Ambiguity in time dilation due to relative velocity

[davidf32]

I would like to see some comments on this observation that appears to lead to an ambiguity re: time dilation: The usual definition for time dilation is the expression:
t =t'/(1-V^2/c^2)^1/2 where an individual in the unprimed coordinate system "at rest" in empty space, sees a clock in the primed coordinate system moving at velocity "v" relative to him, running slower than his identical clock. Fine:
However, unless the observers know the history of HOW there came to be a velocity difference, they cannot know if a calculation using the above equation provides the right answer. Here are two examples demonstrating this ambiguity.

Case 1:
Two individuals "at rest" in empty space adjacent each other, BOTH accelerate the same magnitude for the same length of time in opposite directions. After some time they both turn off their engines and again are "at rest", but there now is a relative velocity between them. Because they both have their energies increased the same amount (and because this form of time dilation is a scalar), there is not time dilation between them even thoguh they no longer are "at rest" relative to one another.

Case 2: Two indiviuals are "at rest" relative to one another as in the first case and ONE OF THEM accelerates away from the other until he reaches the same relative velocity re: the other observer at which time he turns off his engine. Now the twwo observers have the same relative velocity as in case 1, BUT there now is a time dilation effect between them which is defined by the above equation.

Any comments? If this s correct it would seem to say something about cosmological observations of blue/red shifts from ditant objects because calculating relative velocity using red/blue shifts also involves time dilation effects. davidf32

 

[zhermes]

However, unless the observers know the history of HOW there came to be a velocity difference, they cannot know if a calculation using the above equation provides the right answer.

Nothing in the equation makes mention of 'history', nor is it required. All you need to know is the relative velocity.

Case 1:
Two individuals "at rest" in empty space adjacent each other, BOTH accelerate the same magnitude for the same length of time in opposite directions. [...] there is not time dilation between them even thoguh they no longer are "at rest" relative to one another.[/QUOTE]
Because they are not at rest, there is a 'time dilation' between them.

Case 2: Two indiviuals are "at rest" relative to one another as in the first case and ONE OF THEM accelerates away [...]

In the end, both of these cases are equivalent.

 

[Janus]

There is no such thing as being at rest with respect to space. When we talk about a coordinate system being "at rest", this is just a arbitrary choice for convenience. we could just as easily define the clock as being "at rest" and the invidual as moving.

The "v" in the time dialtion formula is the relative velocity between the two frames, and the formula tells us how time passes in one frame as measured from the other.

So in Case 1, there is a relative velocity between the two individuals and thus each measures a time dilation in the other (Both will measure the other individual's clock as running slow.

Case 2 ends with the same result. Both will see each other's clocks as running slow once they stop accelerating.

Once they reach their final relative velocity, it doesn't matter how it was attained as far as time dilation is concerned. (We won't deal with what each measures while accelerating at this point because it is a fair bit more complicated. )

The upshot is that while they are moving relative to each other, there is no absolute way to say which one is aging faster than the other. It is only when when you bring them back together will you being able to make that determination. It is then that "how" they parted and came back together counts.

In case 1, if they both reverse and return to the starting point in the same way, they will end up the same age. (If they don't return the same way, one can end up older than the other.)

In case 2, if the individual who accelerates away turns around and returns, he will have aged less than the other.

 

[davidf32]

That is the point I'm trying to make: The equation of course does not require history be known, but my case 1 vs case 2, (that time dilation due to velocity differences is a scalar), results in the ambiguitiy. For further example: In case 1 if the two observers accelerate in the same direction etc, they end up adjacent to each other with NO RELATIVE velocity. QED: If time dilatation is a scalar (and it is) then the relative direction of the acceleration doesn't matter! If there is no time dilaton when they end up next to each other, than there similarly is no time dilation between them if they end up far apart. I get it that you don't agree, but can you please people your argument with an explanation as to why you disagree? It is not sufficient to simply refer to that equation! My point, of course, is that I can and do demonstrate the equation is ambiguous UNLESS you know the history. Knowing the history in the case of the twin paradox is the solution to that effect, so in this case I claim the same issue is in play.
davidf32

 

[zhermes]

I get it that you don't agree, but can you please people your argument with an explanation as to why you disagree? It is not sufficient to simply refer to that equation!

1) Its not just that we're disagreeing; we're telling you the way it is, in nature.
2) I provided an explanation, what aspect of it didn't you understand?

(that time dilation due to velocity differences is a scalar), results in the ambiguitiy.

It doesn't matter that the dilation is a scalar, and there is no ambiguity.

For further example: In case 1 if the two observers accelerate in the same direction etc, they end up adjacent to each other with NO RELATIVE velocity. QED: If time dilatation is a scalar (and it is) then the relative direction of the acceleration doesn't matter!

The relative direction of the acceleration does matter, and has nothing to do with the scalar nature of the dilation. If they accelerate in the same direction the end up with zero relative velocity; unlike accelerating in different directions in which case they end up with a non-zero relative veloctiy---and therefore a time dilation.

v = v_\textrm{rel} \equiv v_2 - v_1 Relative velocity...

v_i = a_i \cdot t Let's assume a constant acceleration...

if a_1 = a_2 (same direction), then v_1 = v_2 and v_\textrm{rel} = 0 Thus no time dilation.

if a_1 = - a_2 (opposite directions), then v_1 = -v_2 = v_0 and v_\textrm{rel} = 2 \cdot v_0 for whatever velocity results (v_0); and there is time dilation.

If there is no time dilaton when they end up next to each other, than there similarly is no time dilation between them if they end up far apart.

Their displacement has nothing to do with it, only their relative velocity.

 

[davidf32]

QUOTE: "There is no such thing as being at rest with respect to space. When we talk about a coordinate system being "at rest", this is just a arbitrary choice for convenience. we could just as easily define the clock as being "at rest" and the invidual as moving." END OF QUOTE
"Being at rest" simply means one is not subject to any forces. "Being at rest relative to some other observer or clock" simply means there is no relative velocity between them. Two observers in empty space can each claim to "be at rest" even though there is constant velocity betweeen them. They cannot, however claim to "be at rest relative to one another".

In either case 1 or 2, one can envision an experiment to check the relative rates of the clocks without bringing them back together by measuring red/blue shift of a known signal transmitted between them. One, then, has to take into acount relative velocity which, since it is a vector, changes the received signal in a known way PLUS OR MINUS the time dilation effect. IF THERE IS TIME DILATION between the two systems AND one measures the relative velocity by other independant means (a doppler radar signal for example) one in concept can extract information about the time dilation effect.

My claim is that in case 1, one would discover NO TIME DILATION between the two coordinate systems; While in case 2, there would be a meassurable time dilation effect.

To repeat my earlier arguement: Time dilation is a scalar and does not depend on the relative direction of motion. QED: If the two observers are side by side after the acceleration is finished (they are "at rest" relative to one another, than if the same model plays out as in case 1 wherein the end up with relative velocity, THERE CANNOT BE TIME DILATION BETWEN THEM BECAUSE--- TIME DILATION IS A SCALAR!
Now, I'm willing to accept that there is something wrong with this logic, but what is it?? Please don't just spit the equation abck at me--that is not adequate. Thanks, davidf32

 

[Mentz114]

davidf32, it looks as if you are confusing time-dilation with differential ageing. Time-dilation is an instantaneous reciprocal effect between frames, but differential ageing depends on the history of the clocks between comparisons.

 

[JesseM]

In either case 1 or 2, one can envision an experiment to check the relative rates of the clocks without bringing them back together by measuring red/blue shift of a known signal transmitted between them.

How would that work? There must be some mistake in your thinking, because while you can use red/blue shift to determine their rate of ticking relative to some particular observer receiving signals from them, there is no way to determine in any objective frame-independent way which is ticking slower, and in fact relativity says there is no physical "truth" about this matter. Keep in mind that observers moving at different velocities relative to the clocks would observe different red/blue shifts from each one...

 

[davidf32]

Gad zooks! What have I gotten myself into?? I have to think this stuff through a bit more. This is the first time I have entered into this kind of discussion not face to face, and I have to think a bit more. At this point I am not convinced by any arguements any of you have presented, but let me work on it for the nonce. I just say this for the moment: Truths in mathematics are not always truths in physics. Just because the time dilation equation says what it does, isn't always correct. An example when history has to be known is the so-called "twin paradox" that (once you know the history of how the velocity differences occured) ceases to be a paradox. The twin who got accelerated (and thus gained energy) ages less than his bro. Here, clearly history DOES matter. if one takes the view that it is energy increase that matters, not velocity difference, the mystery vanishes. That is the principle I'm applying when I say their exists an ambiguity in the notion of time dilation due to velocity. I'm signing off for now, but if you guys are into this I shall return. davidf32 P.S. It DOES matter that time dilation is a scalar (say I) df

 

[JesseM]

The twin who got accelerated (and thus gained energy) ages less than his bro. Here, clearly history DOES matter. if one takes the view that it is energy increase that matters, not velocity difference, the mystery vanishes.

Except in the twin paradox, it's not just the magnitude but the timing of the accelerations that matters, because the decreased aging is determined by the amount that the acceleration creates a deviation from a "straight" path through spacetime. For example in this illustration, triplets A,B,C start together, A accelerates initially in 2000, later in 2010 B accelerates away from C as well, finally both A and B accelerate back towards C and they reunite at the top in 2020...you can see that A and B's three accelerations (the red sections of their worldlines) each had identical magnitudes and times, but A will have aged less than B in this scenario (and of course they both age less than C).

 

[davidf32]

davidf32, it looks as if you are confusing time-dilation with differential ageing. Time-dilation is an instantaneous reciprocal effect between frames, but differential ageing depends on the history of the clocks between comparisons.

No I don't think so. I understand the difference.

 

[davidf32]

davidf32, it looks as if you are confusing time-dilation with differential ageing. Time-dilation is an instantaneous reciprocal effect between frames, but differential ageing depends on the history of the clocks between comparisons.

I don't think so.

How would that work? There must be some mistake in your thinking, because while you can use red/blue shift to determine their rate of ticking relative to some particular observer receiving signals from them, there is no way to determine in any objective frame-independent way which is ticking slower, and in fact relativity says there is no physical "truth" about this matter. Keep in mind that observers moving at different velocities relative to the clocks would observe different red/blue shifts from each one...

Here is the experiment: Consider two observers in empty space at rest and close to each other. They both have on-board "instrumentation"
1. They agree to transmit signals using a finally controlled single frequency transmitter.
2. They accelerate away from each other symmetrically
3. They both stop accelerating after an agreed upon time period (each using an identical on-board clock)
4. Now they have a well defined relative velocity which they measure with an on-board doppler system.
5. At the same time they each receive the well calibrated single frequency signal transmitted from the other ship.

6. They measure the frequency that they receive and note the effective frequency shift that (since they are moving away from one another) is to the red.

Knowing their relative velocities (from the doppler measurements) they can predict the expected frequency shift from the doppler equation: fr=f(1-v/c). At the same time, IF there is a time dilation effect in operation, it will add to this shift making the observed frequency (clock rate) slower by a factor t =t'/(1-v^2/c^2)^1/2

comparing the measured frequency shift to the equations they will know if there is or is not time dilation between the two moving vehicles.

Since the accelerations are symmetric, and time dilation due to velocity is a scalar, I preddict they will deduce no time dilation is present.

is there anything wrong with this experiment? Note that they do not have to know the magnitude of the difference from the predicted doppler effect, only that it exists.
davidf32

 

[JesseM]

Here is the experiment: Consider two observers in empty space at rest and close to each other. They both have on-board "instrumentation"
1. They agree to transmit signals using a finally controlled single frequency transmitter.
2. They accelerate away from each other symmetrically
3. They both stop accelerating after an agreed upon time period (each using an identical on-board clock)
4. Now they have a well defined relative velocity which they measure with an on-board doppler system.
5. At the same time they each receive the well calibrated single frequency signal transmitted from the other ship.

When you say "at the same time" in part 5, do you mean the same time according to their own onboard clocks, or the same time in some frame? Probably you meant the first, but if you mean the second you have to specify the frame because different frames disagree about whether two events separated in space happened "at the same time", this is known as the relativity of simultaneity.

6. They measure the frequency that they receive and note the effective frequency shift that (since they are moving away from one another) is to the red.

Knowing their relative velocities (from the doppler measurements) they can predict the expected frequency shift from the doppler equation: fr=f(1-v/c). At the same time, IF there is a time dilation effect in operation, it will add to this shift making the observed frequency (clock rate) slower by a factor t =t'/(1-v^2/c^2)^1/2

Yes, that's right, the relativistic Doppler equation is fr=f*sqrt[(1-v/c)/(1+v/c)] (with positive v taken to be moving apart, as in your classical Doppler equation fr=f(1-v/c)), but this can be simplified to:

fr = f*sqrt[(1-v/c)*(1-v/c)/(1+v/c)*(1-v/c)] = f*sqrt[(1-v/c)^2/(1-v^2/c^2)] = f*(1-v/c)/sqrt[1-v^2/c^2]

comparing the measured frequency shift to the equations they will know if there is or is not time dilation between the two moving vehicles.

Since the accelerations are symmetric, and time dilation due to velocity is a scalar, I preddict they will deduce no time dilation is present.

Well, your prediction definitely contradicts relativity, which has a huge amount of experimental evidence in its favor. In your scenario SR says they would both measure the signals from the other to be redshifted by the amount given by the relativistic Doppler shift equation, not the classical one. SR also predicts that the rate they measure signals from the other once they are moving inertially has nothing to do with their acceleration history, only their relative velocity.

 

[davidf32]

When you say "at the same time" in part 5, do you mean the same time according to their own onboard clocks, or the same time in some frame? Probably you meant the first, but if you mean the second you have to specify the frame because different frames disagree about whether two events separated in space happened "at the same time", this is known as the relativity of simultaneity.

Yes, that's right, the relativistic Doppler equation is fr=f*sqrt[(1-v/c)/(1+v/c)] (with positive v taken to be moving apart, as in your classical Doppler equation fr=f(1-v/c)), but this can be simplified to:

fr = f*sqrt[(1-v/c)*(1-v/c)/(1+v/c)*(1-v/c)] = f*sqrt[(1-v/c)^2/(1-v^2/c^2)] = f*(1-v/c)/sqrt[1-v^2/c^2]

I mean the "same time" according to their on-board clocks that (because of the symmetry of experiment) are sychronized.

Well, http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.htmlyour prediction definitely contradicts relativity, which has a huge amount of experimental evidence in its favor. In your scenario SR says they would both measure the signals from the other to be redshifted by the amount given by the relativistic Doppler shift equation, not the classical one. SR also predicts that the rate they measure signals from the other once they are moving inertially has nothing to do with their acceleration history, only their relative velocity.

So far as whether what I am saying contradicts either SR or GR, I don't think so. All it really says is that one should be careful as to how one uses equations: Generally speaking one has to know something about the circumstances of the observer and, in this particular case, some history of how energies got increased. Here is another thought experiment that I believe also makes my point. That is, be careful with using equations.

Consider the symmetric situation in which two twins out in empty space accelerate away from one another; then stop accelerating and drift for a while; then accelerate towards one another until they come back to rest (via appropriate symmetric manouvers) at their original position. An observer who remained at rest at the starting place would observe that both had aged the same amount (somewhat less than he had), but each of the twins would find they had aged the same amount. OK so far? Now, while they were on their respective ships, either could measure the velocity of the other twin (with appropriate instrumentation) and conclude the other one was aging less than he was. BUT, when they arrived home, they would of course discover otherwise. QED: There never was any time dilation effect between them! while they were traveling apart! davidf32

 

[davidf32]

jesseM hey, let me read some about the relativistic doppler shift and see if I am wrong in what I am saying. At this moment I don't think so, but I'm open to changing my mind if needs be. for the moment let this rest. davidf32

 

[JesseM]

So far as whether what I am saying contradicts either SR or GR, I don't think so.

Well, you're wrong, and I'm 100% sure about that. It would be possible to show this without even using the Doppler effect equation, just by calculating the time each one emits two successive signals in some inertial frame (say the frame where they have equal and opposite velocities), and the times they each must receive the two signals sent by the other, and what their clocks will read at these times. Let me know if you want a simple numerical example showing something like this.

Consider the symmetric situation in which two twins out in empty space accelerate away from one another; then stop accelerating and drift for a while; then accelerate towards one another until they come back to rest (via appropriate symmetric manouvers) at their original position. An observer who remained at rest at the starting place would observe that both had aged the same amount (somewhat less than he had), but each of the twins would find they had aged the same amount. OK so far? Now, while they were on their respective ships, either could measure the velocity of the other twin (with appropriate instrumentation) and conclude the other one was aging less than he was. BUT, when they arrived home, they would of course discover otherwise. QED: There never was any time dilation effect between them! while they were traveling apart!

Wrong, they cannot use the time dilation to calculate the amount that the other ages from start to beginning if they accelerate at the midpoint of the journey, the time dilation equation only works in inertial frames. If you imagine a third observer who was at rest relative to one of the twins as they moved apart, but who did not accelerate along with the twins but continued to move inertially, in his frame the twin #1 that he was at rest to before the acceleration was aging faster than the other twin #2, but after twin #1 accelerated his aging rate slowed down in this observer's frame (and in his frame twin #2's aging speeds up after he accelerates). This observer will end up predicting that their different aging rates during different phases cancel out, so he will also predict that they are the same age when they reunite, even though he thinks they were aging at unequal rates during different phases of the journey.

 

[davidf32]

Please! If all of you would only deal with the SYMMETRIC cases where I say there is a problem, I could follow you all a good deal more easily. So, can we narrow this discussion somewhat?
I think collectively you are raising some interesting points but I am having difficulty relating them to my original issue. I refer back to the first example I gave (with case 1 and case 2) and the latest example I gave regarding two twins. If there are errors in either of those models please address them: Please?

The comment by (I think Jesse M) about an inertial observer (not symmetric to the problem as stated) being able to see different dilations during the trip, but same aging at the end, doesn't really address what the two twins experience. I still maintain that in as much as time dilation is due to energy increases, the twins cannot have any intervals during which they have time dilation relative to one another. The idea is testable via the experiment I suggested. If I am correct, I am forced to agree that this violates SR for this kind of situation, but are there any experiments that show I am wrong? I know that SR has been verified many times, but what about this specific case of symmetry?

That space-time diagram appears to be suggesting that all three indiviuals arrive at 2020 at the same time. Do you mean that? If so, and you are right, I have a lot more to learn about SR and GR.
Peace davidf32

 

[Mentz114]

I still maintain that in as much as time dilation is due to energy increases, the twins cannot have any intervals during which they have time dilation relative to one another.

Anytime two observers are in motion relative to each other they will see the other's clock running slowly ( time dilation). It is an effect only of relative velocity. Your statement certainly contradicts that.

 

[JesseM]

Please! If all of you would only deal with the SYMMETRIC cases where I say there is a problem, I could follow you all a good deal more easily. So, can we narrow this discussion somewhat?
I think collectively you are raising some interesting points but I am having difficulty relating them to my original issue. I refer back to the first example I gave (with case 1 and case 2) and the latest example I gave regarding two twins. If there are errors in either of those models please address them: Please?

Case 1 is ill-defined because they don't meet up again to compare ages, so what do you mean by "there is not time dilation between them"? In either one's rest frame the other one is aging slower, and is actually younger at any given moment. In the frame where they were originally at rest, they are both aging at the same slowed-down rate, and they have the same age. You need to specify what frame you want to use to determine the time dilation, "time dilation between them" doesn't have any clear meaning.

For case 2, it's exactly the same, so whatever you mean when you talk about the "time dilation between them", I think you're probably wrong to say the two cases would be different.

The comment by (I think Jesse M) about an inertial observer (not symmetric to the problem as stated) being able to see different dilations during the trip, but same aging at the end, doesn't really address what the two twins experience.

What does "experience" mean? If you're just talking about how much each has aged by the time they reunite, then I told you, in that scenario it will be equal no matter what frame is used. But if you're trying to talk about how each one "experiences" the other one's rate of aging relative to their own, you need to be specific about what frame this "experience" is supposed to refer to (unless you're just talking about what each one sees of the other one visually, which is determined by the Doppler shift).

I still maintain that in as much as time dilation is due to energy increases, the twins cannot have any intervals during which they have time dilation relative to one another.

Again "time dilation relative to one another" has no clear meaning, you need to specify a frame to talk about time dilation. If at some point when they are moving apart you pick an inertial frame where one twin is temporarily at rest for some time, then during that time the other twin is aging slower in that frame. But as I said above, in this frame things would change when the twins changed velocities.

That space-time diagram appears to be suggesting that all three indiviuals arrive at 2020 at the same time.

What do you mean by "at the same time"? 2020 is the coordinate time that they all reunite in the frame where C is at rest, but their ages are not the same when they meet, that's why I said "but A will have aged less than B in this scenario (and of course they both age less than C)" at the end of that post.

 

[JesseM]

Anytime two observers are in motion relative to each other they will see the other's clock running slowly ( time dilation).

Well, they won't necessarily see that in a visual sense (if they're moving towards each other then visually they see each other's clocks running faster, not slower), they'll calculate it if they use an inertial frame where they are at rest. But I think davidf32 is getting confused because he is trying to apply this to an entire journey where they don't remain at rest in a single inertial frame, and to say in this case they should still say the other one's clock is running slower the whole time according to relativity, but that this is proven wrong since they are the same age when they reunite. This argument isn't valid, because the rule that clocks in motion relative to you run slower is only intended to work in inertial frames.

 

[davidf32]

QUOTE Case 1 is ill-defined because they don't meet up again to compare ages, so what do you mean by "there is not time dilation between them"? In either one's rest frame the other one is aging slower, and is actually younger at any given moment. In the frame where they were originally at rest, they are both aging at the same slowed-down rate, and they have the same age. You need to specify what frame you want to use to determine the time dilation, "time dilation between them" doesn't have any clear meaning.
END of QUOTE

I am using the frame of each of them as measured via means given in the proposed experiment. Hence, the description is not poorly defined. Same anwer for case 2.
-------------------------------------------------------------------------------
Originally Posted by davidf32
That space-time diagram appears to be suggesting that all three indiviuals arrive at 2020 at the same time.

What do you mean by "at the same time"? 2020 is the coordinate time that they all reunite in the frame where C is at rest, but their ages are not the same when they meet, that's why I said "but A will have aged less than B in this scenario (and of course they both age less than C)" at the end of that post.
What I mean by "same time" is an observer "at rest in 2020 at the landing site" who gets shmooshed by three arriving space ships "simulataneously" from his point of view. Is that what that diagram is suggesting? Or is it suggesting that the space ships arrive sequentially (from the point of view of our smooshed observer) who thusly gets smooshed three times, not just once?

 

[Mentz114]

Well, they won't necessarily see that in a visual sense (if they're moving towards each other then visually they see each other's clocks running faster, not slower), they'll calculate it if they use an inertial frame where they are at rest. But I think davidf32 is getting confused because he is trying to apply this to an entire journey where they don't remain at rest in a single inertial frame, and to say in this case they should still say the other one's clock is running slower the whole time according to relativity, but that this is proven wrong since they are the same age when they reunite. This argument isn't valid, because the rule that clocks in motion relative to you run slower is only intended to work in inertial frames.

Yes. But time dilation has a generally accepted meaning as the Lorentz transformed time of the reciprocal frame and the poster said

I still maintain that in as much as time dilation is due to energy increases, the twins cannot have any intervals during which they have time dilation relative to one another.

which is wrong.

 

[JesseM]

I am using the frame of each of them as measured via means given in the proposed experiment. Hence, the description is not poorly defined. Same anwer for case 2.

Well, then you are wrong in your answer to case 1, as I already said, "In either one's rest frame the other one is aging slower, and is actually younger at any given moment". And the same would be true in case 2, whether they both accelerated symmetrically or only one accelerated is irrelevant to the answer.

What I mean by "same time" is an observer "at rest in 2020 at the landing site" who gets shmooshed by three arriving space ships "simulataneously" from his point of view.

Why do you say "three arriving ships"? You can see that ship C never moves at all in this frame, so if this is the frame of the landing site, C would just remain at rest parked there. Meanwhile A and B would both arrive simultaneously at the landing site in 2020, with B having aged less than C, and A having aged even less than B.

 

[davidf32]

[Why do you say "three arriving ships"? You can see that ship C never moves at all in this frame, so if this is the frame of the landing site, C would just remain at rest parked there. Meanwhile A and B would both arrive simultaneously at the landing site in 2020, with B having aged less than C, and A having aged even less than B.[/QUOTE]

Got it! Thanks--I misread the diagram. davidf32

 

[darkhorror]

In ether case how would a light clock work after the ships stopped accelerating? well depending on the frame of reference.

 

[bcrowell]

A few gut reactions/simple observations/opinions:
-The gamma factor is not a scalar. A scalar would mean a Lorentz scalar, and gamma isn't one. Just because something has no direction in space, that doesn't mean it transforms as a Lorentz scalar. For example, energy has no direction in space, but it isn't a Lorentz scalar.
-Using a gamma as a time dilation factor is not a fundamental principle of SR. It's more like an interpretation of the Lorentz transformation in certain simple cases.
-The experimental observables are comparisons of clocks that were initially together and were later reunited. It's a waste of time to talk about any other form of clock comparison.
-To compute comparisons of clocks that were initially together and were later reunited, all you need to do is integrate the spacetime interval, \int \sqrt{dt^2-dx^2} (in units where c=1), for each clock. Doing it according to any other prescription is just making life hard for yourself.

 

[harrylin]

That is the point I'm trying to make: The equation of course does not require history be known, but my case 1 vs case 2, (that time dilation due to velocity differences is a scalar), results in the ambiguitiy. For further example: In case 1 if the two observers accelerate in the same direction etc, they end up adjacent to each other with NO RELATIVE velocity. QED: If time dilatation is a scalar (and it is) then the relative direction of the acceleration doesn't matter! If there is no time dilaton when they end up next to each other, than there similarly is no time dilation between them if they end up far apart. I get it that you don't agree, but can you please people your argument with an explanation as to why you disagree? It is not sufficient to simply refer to that equation! My point, of course, is that I can and do demonstrate the equation is ambiguous UNLESS you know the history. Knowing the history in the case of the twin paradox is the solution to that effect, so in this case I claim the same issue is in play.
davidf32

1. Acceleration itself doesn't matter (in ideal cases, which is what we are looking at here).
2. The relative direction of acceleration determines their velocities, and thus also their relative speed. And that does matter for what they will measure with their proper reference systems (the direction of their relative speed does not matter).

To get back to your first two cases:

- Observed from the original rest system, in case 1 both have equal time dilation while in case 2 only one of the two has time dilation.
- In both cases, if next each of them sets up a new inertial rest system (for themselves), each will then measure the other as undergoing time dilation.

The problem may be due to using equations without understanding their basis. Do you understand relativity of simultaneity?

Cheers,
Harald

 

[davidf32]

Yes Harald, I do know about the relativity of simultaneity.

Let me narrow this myself and find out if you agree with me about the importance of history in a thought experiment. Here goes and I would appreciate answers about this scenario:

Two twins are located in empty space in an inertial frame. There are no visible masses, so they do not know where they are other than adjacent to one another.
1. Each gets into an identical spaceship, gets put to sleep, and when they awake they discover they are no longer adjacent to one another. They are each now in inertial frames and off in the distance they see each other's ship.
2. A third party has manouvered into a position midway between the two distant ships and is in an inertial frame. He transmits an RF signal which reaches each of the distant ships SIMULTANEOUSLY (because of the symmetry of the scenario), starts their engines remotely, and the twin's ships accelerate back towards each other SYMMETRICALLY coming to rest adjacent one another.
3. Not knowing if one or both of their ships had accelerated while they were asleep, they cannot know if they will be the same age or not. Further, since there are no sign-posts, they cannot know if they are at the same location from whence they started.
4. We outside observers, on the other hand, know that while they were asleep, only one of them was accelerated, so when the are once again face-to-face, one of the twins will have aged less than the other.
CONCLUSION: Knowledge of the past history in this situation is of importance in knowing the outcome.

YES? NO?

 

[JesseM]

Yes Harald, I do know about the relativity of simultaneity.

Let me narrow this myself and find out if you agree with me about the importance of history in a thought experiment. Here goes and I would appreciate answers about this scenario:

Two twins are located in empty space in an inertial frame. There are no visible masses, so they do not know where they are other than adjacent to one another.
1. Each gets into an identical spaceship, gets put to sleep, and when they awake they discover they are no longer adjacent to one another. They are each now in inertial frames and off in the distance they see each other's ship.
2. A third party has manouvered into a position midway between the two distant ships and is in an inertial frame. He transmits an RF signal which reaches each of the distant ships SIMULTANEOUSLY (because of the symmetry of the scenario)

Do you mean "simultaneously" in the third party's frame? Or do you mean they are the same age when the signal reaches them? Or both? And after they wake up, what are their velocities in the third party's frame?

starts their engines remotely, and the twin's ships accelerate back towards each other SYMMETRICALLY coming to rest adjacent one another.
3. Not knowing if one or both of their ships had accelerated while they were asleep, they cannot know if they will be the same age or not. Further, since there are no sign-posts, they cannot know if they are at the same location from whence they started.
4. We outside observers, on the other hand, know that while they were asleep, only one of them was accelerated, so when the are once again face-to-face, one of the twins will have aged less than the other.
CONCLUSION: Knowledge of the past history in this situation is of importance in knowing the outcome.

YES? NO?

If I'm understanding the question, I would say no. Just as in the twin paradox, the question of who accelerated initially is basically irrelevant to who will have aged less when they reunite (completely irrelevant if we assume an instantaneous acceleration that immediately takes one up to the outbound "cruising speed"), it's the accelerations that happen when they are a significant distance apart that matter. To find their ages upon reuniting in this scenario you just need to know, at some time after they have woken up, what their ages and velocities and separation are in some inertial frame (perhaps the third party's frame), and at what time the signal to turn around reaches each one in this frame, and what their new velocities after turning around are (again assuming an instantaneous change in velocity to make the problem simpler). With this information you can calculate their ages upon reuniting without any knowledge of what happened when they were asleep.

Perhaps you would say that their ages in the third party's frame at some moment after they wake up is itself dependent on their past history, and that's true. But you could imagine two different past histories, one where twin #1 initially accelerated away and one where twin #2 initially accelerated away, that would both result in identical ages at some later time t in the third party's frame after both had woken up. So in this sense the question of who accelerated initially makes no difference.

 

[harrylin]

Yes Harald, I do know about the relativity of simultaneity.

That's good - for then you know why your remark was mistaken that in one case no time dilation would be measured.

Let me narrow this myself and find out if you agree with me about the importance of history in a thought experiment. Here goes and I would appreciate answers about this scenario:

Two twins are located in empty space in an inertial frame.

I take that to mean: in rest in an inertial frame.

There are no visible masses, so they do not know where they are other than adjacent to one another.
1. Each gets into an identical spaceship, gets put to sleep, and when they awake they discover they are no longer adjacent to one another. They are each now in inertial frames and off in the distance they see each other's ship.

I take that to mean: in rest in inertial frames S and S' that are in relative motion (note that both are in S as well as in S').

2. A third party has manouvered into a position midway between the two distant ships and is in an inertial frame.

I take that to mean: is in rest in an inertial frame S'' that is moving relative to both S and S' (at exactly intermediate speed, in view of what follows).

He transmits an RF signal which reaches each of the distant ships SIMULTANEOUSLY (because of the symmetry of the scenario), starts their engines remotely, and the twin's ships accelerate back towards each other SYMMETRICALLY coming to rest adjacent one another.

Simultaneously according to S'', OK. That also means that they come to rest at the place where the third party is.

3. Not knowing if one or both of their ships had accelerated while they were asleep, they cannot know if they will be the same age or not. Further, since there are no sign-posts, they cannot know if they are at the same location from whence they started.
4. We outside observers, on the other hand, know that while they were asleep, only one of them was accelerated, so when the are once again face-to-face, one of the twins will have aged less than the other.
CONCLUSION: Knowledge of the past history in this situation is of importance in knowing the outcome.

YES? NO?

Yes indeed - although in this particular example the twins will actually have aged the same if the acceleration was nearly instant at the start with a constant velocity next. You can see that by considering that in the third observer's reference system their velocity history was then symmetrical.

Note that although the velocity history is important for how much one twin of a twin paradox situation will be behind the other, it does not matter for the rate of a moving clock as measured with an inertial reference system, compared to its rate at rest in that system - which is what is usually meant with "time dilation".

Harald

 

[davidf32]

JessieM, Unfortunately you are doing exactly what I hoped would not happen: You are variously wrong in your statements and bringing in irrelevancies. Here are my responses:

QUOTE Do you mean "simultaneously" in the third party's frame? Or do you mean they are the same age when the signal reaches them? Or both? And after they wake up, what are their velocities in the third party's frame? END OF QUOTE.

ANSWER: Since the velocity of light is the same for all observers, and the third party is midway between the twins, and RF energy travels spherically from an omnidirectional anetenna, it is clear that, from the point of view of the third party, the signal arrives SIMULTANIOUSLY at each ship. Hence, from the third parties point of view, the subsequent accelerated motions of the two ships are identical both as to timing and magnitude. It is irrelevant as to the relative velocities of the twins ships and also irrelevant as to the twins ages in their own inertial reference systems. What they can and do know is that they are both accelerating towards one another and eventually meet (again at rest) at some point in space that is adjacent to the third party. They do not know if that is the place they started from. END OF ANSWER

QUOTE Just as in the twin paradox, the question of who accelerated initially is basically irrelevant to who will have aged less when they reunite (completely irrelevant if we assume an instantaneous acceleration that immediately takes one up to the outbound "cruising speed") END OF QUOTE

Answer: Oh, Really? Do you really believe in the so-called twin paradox that if there is assymmetry in their initial acceleration that when they get back together they will still have aged the same amount? I cannot believe you really believe that. It's wrong. PROOF: If one twin stays at home and the other accelerates out and then returns, the traveling twin will have aged less. Symmetry is important QED! END OF ANSWER

QUOTE it's the accelerations that happen when they are a significant distance apart that matter. END OF QUOTE

ANSWER; Yes, that is true. If that acceleration is symmetric in both timing and magnitude (relative to the third parties reference frame) than it will cancel out for the final answer. If it is not symmetric, it will result in an offset one way or other. In my example I made it symmetric both for the third party and each of the twins EVEN IF the twins don't know it. END OF ANSWER

The remainder of your coments are irrelevant to the point of my thought experiment: The point of the thought experiment was that the twins could not know apriori if their ages would be the same or different when the came back together BECAUSE they didn't know what happened while they were asleep. In other words, without some historical knowledge of the model. Since the ouside observers (us) did know that history, we COULD properly predict the outcome.
Peace davidf32

To find their ages upon reuniting in this scenario you just need to know, at some time after they have woken up, what their ages and velocities and separation are in some inertial frame (perhaps the third party's frame), and at what time the signal to turn around reaches each one in this frame, and what their new velocities after turning around are (again assuming an instantaneous change in velocity to make the problem simpler). With this information you can calculate their ages upon reuniting without any knowledge of what happened when they were asleep.

 

[JesseM]

JessieM, Unfortunately you are doing exactly what I hoped would not happen: You are variously wrong in your statements and bringing in irrelevancies. Here are my responses:

QUOTE Do you mean "simultaneously" in the third party's frame? Or do you mean they are the same age when the signal reaches them? Or both? And after they wake up, what are their velocities in the third party's frame? END OF QUOTE.

ANSWER: Since the velocity of light is the same for all observers, and the third party is midway between the twins, and RF energy travels spherically from an omnidirectional anetenna, it is clear that, from the point of view of the third party, the signal arrives SIMULTANIOUSLY at each ship.

OK, that's all I was asking, I don't know why you denigrate this as an "irrelevancy". You never specified that the velocities of the two ships were equal and opposite in the frame of the third party, if they weren't then the signals wouldn't reach the ships simultaneously in the third party's frame.

Hence, from the third parties point of view, the subsequent accelerated motions of the two ships are identical both as to timing and magnitude. It is irrelevant as to the relative velocities of the twins ships and also irrelevant as to the twins ages in their own inertial reference systems.

I didn't ask about their ages in any particular frame, I just mean you needed to specify their ages some way or another. For example, you could specify their ages in the third party's frame at the moment he sends the signals, or you could specify their ages at the moment they receive the signals. Obviously this is relevant to the final answer--if one is 20 and the other 80 at the moment they receive the signals, and their subsequent motions are "identical both as to timing and magnitude" in the third party's frame, then one will still be 60 years older when they reunite. On the other hand if they are both the same age when they receive the signals, they'll be the same age when they reunite. Without specifying something about their ages (again, it needn't be in their frame) the question doesn't provide enough information for a definite answer about whether they'll be the same age on reuniting.

QUOTE Just as in the twin paradox, the question of who accelerated initially is basically irrelevant to who will have aged less when they reunite (completely irrelevant if we assume an instantaneous acceleration that immediately takes one up to the outbound "cruising speed") END OF QUOTE

Answer: Oh, Really? Do you really believe in the so-called twin paradox that if there is assymmetry in their initial acceleration that when they get back together they will still have aged the same amount?

Huh? In the twin paradox they have not aged the same amount upon return, because one accelerated midway through the journey while the other didn't (did you miss that I was talking specifically about who "accelerated initially" in the quote above, which I contrasted with the very relevant issue of which one accelerates "when they are a significant distance"?) If their initial difference in velocity is caused by A instantaneously accelerating away from B, and then after they have moved apart for X years B instantaneously accelerates in the direction of A and then cruises until catching up with A, we'll find that B has aged less than A when they reunite, because B was the one who accelerated midway through the journey. A's initial acceleration is totally irrelevant here, in fact if you changed this scenario so that B was the one who initially accelerated instantaneously to create the initial velocity difference between them, but kept all the other aspects of the problem the same, then when they reunited B's age would be behind A's age by exactly the same amount as in the first scenario. I can give a numerical example illustrating this if you're familiar with how to solve problems in SR using inertial coordinate systems and the time dilation equation.

I cannot believe you really believe that. It's wrong. PROOF: If one twin stays at home and the other accelerates out and then returns, the traveling twin will have aged less. Symmetry is important QED! END OF ANSWER

But here again you are talking about an acceleration midway through the journey. I said that the initial acceleration, when they were starting at the same location, was irrelevant (it would make a slight difference to the total aging if it occurred over an extended period of time, but usually in these problems we treat accelerations as instantaneous, in this case the question of who accelerated initially is 100% irrelevant to all questions about aging)

QUOTE it's the accelerations that happen when they are a significant distance apart that matter. END OF QUOTE

ANSWER; Yes, that is true. If that acceleration is symmetric in both timing and magnitude (relative to the third parties reference frame) than it will cancel out for the final answer. If it is not symmetric, it will result in an offset one way or other. In my example I made it symmetric both for the third party and each of the twins EVEN IF the twins don't know it. END OF ANSWER

Yes, but you didn't answer the question of whether their ages were also identical in the frame of the third party to begin with, that's important to answering the question of whether they'll be the same age when they reunite.

The remainder of your coments are irrelevant to the point of my thought experiment: The point of the thought experiment was that the twins could not know apriori if their ages would be the same or different when the came back together BECAUSE they didn't know what happened while they were asleep. In other words, without some historical knowledge of the model. Since the ouside observers (us) did know that history, we COULD properly predict the outcome.

But we don't need to know the history either, if we knew their ages on receiving the signals (or at any specific time in the frame of the third party after they wake up), that would suffice to allow us to predict their ages when they reunite, without knowing anything else about the prior history.

 

[davidf32]

Everybody, You all win up to a point. I agree that for the last example I gave the issue is symmetry and neither the beginning acceleration nor the later acceleration matter by themselves. There are an infinite number of ways to have symmetric situations and the test of it ultimately occurs when the two twins get back together. If they have aged to the same degree the situation was symmetric: If they have aged differently, the situation was not symmetric. "SYMMETRY" can be obtained by varying the accelerations, the lengths of time each twin is coasting and so on. Although this is close to being a tautology, the definition of symmetry I am using is simply this--if the twins have aged the same when they meet, they both have traversed space-time in such manners to arrive back at some place (not necessarily where they started from) having aged to the same degree. Are all of you satisfied that you have convinced me of something?
1 for the gang and 0 for david32.

The next part of this, my original thesis, that there is an ambiguity in the time dilation concept, I am not yet ready to concede and I have to think a bit more about it. if you guys (and gals if there are any) want to go on about this, so do I.
david32-who at least in part has been wrong in much he has said.

 

[harrylin]

Everybody, You all win up to a point.

This wasn't about winning but about giving you "some comments on this observation that appears to lead to an ambiguity", in the hope to clarify matters for you...

[..] "SYMMETRY" can be obtained by varying the accelerations, the lengths of time each twin is coasting and so on. [..]

Tinkering isn't symmetry... I gave you an example of symmetry in my last message.

[..] The next part of this, my original thesis, that there is an ambiguity in the time dilation concept, I am not yet ready to concede and I have to think a bit more about it. if you guys (and gals if there are any) want to go on about this, so do I.
david32-who at least in part has been wrong in much he has said.

I take that to mean that some of our comments were helpful.

Harald

 

[davidf32]

Harald, yes you all have been most helpful and I appreciate it greatly. So far as my comment about "winning and losing", that was meant as a joke and the joke was on me. As I commented earlier in this discussion I am new to this mode of communication: This is the first time I have ever used a chat site. I find the experience a bit strange--a like learning a new language. Some of the nuance in face to face gets lost. I will be more careful in the future. So far as the next stuff I want to present---I;m working on it now and trying to do an expansion on the time dilation equation using gamma. I'm a bit uneasy about using this expression because of the comments from Bcrowell re: that expression and what is meant by scalar. That issue, however, will come out in the wash.
In the meantime--again thinks. davidf32-the dolt! (lol)

 

[davidf32]

To all, I am wrong about the ambiguity. I was assuming that time dilation between two inertial frames was proportional to v^2 (energy). That of course is incorrect. However, this discussion was very useful to me in that I learned a lot about a number of things (including me). So I thank you all.
davidf32