)), h' 是投影模型与切片模型之间沟通的桥梁.
According to (8.4.4.2-2)), h' acts as a bridge between the projection model and the slicing model.
|
1. 杨步恩得出了 η 的表达式. (见(11.1-1).) 2. ( h' / m ) 的量纲与 η 的量纲是相同的. (11.2(3)-8) |
|
1. YANG Buen obtained the expression for
η
. (See (11.1-1).) 2. The dimension of ( h' / m ) is the same as that of η . (11.2(3)-8) |
彭罗斯指出:
| 在外尔几何里,不只是时钟频率,而且连粒子的质量都依赖于其历史.用这种非常异乎寻常的想法,外尔能够把麦克斯韦电磁理论的方程并入到时空几何里.(《通向实在之路》§19.4.) (11.2(3)-9) |
Penrose pointed out:
| In Weyl's geometry, not just clock rates but also a particle's mass will depend upon its history. Using this very striking idea, Weyl was able to incorporate the equations of Maxwell's electromagnetic theory into the spacetime geometry (The Road to Reality. §19.4.) (11.2(3)-9) |
参考文献
References
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.
(4)
(4)
由(11.2(3)-7)得到
h = h' / ( b1 m2 v ); (11.2(4)-1)
h' = h ( b1 m2 v ); (11.2(4)-2)
式中b1 = 2 ε0 G me / ( c e2 mp ) ≈ 262 774.26 s / ( kg2 · m );
From (11.2(3)-7), one obtains
h = h' / ( b1 m2 v ); (11.2(4)-1)
h' = h ( b1 m2 v ); (11.2(4)-2)
where b1 = 2 ε0 G me / ( c e2 mp ) ≈ 262 774.26 s / ( kg2 · m );
由(11.2(3)-7)得到
h = b G m2 v / ( c2 b1 m2 v ),
h = ( b / b1 ) ( G / c2 ).
G = b1 h c2 / b . (11.2(4)-3)
From (11.2(3)-7), one obtains
h = b G m2 v / ( c2 b1 m2 v ),
h = ( b / b1 ) ( G / c2 ).
G = b1 h c2 / b . (11.2(4)-3)
更多的信息请参看本网站的第7章第7.6和7.10节.
For more information, please see Sections 7.6 and 7.10 of Chapter 7 on this website.
(5)
(5)
(11.2(3)-7)给出
m惯性 = ± ( h' c2 / (b G v ) )(1/2). (11.2(5)-1)
(11.2(3)-7) yields
minertial = ± ( h' c2 / (b G v ) )(1/2). (11.2(5)-1)
由此可以知道(11.2(5)-1)对于物质而言取正号,对于反物质而言取负号.
Hence one can know that in (11.2(5)-1) the positive sign is taken for matter, and the negative sign is taken for antimatter.
关于负质量和负能量,参看倪光炯等的著作[1][2][3]和邓昭镜等的著作[4][5].
For negative mass and negative energy, see the works of Ni Guangjiong etc.[1][2][3] and the works of DENG Zhaojing etc.[4][5].
| 反引力空间是具有螺旋度 nh' 的"气球",因而是具有特定螺旋度的无质量粒子.粒子具有自旋 nh .由(11.2(3)-2),粒子是具有螺旋度 n1h' 的"气球",因此粒子具有反引力空间,并因而具有扭量空间. (11.2(5)-2) |
| An antigravitational space is a "balloon" having helicity nh' , and hence is a massless particle of specified helicity. A particle has spin nh . From (11.2(3)-2), a particle is a "balloon" having helicity n1h' . Therefore a particle has antigravitational space, and hence has twistor space. (11.2(5)-2) |
[1] 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.
[1] Ni, Guangjiong and Chen, Suqing. Advanced Quantum Mechanics. Rinton Press. 2002. Sections 9.5B and 9.5C.
[2] Guang-jiong Ni, Hong Guan. Einstein-Podolsky-Rosen Paradox and Antiparticle http://cds.cern.ch/record/376760/files/9901046.pdf
[3] 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.第381页
[3] Guangjiong Ni and Suqing Chen. Advanced Quantum Mechanics. Rinton Press. 2002. page 359.
[4] 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.
[4] Deng, Zhaojing. Thermodynamics of energy states in celestial evolution—Collection of Li Ming's Essays. Nanjing University Press. Sept., 2015. (In Chinese.)
[5] 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.
[5] Deng, Zhaojing; Chen, Hualin; Chen, Hong; Xiong, Zuhong. Negative Energy Spectrum and Negative Energy Spectrum Thermodynamics. Southwest Normal University Press. Apr., 2007. (In Chinese.)
11.3 事件粒子加速度的测量间隔
11.3 The measurement interval when measuring the acceleration of an event-particle
在反引力场中,事件粒子的动量 p' 和能量 E' 的变化是
Δp' = mRSB ( Δv ) ;
ΔE' = (1/2) mRSB ( Δv )2 .
In the antigravitational field, the changes in the momentum p' and in the energy E' of an event-particle are
Δp' = mRSB ( Δv ) ;
ΔE' = (1/2) mRSB ( Δv )2 .
将(10.2-2)代入上面的两个方程,得到
Δp' = m v3 / c2 (a反引力 ≠ 0), (11.3-1)
ΔE' = m v4 / ( 2 c2 ) (a反引力 ≠ 0), (11.3-2)
根据(8.6.2-2),式中 Δ 的意思既是"......的变化"又是"......的不确定度"; 当 aantigravitational = 0 时,粒子或物体的质量是 m , 速率是 v .
Substituting (10.2-2) into the above two equations, one obtains
Δp' = m v3 / c2 (aantigravitational ≠ 0), (11.3-1)
ΔE' = m v4 / (2 c2) (aantigravitational ≠ 0), (11.3-2)
where Δ means, according to (8.6.2-2), both "the change in" and "the uncertainty in"; m and v are mass and speed of a particle or an object if aantigravitational = 0 .
如果反引力是由运动物体本身产生的,那么对于事件粒子而言,由(8.6.2-2)、(8.4.4.3-2)、(11.2(3)-7)和(11.3-2)可以得到
t'lifespan = (1/2) (h'/ (2)) (1/E) = (bGm2v/c2)/(4E) = (bGm2v) / (4c2E) = (bGm2v/(4c2)) / E = (bGm2v/(4c2)) / (mv4/(2c2)) = bGm2v(2c2) / (4c2mv4) ;
t'lifespan = b G m / ( 2 v3) (a反引力 ≠ 0);
(11.3-3)式中 m 是(11.2(1)-1)中的 m.
If the antigravitation is generated by a moving object itself, then for an event-particle, (8.6.2-2), (8.4.4.3-2), (11.2(3)-7) and (11.3-2) yield
t'lifespan = (1/2) (h'/ (2)) (1/E) = (bGm2v/c2)/(4E) = (bGm2v) / (4c2E) = (bGm2v/(4c2)) / E = (bGm2v/(4c2)) / (mv4/(2c2)) = bGm2v(2c2) / (4c2mv4) ;
t'lifespan = b G m / ( 2 v3) (aantigravitational ≠ 0);
(11.3-3)where m is the m in (11.2(1)-1).
因此
|
命 μ时间 为计算事件粒子加速度时的测量间隔. μ1,时间 = 1 秒 , (对于扭量光影的中循环而言); μ2,时间 = t' lifespan , (对于扭量光影的全循环而言);其中 μ 是跑动耦合常量, t'lifespan = b G m / ( 2 v3). (11.3-4) |
Hence
|
Let μtime be the measurement interval when calculating the acceleration of an event-particle μ1,time = 1 second , (for the middle cycle of the twistor-light-silhouette);
μ2,time = t'lifespan , (for the complete cycle of the twistor-light-silhouette); where μ is the running coupling constant; t'lifespan = b G m / ( 2 v3). (11.3-4) |