Time paradox

PeterDonis

But this assumption would violate the classical PoR, because velocity appears in the Lorentz force law, which you have to use to combine Maxwell's Equations with mechanics. You would end up predicting a different motion for the same charged particle depending on which frame you did the computation in, so you could tell whether or not you were in the ether frame by measuring charged particle motion.

PAllen

In this universe, it would not be problem to detect motion relative to aether using EM phenomena, any more than it is a problem to detect motion relative to air. Put another way, Lorentz force law would take a different form in a frame moving relative to the aether.

PeterDonis

Hm. I'll have to think about this some more; I'm still not sure this can all fit together consistently, because there are also EM waves to be considered, and Maxwell's Equations do predict Lorentz invariance for those (just consider Einstein's thought experiment about trying to ride alongside a light beam).

PeterDonis

No, the statement you just made here is what inverts reality. The Doppler effect, including symmetry and reciprocity, is a direct observable. It is more fundamental than any theory we have about it. Time dilation is not a direct observable; it's a derived quantity that occurs in our theory.

Yes, because relative motion itself (which is a direct observable) is not the same as time dilation (which is not). I would agree that relative motion causes the Doppler effect and differential aging, but not that time dilation does.

PAllen

But I think Einstein was implicitly assuming Maxwell's equations must hold in such frame, or nature should be familiar in such a frame. Phenomena involving sound, when traveling at the speed of sound, are radically different than in rest frame of air.

Austin0

Quote by Austin0

But the assumption of Doppler symmetry and reciprocity are clearly out of thin air and contradictory to classical physics

i understand that the gamma function is derived from Maxwell's equations. ANd have already stated that the symmetry and reciprocity of Doppler (like contraction and time dilation) are also derived within that structure with the gamma function as well as being fundamental properties of motion through spacetime. That is not the argument.
When you say verified experimentally what are you referring to???
.Were the Doppler properties derived directly from Maxwell or were they derived later with the inclusion of the gamma function???

What do you mean when you say"only requires Maxwell's Equations" Are you speaking literally and suggesting that the relativistic Doppler equation was directly derived from them???/
or are you talking about the Lorentz maths derived from them. The gamma function????
When you say "But you don't need SR to derive it" are saying you don't need the Lorentz math which is an integral part of SR???

Austin0

Quote by Austin0 View Post


This unambiguously inverts reality. The Doppler effects, symmetry and reciprocity are the end of the line. They are consequences of , not causes of time dilation. Yes there is a correlation between the asymmetry of the observations and the asymmetry of the differential aging but this is a correlation without causation.
And is unsurprising because ultimately both the Doppler effects and the final aging are caused by the same thing: The time dilation factor intrinsically resulting from relative motion.. Do you disagree??
so actually the gamma factor does "explain" both the differential aging and the Doppler effects.

Even in an SR context , the Twins scenario, the effects directly resulting from relative motion (without the introduction of dilation) are neither symmetric nor reciprocal. Would you agree???

Well I not only agree with all of the above but have explicitly stated the same things in the course of this thread.
Eg.
YOU "Time dilation and length contraction and Einstein simultaneity convention are part of the coordinate expression of a model to explain a range of measurable phenomena: symmetric and reciprocal Doppler, differential aging,"
ME "so actually the gamma factor does "explain" both the differential aging and the Doppler effects."
Here I was explicitly referring to the time dilation aspect of the gamma factor. SO not only are we in agreement but you are supporting my point. Time dilation explains Doppler symmetry not the other way around.

"An important one is that symmetric and reciprocal Doppler (along with emitter speed independence of light transmission) implies differential aging" ----yes i have repeatedly stated that given these assumptions you get differential aging.
That is not the question. Which is:Do the Doppler effects explain dilation or does dilation explain the symmetric Doppler effects???Do those effects cause dilation or does dilation cause those effects??

As far as I know the gamma function, time dilation and length contraction were derived by Lorentz from the Maxwell math without need of any assumptions at all. is this not the case??

As such they are mathematical descriptions of fundamental phenomena and so precede and determine derivative theorems and coordinate conventions.

So i can't really understand a perspective where they are determined by something else other than the intrinsic properties of spacetime????

PAllen

No, this is not true. If Bradley's derivation of aberration was correct, one would expect symmetry in Doppler. If no one thought waves needed an aether, then Maxwells equations + POR should have led quickly to the Lorentz transform. Thus, any 'unnaturalness' of symmetry and reciprocity came from the belief that some form of medium was needed for wave propagation.
It can be. But Einstein first derived it without any reference to Maxwell's equations. Lorentz, and others also derived it without reference to Maxwell's equations.
Doppler properties follow directly from Maxwell if you assume Maxwell's equations hold in any inertial frame. You do not need to first derive the Lorentz transform or gamma.

Historically, I believe derivation of Lorentz transform preceeded relativistic Doppler equation. But history is not causation. It is a mathematical fact that Maxwell's equations holding in any inertial frame leads directly to relativistic Doppler, without need to derive the Lorentz transform.

PAllen

No, this is not true. Lorentz believed (initially) that Maxwell's equations held only in the 'aeither frame'. He (and others, before Einstein) derived the length contraction, time dilation, and the Lorentz trasnform from analysis of experiments. I believe the only person before Einstein to realize that Maxwell's equations were invariant under the Lorentz transform was Poincare.
Spacetime is a human invention to describe our experience. If you want to boggle your mind, any number of BSM theories suggest the effective dimensionality of space is emergent; and that it may also depend on the scale on which you examine physics; and that (per some approaches) a continuous manifold is emergent, not fundamental.

PeterDonis

He was assuming that whatever would be observed in his thought experiment would have to be a solution of Maxwell's Equations, yes. The fact that those equations have no solutions corresponding to a static EM wave (varying only in space, not time) clued Einstein in to the fact that Maxwell's Equations were Lorentz invariant, not Galilean invariant. That conclusion does not depend on any additional mechanical assumptions; but I agree that that conclusion by itself is not enough to show that mechanics must be Lorentz invariant.

PAllen

I agree with all of that, but I think plenty of physicists at the time were assuming that an EM field in a frame moving rapidly relative to the aether need not look anything like a solution of Maxwell's equations (it would be a solution of some more complex equation). Further, this need not be viewed as a violation of POR if you hold that aether provides a material 'absolute frame', in which EM follows Maxwell.

DrGreg

I could be wrong, but I thought Lorentz was motivated to come up with his final form of the Lorentz transformation specifically to find a transformation to leave Maxwell's equations invariant. Length contraction and time dilation (relative to a supposed aether) had already been found, in order to explain the Michaelson-Morley result, but the final step of a time offset (what Lorentz called "local time" and equivalent to Einstein's relativity of simultaneity) was needed to get invariant Maxwell's equations.

Austin0

would you agree that on an essential level physics is a study of causality?

Quote by Austin0

You will note that I was talking about causality here. Are you suggesting that The Doppler effect, including symmetry and reciprocity should considered as cause rather than effect simply because they are directly observable and time dilation is not???

yes in a sense observables are more fundamental,frame invariant, but observations in themselves have little meaning.
That meaning is also derived from our theory , yes???


Quote by Austin0

Note i did not say or imply that relative motion was the same as time dilation.
I said that time dilation resulted from relative motion.

relative motion---->time dilation------>Doppler effect and differential aging

You seem to be implying that time dilation and differential aging are unrelated phenomena. That because we cannot observe or quantify time dilation that it is not the same thing.
DO you doubt that differential aging is simply the cumulative result of time dilation???

PeterDonis

Causality is certainly one thing physics can study. I don't know that I agree that causality is all there is to it on an essential level. Physics is the study of whatever reality turns out to be; if reality includes causality, then physics studies causality. But if reality turns out not to include causality in some cases (for example, in quantum gravity theories causality may turn out to be an emergent property, not fundamental, and not present in all cases), then physics will not just be the study of causality on an essential level.

I didn't say the Doppler effect was a cause; later on in your post you quoted me as saying it is an effect, caused by relative motion. But the Doppler effect is indeed a direct observable and an invariant; time dilation is a frame-dependent convention. See further comments below.

An observed Doppler shift does not seem to me to be a very "theory-laden" observation. There are some observations in physics that require a lot of theory to interpret--results from particle physics experiments like the LHC, for example--but we're not talking about those kinds of observations here. We're talking about pretty simple and straightforward ones.

Yes, I understand that this is your interpretation of the causality involved. Mine is:

relative motion --> Doppler effect and differential aging

Time dilation does not appear because it is frame-dependent, so it is a convention, not a "real thing" that needs to have a cause.

I don't "doubt" this in the sense of thinking it's a purported factual statement that might not be true. I think it's "not even wrong" in the sense that it attributes causality to a frame-dependent convention.

PAllen

After a bit of research, yes, it appears you are correct. So perhaps Einstein was the first to show their derivation without any reference to Maxwell's equations.

zonde

And this more complicated formulation of Doppler is explained using SR.

Hmm, you will have to be more specific. There is Bondi argument and there is your argument and your interpretation about Bondi argument.

I guess I understand Bondi argument just fine as he does not seem to be claiming much. He just says without any argument:
"Note that the Principle of Relativity, by insisting on the equivalence of all inertial observers, makes it quite clear that the ratio must be the same whichever of a pair of inertial observers does the transmitting."

As I already said he provides no explanation how it can be considered consistent with classical Doppler.

And he makes quite clear distinction between classical Doppler and relativistic Doppler contrary to you:
"It is trough this rule [PoR] that our work on light differs so sharply from the work on sound where, it will be remembered, the speed of transmitter and receiver relative to the air had also to be taken into account."


On the other hand your claim is that one can predict that the travelling twin will be younger than stay at home twin just from PoR and SR second postulate by some shorter route than SR.
So I have to "forget" SR and try to understand your argument. And this is a bit complicated as you keep referring to things that I learned from SR as given.

ghwellsjr

Yes, and when writing a book to explain relativity, Bondi started with the simplified formula.
In between the above two quotes of mine is this qoute which you left out:
That clearly provides that answer to your question.
Are you saying that there are two kinds of Doppler, classical which applies to sound and relativistic which applies to light and since I'm saying to "forget" SR then I must, by default, be limited to the Doppler that applies to sound and not to light?