Symmetry of motion in the special theory of relativity

[PeroK]

I have attempted to address most of the issues you pointed out. However, it is evident that my reasoning still does not fully align with the special theory of relativity—perhaps precisely because of the introduction of acceleration into the analysis.

In fact, I might be progressing towards a proper understanding of that topic. In the special theory of relativity, the symmetry of motion arises from the postulate that the laws of physics are identical in all inertial reference frames. This symmetry holds true in purely inertial scenarios but breaks down when acceleration is introduced. Since I introduced acceleration through the concept of "acceleration history," this could allow a parallel to be drawn between the perceived illogicality of the symmetry of motion in my reasoning and the symmetry of motion as interpreted by the special theory of relativity.

The following represents a revised version of my thinking, which may align with the principles of special relativity in some aspects while diverging in others.

1. Consistency with the special theory of relativity:

The example I provided begins with a special case where both observers were initially at rest relative to each other, meaning their relative velocity was zero. This initial condition allows us to analyze subsequent motion transitions using the principles of classical dynamics, assuming relativistic effects are negligible.

From this state of rest, one or both observers may undergo different accelerations (positive or negative). If both observers possess complete knowledge of their acceleration histories (both their own and the other's) during the transition from rest to a new state, they can apply the laws of classical dynamics to draw physically accurate conclusions about their respective velocities.

Specifically, they can determine which observer is moving with greater relative velocity or whether both have returned to rest with respect to the initial reference frame. By "greater" or "lesser" velocity, I refer to relative velocity measured with respect to the reference frame of the initial state of rest.

2. Divergence from the special theory of relativity:

If these same observers lack information about the history of acceleration (the case of motion symmetry), then their conclusions are not physically relevant. As a result, the symmetry of motion does not provide a meaningful answer about the actual situation.

This lack of acceleration history is also the reason why the twin paradox arises. Relevant information about acceleration history is essential to obtain an accurate picture of the twins' motion. Once this history is included—where both twins know their past accelerations and current relative velocities—the twin paradox ceases to be a paradox.

There is a version of the twin paradox without acceleration.

Also, in general relativity, two clocks can remain in freefall, with no proper acceleration and yet can measure differential ageing.

Moreover, particles can be created in high-energy collisions with different velocities. They have no acceleration history.

This whole line of investigation can't lead anywhere useful. It must have been considered by thousands of students.

 

[Dale]

I have attempted to address most of the issues you pointed out

Have you though? You have never once addressed the fact that your repeated claims of what is “physical” go against the evidence of physical experiments.

If these same observers lack information about the history of acceleration (the case of motion symmetry), then their conclusions are not physically relevant. As a result, the symmetry of motion does not provide a meaningful answer about the actual situation.

And yet, using the symmetry principle, Bailey et al showed that muons accelerated at $10^{18} \ g$ have the same physically measured half life in the lab frame as muons traveling inertially at the same speed.

Your opinion doesn’t dictate what is physical. Experiments do