Contents　

Chapter 4

　Antigravitation engine experiment:

data analysis (to verify the macroscopic quantum mechanical phenomenon)

In this experiment, the rotating body turns at 81 revolutions per second. The boat moves as far as 0.01 metre. The last level of the speed is 0.002 metre / 6 seconds on average. The experiment lasts 36 seconds. The radius of gyration of the metal part of the rotating body is 0.0046 metre. The mass of the metal part of the rotating body is 0.01 kilogram.

The following program is written in Mathematica.

The following are the data got in the experiment and the graph plotted according to the data.

First, the time unit of the antigravitational field is computed.

The gfm (gravitational field matter) ball, which corresponds to the gfm waves caused by the gfm current of the rotating body, and which is a macroscopic particle, hereafter called the gfm ball particle, gains its energy from the beginning to when it is on the last level of speed quantum by quantum, but with uncertainty; its mean life, however, increases from when it is on the last level of speed to the beginning quantum by quantum, but with uncertainty. Hence the mean life of the gfm ball particle on the last level of speed can serve as the time unit.

The gfm ball particle, when on the last level of speed, might gain speed suddenly because of the tunnel effect. Therefore the average speed of the boat towards the end of the experiment is taken as the last level of speed.

The second line of the program below computes the mass of the gfm ball particle, which corresponds to the gfm waves, on its last level of speed, based on Hu Ning's theory of the inertial mass of the gravitational field^[1].  

The third to the sixth line of the program compute, according to the set of equations of the antigravitation engine, the antigravitational acceleration, namely the antigravitational acceleration of the gfm waves caused by the gfm current of the rotating body, which is also the antigravitational acceleration of the de Broglie waves of the gfm current of the rotating body.  

The following two lines beginning with En compute the energies of the gfm ball particle having the above mass according to the theory in quantum mechanics about motion in a homogeneous field. See Ref. [2], p. 140, Eq. (21) and p. 139, line 1. In this line 1, some numbers are given. They are 2.338,4.088,5.521,6.787,.... Using the line of the program below one can get the above numbers and their follow-up numbers by substituting different integers (e.g. 3,4,5,6) for the blue number 2 . 

FindRoot[BesselJ[1/3,2/3*x^(3/2)]+BesselJ[-1/3,2/3*x^(3/2)]==0,{x,2}] 

Substitution of the above numbers (i.e. 2.338,4.088,...) in turn in the following program yields a discrete energy spectrum. See which number, after it has been substituted in the program, gives a probability graph that accords with the data graph.

The line further below is based on the uncertainty principle to compute the mean life of the particle having the above energy.   

The gfm ball particle does not gain its speed continuously; instead, it gets its speed quantum by quantum, with uncertainty.

The first line of the program below tries different lifetime ( nt ) to see which graph thus gained is in accordance with the data graph. In other words, the life of the first generation of the gfm ball particle is computed. 

The second line to the fourth line are based on the solution of the differential equation of a moving particle, in theoretical mechanics, to get the final value of speed of the first generation of the gfm ball particle. This is also the initial value to which the speed of the gfm ball particle jumps from zero value.

The line further below computes the mass of the first generation of the gfm ball particle, based on Hu Ning's theory^[1].

The lines of the program with Greek letters in them compute the relative probability according to the theory in quantum mechanics related to the weak equivalence principle^[3]. 

Below the relative probability graph is plotted.

Below is the comparison between the probability graph of quantum mechanics and the data graph.

At the wave crest, where the probability is larger, the particle is found staying longer, and moving slower. 

At the wave trough, where the probability is smaller, the particle is found staying for a shorter period of time, and moving faster. 

The first wave crest on the left shows that the boat is probably found in the state of stagnation for a rather long period of time at the beginning of the experiment.

References and notes

[1]  Hu Ning, General Relativity and Theory of the Gravitational Field, (Chinese 

       edition,) 1st ed., Science Press, Beijing, January, 2000, pp. 84--85. 

       After making a great many calculations, Hu Ning (1916 ~ 1997), a late 

       academician of the Chinese Academy of Sciences, wrote: 

       "As a form of matter, gravitational field has inertial mass" (p. 84);

       "Gravitational field has not gravitational mass" (p.84);     

       "The above result demonstrates that the order of magnitude of the ratio of the 

       difference between the gravitational mass and the inertial mass to the original 

       mass is  v2/c2 " (p.85).

[2]  Zeng Jinyan, Quantum Mechanics, (Chinese edition,) 3rd ed., Science

       Press, Beijing, January 2000, Vol. 1.

[3]  Yin Hongjun, Quantum Mechanics, (Chinese edition,) 1st ed., University of 

       Science and Technology of China Press, Hefei, China, October, 1999, 

        p. 210, Eq. (3.6.93) and p. 209, Eq. (3.6.91). 

Chapter 1  An introduction to some antigravitation engine experiments that everyone can make

Chapter 2  The setting up of the set of equations of the antigravitation engine

Chapter 3  Know-how of the antigravitational mechanical experiment and range of application

Chapter 4  Data analysis (to verify the macroscopic quantum mechanical phenomenon)

Chapter 5  Data analysis (mainly to verify Eq. (1) in Chapter 1)

Chapter 6  A new state of matter: foggoid state

Chapter 7  More about antigravitational experiments

Photos of the experiments in Chapter 7