Time paradox

Austin0

Quote by Austin0
"on an essential level"..... in this context the word "an" inherently implies other essential levels,yes?

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Your reaction to my quote below

Quote by Austin0
was
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

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

Quote by Austin0

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
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"???

PAllen

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.

zonde

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."

Yes

PAllen

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.

PeterDonis

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.

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.

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.

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.

No, that's not what SR says. Here's the formula for relativistic Doppler:

[tex]\frac{\omega}{\omega_0} = \sqrt{\frac{1 + v}{1 - v}}[/tex]

where [itex]v[/itex] 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?

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.

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.

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.

Propagating signals *are* phenomena, aren't they? (More precisely, detections of such signals are.)

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.

ghwellsjr

Correct.
I can understand that if forgetting SR meant you had to forget relativistic Doppler, then the argument would be cut short. But this would only be true if forgetting SR meant you had to forget PoR which is not the case. Einstein's theory of Special Relativity is just one possible theory based on the Principle of Relativity but it requires another postulate stating that light propagates at c in all Inertial Reference Frames. That's what I was saying to forget which leads to forgetting SR but not PoR. I specifically said this in post #7 and Bondi specifically says this in his book. We are not identifying either the speeds of the traveler or light in this argument and we are not identifying the time that it takes for light to make any part of the trip. That would require a theory such as SR or the Relativistic Doppler equation relating the speed of the observers to the Doppler factor. But we are not deriving that equation, we're only pointing out a conclusion based just on the PoR and that the propagation of the light coming from two sources with relative motion is the same.

Again, I want to emphasize that I was answering the OP's question of which observer would be older. He accepted the PoR and wondered how the symmetry inherent in it could result in the observers accumulating different ages. DaleSpam answered his question and pointed out that the PoR applied to inertial referentials (as the OP called them) but that the traveler is not inertial. This showed the lack of symmetry but did not explain how you could conclude which one would be older. Of course a full blown explanation from SR would provide that answer or even a full blown explanation based just on Relativistic Doppler but I wanted to show that the answer could also be provided just from the PoR and the assumption that light propagated from two different sources at the same speed.

ghwellsjr

Here is a spacetime diagram of a single clock at rest in its Inertial Reference Frame. The blue dots represent one second ticks of Proper Time on the clock:



Now here is another spacetime diagram created by transforming to an IRF moving at -0.6c with respect to the first IRF:



In both diagrams the Time Dilation of the clock can be calculated from the same formula relating Time Dilation to speed. Is this what you meant when you said that time dilation resulted from relative motion?

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Austin0

Quote by Austin0

So are you saying that differential aging is not a process???
Doesn't the fundamental physical concept of process necessarily require an unspecified time interval??

Am i not correct in thinking that the basic mathematical description of processes are differential equations??
Can't we discuss them in their general form without parameterization or convention? What meaning does difference, or change with respect to , etc have without a finite time interval of some duration??
So your comments make sense as related to quantifying results but I was speaking in terms of general principles.

You say:
. Here you are talking about along the world line ,acknowledging the passage of time.
So worldlines are curves on a plane and as such once drawn exist outside of time but don't we still have to assume that differential aging is not an instantaneous event but must occur spread throughout the time represented by those curves???




i am puzzled by the repeated implications that i think or have said anything indicating a belief that theories determine (cause) phenomena.
You say that Doppler symmetry exists independent of theory. WHile i share this belief it is through the theory. POR is itself a theory ,no??
you then say Has this been definitively determined by actual observation at relativistic velocities??

In any case I agreed from the beginning that given symmetry and reciprocity time dilation was an inevitable result. i have yet to see how this alone leads to the actual gamma factor (it didn't in bondi or the quick calcs I did) so would like to see how you arrived there in your your derivation when finished.

I think all the Lorentz effects exist independent of theory and would have been directly derived from observation eventually through increased clock precision, particle acceleration, actual relativistic travel etc.

This is exactly how I see it and am simply trying to understand the full implications of that explanation in a coherent whole. You mentioned in another post the inherent limitations of our abstract constructs as far as correspondence to reality. WHile I certainly agree and at the end of the day it may be revealed that our current models have little or no correspondence to the actual universe , still we proceed with the assumption that there is some actual correspondence even into areas where there is no possibility of observation Eg. interior of a black hole.

You seem to be concerned here with the precedence of derivation of the theory itself. I am not disagreeing with anything you are presenting but I am looking at causality and time ordering on a more physical level.

Is it possible to arrive at an alternative explanation without being tendentious?? if so I guess in my case it is simply my personal limitations in communication which i will strive to improve ;-)

Austin0

Quote by Austin0

I was neither being argumentative nor playing word games. So i would like to clarify this matter as it bothers me you would think that.

Quote by Austin0

This was my original statement. It appears to me that to argue the contrary is necessarily equivalent to asserting that :

a study of causality is not an essential level of physics.


From you response it appears that you misread my statement as ...On the essential level, physics is a study of causality.

IF that had been my statement I would completely agree with your arguments but as actually stated that interpretation is essentially precluded.

So rather than trying to create an argument I was trying to indicate there was no real argument but only a semantic misinterpretation.
...
i have too high a regard for your input and this opportunity for discussion to seek out trivial and unnecessary arguments. I am sorry if my mode of expression seemed to imply otherwise.

Quote by Austin0

Certainly observations come first in construction of a theory regarding actual empirical observations.
But i was talking about the theory as it exists ....SR and how it provided context and meaning to the raw Doppler observations.

Quote by Austin0

It explicitly appears in the derivation presented in hyper Physics. so i think it is intrinsically embedded in the equation just as it is in the Addition of Velocities equation. Certainly there may be other possibly derivations that do not directly involve gamma but I think that in any case the implicit presence can be revealed through decomposition into gamma and the classical kinematic Doppler component.


I am asking this again:
Quote by Austin0
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.

I think that because when i said"the observed values are the result of two distinct factors ---relative motion and the dilation factor." you said I was incorrect.that seems to imply you are dismissing the kinematic element as well??

I am unsure of what you mean when you say "time dilation is a frame dependent convention" in this specifically limited context (Doppler analysis)
The gamma factor between source and observer is as invariant as the Doppler factor ,yes??
SO are you disassociating the gamma factor from any connection to time dilation here??

Also,,,, observing inertial frames can directly apply the Doppler equation to arrive at the correct result but am I incorrect in thinking that they could instead directly do a kinematic and gamma analysis and arrive at the same end result??
SO although they would derive different quantitative results during the process they would all agree that the two factors validly applied as I am suggesting. yes???

Quote by Austin0

Quote by Austin0

Yes this is different. I was not attributing any position to you but just asking what that position was.

In actuality i was somewhat expecting this response but did not presume. I share this view but it seems that others may question it. PAllen mentioned Singhe for one.

Actually in the static Sc case isn't the standard interpretation of this to be Doppler shift? SO in this case it appears you are making an analytical choice of interpretation of dilation even though it is also not directly observable in the sense you are talking about with relativistic Doppler observation.

AsI said I have no problem with this at all.
But this leads to another question.

Do you think that relativistic dilation from relative motion is a fundamentally different phenomenon from gravitational dilation???

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Yes no need for any more worms

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Of course propagating waves and observations of the same are phenomena. My point was that the propagation had no possible effect on the outcome. No change in transit,,,yes??

Quote by Austin0

You are addressing a separate question. Yes it is understood that comparison during transit is impossible in any frame independent way.
But I am talking about simple physical causality. Independent of observation.it would seem that the causality and temporal ordering were unambiguous.
Actual number transmitted----->Propagation----->Observation. that propagation and observation can have no possible causal influence on the numbers at the sources.

Would you propose that this could somehow not be the case????
That the asymmetry at the end was not a result of an actual different number of signals sent ?
sorry for my delayed response i have been a bit under the weather

Austin0

Quote by Austin0

I said that time dilation resulted from relative motion.



Hi
i was speaking on a much simpler level of causality.
My own personal view is that the gamma function describes intrinsic attributes of spacetime.

I am aware there are alternative concepts held by many that these atrributes are purely kinematic. I.e. coordinate artifacts resulting from relative velocity between coordinates systems without physical significance or causality.

While I completely understand the logic and recognize that in the end this may actually be correct, it seems that this view runs into problems in certain areas. The Twins for one, where it is pretty hard to consider the difference in physical ages a coordinate artifact.

Hence the plethora of explanations which all share a common attribute. That being an attempt to remove time dilation from the concept of differential aging . Thus implying that the exact quantitative correspondence between the cumulative results and the gamma time dilation factor is simply a disconnected coincidence.

Most of these explanations seem to be irrelevant on a causal level , which is necessary for an explanation.
The only relevant ones appear to be the world line analyses, triangle inequality, integration etc.while perfectly valid as abstract representations of events they obscure the fact that what is being represented is time dilation. What is being integrated is momentary gamma as represented by the slope of the worldlines

Infinitesimal intervals of dilated proper time. yes???

PAllen

1) If two travelers pass and never meet up, whose gamma is a feature of spacetime?

2) In any coordinates in which a non-inertial observer has a fixed spatial coordinate, the time dilation formula is not given by gamma.

3) The SR Doppler formula is readily derived from coordinate independent facts never implicitly involving gamma.

PeterDonis

Sorry if it bothered you, but I still don't have anything to add to what I already said on these points. I understand you did not intend to be playing word games, but it does seem to me that you are focusing too much on the definitions of words and not enough on the actual physics. For example:

To put it bluntly, who cares? We're not talking about "causality". We're talking about a specific physical scenario, which can be discussed in terms of specific observable facts about the scenario, without having to bring in any abstract philosophical terms like "causality". I don't know whether "causality" is "an essential level of physics" or not; that seems to me to be a question about words, not about physics. Your mileage may vary, I suppose, but that's where I'm coming from.

That's not the only possible derivation, so I don't think this claim follows. For it to be "intrinsically embedded", there would have to be no derivation that did *not* use time dilation.

(Also, the derivation in hyper physics uses gamma, but that does not necessarily mean it uses time dilation; interpreting gamma as a "time dilation factor" is an interpretation which is not necessary to the physics. It's an extremely common interpretation, yes, but it's still an interpretation.)

See above. Also, remember that in reality spacetime is not flat, and this decomposition of the relativistic Doppler effect into "components" can't be done in a general curved spacetime.

The relativistic Doppler effect, taken by itself, is symmetric and reciprocal, because relative velocity itself is. The elapsed proper time of the twins is not symmetric and reciprocal, but that's because the twins' trajectories are not symmetric and reciprocal. One twin fires rockets to turn around, the other doesn't. What else do you need?

The fact that the twins' trajectories are not symmetric is sufficient to explain the difference in elapsed time. The exact asymmetry in the trajectories can be observed entirely in terms of the difference in when each twin observes the change from Doppler redshift to Doppler blueshift: the traveling twin observes it when he turns around, halfway through his trip, but the stay-at-home twin doesn't observe it until the light signal from the traveling twin's turnaround reaches him, much *more* than halfway through his trip. You can calculate the difference in elapsed time just from these observables alone; no need for "time dilation" or anything else. So what is being left out?

The point you seem to be missing is that there is no one single way of "explaining" a scenario like the twin paradox. The only real "anchors" are the direct observables; everything else is interpretation. You are trying to claim that your preferred interpretation, in terms of time dilation and its associated kinematics, is "more real"; it isn't. It's just an interpretation.

See above.

No, I'm saying that "time dilation" doesn't just involve gamma. It also involves a standard of simultaneity. In order to compare "rates of time flow" along two spatially separate worldlines, you have to have a common standard for comparison. In the twin paradox, the common standard is that the worldlines meet at two events, the start and end of the trip. But if the traveling twin never turns around, there is no common standard of simultaneity, so there's no invariant way to compare their rates of time flow.

Sure, there is more than one way to compute the same result, as I said above.

No, because there's no relative motion between the two static observers.

Fundamentally? No, because as I said above, the split between "dilation from relative motion" and "gravitational dilation" doesn't work in a general curved spacetime. The more fundamental method, which works in any spacetime, is to assign a given light signal a 4-momentum vector determined at the source, then parallel transport that 4-momentum along the light signal's worldline to the detector, then take the inner product of the parallel transported 4-momentum and the detector's 4-velocity to get the observed energy of the signal (or its frequency if you divide by Planck's constant). You can then compare this with the inner product of the light signal's original 4-momentum at the source and the source's 4-velocity, which gives the energy (or frequency) of the signal at the source.

In flat spacetime, yes, this is a valid assumption. It's not in a general curved spacetime; in order to compare vectors at different events, you have to parallel transport one of them, as in the example I gave above; that can "change" the vector, in the sense that the two inner products I described above can be different.

I don't understand what any of this has to do with the point I was making. Sure, propagation doesn't affect what happens "at the sources", but if the sources are spatially separated, you can't directly compare what happens "at the sources" without first adopting some convention for which points on the two source worldlines "correspond"; in other words, without adopting some convention for simultaneity. If the two twins are not at rest with respect to each other, there's no invariant way to do that.

ghwellsjr

If so, then how do you answer the OP's question: who will be older?

DaleSpam

That is my personal prefered analysis.

Not necessarily. [itex]\gamma=(1-v/c)^{-1/2}[/itex] only shows up if the integration is being done in an inertial frame in flat spacetime. Otherwise other functions can be involved. In fact, you can carry out this integration in null coordinates where there is no time coordinate for clocks to dilate relative to. The geometry remains, although the description in terms of γ may not.

phyti

Does the earth twin, feeling the constant G field and orbiting the sun, really qualify as an inertial frame?

PeterDonis

No, but the standard twin paradox scenario idealizes the stay-at-home twin as following an inertial path in flat spacetime; the term "Earth" doesn't refer to the real Earth but to a fictitious Earth whose gravity doesn't affect the scenario and which is not orbiting the Sun but just floating in flat spacetime.