Exploring Possible Causes of AF's Time Dilation in yuiop's Thread

[Austin0]

This is related to another current thread

https://www.physicsforums.com/showthread.php?t=426307"

wherein yuiop presents a very convincing demonstration of non-reciprocal proper time differential between an accelerated system AF and an inertial system IF between two points A and B

In sysnopsis: At point A ,,,, AF and IF are colocated with IF having a relative v =0.9512 c wrt AF and at which point AF initiates a constant proper acceleration of 2c/s² along the same spatial path traveled by IF
At point B they are again colocated with IF having now a relative velocity of v=-0.9512 wrt the instantaneous velocity of AF.
AT this point it is shown that AF has an elapsed proper time significantly less than that of IF.

Given an assumption of generality and the validity of the clock hypotheses it would seem to mean that there was a real dilation differential as a result of the relative velocities during the period of translation.
Viewed as a series of instantaneous relative velocities and the same spatial distance traveled , how then could there be a cumulative difference in elapsed proper time at recolocation??

One perspective could be that the difference was a result of the gamma³ reduction of coordinate acceleration wrt IF So initially If was rapidly moving away from AF [AF v being negative]. In order to catch up AF would neccessarily have to attain a positive velocity relative to IF
In the course of acheiving this relative v , because of the dropoff factor it would neccessarily have to spend a larger part of the time with a greater relative velocity and an increased gamma factor.
In this view , initially AF's clock would have to have a faster rate than IF's.
Clock AF would then slow down relative to its initial rate until reaching a momentary state of comovement and an equal rate and then slow down relative to clock IF from that point.

Given the final result is there any way to look at it other than an actual difference in clock rates?
ANy other niews appreciated

 

[JesseM]

Given an assumption of generality and the validity of the clock hypotheses it would seem to mean that there was a real dilation differential as a result of the relative velocities during the period of translation.

What does "real dilation differential" mean? Do you agree we can analyze the whole trip from any inertial frame and get the same answer as to the total elapsed time of each clock? Do you agree that for any point on the accelerating clock's worldline, there is some inertial frame that says the inertial clock is instantaneously ticking slower at that moment, and some other inertial frame that says the accelerating clock is instantaneously ticking slower at that moment?

Viewed as a series of instantaneous relative velocities and the same spatial distance traveled , how then could there be a cumulative difference in elapsed proper time at recolocation??

Why do you think there wouldn't be? What does "a series of instantaneous relative velocities" have to do with your belief? You need to explain your argument in detail, not just assume others will share your intuitions!

 

[Austin0]

Given an assumption of generality and the validity of the clock hypotheses it would seem to mean that there was a real dilation differential as a result of the relative velocities during the period of translation.

What does "real dilation differential" mean?

((1))Do you agree we can analyze the whole trip from any inertial frame and get the same answer as to the total elapsed time of each clock?

((2))Do you agree that for any point on the accelerating clock's worldline, there is some inertial frame that says the inertial clock is instantaneously ticking slower at that moment, and some other inertial frame that says the accelerating clock is instantaneously ticking slower at that moment?

Real meaning; not reciprocal, not simply a matter of kinematics. Would you say a returning twin being physically younger was not real differential aging ??

((1)) Of course

((2)) Total agreement. That is part of the question. Those evaluations from various inertial frames are purely relative and reciprocal. Symmetrical.
But the final cumulative result is not reciprocal or symmetrical and I am curious as to the reason.
Those measurements from other frames are not direct comparisons between clocks but must neccessarily involve more than one, spatially separated clocks, so simultaneity becomes an issue ,while the final result here is a matter direct colocated comparisons between two single clocks.

The aspect of the scenario that is not symmetrical is the coordinate acceleration profile.
This leads me to consider how this might be relevant to the end result.

Viewed as a series of instantaneous relative velocities and the same spatial distance traveled , how then could there be a cumulative difference in elapsed proper time at recolocation??

Why do you think there wouldn't be? What does "a series of instantaneous relative velocities" have to do with your belief? You need to explain your argument in detail, not just assume others will share your intuitions!

It is not a matter of thinking there wouldn't be. I have no problem with the end result.
It is a question of trying to find a consistent reason ,given the clock hypotheses and the reciprocal concept of dilation , that there would be.


If we eliminate acceleration as a relevant factor in itself and look at the total course of events as a series of purely relative , reciprocal instantaneous dilations, what would be the basis for an assumption of a cumulative difference at the end?
The inertial velocity is simply the average of the instantaneous accelerated velocities.

Given the final result is there any way to look at it other than an actual difference in clock rates?

You didn't mention this question.

Thanks

 

[JesseM]

Real meaning; not reciprocal, not simply a matter of kinematics. Would you say a returning twin being physically younger was not real differential aging ??

So by "real differential aging" you just mean a difference in elapsed aging over the course of the entire trip, you don't mean to imply a real fact of the matter about which was aging slower or faster during any small subsection of the trip? If so, of course there is a difference, that's just what the standard twin paradox illustrates, why do you see this variation as any different?

((1)) Of course

((2)) Total agreement. That is part of the question. Those evaluations from various inertial frames are purely relative and reciprocal. Symmetrical.
But the final cumulative result is not reciprocal or symmetrical and I am curious as to the reason.

Again, it's no different than the standard twin paradox. They take two different paths through spacetime and the lengths of the paths are different. Do you think it's puzzling in Euclidean geometry that if you pick a pair of points A and B and draw two paths between them which both cover the same range of x-coordinates (but with each x reached at a different y-coordinate for the two paths), one of which is a straight line while the other is non-straight, then the straight line path will have a shorter length than the curved one? And just as a straight line through space is always the shortest distance between points, so a straight line through spacetime always has the greatest proper time. One can expand on this analogy to 2D Euclidean geometry to include things like an analogy for the way each frame calculates total elapsed time by integrating an instantaneous rate of ticking relative to coordinate time, [tex]d\tau /dt[/tex], which is only a function of velocity in the chosen frame...in the geometric analogy this converts to the fact that each Cartesian coordinate system can calculate total elapsed path length by integrating the instantaneous rate that a car with an odometer moving along the path would accumulate odometer distance D as its x-coordinate changes, with the instantaneous dD/dx being solely a function of the path's slope at that point in the chosen Cartesian coordinate system. See my post #8 on this thread for more detail on the geometric analogy.

The aspect of the scenario that is not symmetrical is the coordinate acceleration profile.
This leads me to consider how this might be relevant to the end result.

Sure, the fact that one changes velocity and the other doesn't means that the one that accelerated must have aged less. Similarly, in geometry if you have two paths between points on a plane, and one has constant slope while the other has a change in slope somewhere, the one with constant slope (the straight line) will have a shorter distance. I still don't really understand what you're asking, or why/if you think this is any different from the standard twin paradox scenario.

It is a question of trying to find a consistent reason ,given the clock hypotheses and the reciprocal concept of dilation , that there would be.

Why would there be any lack of consistency between the clock hypothesis and reciprocal time dilation and differential aging? Again take a look at the geometric analogy--hopefully you don't see an inconsistency between the fact that a straight path between two points has a shorter total distance than a non-straight path, and the fact that dD/dx (rate of path length increase relative to change in x-coordinate) at each point is just a function of the slope of the path dy/dx at that point (analogous to the clock hypothesis which says that [tex]d\tau /dt[/tex] is a function of the velocity, which is just dx/dt if motion is along the x-axis), or that at each point on the path you can find a Cartesian coordinate system where the path is parallel to the x-axis at that point so dD/dx = 1 (analogous to the fact that at any point on the path of a moving object you can find an inertial frame where the object is instantaneously at rest so [tex]d\tau /dt = 1[/tex]).

If we eliminate acceleration as a relevant factor in itself and look at the total course of events as a series of purely relative , reciprocal instantaneous dilations, what would be the basis for an assumption of a cumulative difference at the end?

I don't understand what you mean by "eliminate acceleration as a relevant factor in itself and look at the total course of events as a series of purely relative, reciprocal instantaneous dilations". Can your "look at" be explained in some sort of quantitative mathematical terms? For example, are you just talking about the fact that we can calculate total elapsed time in terms of v(t) for each path, using [tex]\int_{t_0}^{t_1} \sqrt{1 - v(t)^2 /c^2} \, dt[/tex]?

The inertial velocity is simply the average of the instantaneous accelerated velocities.

Sure, but what does that have to do with anything? If the inertial twin has a constant v_I(t) while the accelerating twin has a varying v_A(t), then setting the averages equal just means that:

[tex]\frac{1}{t_1 - t_0} \int_{t_0}^{t_1} v_I(t) \, dt = \frac{1}{t_1 - t_0} \int_{t_0}^{t_1} v_A(t) \, dt[/tex]

But this in no way implies that [tex]\int_{t_0}^{t_1} \sqrt{1 - v_I(t)^2/c^2 } \, dt[/tex] should be equal to [tex]\int_{t_0}^{t_1} \sqrt{1 - v_A(t)^2/c^2 } \, dt[/tex] (the total elapsed times for each clock). If you think the equality of the first two would somehow imply the equality of the second two, why? Once again, keep in mind the geometric analogy--if you have a straight path and a non-straight path between two points, the two paths can have the same average slope in a given Cartesian coordinate system, and the total length of each path can be calculated as a function of the slope S(x) using the formula [tex]\int_{x_0}^{x_1} \sqrt{1 + S(x)^2} \, dx[/tex], but obviously a straight line path is going to be shorter since a straight line is the shortest distance between two points in Euclidean geometry.

Given the final result is there any way to look at it other than an actual difference in clock rates?

You didn't mention this question.

Well, I had already mentioned I didn't really understand what you meant by "real dilation differential", I took "actual difference in clock rates" to be basically synonymous. Again, if you're just talking about a difference in total elapsed times between meetings, then by definition there is such a difference, but if you're talking about an actual difference in instantaneous rates or in rates over some short subsection of the trip, then there's no need to assume any "actual" truth about which clock had a slower rate.

 

[Austin0]

So by "real differential aging" you just mean a difference in elapsed aging over the course of the entire trip, you don't mean to imply a real fact of the matter about which was aging slower or faster during any small subsection of the trip? If so, of course there is a difference, that's just what the standard twin paradox illustrates, why do you see this variation as any different?

I don't see it as qualitatively different, simply more direct and unambiguous.
ANother context for the idea of real differential dilation and clock rates is at different potential heights in a gravitational filed. In this case would you argue that there was no assumption of reality [non-reciprocality] to both the total elapsed time difference and the assumption of actual difference in periodicity?
Perhaps it would help if I gave you the context of my enquiry;
In my mind the Equivalence Principle is not simply a fantastic leap of logic and conceptualization but also a promise of the possibility of a bridge between GR and SR. \Between our earthbound environment and actual inertial motion in the flat reaches of space.
But so far it seems that this is still a bridge halfway to nowhere.
That in the minds of most this is a worthless pursuit because it is an accelpted fact that there is no "there " on the other end.
That it is certain that there is no physicallity to inertial motion. No effects of causality,,no effects from acceleration.
That all inertial fundamental particles [electrons etc] are absolutely identical, not only in charge and spin but in intrinsic periodicity and wave symmetry.
The only distinctions being apparent ones due purely to the relative motion of the observing frame.
Now I have no illusions of knowing the true nature of reality and would not question that this may be absolutely true .
Nor do I question the empirical reality of the limitation to purely relative quantitative measurements of bodies and systems in uniform motion.
But at the same time I see no compelling reason to completely reject the possibility that motion might be both real and relative. That there might be a truly unified spacetime.
I recognize that this may simply be an intellectual desire or hope on my part.
I have no belief or certainty that this is the neccessarily the case and any attempt to add to the bridge may be completely misdirected energy, but I think there are questions that need to be pursued even if there is slight chance of answers . This obviously applies to many of the fundamental questions of physics. SHould we stop asking?

Originally Posted by Austin0
The aspect of the scenario that is not symmetrical is the coordinate acceleration profile.
This leads me to consider how this might be relevant to the end result.

Sure, the fact that one changes velocity and the other doesn't means that the one that accelerated must have aged less.

I wasn't talking about simply accelerating but the asymmetry of the coordinate rate of acceleration.
I think this itself could be the subject of interesting study . Looking at different accelerated systems from various relative frames and the differences in observed profiles.

Originally Posted by Austin0
Given the final result is there any way to look at it other than an actual difference in clock rates?

Well, I had already mentioned I didn't really understand what you meant by "real dilation differential", I took "actual difference in clock rates" to be basically synonymous. Again, if you're just talking about a difference in total elapsed times between meetings, then by definition there is such a difference, but if you're talking about an actual difference in instantaneous rates or in rates over some short subsection of the trip, then there's no need to assume any "actual" truth about which clock had a slower rate.

I do understand the geometric concept and the integration of worldlines etc. This is not in question.
I also understand that assigning instantaneous clock rates, in a frame independant way cannot be done.
But am I wrong in assuming that this would be difficult or impossible with clocks at different potentials in gravitation as well?

Without any quantitative evaluations at specific sections of the path would you disagree
that there was an actual difference in frequencies during the interval under question ??
A physical effect ,change in atomic periodicity, that would seem to have to be due to either acceleration or instantaneous relative motion .
If not what else??

 

[JesseM]

ANother context for the idea of real differential dilation and clock rates is at different potential heights in a gravitational filed. In this case would you argue that there was no assumption of reality [non-reciprocality] to both the total elapsed time difference and the assumption of actual difference in periodicity?

Again, does "real differential dilation" simply refer to the idea that if two clocks meet and compare times locally twice in succession, the total elapsed time between meetings may be different for the two clocks? That's all you said it meant when you asked before, and if that's all you mean here then of course there can be a difference if the clocks spend some time at different heights in a gravitational field between meetings. But if "actual difference in periodicity" is intended to mean something different, then you are using vague pseudo-technical language as a substitute for actually spelling out what you mean, which makes your posts very difficult to follow (you probably remember I cautioned you against this in a previous thread). Do you mean that in this case we could talk about an objective difference in clock rates even for very short segments of their worldlines when they are far apart, or perhaps even a difference in instantaneous rates of ticking when they are at different heights? If so, no we can't, this would involve picking a preferred definition of simultaneity as I said in a recent post to A-wal on the "arrow of time" thread:

A little thought shows that believing there is a "real truth" about the relative rate of ticking of clocks in different regions of spacetime is equivalent to believing there must be some "real truth" about simultaneity--for example, if I say clock A is running half as fast as clock B, that's equivalent to saying that if clock A showing a time T is simultaneous with clock B showing a time T', then clock A showing a time T + delta-t must be simultaneous with clock B showing a time T' + 2*delta-t. But as long as there is no objective truth about simultaneity, what's to stop you from picking a different definition of simultaneity where clock A showing T is still simultaneous with clock B showing T', but clock A showing T + delta-t is now simultaneous with B showing T + 0.5*delta-t or T + 3*delta-t?

Perhaps it would help if I gave you the context of my enquiry;
In my mind the Equivalence Principle is not simply a fantastic leap of logic and conceptualization but also a promise of the possibility of a bridge between GR and SR. \Between our earthbound environment and actual inertial motion in the flat reaches of space.
But so far it seems that this is still a bridge halfway to nowhere.

Well, it would help if you'd spell out in detail what you mean by "bridge between GR and SR"--I would say the equivalence principle already constitutes such a bridge since it says the laws of physics seen by a freefalling observer in any local region of curved GR spacetime reduce to those of an inertial observer in flat SR spacetime.

That in the minds of most this is a worthless pursuit because it is an accelpted fact that there is no "there " on the other end.

I don't know what pursuit it is you're talking about. As always, details details details!

That it is certain that there is no physicallity to inertial motion. No effects of causality,,no effects from acceleration.

What does "physicality" mean? Just that there is no frame-independent sense in which we can say something is moving inertially or at rest? And what does "no effects of causality" mean? There certainly is a frame-invariant truth about whether causality is respected or violated in a given spacetime, likewise there's a frame invariant-truth about whether something is experiencing nonzero proper acceleration, but you presumably knew that, so you must have meant something else by "no effects from acceleration". I can't think what though, again you are being way too laconic in your comments for your thoughts to be comprehensible to others.

That all inertial fundamental particles [electrons etc] are absolutely identical, not only in charge and spin but in intrinsic periodicity and wave symmetry.

Not clear why you say "inertial" fundamental particles, an electron moving non-inertially still has the same charge and spin. And "intrinsic periodicity" seems to be another pseudo-technical term you've invented, it's really a bad habit! If you don't know for sure that something is an existing technical term regularly used by physicists, don't try to coin a new one, just explain in English (and math, perhaps) what you are talking about in detail. I would guess you are referring to the quantum equation E=hf which shows frequency is proportional to energy, so that in a frame where a massive particle's kinetic energy is very small compared to its rest-mass energy (like a frame where it's moving at a speed that's very small compared to c), the frequency should be closely proportional to the particle's rest mass. I don't really know what "wave symmetry" would refer to, it would be possible for a quantum particle to be measured in such a way that its position wavefunction would be asymmetrical about the point of maximum amplitude, for example.

The only distinctions being apparent ones due purely to the relative motion of the observing frame.

"Distinctions"? Between what and what?

But at the same time I see no compelling reason to completely reject the possibility that motion might be both real and relative. That there might be a truly unified spacetime.

Are you talking about some notion of absolute space, so there'd be an absolute truth about whether a given particle has remained at the same point in space or moved? If so I don't understand what this would have to do with creating a "unified spacetime", that's another phrase that doesn't mean anything to me without more explanation of your thinking.

I recognize that this may simply be an intellectual desire or hope on my part.
I have no belief or certainty that this is the neccessarily the case and any attempt to add to the bridge may be completely misdirected energy, but I think there are questions that need to be pursued even if there is slight chance of answers . This obviously applies to many of the fundamental questions of physics. SHould we stop asking?

I have no problem with your asking questions, but you need to explain your thinking in sufficient detail so people can understand what it is you're trying to ask!

I wasn't talking about simply accelerating but the asymmetry of the coordinate rate of acceleration.

Don't understand why you are making this distinction, since one of the two clocks in your thought-experiment had a coordinate rate of acceleration of 0, i.e. it wasn't accelerating at all.

I think this itself could be the subject of interesting study . Looking at different accelerated systems from various relative frames and the differences in observed profiles.

Profiles of what, exactly? Elapsed clock time vs. coordinate time?

I do understand the geometric concept and the integration of worldlines etc. This is not in question.
I also understand that assigning instantaneous clock rates, in a frame independant way cannot be done.
But am I wrong in assuming that this would be difficult or impossible with clocks at different potentials in gravitation as well?

What would be difficult or impossible? Showing that instantaneous clock rates are frame-dependent? If so that wouldn't be difficult at all, you have the freedom to use any arbitrary continuous coordinate system in GR thanks to diffeomorphism invariance (see here), so for any brief section of one clock's worldline you could pick different coordinate system which assigned simultaneity in different ways, leading the other distant clock to either have elapsed more or less time in the section of its worldline simultaneous with the section of the first clock's worldline you had chosen (that's what I was discussing in the quote from the post to A-wal).

Without any quantitative evaluations at specific sections of the path would you disagree
that there was an actual difference in frequencies during the interval under question ??

"Difference in frequencies" is an intrinsically quantitative statement, I don't see how the question can be meaningfully evaluated "without any quantitative evaluations at specific sections of the path".

A physical effect ,change in atomic periodicity, that would seem to have to be due to either acceleration or instantaneous relative motion .

Does "change in atomic periodicity" refer to something coordinate-independent like a difference in total number of cycles between two local meetings of atomic clocks? If not, I wouldn't call it a "physical effect" if it's not frame-independent.

 

[Passionflower]

But at the same time I see no compelling reason to completely reject the possibility that motion might be both real and relative. That there might be a truly unified spacetime.
I recognize that this may simply be an intellectual desire or hope on my part.
I have no belief or certainty that this is the neccessarily the case and any attempt to add to the bridge may be completely misdirected energy, but I think there are questions that need to be pursued even if there is slight chance of answers . This obviously applies to many of the fundamental questions of physics.

It seems that my anticipation was right on the money when I wrote in a prior (and similar) topic:

I get the impression based on several of your postings, that you really have not fully come to terms with the fact that inertial motion is completely relative.