by jaumzaum
PF Gold
P: 4,778
 Quote by 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).
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.
P: 1,162
Quote by Austin0

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

 Quote by PeterDonis 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???

 Quote by PeterDonis 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???
P: 1,162
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???

 Quote by PAllen 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??

 Quote by PAllen 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????
PF Gold
P: 4,778
 Quote by Austin0 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.
 Quote by Austin0 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.
 Quote by Austin0 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.

 Quote by Austin0 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.
PF Gold
P: 4,778
 Quote by Austin0 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.
 Quote by Austin0 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.
Physics
PF Gold
P: 5,322
 Quote by PAllen 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 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.
PF Gold
P: 4,778
 Quote by 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.
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.
PF Gold
P: 1,795
 Quote by 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.
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.
P: 1,162
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.
 Quote by 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..
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??
 Quote by PeterDonis 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???
Physics
PF Gold
P: 5,322
 Quote by Austin0 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.

 Quote by Austin0 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.

 Quote by Austin0 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.

 Quote by Austin0 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.

 Quote by Austin0 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.
PF Gold
P: 4,778
 Quote by 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.
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.
PF Gold
P: 1,376
 Quote by ghwellsjr 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.

 Quote by ghwellsjr 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 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.
PF Gold
P: 4,431
Quote by zonde
 Quote by ghwellsjr 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.
Yes, and when writing a book to explain relativity, Bondi started with the simplified formula.
Quote by zonde
 Quote by ghwellsjr 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.
In between the above two quotes of mine is this qoute which you left out:
 Quote by ghwellsjr But I don't want to get sidetracked on this issue as it has no relevance to Bondi's argument concerning the inverse relationship of the Doppler shifts for coming and going at the same speed.
 Quote by zonde 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.
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?
P: 1,162
Quote by Austin0
 would you agree that on an essential level physics is a study of causality?
 Quote by 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.
"on an essential level"..... in this context the word "an" inherently implies other essential levels,yes?

Quote by Austin0

 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???
 Quote by PeterDonis 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.
Your reaction to my quote below

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.
was
 Quote by PeterDonis No, the statement you just made here is what inverts reality.
if you say I am inverting reality ,this would only be true if the inverse of what I said was true, Yes?

The Doppler effects, symmetry and reciprocity ---->time dilation

instead of time dilation----->Doppler effects, symmetry and reciprocity which is what I said.

Quote by Austin0

 observations in themselves have little meaning. That meaning is also a derived from our theory , yes???
 Quote by PeterDonis 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.
What could be simpler than a temperature reading?
But what does that bare value tell us about what is being measured other than that you may not want to stick your fingers in it?
What does the word temperature or heat even mean without a theory? A molecular model, mechanics,etc, etc.

With Doppler the theoretical context in this case is SR .

According to which it appears that the observed values are the result of two distinct factors ---relative motion and the dilation factor.
Now the quantitative evaluation of the relative effect of these components is of course conventional and not to be understood as having any absolute significance quantitatively.
but you seem to want to throw out this understanding completely. Not only the implication that time dilation is a phenomenon which exists independent of convention but also the fundamental kinematics involved in this analysis and understanding.

You missed this one;
Quote by Austin0
 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???

Quote by Austin0

 relative motion---->time dilation------>Doppler effect and differential aging
 Quote by PeterDonis 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.
so do you think that there is no causality involved in relative rates of static clocks in a gravity field?
That those rates are not "real" ( don't occur) until a clock is transported and returned ?

That the returning twins age is only a "real thing" after he arrives and it becomes observable??

Do you think that the existence of phenomena is dependent on or determined by convention?

Quote by Austin0 View Post
 DO you doubt that differential aging is simply the cumulative result of time dilation???
 Quote by PeterDonis 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.
Well i think that you must agree that observation certainly does NOT cause phenomena. And propagation of signals of itself doesn't either.

Ultimately the asymmetry, the difference in signals received is solely dependent on the actual difference in the number of signals sent at the sources. YES?

This difference in number must be spread out over the course of travel ...........Agreed?

This seems to lead to two inevitable inferences:

1)There must be differences in relative rates during that transit.
The fact that we can't quantify or locate these differences in a frame independent way during transit does not negate the conclusion they must occur somewhere in that course.
2) These differences occur at the sources. Simply mechanisms (observers and clocks) and relative motion. No other intermediate factors or influences. You agreed that differential aging was a consequence of relative motion, yes/
Well differential aging is a process occurring over time.
As a process it is a difference in rates (biological or mechanical) over intervals. Time dilation by definition ,,,yes"???
PF Gold
P: 4,778
 Quote by Austin0 This seems to lead to two inevitable inferences: 1)There must be differences in relative rates during that transit. The fact that we can't quantify or locate these differences in a frame independent way during transit does not negate the conclusion they must occur somewhere in that course. 2) These differences occur at the sources. Simply mechanisms (observers and clocks) and relative motion. No other intermediate factors or influences. You agreed that differential aging was a consequence of relative motion, yes/ Well differential aging is a process occurring over time. As a process it is a difference in rates (biological or mechanical) over intervals. Time dilation by definition ,,,yes"???
I can agree with (1) in following sense: any mapping from a parameter to each (twin) world line that meets the requirements of implementing a simultaneity convention will show a greater average rate of tau to the parameter for one of the twins.

With (2), I have a big problem. You say differential aging is a process occurring over time. Whose time? The only objective time is the time along each world line. If I draw lines on a piece of paper, we don't talk about length occurring over length. If two curves on a plane have different lengths, we don't say one of them accumulated length faster, or more length per length. We say nothing more than one is longer. That is all we can say of world lines.
PF Gold
P: 1,376
Quote by ghwellsjr
 Quote by ghwellsjr But I don't want to get sidetracked on this issue as it has no relevance to Bondi's argument concerning the inverse relationship of the Doppler shifts for coming and going at the same speed.
But you understood that Bondi explained in detail inverse relationship of the Doppler shifts for coming sender and going receiver at the same speed that works just as well for classical Doppler as relativistic Doppler, right?
And when it cames to the point where one should invoke PoR (reverse sender and receiver) and two Dopplers are not equal any more all the explanations are cut short with this sentence:
"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."

 Quote by ghwellsjr 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?
Yes
 Sci Advisor PF Gold P: 4,778 Theories don't cause anything. They explain observations. Doppler symmetry exists independent of theory, and, if observed, is sufficient to predict differential aging (which might then be observed). Doppler symmetry and reciprocity is sufficient to derive the gamma factor of differential aging, without deriving Lorentz transform or even assuming invariance of light speed (if you don't assume this, you allow that the c in gamma could be frame dependent and not necessarily isotropic). SR is a theory which explains a whole range of phenomena in a unified way. That is what is great about it. But it doesn't cause anything. Within SR, you can, but in no way need to invoke time dilation to explain Doppler. If you look at SR as Einstein did, you have assumptions: (POR applies to all phenomenon including light = can't detect aether, if it exists (I am building in invariance of light speed into this); speed of light is independent of emitter speed). From these, plus a convention, you derive Lorentz transform and the full machinery of SR. Also, from these, without the convention, and without bothering to derive Lorentz transform or time dilation, you can derive symmetry and reciprocity of Doppler, and from that differential aging by gamma factor. It thus seems tendentious to insist the time dilation is the explanation (let alone cause!) of Doppler symmetry and reciprocity.
Physics
PF Gold
P: 5,322
 Quote by Austin0 "on an essential level"..... in this context the word "an" inherently implies other essential levels,yes?
I don't think I have anything to add to what I've already said on this point. I'm not interested in playing word games.

 Quote by Austin0 if you say I am inverting reality ,this would only be true if the inverse of what I said was true, Yes?
I said quite clearly what I thought the causality was, and I made it clear that my main point was that time dilation doesn't belong in the causal chain. If you have something substantive to say in response to that, fine. Again, I'm not interested in playing word games.

 Quote by Austin0 What could be simpler than a temperature reading? But what does that bare value tell us about what is being measured other than that you may not want to stick your fingers in it? What does the word temperature or heat even mean without a theory?
Um, that you shouldn't stick your fingers in it if it's hot? Temperature measurements have obvious pragmatic value even if nobody has a good theory to explain them. Which was, in fact, the case for a significant period of time after thermometers were invented. That did not prevent them from being used. Similar remarks apply to most observations; we can make them, and often make use of the data obtained, without having a theory about them.

 Quote by Austin0 With Doppler the theoretical context in this case is SR.
Not necessarily. The observations come first; they are logically prior to any specific theory that explains them. You are assuming that SR is the correct theory; on that assumption, of course you can turn the logic around and deduce all the observations from the theory. But we're talking about how you know which theory is correct; and you only know that by treating the observations as primary, not the theory.

 Quote by Austin0 According to which it appears that the observed values are the result of two distinct factors ---relative motion and the dilation factor.
No, that's not what SR says. Here's the formula for relativistic Doppler:

$$\frac{\omega}{\omega_0} = \sqrt{\frac{1 + v}{1 - v}}$$

where $v$ is the relative velocity of the observer *towards* the source (i.e., positive v is velocity towards, negative v is velocity away). Now tell me, where in that formula does time dilation appear?

 Quote by Austin0 but you seem to want to throw out this understanding completely. Not only the implication that time dilation is a phenomenon which exists independent of convention but also the fundamental kinematics involved in this analysis and understanding.
What makes you think that? All I have said is that time dilation is a frame dependent convention. I haven't said relativistic kinematics is invalid.

 Quote by Austin0 so do you think that there is no causality involved in relative rates of static clocks in a gravity field?
 Quote by Austin0 That those rates are not "real" (don't occur) until a clock is transported and returned?
Now you're talking about a different scenario where a causal factor (gravity, spacetime curvature, whatever you want to call it) is present that wasn't present in the original scenario. What makes you think that what I said about causal factors in the original scenario applies to this new one? Please don't attribute positions to me that I have not taken.

To answer your questions as you pose them, obviously if gravity (spacetime curvature, whatever) is present, there is another causal factor involved; in the case of static objects (i.e., no relative motion), the causality would be:

varying gravitational potential --> differential aging

Since the situation is static, two observers at different altitudes can establish the same simultaneity convention by exchanging light signals; and when they do, they will find that the one who is higher up experiences more ticks of his own clock between two of the exchanged light signals than the one who is lower down. So there is a set of direct observables corresponding to differential aging in this case even though the two observers don't ever actually meet.

Note, by the way, that this is a key difference from the flat spacetime case; in flat spacetime it is impossible for two observers who remain at rest relative to each other to have differential aging. If two such observers in flat spacetime run the above experiment (exchanging light signals to establish the same simultaneity convention), they will find that both of their clocks tick the same number of ticks between light signals. And if they are in relative motion, they can't synchronize their clocks this way; so the only way they have of detecting differential aging is to actually meet up and compare clocks.

 Quote by Austin0 Well i think that you must agree that observation certainly does NOT cause phenomena.
As long as we're talking about classical physics, yes, this is true. More precisely, we can always make the effects of observation sufficiently small that they can be ignored; but observations are themselves physical phenomena (for example, receiving light signals from an object), so they do have some effect.

If we take quantum mechanics into account, of course, we can no longer always make the effects of observations negligible; but I don't think we need to open that can of worms here.

 Quote by Austin0 And propagation of signals of itself doesn't either.
Propagating signals *are* phenomena, aren't they? (More precisely, detections of such signals are.)

 Quote by Austin0 Ultimately the asymmetry, the difference in signals received is solely dependent on the actual difference in the number of signals sent at the sources. YES?
Difference compared how? There has to be some common standard for comparison. In the case of the standard twin paradox, the standard is that the two twins are together, then they separate, then they come together again; so at the start and end of the scenario they can directly compare their clocks. In the case of the static gravity field, the two observers can establish a common standard of simultaneity that serves as the standard for comparison. Once there is such a standard, then yes, you can compare how many times each observer's clock ticks (or how many light signals he emits) between two standard comparison points. But you have to have those standard comparison points to do it.

PAllen already commented on the rest of your post; I agree with what he said.

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