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According to the equivalence principle, the accelerating field and the gravitational field are considered to be completely equivalent. But after carefully studying the two most classic acceleration systems, i.e. the uniform acceleration elevator and the uniform rotating disc, the author has discovered that there is only partial equivalence instead of complete equivalence between the above two acceleration systems and the gravitational field.

In recent decades, the study of relativity gradually is gradually becoming active. It is generally known that just like Newtonian Mechanics has its limitation, the relativity also has its limitation. So far, there is no experimental basis for the Relativistic space-time outlook, and the author’s study shows that problems exist in the Equivalence principle. When proving equivalence principle, Einstein just used several ideal experiments. The uniform acceleration elevator and the uniform rotating disc are the two most classic acceleration systems among the several ideal experiments. After careful analysis, the author discovered that the two most classic acceleration systems and the gravitational field are not completely equivalent.

According to the General Theory of Relativity, the light spreads out by a straight line in a vacuum without gravity, but it will bend in the gravitational field.

Theoretically, when the elevator is parked on the surface of the planet, the trajectory of the photon in the elevator should be a curve, but the width of the elevator is only 3 meters, in such a short distance when we calculate the deflection angle of the light, we can use a slash instead of a curve, and the result will remain unchanged. For this reason, in

When the elevator is parked on the surface of the planet, we suppose that from point

Where the gravitational force is greater and the gravitational potential is deeper, the bending of the light is more powerful. The General Theory of Relativity predicts that the photon will be deflected at the edge of the sun, and deflection angle is:

In the above formula,

Einstein believed that the gravitational field and the accelerating field are completely equivalent, so the light will also bend in the uniform acceleration rising elevator [

The elevator in

The direction of the arrow in the

Einstein pointed out that in uniform acceleration elevator the propagation path of the light is curved. The observer inside the elevator may think that the bending of light is caused by gravity, and for the observer outside the elevator, the light still travels in a straight line. But because of acceleration movement of the elevator, in this period of time when the photons from the incident point reach the opposite wall, the position of the elevator has changed, so the illumination point of the light on the opposite wall is slightly lower than the point

Assuming that there are three external light pulses along the direction parallel to the floor of the elevator, orderly get in from the point

For ease of calculation, set

In the same way, the distance between the point

And the distance between the point

In the General Theory of Relativity, the bending of the light reflects the bending of the space. If the space-time relationship between the accelerating system and the gravitational field is exactly equivalent, the observers in the acceleration elevator will also find that the trajectories of the three light beams from outside are completely coincident, and the three points

The deflection angle of the 2nd beam is:

The deflection angle of the 3rd beam is:

∙∙∙, ∙∙∙

The deflection angle of the nth beam is:

In the case of

In formula (9),

Comparing

The deflection of light in the gravitational field is not the same as it in the uniform acceleration elevator. So the observer in a closed elevator will know that the elevator is parked on the surface of a planet or in the uniform acceleration movement by observing the light coming from outside, even if he does not look outside. If the light in an elevator is curving and the deflection angle of every beam is coincident or the illumination point on the opposite wall is changeless, it shows that the elevator is parked on the surface of a planet. However, if the light in an elevator is curving, but as time goes on, the deflection angle of light will become bigger and bigger, and the illumination point on the opposite wall is moving down constantly, it shows that the elevator is in the uniform acceleration movement.

According to formulas (2)-(4) and (9), under the condition of

It is not difficult theoretically to use experiments to verify the deflection of light in an acceleration system. Let a small rocket continue a uniform accelerated flight for a period of time. The outside light gets into the rocket from the point

Because the acceleration of the rocket is only 10 m/s^{2}, so the Space-time curvature effect of the General Theory of Relativity can be ignored; after a sustained acceleration of 600 seconds, the speed of the rocket is only 6 km/s, so the length contraction effect of the Special theory can be ignored. So when calculating the data in

In the above example, because the width of the elevator was only 3 m, so when we calculated the deflection angle of the three beams, three curves were replaced by three straight lines. In this section, we will draw out the three curves precisely, thus people can understand that the real trajectories of the photon.

In

In 1 ns time, the photon pass through 30 cm; in 2 ns time, the photon pass 60 cm; and so on. So the x coordinate values of the three curves are very easy to calculate, and the calculation of y coordinate value can refer to formula (2)-(4). The whole calculation process is not described in detail, here we only list the calculation results: the data of the first curve is in the

Accelerating time | 1 s | 10 s | 100 s | 600 s |
---|---|---|---|---|

Downward distance | 0.1 mm | 1 mm | 10 mm | 60 mm |

Deflection angle |

Time | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

x coordinates | 0 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 300 |

y coordinates | 0 | −5 | −20 | −45 | −80 | −125 | −180 | −245 | −320 | −405 | −500 |

Time | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

x coordinates | 0 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 300 |

y coordinates | 0 | −105 | −220 | −345 | −480 | −625 | −780 | −945 | −1120 | −1305 | −1500 |

Time | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

x coordinates | 0 | 30 | 60 | 90 | 120 | 150 | 180 | 210 | 240 | 270 | 300 |

y coordinates | 0 | −205 | −420 | −645 | −880 | −1125 | −1380 | −1645 | −1920 | −2205 | −2500 |

In above three tables, the x coordinate unit is

According to the data in above three tables, we draw out three curves accurately in

Comparing

Suppose that there is a room on the surface of a planet, and a sagging spring connects a small ball

there is a disc in a so-called free space, and a spring connects a small ball

An observer on the disc may think that the disc is stationary, and the small ball is subject to the forces of gravitation and bounce. The two forces balance so that the ball is in a stationary status. Modern physicists generally believe that the uniform rotating disc and the gravitational field are completely equivalent. If the disc is enclosed, the observer on the disc will never be able to use any experiment to distinguish between the centrifugal force and the gravity.

But in fact, it is not the truth. Even if the disc is enclosed, the observer can still distinguish between the centrifugal force and the gravity in free fall experiments of objects. As long as cutting off the spring connecting the roof and the small ball, the observer in the room will see that the ball goes into the free fall status under the action of gravity. The direction of the free fall is consistent with the direction of the gravity. In the whole process of falling, the speed of an object is getting faster and faster, thus the kinetic energy is getting bigger and bigger. But on the uniform rotating disc this scene can’t be sawn. At the moment the spring is cut off, the ball will not do the free fall movement in the direction of the centrifugal force, but will fly away instead at the original speed along the direction of tangent line of the circular motion. If the closed disc is large enough, the observer will find that the moving path of the ball is a spiral line and the kinetic energy of the flying ball is constant. On the surface of a planet, an object will do free fall movement under gravity action, but on a uniform rotating disc, it is not possible for an object to do the free fall movement under centrifugal force action. According to this, the observer on the disc can distinguish between gravity and centrifugal force. It shows that the uniform rotating disc and the gravitational field are not completely equivalent.

According to the General Theory of Relativity, the intensity of the gravitational field affects the rhythm of the clock. The bigger the gravity, the slower the clock goes. Based on the principle of equivalence, some physicists have come to the conclusion that the more the acceleration is, the more the time expands [

Suppose that a meson is in a uniform circular motion in a cyclotron. If the acceleration does affect the rhythm of the clock, as long as the radius of the circular motion of the meson is shortened, under the condition of constant line speed, the average life will be extended. But that never happened. By further analysis of these experiments you will also find that even in the case of 10^{16} g acceleration, it does not produce any impacts on the clock rate [

The author makes some analysis on the equivalence of the acceleration system and the gravitational field, and the results are as follows:

1) According to the author’s estimate, the deflections of light in the gravitational field and in the uniform acceleration elevator are not consistent, the uniform acceleration elevator and the gravitational field are not completely equivalent.

2) The object can go into the free fall under the action of gravity, but the centrifugal force on a uniform rotating disc does not have the function. This shows that the uniform rotating disc and the gravitational field are not completely equivalent.

3) According to the General Theory of Relativity, the intensity of the gravitational field affects the rhythm of the clock. In a place where the gravity is bigger, the clock goes more slowly. But in the experiment, it was discovered that acceleration had no effect on the clock rhythm. Even when the acceleration reached 10^{16} g, it is still the case. This shows that the time-space relationship between the acceleration system and the gravitational field is not completely equivalent.

4) In the book “Analysis of Relativity Theory” published in 2015, the author carefully thinks about the equivalence relationship between the uniform rotating disc and the uniform acceleration elevator, and gets to the conclusion that there is only a partial equivalence in the acceleration systems and in the gravitational field. There is no completely equivalent relationship [

5) The principle of equivalence is an extremely important principle in modern physics. If there are several experiments which can prove that the gravitational field and the accelerating system are not completely equivalent, it will lead to a major change in Physics.

Zhu, J.D. (2016) A New Understanding of Equivalence of the Accelerating Field and the Gravitational Field. Open Access Library Journal, 3: e3034. http://dx.doi.org/10.4236/oalib.1103034