Constant speed between 2 objects close to the speed of light

[roineust]

If i am moving away from an object at a certain constant speed close to the speed of light, is that object also moving away from me at the same constant speed?

 

[PAllen]

Yes.

 

[roineust]

Yes.

How do we know that is correct? How do we know that the answer is yes?

 

[PAllen]

This symmetry has been a fundamental feature of physics since Galileo. All of classical mechanics, special relativity, general relativity (for nearby objects), quantum field theory and the standard model depend on it. It is directly testable up to some speed. So to hypothesize otherwise you need to find alternatives to all validated physical theories that make the same predictions for all observations, yet incorporates some mechanism where this symmetry breaks down in some way above some sublight relative velocity. Such an alternative would require abandonment of homogeneity and isotropy, because this velocity symmetry can be derived from those assumptions alone. This would then imply that Noether’s theorem is irrelevant to our universe, so conservation laws would no longer be related to symmetry. Almost certainly, such a program is impossible, and it is certainly pointless.

 

[roineust]

This symmetry has been a fundamental feature of physics since Galileo. All of classical mechanics, special relativity, general relativity (for nearby objects), quantum field theory and the standard model depend on it. It is directly testable up to some speed. So to hypothesize otherwise you need to find alternatives to all validated physical theories that make the same predictions for all observations, yet incorporates some mechanism where this symmetry breaks down in some way above some sublight relative velocity. Such an alternative would require abandonment of homogeneity and isotropy, because this velocity symmetry can be derived from those assumptions alone. This would then imply that Noether’s theorem is irrelevant to our universe, so conservation laws would no longer be related to symmetry. Almost certainly, such a program is impossible, and it is certainly pointless.

How does that fundamental symmetry relate to SR postulate no.1? Is it a part of it, all of it or a different entity from it?

 

[PAllen]

How does that fundamental symmetry relate to SR postulate no.1? Is it a part of it, all of it or a different entity from it?

It is different, since it is true for all relative velocities in Newtonian physics. It is even true in Lorentz ether theory. In fact, I no of know serious speculative proposal for which velocity symmetry is not taken for granted.

edit: I missed that you said postulate 1, which is just plain equivalence of inertial frames. In that case, yes, velocity symmetry is related to this postulate.

 

[Mister T]

If i am moving away from an object at a certain constant speed close to the speed of light, is that object also moving away from me at the same constant speed?

That's true by definition. If A moves relative to B with speed $v$ then B moves relative to A with the same speed $v$.

 

[PAllen]

That's true by definition. If A moves relative to B with speed $v$ then B moves relative to A with the same speed $v$.

It can be taken as a definition, but much serious analysis has been done on the relation of this velocity symmetry to other assumptions. The following well known paper (which calls this symmetry reciprocity) is an example of its relation to homogeneity, isotropy, and the principle of relativity. It derives reciprocity from these, rather than just defining it. It thus supports the statements I made above about what you would have to give up if you wanted to hypothesize that reciprocity was false:

http://physics.sharif.edu/~sperel/91/paper1.pdf

 

[FactChecker]

There is a long and stubborn history of people trying to establish a preferred reference frame on which absolute motion could be defined. The theory of Aether is a good example. It never worked out. Without a preferred reference frame, all inertial reference frames are considered equally valid.

 

[PeroK]

That's true by definition. If A moves relative to B with speed $v$ then B moves relative to A with the same speed $v$.

Here is a simple justification. First, we can take the relative motion to be along a shared x-direction. If A measures B's speed to be $v$ and B measures A's speed to be greater than $v$, say, then there is no factor to use to justify this. Who is traveling in the positive or negative direction can be switched by changing the orientation of the shared axis. And then it's B who should be traveling faster. The same argument applies for a measurement of less than $v$.

In other words, different measured speeds would imply that there must be a fundamental, non-homogeneous left and right in space. As this is assumed not to be the case, then B must measure the same relative speed as A.

 

[roineust]

It can be taken as a definition, but much serious analysis has been done on the relation of this velocity symmetry to other assumptions. The following well known paper (which calls this symmetry reciprocity) is an example of its relation to homogeneity, isotropy, and the principle of relativity. It derives reciprocity from these, rather than just defining it. It thus supports the statements I made above about what you would have to give up if you wanted to hypothesize that reciprocity was false:

http://physics.sharif.edu/~sperel/91/paper1.pdf

If that was hypothetically true (this speed symmetry brake close to the speed of light), does it necessarily imply that the ratio between time dilation and length contraction is not linear?

 

[PeroK]

If that was hypothetically true (this speed symmetry brake close to the speed of light), does it necessarily imply that the ratio between time dilation and length contraction is not linear?

Could you explain what you mean by that? What is "this speed symmetry brake"?

 

[roineust]

Could you explain what you mean by that? What is "this speed symmetry brake"?

If an experiment had shown that the measured constant speed between 2 objects, does not have the same value as measured from these 2 different frames of reference, when approaching the speed of light.

 

[PeroK]

If an experiment had shown that the measured constant speed between 2 objects, does not have the same value as measured from these 2 different frames of reference, when approaching the speed of light.

That's exactly the sort of experiment that was tried before 1905. No such asymmetry could ever be found.

 

[roineust]

That's exactly the sort of experiment that was tried before 1905. No such asymmetry could ever be found.

Was there such an experiment executed, where the same or identical equipment has been taking measurements of the relative speed, while situated on both objects that move at close to the speed of light relative to each other? One object could be earth, what was the other object?

If such a question sounds weird, why doesn't Michelson Mroley experiment, which claims not to find difference of observations between 2 objects, while measuring results situated only from 1 object, not sound twice as weird?

 

[PeroK]

Was there such an experiment executed, where the same or identical equipment has been taking measurements of the relative speed, while situated on both objects that move at close to the speed of light relative to each other? One object could be earth, what was the other object?

If such a question sounds weird, why doesn't Michelson Mroley experiment, which claims not to find difference of observations between 2 objects, while measuring results situated only from 1 object, not sound twice as weird?

I don't know where this is leading. There's a fundamental question about whether space is the same in every direction. Or, whether let's say there is an up and a down in the universe. If there really were an up and a down, then experiments across the surface of the Earth would show different results. Particle accelerators would operate differently depending on their relative orientation to each other. Nothing like that has ever shown up.

If it had, then it would be part of our physics. In the same way that there is an up and down relative to the surface of the Earth.

All physical theories either assume (or have shown no contradiction to) the basic idea that space is the same in every direction.

 

[PAllen]

If that was hypothetically true (this speed symmetry brake close to the speed of light), does it necessarily imply that the ratio between time dilation and length contraction is not linear?

To answer this question, one would need a particular speculative model or theory that had a violation of reciprocity of relative velocity that became significant above some cutoff near c. Despite a great many speculative models physicists have created (some for the sole purpose of having something to compare to the current best theory in experiments - so called test theories), including theories of absolute frames of reference, and several varieties of Lorentz violating theories, etc. none that I have ever seen reference to have the feature you propose. The reason is that this just seems patently silly even to the most speculative physicists. I would say it seems as silly to me as a theory of spontaneous generation of pink unicorns.

Without a worked out test theory, nothing can be said about the implications. So, unless you can find a reference to one, there is just nothing more to discuss.

Your questions about why reciprocity is believed, the type of evidence, and the relation to other assumptions, have all been answered fully. Thus, constructive discussion seems to be at an end.

 

[PeterDonis]

Was there such an experiment executed, where the same or identical equipment has been taking measurements of the relative speed, while situated on both objects that move at close to the speed of light relative to each other?

How would you measure the relative speed?

The most common way of doing it is to have light signals make round trips between the two objects, and measure the round-trip travel times and observed frequencies/wavelengths of the light signals. Any such experiment will obviously give you just one answer for "relative velocity", which will apply to both objects.

Michelson Mroley experiment, which claims not to find difference of observations between 2 objects, while measuring results situated only from 1 object

Where are you getting this from? What "objects" are you taking about?

 

[roineust]

I was told that the Mossbauer effect proves the question in this thread, namely: that if person A measures to be moving away from person B at a certain constant speed close to the speed of light, then person B will be measuring to be moving away from person A at the exact same speed.

Can anyone explain to me how this effect proves my question?

 

[Ibix]

I was told that the Mossbauer effect proves the question in this thread,

It would be helpful to say who told you and where.

I don't think the Mossbauer effect itself proves anything. It is, however, an integral part of several tests of relativity because it allows very high precision measurement of frequency. It has been used in tests of the clock hypothesis, which I'd guess is what you are talking about.

 

[Nugatory]

I was told that...

Told by whom? Can you give us a link or other reference? Without that, it’s going to be hard to say anything sensible.

 

[FactChecker]

I was told that the Mossbauer effect proves the question in this thread, namely: that if person A measures to be moving away from person B at a certain constant speed close to the speed of light, then person B will be measuring to be moving away from person A at the exact same speed.

Measured how and by whom? When special relativity is discussed, the symmetry of the situation you describe is a fundamental assumption that seems to hold. No experiment has shown that there is a preferred inertial reference frame. Therefore, it is assumed true that person B will be measured to be moving away from person A at the exact same speed. Something that is true can often be proven in a multitude of ways.

 

[Dale]

I was told that the Mossbauer effect proves the question in this thread, namely: that if person A measures to be moving away from person B at a certain constant speed close to the speed of light, then person B will be measuring to be moving away from person A at the exact same speed.

Can anyone explain to me how this effect proves my question?

Yes, that was me. Sorry I didn’t see this post until just now.

The Mossbauer effect allows very precise measurements of frequency. I can go into detail about how it allows precise measurements of frequency, but the point for proving the point is that it does.

There are several important Mossbauer rotor tests, for example Kuendig, Phys. Rev. 129 no. 6 (1963), pg 2371. In that one they put a piece of iron on the edge of a high speed rotor and used the Mossbauer effect to precisely measure the transverse Doppler shift seen by the moving piece of iron at different speeds. The relativistic value was confirmed to within about 1%.

The transverse Doppler shift (aka time dilation) is zero in Newtonian physics, and its precise value predicted by relativity is directly determined by the first postulate. Therefore, confirmation of the transverse Doppler shift at the specific relativistic value validates the first postulate, including the reciprocity of relative velocity.