I Symmetry of motion in the special theory of relativity

[pervect]

TL;DR Summary: Does the symmetry of motion in the special theory of relativity correspond to the real physical state?

It is evident that observers lack sufficient information about their past movements. This lack of information is the reason they arrive at contradictory conclusions.

What contradictory conclusions are those? Are you under the impression that relativity is not self consistent, or are you just disturbed that it contradicts your philosophy?

 

[PeroK]

Note that an object like a planet or spaceship or an astronaut is a collection of a huge number of elementary particles. It doesn't really make sense to talk about the acceleration history of an elementary particle.

If elementary particles depended in some way on their history, then this would show up instead of the quantum mechanical evidence that all electrons, say, are fundamentally indistinguishable.

Modern research is interested in trying to reconcile general relativity with quantum mechanics, rather than trying to restore the limited knowledge of the ancient Greeks, for example.

 

[qnt200]

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.

 

[jbriggs444]

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.

No. The lack of information on the twin's acceleration history is irrelevant.

If all we end up knowing is that the two twins started next to each other co-moving and ended next to each other co-moving and that the stop watches on their wrists have different readings then there is no paradox. There are any number of trajectories that could deliver the observed result.

If we also know their acceleration history, there is still no paradox. We know the trajectories that delivered the observed result.

The "paradox" is in the various tempting shortcuts where the situation is analyzed incorrectly. Almost certainly, the relativity of simultaneity will not have been taken into account.

 

[Ibix]

1. Consistency with the special theory of relativity:

This seems like a very long-winded way of saying that if you don't have any information with which to determine your velocity relative to some frame then you can't do it. Again, it seems to miss the point that this is true of any arbitrary frame, not just some past rest frame.

This lack of acceleration history is also the reason why the twin paradox arises.

No, the twin paradox needs a velocity history, not an acceleration history, to resolve. An acceleration history alone cannot resolve it.

 

[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

 

[pervect]

TL;DR Summary: Does the symmetry of motion in the special theory of relativity correspond to the real physical state?

Does the symmetry of motion in the special theory of relativity correspond to the real physical state?

I assume that the principle of symmetry of motion leads to the following consequences:

Observers in relative motion cannot definitively determine which one is "at rest" and which is "in motion." Each observer can consider their own frame as stationary and the other as moving. In other words, neither observer has sufficient information to definitively describe the true nature of the motion. Therefore, it can be said that both observers can only guess—rather than truly know—what is happening in reality.

This leads to the following problem:

So far, so good. You have described the symmetry principle of relativity well. And it is indeed puzzling how this is possible - at first glance, it does seem paradocixal.

It is evident that observers lack sufficient information about their past movements. This lack of information is the reason they arrive at contradictory conclusions.

OK, here's where you made a giant logical leap. I'm not sure what you're trying to say here. Symmetrical motion is puzzling - but the resolution of this is well known, and it is called the "relativity of simultaneity". I've skimmed through the thread, and nobody else seems to have mentioned this particular, very important phrase, but possibly I missed it. Regardless, it's something that is worth another mention if someone did already mention it.

We can express this abstractly in terms of maps. In any frame of reference, there is a map from "reality", four dimensional space time, to a subset of reality, the set of events at that specific time.

Symmetrical motion can only be self-consistent when different observers, observers use different maps from the 4 dimensional space-time to a particular instant in time, when they have different notions of simultaneity.

I wrote about this a while ago in https://www.physicsforums.com/threa...on-implies-relativity-of-simultaneity.805210/

But I make a few clarifications later.

I suppose my observations aren't complete, as what you are saying doesn't seem to be "the relativity of simultaneity" but something else, and you, at least believe it resolves the problem. So, possibly there are other ways of resolving the apparent issues, but the one I outlined is the standard one

Basically, it seems to me you haven't considered this possibility. So, it's something to look at. There are numerous attempts to explain it, some in the literature such as Einstein talking about moving trains, to studies about how to teach the concept. And an additonal very large number of various things that people have written on the forums and elsewhere. I would say that saying "realtivity doesn't model reality" is not an acceptable resolution to the issue. The theory would not have become not only popular but dominant if it obviously didn't reflect reality.

Einstein's discussion is at https://www.bartleby.com/lit-hub/re...ral-theory/ix-the-relativity-of-simultaneity/. It's well known, but it tends to cause confusion in readers. I can't say why, but people struggle with Einstein's exposition.

Possibly less confusing, but demanding some work, is a study on how to best teach the topic. Scherr, et al, wrote about this in https://arxiv.org/abs/physics/0207081, "The challenge of changing deeply held student beliefs about the relativity of simultaneity".

There are countless other references and writings, both formal and informal, as well. Einstein's has the most historical significance. Scherr's approach is my current favorite from a learning (pedagogical) standpoint. However, I can't say that I've often seen people state that they've read it and that it's solved their problem. I'm hoping that it may, eventually, llead them in the right direction - I usually don't get much feedback from readers, but I h ave a suspicion that peole don't track it down, or if they do, they don't see the relevance :(.

Closely related to the issue of simultaneity is the issue of isotropy. Isotropy determines a favored notion of simulateity for any particular frame. It's the notion of "fair" clock syncrhonization. A more percise statement of the relativity of simultaneity is that the unique "fair" or "isotropic" notion of simultaneity associated with each said observer is differfent.

So, I would stress these two key phrases: "The relativity of simultaneity" and "isotropy" as the resolution of your issue.