A Possible Method to Solve Twin Paradox in Micro-Gravitational Field

[DongchengZhao]

Twin paradox is a corollary of kinematic time dilation effect of special relativity, it is a thought experiment, which cannot be completed with current technology, can only be confirmed or denied by theory at present.  Twin paradox usually has two moving objects (two brothers), incase more moving objects are added, then the chaos level of the result will be greatly increased, then some current solutions may be no longer in force. 

Here is a possible method to solve twin paradox in micro-gravitational field.  The premise of this method is that the kinematic time dilation effect in the gravitational field will be affected by a coefficient of k.  The kinematic time dilation effect of special relativity has been tested by Hafele-Keating experiment and some other related experiments, all these experiments were all carried out in earth's gravitational field, due to the influence of the earth’s gravitational field, there may be a small drift between the measured results and the theoretical predictions of the special relativity.  This drift can be expressed with the aid of a coefficient k, bring k into the kinematic time dilation equation which used in Hafele-Keating experiment, we will get an equation E:

τ-τ₀=- k.v^2/(2c^2 ).τ₀

When k=1, the original equation and its calculation results remain unchanged, it expresses the kinematic time dilation effect in the flat space-time of special relativity, when this effect is affected by the earth’s gravitational field, it will lead to a deviation of k toward 0 and less than 1.  However, due to the limitation of the accuracy of the early cesium clocks and the experimental process, the highest accuracy of the experiment in 1971 only reached nanoseconds level, it has not met the accuracy requirement and could not be the valid proof for coefficient k, so it needs to be proved by an experiment with much higher precision.

In case the kinematic time dilation effect in the gravitational field has been affected by the value of k, since twin paradox is a result of the kinematic time dilation effect, a corollary related to k is that if twin paradox is carried out in gravity (or micro-gravity) environment, theoretically the twins still will be constrained by k.  When they travelling in (micro) gravitational field O, their clocks A and B will always under the influence of the gravitational field, with the aid of k, the relative speed between AO or BO will directly affect the kinematic time dilation effect of A and B, but cannot affect time of O, so the gravitational field O has strong anti-interference, it can be their primary relative frame of reference.  For the primary reference frame O, whatever how A and B moving (even if more clocks with different motion states are added), it will not lead to contradictory and chaotic results, so twin paradox may not exist in (micro) gravitational field.  In the universe, there is no place where absolutely without gravity, so it can be approximately considered that twin paradox may not exist in the universe, in case the kinematic time dilation effect can be affected by gravitational field.

To detect the value of k in earth’s gravitational field with experiment, will be helpful for solve the twin paradox and even more.  The detail method and experiments to detect value of k is at the under address:

https://arxiv.org/abs/2010.00228

 

Edited August 22, 2022 by DongchengZhao

[swansont]

6 hours ago, DongchengZhao said:

Twin paradox is a corollary of kinematic time dilation effect of special relativity, it is a thought experiment, which cannot be completed with current technology, can only be confirmed or denied by theory at present. 

...

The kinematic time dilation effect of special relativity has been tested by Hafele-Keating experiment and some other related experiments, all these experiments were all carried out in earth's gravitational field, due to the influence of the earth’s gravitational field, there may be a small drift between the measured results and the theoretical predictions of the special relativity.

Do you see the contradiction here? "Cannot be completed" and then a citation of an experiment where it was completed? i.e. the separate gravitational and kinematic effects on the clocks allows one to show that the kinematic effect is real, since the gravitational effect can be separately confirmed (e.g. the Pound-Rebka experiment)

Further, the kinematic effect was confirmed where there was no difference in the gravitational time dilation (and there was a separate experiment where the gravitational time dilation was measured)

https://www.nist.gov/publications/relativity-and-optical-clocks

direct link to a pdf of the paper https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=905055

"Here we report the detection of relativistic time dilation due to velocities of several meters per second and, separately, due to a change in height of 0.33 m by comparing two optical clocks based on ²⁷Al⁺ ions."

 

 

[DongchengZhao]

Thanks very much for your reply, your questions are very valuable. There may be some ambiguities in my previous statements, a more specific statement can be found in the paper linked at the bottom of the original text.  

The thought experiment of twin paradox is impossible to directly complete at present, the current technology cannot support a brother to travel far away from the earth at an extremely high speed in the universe, and then returning to the earth to compare with another brother many years later.  What has been completed are some verification experiments of the kinematic time dilation effect.  the objects of the two statements are not the same, so there is no contradiction.

The main discussion here is the possible influence of the gravitational field on the kinematic time dilation effect of special relativity, the gravitational time dilation effect of general relativity needs to be eliminated as the main interfering factor.  In the paper, by keeping the stationary clock and flying clocks at the same distance from the earth center, to realize that they receive the same gravitational force to eliminate the interference caused by gravitational time dilation effect. 

The experiment in the link you post is very rigorous and precise, however, Hafele-Keating experiment maybe more suitable for twin paradox, because the flying clocks in this experiment have gone trough the process of departure, long-time flight and return, it can imitate the trajectory of the interstellar travel brother in a similar way. There is still high value in redoing this experiment at higher precision.

[swansont]

6 hours ago, DongchengZhao said:

Thanks very much for your reply, your questions are very valuable. There may be some ambiguities in my previous statements, a more specific statement can be found in the paper linked at the bottom of the original text.  

The thought experiment of twin paradox is impossible to directly complete at present, the current technology cannot support a brother to travel far away from the earth at an extremely high speed in the universe, and then returning to the earth to compare with another brother many years later.  What has been completed are some verification experiments of the kinematic time dilation effect.  the objects of the two statements are not the same, so there is no contradiction.

We don’t need to do that exact experiment to confirm the effect.

6 hours ago, DongchengZhao said:

The main discussion here is the possible influence of the gravitational field on the kinematic time dilation effect of special relativity, the gravitational time dilation effect of general relativity needs to be eliminated as the main interfering factor.  In the paper, by keeping the stationary clock and flying clocks at the same distance from the earth center, to realize that they receive the same gravitational force to eliminate the interference caused by gravitational time dilation effect. 

 

Doing the experiment at the same gravitational potential also eliminates it.