Understand Special Relativity and Time paradox

[PAllen]

Yes, it's the same principle. Just because Einstein applied it to all phenomena whereas other people didn't, doesn't change the principle. And by itself, there is no Special Relativity. SR requires another principle which includes the propagation of light which I was purposely excluding from my discussion of how to prove that the traveling twin ends up younger.

I guess it is more useful to think strictly of one POR, but it's implications then depend on what other laws nature is assumed to follow. If you believe a wave travels in some material medium, then to apply POR, you treat the motion of the medium in laws that respect POR. The POR plus this wave model has different consequences than POR plus a wave model where either a transmission medium doesn't exist or is undetectable.

The issue that zonde is concerned about is whether the Principle of Relativity plus the principle that light from two sources with relative motion propagates at the same speed is enough to prove that the traveling twin will come back younger. Can I get some help on that score instead of this side track?

There is another assumption involved. You have to assume either that Doppler is symmetric between two observers, or that Doppler follows the POR directly, without need to include motion of a transmission medium. Especially if you take the view that POR applies to sound in air, you must have some additional assumption about how light is different from sound, because speed independent of emitter velocity is true for sound in air, yet Doppler is asymmetric for sound in air.

 

[phyti]

another look:

B moving at .8c relative to A, experiences a clock rate (via gamma) of .6 relative to the A clock.

Fig. 1 shows observer B with instant acceleration at B-time 0 and 24, and instant deceleration at B-time 12. B receives 4 A-ticks outbound (blue) and 36 ticks inbound. The doppler rate is therefore 4/12=1/3 out and 36/12=3 back, i.e. reciprocal as expected. The notion of A aging rapidly when B reverses direction is false. The simultaneity axis (gray) reverses from A 7.2 backward to A 32.8 forward, to FUTURE events.

Fig. 2 is from B's perspective, showing A approaching at .8c and tick 4 received at B 12. B has yet to receive ticks 5 thru 40. The extreme time and space excursions such as event A tick 4 ocurring 36 ticks before B departs, are a result of the simultaneity convention in SR. It must be remembered that the convention is a stipulation, not physics, and therefore the time and space coordinates of the remote events are bogus. The only meaningful measurement is the round trip time for light. Any division of that time into separate out and return paths is speculation if an absolute observer speed is unknown.

Fig. 3 shows the fig.2 scenario without the SR convention and using relative light speed (magenta).Fig. 3 maintains temporal order where fig.2 does not. Using my own stipulation, if b is greater than 0, I don't expect equal out and return paths. From a momentum comparison, with m the mass of the B system and M the mass of the rest of the universe, mv does not equal Mv. It's more logical and realistic that enough energy is available to accelerate a single observer system to .8c. (Why do physicists always accelerate the particles and not the lab?)

Fig. 4 shows B experiencing an equivalent G-field during his deceleration period, while perceiving A to follow a curved return path.
https://www.physicsforums.com/attachments/55394

 

[ghwellsjr]

I guess it is more useful to think strictly of one POR, but it's implications then depend on what other laws nature is assumed to follow. If you believe a wave travels in some material medium, then to apply POR, you treat the motion of the medium in laws that respect POR. The POR plus this wave model has different consequences than POR plus a wave model where either a transmission medium doesn't exist or is undetectable.


There is another assumption involved. You have to assume either that Doppler is symmetric between two observers, or that Doppler follows the POR directly, without need to include motion of a transmission medium. Especially if you take the view that POR applies to sound in air, you must have some additional assumption about how light is different from sound, because speed independent of emitter velocity is true for sound in air, yet Doppler is asymmetric for sound in air.

I'm assuming what Einstein assumed in his first postulate, the PoR, plus part of what he assumed in his second postulate, but not the part that says light propagates at c. Are you now saying that the additional assumption I need is the part of Einstein's second postulate that I left out or that Einstein also needs another assumption?

 

[PAllen]

I'm assuming what Einstein assumed in his first postulate, the PoR, plus part of what he assumed in his second postulate, but not the part that says light propagates at c. Are you now saying that the additional assumption I need is the part of Einstein's second postulate that I left out or that Einstein also needs another assumption?

I'm saying you need some additional assumption. Any of several are sufficient. You have to say something about how light follows the POR. You need not assume 2 way light speed speed follows the POR, but you do need something. You can simply assume Doppler directly follows the POR (without having to allow for Aether speed). If Aether is assumed to be material, it is not a violation of POR to be able to detect your speed in relation to it.

 

[Dale]

And if the net effect of the two back-to-back reversals is that the home twin's age is the same after the second reversal as it was before the first reversal, then that means that the decrease in the home twin's age during the second reversal must be equal to the increase in the home twin's age during the first reversal, because they have to sum to zero. So that seems to imply that either both of the two results are valid, or else they are both invalid. Is my reasoning wrong somewhere here?

Did you read my earlier post? I already responded directly to this question.

Please don't ask a question if you are going to just ignore the answers. Please read my previous explanation as well as the material I linked to.

 

[PAllen]

Fig. 1 shows observer B with instant acceleration at B-time 0 and 24, and instant deceleration at B-time 12. B receives 4 A-ticks outbound (blue) and 36 ticks inbound. The doppler rate is therefore 4/12=1/3 out and 36/12=3 back, i.e. reciprocal as expected. The notion of A aging rapidly when B reverses direction is false. The simultaneity axis (gray) reverses from A 7.2 backward to A 32.8 forward, to FUTURE events.

The time reversal under discussion in this thread is to the right of your B world line, where the simultenaity lines per this convention intersect. Also note that if you make a sideways W shaped path for the B twin, you can have the intersecting simultaneity lines occur to the left of the B world line, covering part of the A world line (you don't have the central peak of the W go all the way back to the A world line).

Most of us here are saying a few things about this:

- there is no anomaly using any inertial frame, and no need to use anything else.
- the Einstein simultaneity convention was defined for inertial frames (which cover all of spacetime). Einstein never used 'lines of simultaneity' in this way.
- if you want to describe a convention for simultaneity from a non-inertial world line, you can use this or many other conventions, but not all conventions cover all of spacetime. It is perfectly reasonable for a simultaneity convention not to cover all of spacetime.
- SR does not replace universal absolute simultaneity with observer dependent absolute simultaneity. It says there is no objective simultaneity at all, only conventions. Relativity of simultaneity means nothing more than If two observers in relative motion use the same convention, they will get different results for which events are simultaneous.

 

[Austin0]

Quote by Austin0

Well I have no doubt that both symmetry and reciprocity are actualities in the real world. But that is only because I think that SR accurately describes that world.
In SR both these properties of the Doppler effect are not assumptions but can be directly derived and demonstrated through the application of fundamental kinematics.
In a classical context they are purely ad hoc assumptions . Assumptions which in themselves directly predetermine the end results.
As far as I can see Bondi does not derive them from first principles, he simply introduces them as assumptions.

I think the value of the exercise is the show there are multiple sets of physical assumptions that can lead the the same prediction (differential aging, in this case). As to which is adhoc in the pre-relativity sense, this is subjective. Neither Bondi's assumptions nor Einstein's were expected in the 1800s. Aether theories did predict that light speed should be source independent, but they also predicted that Doppler would not be symmetrical, and that motion through the aether could also be detected by measurements of the two way speed of light. Either of these is measurable. Both get at the issue of the aether becoming undetectable. Either, combined with other assumptions, can lead to SR. Since Doppler is part of what is seen in the twin scenario (extra signals not needed - they just have to be able to see each others clocks), it is instructive work from this. The twins are not making measurements light speed unless this is added. The one that turns around will have some difficulties measuring two way light speed as well.

I assume you realize that Einsteins arrived at SR by making 3 main assumptions (undetectability of inertial motion; constancy of two way speed of light; light speed independent of emitter velocity). He also added a convention that put the theory in a particular [arguably, the simplest] form. He could have chosen a different convention, and gotten a theory with slightly different equations, that made the same predictions. So it really boils down to which sets of unexpected assumptions to make. My view is it is useful to understand that there are multiple choices.

Well I certainly agree on the subjectivity of ad hocness.
This case for example:
I would say that the first postulate was not at all ad hoc. It was founded on the observed reality of inertial frame equivalence regarding applied physics, mechanics etc. The only assumption part of it was the projection that it would continue to apply in the domain outside our limits of experimental verification.Achievable velocity range.

Likewise with the second postulate. The independence from source. This was a sound logical deduction (not ad hoc) founded on established wave theory and also observation, as it also applies to sound .

I agree that the constancy of the two way speed of light would be ad hoc if it was a foundational assumption, as it's validity is dependent on the condition of length contraction and time dilation. But I see it rather as a derivative theorem, arising from the gamma function and resulting kinematics (not to mention observation I.e. the M-M results). Not a pure assumption
Unless my memory leads me astray , Poincarre had previously proposed a similar synch convention based on the same principles.
In this light the actual assumptions (the two postulates) were not themselves ad hoc or inconsistent with classical physics and so were not unexpected in the sense you mean.

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

I take your point that if presented as an exercise in the importance and effect of initial assumptions regarding the development of a theory, such a demonstration could be valuable and instructive. But that is not the perspective that Bondi or ghwellsjr are taking in their demonstrations.

They are proposing that symmetry and reciprocity are inherent properties of signal exchange and inertial motion and that differential aging (time dilation) can be expalined on that basis without need or reference to the gamma factor (time dilation)

But it appears that in fact those properties are a consequence of time dilation so the logical equivalence of their derivation is:
If it is true that A---( Doppler symmetry and reciprocity) are only possible on the condition of B ---(time dilation)

A only if B ... then (assuming ) Aand proving that A implies B is an empty tautology as far as I can see.

 

[PAllen]

Quote by Austin0

Well I certainly agree on the subjectivity of ad hocness.
This case for example:
I would say that the first postulate was not at all ad hoc. It was founded on the observed reality of inertial frame equivalence regarding applied physics, mechanics etc. The only assumption part of it was the projection that it would continue to apply in the domain outside our limits of experimental verification.Achievable velocity range.

Many physicists in the late 1800s believed the POR was valid at all velocities, but didn't apply to EM phenomenon because Aether was an exotic material medium. It is normally considered that the ability to detect motion through air is not a violation of the POR.

Likewise with the second postulate. The independence from source. This was a sound logical deduction (not ad hoc) founded on established wave theory and also observation, as it also applies to sound .

Agreed, as the wave theory of light culminating in Maxwell's equations were near universally accepted. However, Newton and Bradley (sans later data ) would have disagreed. Interestingly, Bradley's derivation of aberration relied on a Newtonian corpuscular model which did not have source independent velocity; and it remained a difficulty for wave models to account for aberration until SR (there were approaches involving introduction of Aether wind, or Aether dragging).

I agree that the constancy of the two way speed of light would be ad hoc if it was a foundational assumption, as it's validity is dependent on the condition of length contraction and time dilation. But I see it rather as a derivative theorem, arising from the gamma function and resulting kinematics (not to mention observation I.e. the M-M results). Not a pure assumption

Nonsense. It was the foundational assumption from which Einstein derived gamma and time dilation and length contraction. Which all goes to show how freely one can interchange consequences and assumptions.

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

Can't argue about taste. Constant two way speed of light was unexpected. Exactly symmetric Doppler was unexpected. Both for exactly the same reason (naive Aether theory). Note that Bondi's contribution (which I wasn't aware of before gwellsjr's link) is that assuming Doppler phenomena directly follow the POR you get both symmetric Doppler and reciprocal Doppler for approach versus recession at the same speed.

I take your point that if presented as an exercise in the importance and effect of initial assumptions regarding the development of a theory, such a demonstration could be valuable and instructive. But that is not the perspective that Bondi or ghwellsjr are taking in their demonstrations.

They are proposing that symmetry and reciprocity are inherent properties of signal exchange and inertial motion and that differential aging (time dilation) can be expalined on that basis without need or reference to the gamma factor (time dilation)

Well they are right. Recall, gamma factor and time dilation are derived features in Einstein's 1905 paper. You can replace 2-way light speed follows POR with Doppler follows POR, and get differential aging. It is an assumption that Doppler directly follows POR, but I don't find it adhoc or unnatural.

But it appears that in fact those properties are a consequence of time dilation so the logical equivalence of their derivation is:
If it is true that A---( Doppler symmetry and reciprocity) are only possible on the condition of B ---(time dilation)

A only if B ... then proving that (assuming ) A implies B is an empty tautology as far as I can see.

I disagree. If you don't know about diffential aging, gamma factors, etc. You can assume Doppler follows POR and arrive at differential aging. By the way, time dilation is a coorinate dependent quantity, not a physical observable the way differential aging is.

 

[PeterDonis]

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

This is not correct. Doppler symmetry and reciprocity are consequences of Maxwell's Equations, which were verified experimentally well before relativity was even considered.

 

[Austin0]

Quote by Austin0
...

You propose that in a classical context (pre SR) with a single postulate of constant finite signal propagation independent of the source or any medium, that time dilation and differential aging can be derived as well as symmetry and reciprocity of signal reception ratios. WOuld you say this was an accurate appraisal?

No.

I never proposed a single postulate of constant finite signal propagation... That is Einstein's second postulate. I said in post #7 that I was proposing only a portion of Einstein's second postulate, the part that says that the propagation of light is independent of the source but I was not identifying that speed as Einstein did and which is necessary to establish SR..

The constancy of propagation as I used it and in the 2nd P refers to the intrinsic property of the signal not referring to any specific quantification or measurement. Both you and Bondi implicitly apply this assumption when you attribute equal propagation between Alfred and Brian in both directions. If you will notice I also did not assign any specific value but only said it must be finite.
But this is all really inrrelevant to the question at hand.

This is probably a confusing issue. I would recommend that you look up the wikipedia article on the One-Way Speed of Light and look down to the section called "Experiments that can be done on the one-way speed of light". There you will see that it is possible to determine experimentally that light from two different sources with relative velocity propagate at the same speed but we cannot measure what that speed is. This is also assumed to be true both in a classical context (pre SR) where ether is affirmed and in a relativistic context (SR) where ether is denied. Bondi did not specifically state that he was adopting this assumption but it is obvious that he is..

There is absolutely zero confusion in my mind and all of this is well known and understood. But as it is also not germane to the issue. The only purpose I see in this digression is the unfortunately common one of implying that disagreement must stem from ignorance or misunderstanding.

Quote by Austin0

Well I have no doubt that both symmetry and reciprocity are actualities in the real world. But that is only because I think that SR accurately describes that world.
In SR both these properties of the Doppler effect are not assumptions but can be directly derived and demonstrated through the application of fundamental kinematics.
In a classical context they are purely ad hoc assumptions . Assumptions which in themselves directly predetermine the end results.
As far as I can see Bondi does not derive them from first principles, he simply introduces them as assumptions.

Yes, the Doppler effects of symmetry and reciprocity are actualities in the real world and SR accurately describes that world but SR is not what makes those effects real.

As long as we adopt the Principle of Relativity (apart from SR), then even in a classical context the correct conclusion can be drawn that the traveling twin's clock will accumulate less time than the inertial clock. The Principle of Relativity predates SR and is part of the classical context. Based purely on that principle plus the assumption that light from different sources propagates at the same speed but without identifying that speed (as explained previously) and even with a belief in an absolute ether, it can be proven that a non-inertial clock will accumulate less time than an inertial clock..

yes you continue making unqualified assertions that it can be "proven" without providing any additional support or explanation. As others have pointed out you are applying your own interpretation of the classical Principle of Relativity which in effect is indistinguishable from the SR version.

As far as symmetry and reciprocity are concerned; your assertion of their actuality is a mere assumption (which I happen to share) on your part.
This is not a fact of your direct observation nor of experimental observation as our technology is yet insufficient for definitive verification. SO your assumption , like mine , rests on your belief in the validity of a theory. Either SR or Bondi but
in either case a theoretical 'actuality"

Quote by Austin0

He assumes that the ratio observed by Alfred of signals received from Brian (traveling away towards Charles) is the reciprocal of the ratio observed by Charles of the Brian signals received (as Brian is approaching).

Likewise he assumes that the ratio observed by Alfred of Brian signals is symmetrical (equivalent) to the ratio observed by Brian of Alfred signals.
I submit both these assumptions are unwarranted in a classical framework.

Yes, Bondi does make more assumptions as he continues his discussion that includes Charles because he wants to eventually give a full explanation of the Twin Paradox which includes the Doppler that both twins see. But I didn't do that because that was not my goal. I was only using his proof that the Doppler ratios are inverses for coming and going at the same speed. And then I only expressed the Doppler that one twin sees. That is sufficient to prove which twin is older when they reunite. But the limited assumptions that I made are warranted in a classical framework..

here you again claim that Bondi proved that the Doppler ratios are inverse for coming and going.
What I saw was that from first principles he demonstrated that the ratio of signals received from Brian by David was the reciprocal of the ratio of signals received from Alfred by Brian.This is also consistent with classical kinematics.
He then simply assumes symmetry and from this then makes the ratio of signals received by Alfred from Brian equivalent to the ratio that was shown to be received by Brian from Alfred. Which is not consistent with classical physics.

Quote by Austin0

In SR both the symmetry and reciprocity of observed signal ratios is directly a consequence of time dilation.
Introduced through the gamma factor embedded in the Relativistic Doppler equation and the LT kinematics.

They are not inherent properties of signal exchange between inertial observers but can only occur with the necessary condition of time dilation taking effect.

it would seem then, that to adopt them as initial premises or assumptions is to implicitly introduce time dilation to derive time dilation. Also to invoke SR as these properties are only valid in that context.

SR works because it accurately reflects the Doppler effects--not the other way around. The horse is the Doppler effects, the cart is SR. Don't get the cart before the horse. The Doppler effects occur no matter what theory we invent to explain them..

This is an absurd interpretation of what I said. A straw horse. No one would propose that theory determined reality.
On the other foot:
Your claim to explain the asymmetry of aging by the asymmetry in the Doppler observations makes a direct connection between the two phenomena. This directly implies a causal connection and direction. Otherwise your initial claim is meaningless and invalid.

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?

 

[PAllen]

This is not correct. Doppler symmetry and reciprocity are consequences of Maxwell's Equations, which were verified experimentally well before relativity was even considered.

If you assume Maxwell's equations are valid in any inertial frame, rather than that they are the simplest expression of laws of EM, true only in the Aether frame (similarly, sound is simplest to describe in the rest frame of air; yet this is not normally taken as a violation of POR).

Anyway, I strongly agree they are natural assumptions, but not the most common ones circa e.g. 1870.

 

[PAllen]

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?

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, transverse Doppler, differential aging, invariant two way light speed. The phenomena exist even if we don't have a theory to explain them. Further, the phenomena, by themselves, have relationships. An important one is that symmetric and reciprocal Doppler (along with emitter speed independence of light transmission) implies differential aging ; it even quantifies as I will show in blog I am almost done with. Similarly, invariant two way light speed (along with a couple of undisputed assumptions) implies all the rest.

Time dilation and length contraction are the derived features of a model, that accommodates the truth of all these phenomena. These are derived from various possible sets of assumptions. It is the assumptions that should be taken to impy time dilation and length contractions given a convention for defining inertial coordinates, not vice versa.

 

[PeterDonis]

If you assume Maxwell's equations are valid in any inertial frame, rather than that they are the simplest expression of laws of EM, true only in the Aether frame

I realize a lot of people assumed this, but it isn't actually consistent with Maxwell's Equations. People in the late 1800's didn't fully understand what "Maxwell's Equations are Lorentz invariant" actually meant. They are only consistent if they are valid in any inertial frame. (More precisely, if you want to have any connection between Maxwell's Equations and mechanics at all, they have to be valid in any inertial frame; there is no way to have them only be valid in one chosen aether frame.)

 

[PAllen]

I realize a lot of people assumed this, but it isn't actually consistent with Maxwell's Equations. People in the late 1800's didn't fully understand what "Maxwell's Equations are Lorentz invariant" actually meant. They are only consistent if they are valid in any inertial frame. (More precisely, if you want to have any connection between Maxwell's Equations and mechanics at all, they have to be valid in any inertial frame; there is no way to have them only be valid in one chosen aether frame.)

Can you clarify what you mean? To me, it is logically possible (in some alternate universe) to posit that Maxwell's equations only hold in an aether rest frame (and would take some other form in other inertial frames). That, without having derived time dilation for a moving body, when an aether rest observer and a moving observer exchange light signals, Doppler will be asymmetric.

 

[PeterDonis]

To me, it is logically possible (in some alternate universe) to posit that Maxwell's equations only hold in an aether rest frame (and would take some other form in other inertial frames).

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]

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.

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]

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.

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]

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.

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.

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??

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]

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).

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

This is not correct. Doppler symmetry and reciprocity are consequences of Maxwell's Equations, which were verified experimentally well before relativity was even considered.

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?

There is no "classical Doppler". What we call the "relativistic" formula for the Doppler effect does not actually require SR. It only requires Maxwell's Equations. Those equations are Lorentz invariant, so of course the Doppler formula derived from them is consistent with SR. But you don't need SR to derive it.

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?

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, transverse Doppler, differential aging, invariant two way light speed. The phenomena exist even if we don't have a theory to explain them. Further, the phenomena, by themselves, have relationships. An important one is that symmetric and reciprocal Doppler (along with emitter speed independence of light transmission) implies differential aging .

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??

Time dilation and length contraction are the derived features of a model, that accommodates the truth of all these phenomena. These are derived from various possible sets of assumptions. It is the assumptions that should be taken to imply time dilation and length contractions given a convention for defining inertial coordinates, not vice versa..

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]

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

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.

i understand that the gamma function is derived from Maxwell's equations.

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.

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?

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.

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?

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]

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??

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.

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?

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]

But I think Einstein was implicitly assuming Maxwell's equations must hold in such frame

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 into 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]

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 into 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.

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]

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.

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

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.

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..

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

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??

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..

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]

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

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.

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?

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.

observations in themselves have little meaning.
That meaning is also a derived from our theory , yes?

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.

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

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.

DO you doubt that differential aging is simply the cumulative result of time dilation?

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]

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.

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]

The classical Doppler formulation is no exception. It had a simplified formula, which is still used today, just like F=ma is still used today, but we realize it is only a very good approximation and useful because the more complicated formula won't make any difference in our computation, as long as the speeds are small compared to the speed of light. However, there is a more complicated formulation that works at all speeds which you can read about here.

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

Tell me something zonde, do you understand the argument, whether or not you agree with it?

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 traveling 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.