Undergrad Time dilation again, Einstein or Resnick?

[Herman Trivilino]

So are you saying when they set off on their journey across one light year they perceive they got there in less than a year?

What they perceive is not relevant. What happens is that they age less than a year during the journey because less than a year of proper time passes on their clocks. But also note that if they were racing a light beam, they would lose the race.

 

[Good Elf]

It is simple if you consider accelerations (both variable and constant) in "Special Relativity" as being made of piecemeal jumps in velocity. You can then apply Special Relativity to each velocity plateau where you may theoretically consider deferentially short periods of time where velocity is constant. You then sum up the small steps between one constant velocity and another different constant velocity (this is an acceleration) where a Special Relativistic System has been subject to acceleration (constant or otherwise). Special Relativity becomes an analytical form of General Relativity from the POV of a fixed "observer" frame of reference. Movements of clocks from one step in a high rise building to the next involves a change of acceleration due to "Gravity"... a small but measurable amount of "differential" time dilation is nowadays easily measurable.

According to the Einstein Convention you can only compare clocks in the same "mutual rest frame". If two frames are in relative motion then to set the zero on clocks you will need to bring one of the two frames into the chosen "rest frame". When clocks are moving relative to each other the "ticks" of their clocks are of different relative length but appear the same when considered from each other's frame of reference because "everything is relative". What is not accounted for is bringing one or other of these moving systems into the frame of the observer. There are two ways to do that, an observer in relative motion can either accelerate UP (or DOWN) to the speed of the relatively moving frame and then you may synchronize clocks, or you can decelerate or accelerate the moving (observed) frame UP (or DOWN) to the velocity of the observer frame. In the first case the observer undergoes an acceleration. In the latter case the observed frame undergoes the acceleration. Once this has occurred you use Einstein Synchronization light pulses, at least in theory. In practice this never really happens but please bear with me on this. In terms of General Relativity and the Equivalence Principle (the one on which GR is based and linked in Wikipedia below), the systems are entirely distinguishable. It is not an arbitary decision as to how the clocks are brought into the same rest frame and synchronization in the one place and at relative rest. After that synchronization instant, the two respective clocks return to their respective moving frames. You me only one of these frames actually undergo acceleration (not "in fact" but only "on paper"). One or the other of the two frames and it's contents undergoes extreme acceleration. You then "assign" the same initial time to both systems. After that it is clear which system is undergoing time dilati0on and which one is not. Here is a full mathematical description of the case which is completely acceptable way in which Special Relativity and General Relativity agree. See:
How Do You Add Velocities in Special Relativity?
This reference is taken directly from John Baez's own thread. If you look you will find other sources following the direction of this treatment too. You can split the accelerations up into small steps (as per calculus) and the result is identical to the way you do it in General Relativity in the end, outcome is the same. You can use the fact that systems are instantaneously at rest to synchronize clocks and this is the way Special Relativity deals with Einstein Synchronization of clocks, it just does not state it explicitly. Consider that you bring to rest one of the two systems as they pass in close proximity to each other. Your choice of "rest frame" affects the zero time synchronization on the pair of clocks. Then semi-instantaneouly accelerate that temporary quasi-rest frame back up to speed (a significant fraction of the speed of light if you want to see a big jump) or through a series of incremental equal steps in velocity (a constant acceleration) or just one single BIG change in velocity. In the latter case that one step in velocity better not be the observer frame because it would crush to a fine powder every bone in your (observer) body, that is just the real effect of relativity - special or general on matter. Capiche?

It rams home Einstein's Equivalence Principle and the way physicists like Einstein have chosen a very elegant means of solving the problem for highly symmetric systems. So "Beauty" conquers "Truth" in this case. The not so beautiful is more instructive when you understand the "under-story" of Special Relativity. Unfortunately in the general case where we have an ideal gas where "billiard ball-like" particles are in relativistic motion all the time and changing velocity through mutual scattering, time dilation is a much more involved problem, tiny time dilations accumulate between "impacts" and frames are shuffled around (consider that as quantum entanglement shuffling about), and exact solutions using General Relativity become the more complex approach. This Special Relativistic Approach is "easier" provided you have a way to equate mass and acceleration, it is just that the "rest frame still must be chosen in order to determine which "twin clock" is to undergo time dilation and which one is the reference clock.

The way you should consider time should be understood in the context of a Page & Wootters Mechanism for those who have an interest. From that you can gain an "overview" of the real mechanisms behind the processes of time dilation through quantum entanglement frame changing. Check out this easy read reference:
Quantum Experiment Shows How Time ‘Emerges’ from Entanglement - Medium - Oct 13 - 2013.
And so we come "full circle".

 

[Herman Trivilino]

According to the Einstein Convention you can only compare clocks in the same "mutual rest frame". If two frames are in relative motion then to set the zero on clocks you will need to bring one of the two frames into the chosen "rest frame". When clocks are moving relative to each other the "ticks" of their clocks are of different relative length but appear the same when considered from each other's frame of reference because "everything is relative". What is not accounted for is bringing one or other of these moving systems into the frame of the observer. There are two ways to do that, an observer in relative motion can either accelerate UP (or DOWN) to the speed of the relatively moving frame and then you may synchronize clocks, or you can decelerate or accelerate the moving (observed) frame UP (or DOWN) to the velocity of the observer frame.

That seems a long-winded way of saying that the two clocks can't be moving relative to each other? Not at all true. All that matters is position, not motion. If the two clocks share the same location then you simply set them to the same reading, regardless of their relative motion. This is an example of an event: Two co-located clocks read the same!

If, on the other hand, the clocks are separated, then you do need a convention to synchronize them, but using the Einstein Convention (or any other convention) it doesn't matter if they're in relative motion, it can still be done.

 

[Raymond Potvin]

In the muon frame, ground reaches muon before it decays due to length contraction of the atmosphere - the ground travels only a short distance.

Contraction is only needed to explain the null result of the MM experiment, it doesn't affect the way time dilation happens. Time dilation happens to light clocks when they move through space, because then, light takes more time to make the roundtrip between the mirrors, but the clocks also have to make a roundtrip in space for us to be able to tell which clock has suffered more time dilation than the other, and if it is so, then we can conclude that a clock has moved faster than the other even if, during their trip, it was impossible for the clocks themselves to know which one of them was moving.

 

[PAllen]

Contraction is only needed to explain the null result of the MM experiment, it doesn't affect the way time dilation happens. Time dilation happens to light clocks when they move through space, because then, light takes more time to make the roundtrip between the mirrors, but the clocks also have to make a roundtrip in space for us to be able to tell which clock has suffered more time dilation than the other, and if it is so, then we can conclude that a clock has moved faster than the other even if, during their trip, it was impossible for the clocks themselves to know which one of them was moving.

In the muon case, there is no reuniting of clocks, thus no invariant differential aging. There are two alternative frame dependent explanations of the invariant fact that the muons reach the ground. Unless you insist the Earth frame is picked out by some fundamental principle, both explanations are equally valid.

 

[PeroK]

Time dilation happens to light clocks when they move through space, because then, light takes more time to make the roundtrip between the mirrors

This is a common misconception. Time dilation is a result of relative motion between reference frames. All inertial motion through space is relative, so it is never possible to claim that one clock is "really" moving or that one clock is moving faster than another or that one clock is really time dilated more than another.

 

[Raymond Potvin]

In the muon case, there is no reuniting of clocks, thus no invariant differential aging. There are two alternative frame dependent explanations of the invariant fact that the muons reach the ground. Unless you insist the Earth frame is picked out by some fundamental principle, both explanations are equally valid.

The muon itself can be considered as a clock that starts with its creation and stops with its detection. We thus know where it starts and where it stops, and we know it is traveling at a relativistic speed, so we can make a calculation and discover that it lasts longer than in a lab. But we can't make such a calculation if we apply the same reasoning to the earth, because if we did, it is our clocks on Earth that would be suffering time dilation, and the data from the atmospheric muon would be unexplainable.

 

[PeroK]

The muon itself can be considered as a clock that starts with its creation and stops with its detection. We thus know where it starts and where it stops, and we know it is traveling at a relativistic speed, so we can make a calculation and discover that it lasts longer than in a lab. But we can't make such a calculation if we apply the same reasoning to the earth, because if we did, it is our clocks on Earth that would be suffering time dilation, and the data from the atmospheric muon would be unexplainable.

You're still labouring under the delusion that motion is absolute. There is no such thing as absolute inertial motion. And no such thing as a clock "suffering" time dilation.

If you take any clock on Earth and study it in a reference frame in which the Earth is moving at relativistic speed, then (in that frame) the clock run slower than an identical clock at rest in that frame.

No paradoxes or problems arise from considering things from the muon's rest frame, where it is at rest and the Earth is moving.

 

[Raymond Potvin]

This is a common misconception. Time dilation is a result of relative motion between reference frames. All inertial motion through space is relative, so it is never possible to claim that one clock is "really" moving or that one clock is moving faster than another or that one clock is really time dilated more than another.

Hi PeroK,
How could we make predictions if it was so? It is true that it is impossible to tell which clock is moving when we travel with them, but when the clocks are reunited, if one of them has suffered more time dilation, it means that it has traveled at a higher speed, no?

 

[Herman Trivilino]

But we can't make such a calculation if we apply the same reasoning to the earth, because if we did, it is our clocks on Earth that would be suffering time dilation, and the data from the atmospheric muon would be unexplainable.

No, it's fully explainable. Note that you need two Earth clocks, one present at the creation and another at the detection, or the equivalent thereof.

Those clocks are typically synchronized in Earth's rest frame, but if you synchronized them in the muon's rest frame they wouldn't be synchronized in Earth's rest frame. Regardless of how you do it, you can account for why those clocks read what they do when the events occur.

 

[PeroK]

Hi PeroK,
How could we make predictions if it was so? It is true that it is impossible to tell which clock is moving when we travel with them, but when the clocks are reunited, if one of them has suffered more time dilation, it means that it has traveled at a higher speed, no?

No. Two clocks can only be reunited if at least one of them changes its inertial reference frame. But, that's a difefrent matter from time dilation.

In any case, in neither classical physics nor relativity are there special reference frames such as the rest frame of the Earth in which a problem must be studied. In can be studied in any inertial reference frame, including that of a "high-energy" muon.

 

[Raymond Potvin]

Hi MT,
Here is a simulation of the twins paradox experiment that shows why the moving clock registers less tics than the one at rest. Light is moving at c in each clock, but its roundtrip takes more time in the moving one, and it takes exactly twice the time because it is traveling at .866c and because it is contracted at half its original length. If we would reverse the reasoning and consider that it is the other clock that was moving, the data would simply be reversed.
https://lumiere.shost.ca/page 1/Twins paradox.html

 

[PeroK]

Hi MT,
Here is a simulation of the twins paradox experiment that shows why the moving clock registers less tics than the one at rest. Light is moving at c in each clock, but its roundtrip takes more time in the moving one, and it takes exactly twice the time because it is traveling at .866c and because it is contracted at half its original length. If we would reverse the reasoning and consider that it is the other clock that was moving, the data would simply be reversed.
https://lumiere.shost.ca/page 1/Twins paradox.html

That animation assumes that the blue clock remains in an inertial reference frame and analyses the problem from that frame. In that case, the yellow clock does not remain in a single inertial reference frame, but changes its reference frame half way through. The roles cannot be reversed in that case.

You would have to analyse what happens when the yellow clock changes its reference frame.

 

[Raymond Potvin]

That animation assumes that the blue clock remains in an inertial reference frame and analyses the problem from that frame. In that case, the yellow clock does not remain in a single inertial reference frame, but changes its reference frame half way through. The roles cannot be reversed in that case.

You would have to analyse what happens when the yellow clock changes its reference frame.

Acceleration doesn't change the way light bounces between the mirrors, if the speed gets down during acceleration, the light takes less time to make the roundtrip during that time, and if the clock accelerates at .866c on its way back to the other clock, the light takes the same time as on its outward journey.

 

[PeroK]

Acceleration doesn't change the way light bounces between the mirrors, if the speed gets down during acceleration, the light takes less time to make the roundtrip during that time, and if the clock accelerates at .866c on its way back to the other clock, the light takes the same time as on its outward journey.

It's not directly related to acceleration. It's related to changing your reference frame.

There are several ways to analyse this. One option is simply be to use a suitable IRF (inertial reference frame). The frame of the blue clock is the obvious candidate - but that probably won't convince you!

You could choose any other IRF. The one that the yellow clock has for the first half of its journey might be an interesting choice. In that frame, the yellow clock would be at rest for the outward journey, but then move to the left at a greater speed to catch the blue clock that moves to the left the whole time.

In that frame, you would find the same result for the clocks (both blue and yellow) when they meet up.

 

[PeroK]

@Raymond Potvin Here's the calculation (in the reference frame of the first half of the yellow clock's journey); The blue clock sets of to the left at $0.866c$ and continues at that speed throughout:

The first half of the journey takes $8s$ according to the yellow clock. At that time:

The blue clock has traveled $6.928 cs$ (light seconds) and is reading only $4s$ (time dilation in the yellow clock's frame).

For the second half of the journey, the yellow clock sets off at approx $0.99c$ (in its original reference frame, which we are using). It's gamma factor is $7$. This half of the journey lasts 8 seconds according to the yellow clock, so $56s$ in the original frame in which we are analysing this; and $28s$ according to the blue clock.

In any case, after this time:

The blue clock has traveled a total distance of $55.4cs$ and reads $32s$.

The yellow clock has traveled a distance of $55.4cs$ and reads $16s$.

Hence, by analysing things in this frame we get the same answer as in the blue frame. And, we would get the same answer in any IRF.

Note that there is no need to assume that the blue clock is at rest. But, it is neceesary to stick with the same reference frame throughout.
.

 

[Raymond Potvin]

It's not directly related to acceleration. It's related to changing your reference frame.

There are several ways to analyse this. One option is simply be to use a suitable IRF (inertial reference frame). The frame of the blue clock is the obvious candidate - but that probably won't convince you!

You could choose any other IRF. The one that the yellow clock has for the first half of its journey might be an interesting choice. In that frame, the yellow clock would be at rest for the outward journey, but then move to the left at a greater speed to catch the blue clock that moves to the left the whole time.

In that frame, you would find the same result for the clocks (both blue and yellow) when they meet up.

You're right, but we can also do that with the blue clock if we consider that it is the one that is moving, and we will still get reversed data. If we don't know which clock is moving, how can we predict which one will suffer time dilation? When you change reference frames, you're assuming that the yellow clock is accelerating, so why didn't you assume it was accelerating in the beginning?

 

[PeroK]

You're right, but we can also do that with the blue clock if we consider that it is the one that is moving, and we will still get reversed data. If we don't know which clock is moving, how can we predict which one will suffer time dilation? When you change reference frames, you're assuming that the yellow clock is accelerating, so why didn't you assume it was accelerating in the beginning?

It's not to do with acceleration. But, you do know when you change reference frame. This could be due to acceleration. But, for example, there's a neat idea where the yellow clock simply transfers the time it reads to an identical clock moving in the opposite direction. That would do just as well.

In both cases, however the time of the return leg is measured, you know that you have changed reference frames.

Another idea is to use a neutral third IRF. In that IRF, the blue clock has the same velocity throughout but the yellow clock changes direction at some stage. There's no getting away from that. You can't pretend that the blue clock is changing direction when it isn't! And you can't pretend that the yellow clock isn't changing direction.

 

[Raymond Potvin]

It's not to do with acceleration. But, you do know when you change reference frame. This could be due to acceleration. But, for example, there's a neat idea where the yellow clock simply transfers the time it reads to an identical clock moving in the opposite direction. That would do just as well.

In both cases, however the time of the return leg is measured, you know that you have changed reference frames.

Another idea is to use a neutral third IRF. In that IRF, the blue clock has the same velocity throughout but the yellow clock changes direction at some stage. There's no getting away from that. You can't pretend that the blue clock is changing direction when it isn't! And you can't pretend that the yellow clock isn't changing direction.

It is a lot easier to consider that acceleration determines which clock is moving: we get the right result and eliminate all the other possibilities. Relativity is about how light moves between moving bodies, not about determining which one is moving, but if clocks can run slower than others, then they have to be the ones that are moving. Not accepting that logic means facing interminable discussions on relativity. On problems where it is impossible to tell which clock is moving, the discussion is always useless because no prediction can be made.

 

[PeroK]

It is a lot easier to consider that acceleration determines which clock is moving: we get the right result and eliminate all the other possibilities. Relativity is about how light moves between moving bodies, not about determining which one is moving, but if clocks can run slower than others, then they have to be the ones that are moving. Not accepting that logic means facing interminable discussions on relativity. On problems where it is impossible to tell which clock is moving, the discussion is always useless because no prediction can be made.

Well, I'm sorry you feel that way. Physics Forums is a good place to learn about relativity. But not learning SR is, after all, your prerogative.

I've tried my best, but I'll have to leave you in your state of ignorance of the subject!

 

[Janus]

Relativity is about how light moves between moving bodies, not about determining which one is moving, but if clocks can run slower than others, then they have to be the ones that are moving.

Relativity is not about how light moves, it is about the very nature of time and space and how it is measured. Light is used in many examples when discussing it as as a convenience due to the fact that it travels at c.

 

[PAllen]

The muon itself can be considered as a clock that starts with its creation and stops with its detection. We thus know where it starts and where it stops, and we know it is traveling at a relativistic speed, so we can make a calculation and discover that it lasts longer than in a lab. But we can't make such a calculation if we apply the same reasoning to the earth, because if we did, it is our clocks on Earth that would be suffering time dilation, and the data from the atmospheric muon would be unexplainable.

Wrong on both counts. The Earth frame description that the muon traveled for e.g. 10 microseconds is a comparison, implicitly, with two Earth frame clocks - one at the creation event, one at the reception event. Per the muon, both of these clocks run slower than the muon clock, but they are out of synch with each other (relativity of simultaneity). Per the muon frame, the only possible explanation of the result is length contraction. Thus, ther is nothing invariant or preferred about the time dilation explanation compared to the length contraction explanation. This definitively NOT equivalent to twin differential aging.

 

[Raymond Potvin]

Hi Janus,
We use light in our discussions because we think it is the speed at which the information travels between bodies. It is from the light clock mind experiment that the whole relativity was erected, that the nature of space and time was conceptualized. It works because we can make predictions, so it is useful, but the interminable discussions about it on the scientific forums are not really useful. I made the present simulation of the twins paradox in expectation that I would make another one to show what would happen if we would change reference frames, but I finally decided not to make it, and to stick to the idea that the twin that was moving was the one that has accelerated. This way, if two clocks meet in space without knowing where they come from, we can know if one of them has traveled longer or faster while comparing them, but we could not have predicted it.

 

[PeroK]

Hi Janus,
We use light in our discussions because we think it is the speed at which the information travels between bodies. It is from the light clock mind experiment that the whole relativity was erected, that the nature of space and time was conceptualized. It works because we can make predictions, so it is useful, but the interminable discussions about it on the scientific forums are not really useful. I made the present simulation of the twins paradox in expectation that I would make another one to show what would happen if we would change reference frames, but I finally decided not to make it, and to stick to the idea that the twin that was moving was the one that has accelerated. This way, if two clocks meet in space without knowing where they come from, we can know if one of them has traveled longer or faster while comparing them, but we could not have predicted it.

If you build a new clock on board a spaceship that previously accelerated, would your new clock know that it was "really" time dilated and know that it was different from a clock built on Earth?

 

[Raymond Potvin]

Wrong on both counts. The Earth frame description that the muon traveled for e.g. 10 microseconds is a comparison, implicitly, with two Earth frame clocks - one at the creation event, one at the reception event. Per the muon, both of these clocks run slower than the muon clock, but they are out of synch with each other (relativity of simultaneity). Per the muon frame, the only possible explanation of the result is length contraction. Thus, ther is nothing invariant or preferred about the time dilation explanation compared to the length contraction explanation. This definitively NOT equivalent to twin differential aging.

In my simulation, the yellow clock's width is half the width of the blue one. If I wouldn't have made that correction, the yellow one would have ticked less than 16 times, so it would have suffered more time dilation than what the data tells us. Without contraction, the muon would simply last longer than expected, and the same would be happening to the clocks on Earth if we would change reference frames.

 

[Raymond Potvin]

If you build a new clock on board a spaceship that previously accelerated, would your new clock know that it was "really" time dilated and know that it was different from a clock built on Earth?

If we know that the ship has accelerated in a given direction for a while, then we know its speed in this direction with regard to the point where it started accelerating. If a clock was left at that point, we could thus know how much time dilation our clock actually suffers compared to that clock, but if we encounter another clock en route, nothing can help us to predict the two readings.

 

[jbriggs444]

If a clock was left at that point, we could thus know how much time dilation our clock actually suffers compared to that clock,

You are dropping a clock off at a point that you pass by? [Or that passes by you]. How will that help determine anything? How will you compare your clock against the left-behind clock when both are receding into the distance with respect to one another?

 

[Raymond Potvin]

You are dropping a clock off at a point that you pass by? [Or that passes by you]. How will that help determine anything? How will you compare your clock against the left-behind clock when both are receding into the distance with respect to one another?

Hi jbriggs!
Leaving a clock behind in space means put it outside the ship and accelerate away from it. If you return to the point after a while and the clock is still there and has not accelerated, you know your own clock will have dilated.

 

[jbriggs444]

Hi jbriggs!
Leaving a clock behind in space means put it outside the ship and accelerate away from it. If you return to the point after a while and the clock is still there and has not accelerated, you know your own clock will have dilated.

No, you do not. You know that you have differential aging.

 

[Raymond Potvin]

No, you do not. You know that you have differential aging.

Well, if you know you will be younger than somebody left with the clock, then you know your clock will confirm that you are younger.