Understand Special Relativity and Time paradox

[Austin0]

Quote by Austin0

I said that time dilation resulted from relative motion.

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? .

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]

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?

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]

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.

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:

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.

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.

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.

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.)

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.

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.

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?

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?

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.

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.

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??

See above.

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??

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.

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?

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

Actually in the static Sc case isn't the standard interpretation of this to be Doppler shift?

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

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

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.

My point was that the propagation had no possible effect on the outcome. No change in transit,,,yes??

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.

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 ?

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]

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?

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

 

[Dale]

The only relevant ones appear to be the world line analyses, triangle inequality, integration etc.

That is my personal preferred analysis.

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

Not necessarily. \gamma=(1-v/c)^{-1/2} 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]

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

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.