Symmetry of motion in the special theory of relativity

[qnt200]

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:

It is evident that observers lack sufficient information about their past movements. This lack of information is the reason they arrive at contradictory conclusions.
Therefore, it seems to me that the principle of symmetry of motion does not fully correspond to the actual physical state of objects. Moreover, it is clear that drawing reliable conclusions is impossible without adequate information about the motion's history.

I do not understand what led to the principle of symmetry of motion—apparently lacking a solid physical basis—being accepted as a foundational concept in the special theory of relativity.

 

[jbriggs444]

There is a philosophical leap that one should make. It is, perhaps, a variant of Occam's razor.

If there is no experimental test that can distinguish between two possibilities then the distinction does not even exist. It is not that we cannot tell which observer is really at rest. It is that the concept of "really at rest" does not correspond to anything physical.

 

[Dale]

I do not understand what led to the principle of symmetry of motion—apparently lacking a solid physical basis—being accepted as a foundational concept in the special theory of relativity.

That at least is clear. It is accepted as a foundational concept because it successfully explains the result of a wide variety of experiments.

https://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

The evidence supporting it is overwhelming. It does correspond to the physical state, and is an exceptionally solid physical basis.

 

[PeroK]

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:

It is evident that observers lack sufficient information about their past movements. This lack of information is the reason they arrive at contradictory conclusions.
Therefore, it seems to me that the principle of symmetry of motion does not fully correspond to the actual physical state of objects. Moreover, it is clear that drawing reliable conclusions is impossible without adequate information about the motion's history.

I do not understand what led to the principle of symmetry of motion—apparently lacking a solid physical basis—being accepted as a foundational concept in the special theory of relativity.

Einstein deals with that point in the introduction to the 1905 paper. It was partly the unsuccessful attempts to detect an ether and the lack of any sense of absolute motion in the phenomena of electromagnetism.

If you search online, you'll find the paper.

 

[Histspec]

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

The theory says that only "inertial" motions are relative (or symmetric), whereas accelerated motions - as indicated by comoving accelerometers - are "absolute".

In other words, neither observer has sufficient information to definitively describe the true nature of the motion.
...
It is evident that observers lack sufficient information about their past movements.

They don't need anything to know about their past movements, they only need an accelerometer - an indication of zero means they can consider themselves as being at rest in their respective inertial frames; indicating more than zero means they are accelerating and constantly changing there (momentary) inertial rest frames.

I do not understand what led to the principle of symmetry of motion—apparently lacking a solid physical basis—being accepted as a foundational concept in the special theory of relativity.

Experiments couldn't detect any "absolute" inertial motion with respect to a frame in absolute rest ("aether"), so the most easy explanation is that no such motion exists (examples are the Michelson-Morley experiment, Hughes-Drever experiment etc.).

 

[A.T.]

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

This principle is not specific to SR, but much older:
https://en.m.wikipedia.org/wiki/Galilean_invariance

Each observer can consider their own frame as stationary and the other as moving.

It's even better: Each of them can choose from an infinite number of equivalent reference frames to do physics using the same laws.

This leads to the following problem:

It's not problem for physics, but rather a great powerful feature. It's a problem for armchair philosophers with preconceived notions of 'realness' which don't match observations.

 

[robphy]

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

I do not understand what led to the principle of symmetry of motion—apparently lacking a solid physical basis—being accepted as a foundational concept in the special theory of relativity.

The idea of the "principle of relativity" began with Galileo and mechanical experiments
https://en.wikipedia.org/wiki/Galileo's_ship#1632_thought_experiment
which was extended by Einstein to include electromagnetism and all the laws of physics.

The geometric analogue is... on a Euclidean plane, given a circle and two radial directions, which direction is "the horizontal direction"?

 

[qnt200]

That at least is clear. It is accepted as a foundational concept because it successfully explains the result of a wide variety of experiments.

https://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

The evidence supporting it is overwhelming. It does correspond to the physical state, and is an exceptionally solid physical basis.

Your argument is strong, but it is also familiar to me. However, I am looking for a concrete and clear explanation because I am interested in research in this area. Perhaps you could suggest a work that critically addresses this topic.

In principle, we can also ask what else might have been discovered if this principle had not been accepted. We do not know the answer to this (similar to observers in the principle of symmetry of motion).

 

[qnt200]

They don't need anything to know about their past movements, they only need an accelerometer - an indication of zero means they can consider themselves as being at rest in their respective inertial frames; indicating more than zero means they are accelerating and constantly changing there (momentary) inertial rest frames.

In that case, observers can only determine whether they are in the phase of acceleration or uniform motion.
They are unable to assert that one is at rest while the other is moving, or vice versa, nor can they make any other conclusions about motion beyond whether it is uniform or not. The reason is that they lack information about past motion (acceleration).

In other words, their knowledge is insufficient to provide a true physical assessment of the motion of objects. This aligns with the principle of symmetry of motion, but this symmetry does not provide a realistic physical picture, as it is possible that the objects are moving at speeds unknown to the observers.

 

[phinds]

They are unable to assert that one is at rest while the other is moving, or vice versa

Correct, because neither is "at rest" in any absolute sense and each of them is at rest in his own frame of reference and in motion in the others frame of reference.

You are truly wasting your time arguing against Special Relativity. It is reality and has been shown to be such via thousands of experiments. **

** that's probably a gross underestimate.

 

[Nugatory]

In that case, observers can only determine whether they are in the phase of acceleration or uniform motion

yes, but it does not follow from this that….

In other words, their knowledge is insufficient to provide a true physical assessment of the motion of objects.

This conclusion requires an additional assumption: that there is such a thing as absolute motion that is a necessary part of a “true physical assessment” of the motion of objects. So far you have not justified that assumption.

 

[Ibix]

In that case, observers can only determine whether they are in the phase of acceleration or uniform motion.

Yes.

They are unable to assert that one is at rest while the other is moving, or vice versa, nor can they make any other conclusions about motion beyond whether it is uniform or not.

No - both are free to assert that either or neither is at rest.

The reason is that they lack information about past motion (acceleration).

No. The reason is that there is no measureable difference between the state "I am at rest" and "you are at rest". So who is at rest is nothing more than a matter of convention.

 

[FactChecker]

It's very nice that when I am on a commercial airplane I can consider the airplane to be stationary. When I need to walk to the bathroom I do not need to consider the 400mph of the airplane before I take a step. ;-)

 

[robphy]

Reminder:
"able-to-be-at-rest" is not equivalent to "being inertial".

 

[Dale]

Perhaps you could suggest a work that critically addresses this topic.

The link I gave you and all the references therein.

I am looking for a concrete and clear explanation

What explanation can possibly be more concrete than actual experiments?

In principle, we can also ask what else might have been discovered if this principle had not been accepted. We do not know the answer to this (similar to observers in the principle of symmetry of motion)

Sure. That has been studied. Robertson’s famous paper (see the specific citation in the link above) showed how the experimental evidence is sufficient to deduce the math of relativity even without the postulates.

So we would have gotten to the theory of relativity simply from the evidence. The fact that the postulates (in advance) predicted such a large body of evidence is a masterstroke of theory. But at this point, with the existing evidence, we would be here regardless.

This aligns with the principle of symmetry of motion, but this symmetry does not provide a realistic physical picture

Numerous real physical experiments disagree with you. When your opinion about what constitutes a realistic physical picture disagrees with real physical experiments, then it is time to revise your opinion

 

[PeroK]

In principle, we can also ask what else might have been discovered if this principle had not been accepted. We do not know the answer to this (similar to observers in the principle of symmetry of motion).

If a theory is wrong it generally gets disproved. Principles and postulates never stopped the experiments.

Physics is constantly being experimentally tested. It's a common misconception that physicists generally get credit for confirming established theories. It's quite the reverse. The way to make a name for yourself is to do an experiment with a surprising result. Or, at least, a result no one has seen before.

 

[qnt200]

Thank you for your constructive criticism and helpful answers. Unfortunately, I feel that I have not fully received an explanation that provides the real logical reason for accepting the symmetry of motion in the special theory of relativity.

Perhaps this simple example will better illustrate the point I am trying to make:

Initially, two observers are at rest in inertial reference frames. Then, one of the observers briefly accelerates, reaching a relative velocity v with respect to the observer who did not accelerate. After the acceleration phase, both observers are again in inertial reference frames.

Now, considering the velocity relationship between the two observers, the following can be said:

1. If the observers know the history of acceleration, they can conclude that the velocity of the observer who experienced acceleration is greater than that of the observer who did not accelerate. This conclusion reflects the actual physical situation.


2. If the observers do not know the acceleration history (the case of motion symmetry), they cannot draw meaningful physical conclusions about the relationship between their velocities. This lack of information implies that the symmetry of motion lacks physical significance, as observers do not have enough data to provide a relevant answer.

 

[phinds]

1. If the observers know the history of acceleration, they can conclude that the velocity of the observer who experienced acceleration is greater than that of the observer who did not accelerate. This conclusion reflects the actual physical situation.

NO, it most emphatically does NOT. You KEEP forgetting that all motion is relative, so there are objects for which one is seen as moving faster and objects for which the other is moving faster. This is VERY simple relativity and was known long before Einstein.

2. If the observers do not know the acceleration history (the case of motion symmetry), they cannot draw meaningful physical conclusions about the relationship between their velocities. This lack of information implies that the symmetry of motion lacks physical significance, as observers do not have enough data to provide a relevant answer.

There IS ONLY ONE meaningful relationship between the two after acceleration and that is that each sees the other as moving and they see the same relative velocity.

 

[martinbn]

Thank you for your constructive criticism and helpful answers. Unfortunately, I feel that I have not fully received an explanation that provides the real logical reason for accepting the symmetry of motion in the special theory of relativity.

Perhaps this simple example will better illustrate the point I am trying to make:

Initially, two observers are at rest in inertial reference frames. Then, one of the observers briefly accelerates, reaching a relative velocity v with respect to the observer who did not accelerate. After the acceleration phase, both observers are again in inertial reference frames.

Now, considering the velocity relationship between the two observers, the following can be said:

1. If the observers know the history of acceleration, they can conclude that the velocity of the observer who experienced acceleration is greater than that of the observer who did not accelerate. This conclusion reflects the actual physical situation.


2. If the observers do not know the acceleration history (the case of motion symmetry), they cannot draw meaningful physical conclusions about the relationship between their velocities. This lack of information implies that the symmetry of motion lacks physical significance, as observers do not have enough data to provide a relevant answer.

None of this has anything to do with special relativity!

 

[phinds]

None of this has anything to do with special relativity!

Plus the minor fact that it is all wrong

 

[Ibix]

1. If the observers know the history of acceleration, they can conclude that the velocity of the observer who experienced acceleration is greater than that of the observer who did not accelerate.

No. They could have initially regarded themselves as in motion and one braked to a stop. There is no measurement you can make that will tell you whether your description or mine is right or wrong. That is the reason for accepting the principle of relativity. It says there is no experiment that can tell the difference and that prediction has been true in every case we've ever tested.

 

[Dale]

This conclusion reflects the actual physical situation.

This conclusion does not reflect the actual physical situation. It just reflects your personal opinion. An opinion which is not confirmed by actual physical evidence.

You have failed to recognize this point that has been made multiple times now. What you repeatedly call “the actual physical situation” is not actually physical. A mountain of experimental evidence shows it.

 

[qnt200]

No. They could have initially regarded themselves as in motion and one braked to a stop.

I don't think that logic fits. Relative to what could the observers claim they were moving? In the context of the symmetry of motion, there are only two observers in space. Initially, they were at rest relative to each other, with no external reference point to orient themselves.

It is clear that your idea introduces an additional element—a point of orientation—which is absent when considering the symmetry of motion. This additional element changes the nature of the problem, as it implies a reference frame external to the observers, which is not part of the original scenario.

 

[Ibix]

Relative to what could the observers claim they were moving?

The final state of the one who changed speed.

 

[Ibix]

Also, remember that the principle of relativity is a postulate. There is no purely logical reason for accepting it - you simply assume it is true and deduce the consequences if it is so. In this case the consequences are either Newtonian physics or special relativity. We then propose that the speed of light is invariant and therefore reject Newtonian physics.

All we have done so far (edit: or more precisely, all we would have done so far if we'd actually deduced anything rather than merely stating the results of the deduction) is show that the postulates do not lead to self-contradiction. We would have to reject one or other or both if they did, but they do not. We then compare the predictions of special relativity to experiment, and find that it is accurate in all cases we have tested. That is the justification for accepting the postulates of relativity.

In order to challenge the postulates you would have to build a theory that does not rely on them and show that it makes the same predictions as relativity to our current available precision, and then propose an experiment that could differentiate between them. Coming up with new ideas for theories is fairly easy, but the rest of it is hard. Most ideas are instantly falsified because they make incorrect predictions for experiments that have already been done.

 

[PeterDonis]

In the context of the symmetry of motion, there are only two observers in space.

Ok. But--

Initially, they were at rest relative to each other, with no external reference point to orient themselves.

Yes, at rest relative to each other. Not in any absolute sense.

It is clear that your idea introduces an additional element—a point of orientation—which is absent when considering the symmetry of motion.

No, it doesn't. You are the one who is introducing an additional element, by giving a privileged status to the frame in which both observers are initially at rest.

This additional element changes the nature of the problem, as it implies a reference frame external to the observers

No, it doesn't. The second "reference frame" is relative to the observer who, in your scenario, accelerates for a period of time, after they have finished accelerating. It is not external to the observers.

Your additional element changes the nature of the problem, by making an assumption that is not necessary. You have constructed your scenario so that it seems to you like there is no such assumption--by your construction, only one observer experiences proper acceleration, so that is the one that is "moving" after having done so.

But suppose we now have the other observer, who did not experience any proper acceleration initially, do so--just enough so that both observers are at rest relative to each other again. We now have the same condition as the initial condition of your scenario: two observers, at rest relative to each other, nothing else. So by your logic, both observers are now at rest. But that contradicts your claim that experiencing proper acceleration put one observer "in motion", because that observer did not accelerate any more--they stayed inertial while the other observer accelerated. So they did nothing to change their state from "moving" to "at rest". Yet it somehow changed, because of something the other observer did.

When you carefully unpack all of this, you arrive at the principle of relativity: there is no consistent way to assign the states "moving" or "at rest" in any absolute sense. You can only do it relative to some particular object or reference frame--where here "reference frame" means a physical construction that is set up so that all its parts are at rest relative to each other.

 

[Dale]

I don't think that logic fits. Relative to what could the observers claim they were moving?

It does fit. They were initially moving relative to any inertial frame which is moving with respect to their initial rest frame. There doesn’t need to be any object at rest in a frame for you to use it.

Initially, they were at rest relative to each other, with no external reference point to orient themselves.

So what? They are free to use any reference frame they like. Including ones where they were initially moving.

 

[Ibix]

The final state of the one who changed speed.

Just to add, it is often convenient to treat yourself as "at rest", but there is no actual requirement to do so. The observers may simply state that they are initially moving at 3m/s in the direction of one of them'd right arm. Or the other one's left leg. There is no experiment that can tell between these cases.

And why should they simply assume that they are initially at rest? Why privilege the frame they happen to start at rest in? Why not some random frame in which they move in some direction at some speed? Unless there is some test they can do to determine whether they are initially at rest (and there is not), why be so self-centered?

 

[Dale]

Just to add, it is often convenient to treat yourself as "at rest", but no actual requirement to do so.

Indeed. You are free to go to the store, and not required to use a frame where the store comes to you.

 

[Ibix]

Indeed. You are free to go to the store, and not required to use a frame where the store comes to you.

Or "at what time does Oxford stop at this train", as Einstein is said to have asked.

 

[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.