Time dilation again, Einstein or Resnick?

[Janus]

Trying to learn relativity without confronting the issue of simultaneity is like building a house without a key foundation. One day your perceived understanding will collapse.

For example, this thread started with your post, including:
It's clear, therefore, that your knowledge of SR is not yet on a solid foundation. In my view, you do need to confront the simultaneity issue.

As for its being convoluted, all you need is a light source in the middle of a vehicle. In the vehicle's frame light from the source hits both ends of the vehicle simultaneously. Yet, in a frame where the vehicle is moving the light reaches the rear of the vehicle first. Thus, simultaneity is frame dependent. It's that simple.

Relativity of Simultaneity, is likely the hardest concept for people to accept in regards to Relativity. It is so difficult to shake the idea that "now" is universal. But once you get it, the rest is easy.
It somewhat reminds me of back when I was taking flying lessons. Our instructor told us that we would be doing our flight training in a Piper Tomahawk, which was the best plane to learn to fly with, because it was the hardest plane to learn to fly with. If you could learn to fly a Tomahawk, flying anything else would be a piece of cake.

 

[russ_watters]

I think you are completely wrong. In my opinion, when learning relativity, one should learn relativity of simultaneity BEFORE one learns time dilation and length contraction. Indeed, one should learn relativity of simultaneity as an immediate consequence of the two postulates of SR.

I agree with this and go further to say before and separate, as part of Newtonian physics. For whatever reason, we get an awful lot of beginners here thinking that all of SR can be explained with RoS, which eliminates what makes Einstein's relativity different from Newton's. If we use Newton's approach, the twins end up the same age, missing what's really "special" about SR.

 

[russ_watters]

Relativity of Simultaneity, is likely the hardest concept for people to accept in regards to Relativity. It is so difficult to shake the idea that "now" is universal.

While I've seen that is true on PF, I don't get it. People deal with it every day of their lives in other contexts, like estimating the distance to a lightning strike by counting the delay before the thunder gets to them!

I'm losing track of threads, but it might have been you who pointed out in another thread that UTC is the same everywhere on Earth, which assumes a non-rotating Earth and a certain synchronization technique (subtracting-out the signal delay from Grenwhich). Do you think this sort of thing is what causes people to be confused about the existence of a universal "now"? Is putting the signal delay back in an easy way to fix it?

 

[Dale]

Relativity of Simultaneity, is likely the hardest concept for people to accept in regards to Relativity.

There is some evidence to support this
https://arxiv.org/abs/physics/0207109

 

[Ibix]

As others have said, the relativity of simultaneity is absolutely critical to understanding relativity, and if you've missed it then you have a problem. For example, without the relativity of simultaneity the twin paradox is genuinely paradoxical.

 

[PAllen]

I agree with this and go further to say before and separate, as part of Newtonian physics. For whatever reason, we get an awful lot of beginners here thinking that all of SR can be explained with RoS, which eliminates what makes Einstein's relativity different from Newton's. If we use Newton's approach, the twins end up the same age, missing what's really "special" about SR.

I'm not sure I follow. Are you suggesting there is relativity of simultaneity in Newtonian physics??! (signal delays have nothing to do with whether or not there is absolute simultaneity).

 

[asca]

Relativity of simultaneity is the key point. Forget about the twin paradox, and let’s focus on the famous muon decay experiment, (you can see the experiment in a PSSC video here https://www.youtube.com/watch?v=3CeQXsIiGp8 ). So the "traveling" muon, in its own reference system, survives “A” seconds, while in the Earth’s reference system it survives “B” seconds, with B>A. No acceleration is involved, so no GR to help us out. The question is, what if we consider the muon's point of view about the Earth’s clocks? SR says that according to the muon, the Earth’s clock should run slower that the muon’s ones, so we should have B<A! Solution? Ok, bear in mind that the so called time dilation is just one of the consequences of Lorentz’s transformations, especially of the “time” portion, which is the portion that describes the relativity of simultaneity. I hope the first 15 minutes of this video https://www.youtube.com/watch?v=eAkbnVAI0VE could help you visualize the effect of relativity of simultaneity (and the Lorentz transformation space time dependence) and grasp the solution. The confusion arises from the fact that nobody usually uses Lorentz’s transformation to show the time dilation effect. You usually find a simple ( and correct) shortcut that deals with light bouncing back and forth between two mirrors. But that shortcut forces you to miss the “bigger picture” that stays in relativity of simultaneity.

 

[Orodruin]

No acceleration is involved, so no GR to help us out.

It is a common misconception that GR is required to handle acceleration. It is not.

 

[vanhees71]

Indeed, but time-dilation as usually presented is comparing a coordinate time to proper time. This requires a time coordinate and therefore a frame dependent simultaneity convention.

Sure. For this purpose you simply parametrize the timelike trajectory of the clock with the time coordinate of the given reference frame. For the treatment of the twin paradox for a twin moving on a circle as an example, see

https://th.physik.uni-frankfurt.de/~hees/pf-faq/srt.pdf

As hopefully becomes clear, here the "proper times" of two observers, called Alice and Bob in the manuscript is compared, i.e., two physically well defined times!

 

[pm3142]

I am intrigued by perceptions of the consequences of SR. In the A, B, Bob and Alice type example given earlier, it is the case that observations of time dilation (and length contraction) are reciprocal between the two observers due to their relative velocities and the einstein equations do show this. However, from a physical point of view, it seems to me that all such relativistic effects as we observe them (or would if we could) can be interpreted as a function of the doppler shifting of photons emitted from a relatively moving source. As such, relativistic mechanics seems a bit illusory. Maybe I am missing something ?

 

[Orodruin]

Maybe I am missing something ?

Clearly, but unless you show us your misunderstanding, there is no way to correct it.

 

[PeroK]

As such, relativistic mechanics seems a bit illusory. Maybe I am missing something ?

You are missing quite a lot. We are not able to undertake space travel at relativistic speeds, but if we could then the differential ageing of astronauts would be far from an illusion.

Moreover, as you may know, clocks within the GPS satellite system are configured to take into account time dilation.

 

[pm3142]

Heres a thought. Any misunderstanding is tied up with this.

Consider this: Ship A heads off to a point 1 light year away in space (assume rapid acceleration). Once top speed is reached, say 99.9% lightspeed we make an observation through the 'porthole' and we see evidence of dilated time onboard the ship. However, the ship IS moving at almost lightspeed with respect to the stationary observer and WILL reach its destination in 1 year and by turning around, return in another year. So, two years have passed to the stationary observer for the return journey. Onboard ship, time is dilated to the point where the relative scale of time is vastly different from that outside the ship.The journey still apparently takes two years though to those on board. So my question is this: What is it that the stationary observer is actually seeing in this thought experiment?. Its tempting to think that what may be observed is a stretched photonic wavefront that is essentially more static relative to the external (or stationary) time frame. Once the ship returns in two years to the stationary reference frame, this observed wave front collapses and the scale of time is observed to be synchronised again between the reference frames. However, only two years have actually passed for both observers.

 

[PeterDonis]

The journey still apparently takes two years though to those on board.

No, it doesn't. It takes two years (or a little longer since the ship can't quite reach the speed of light) according to those on Earth. It takes a much, much shorter time according to those on board.

 

[pm3142]

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?

 

[PAllen]

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?

Yes, this is shown by how many muons created in the upper atmosphere by cosmic rays reach the ground. Their half life is 2 microseconds. Almost none should reach the ground, yet most of them actually do. We, on the ground see them taking 10s of microseconds to reach the ground, but almost all arrive without decaying because for the muon much less than 2 microseconds elapsed.

 

[pm3142]

Thanks for putting up with my attempts to understand!

I am aware of the muon phenomenon which certainly seems to provide evidence of time dilation. However, they are inanimate. We have no idea what they are 'perceiving'. Doesnt this argument imply that the ship-board observers in my thought experiment would be perceiving FTL travel ?

 

[PeroK]

Thanks for putting up with my attempts to understand!

I am aware of the muon phenomenon which certainly seems to provide evidence of time dilation. However, they are inanimate. We have no idea what they are 'perceiving'. Doesnt this argument imply that the ship-board observers in my thought experiment would be perceiving FTL travel ?

No. If you travel to a star that is 5 light years away from the Earth at a speed close to the speed of light, then you will arrive in less than 5 years by your clock. But, you will not observe a FTL speed at any stage. The key to this is that after you have accelerated to your relativistic speed, the distance to the star, as measured by you, has contracted. Your on board observation is that the star moves towards you at a sub light speed but from a much reduced initial distance.

 

[PAllen]

Thanks for putting up with my attempts to understand!

I am aware of the muon phenomenon which certainly seems to provide evidence of time dilation. However, they are inanimate. We have no idea what they are 'perceiving'. Doesnt this argument imply that the ship-board observers in my thought experiment would be perceiving FTL travel ?

No. In the most fundamental sense, if a radar signal was sent at the same time as a rocket passed earth, the light would arrive before the rocket, obviously ther is no FTL. Another observation is that in the rest frame of the rocket during travel, the Earth star distance is greatly reduced, so distance traveled in this frame divided by trip time measured in this frame is less than c.

 

[pm3142]

Interesting. So we believe the space contraction would appear very real to the voyager and distance would appear reduced, relative to the original (stationary - as viewed on earth) distance to the destination. So, acceleration to high velocity is perceived to actually warp space enough to bring distant objects physically closer?

 

[SiennaTheGr8]

Interesting. So we believe the space contraction would appear very real to the voyager and distance would appear reduced, relative to the original (stationary - as viewed on earth) distance to the destination. So, acceleration to high velocity is perceived to actually warp space enough to bring distant objects physically closer?

No need to use words like "appear" and "perceived." The distance between Earth and distant star really is shorter in the spacefarer's frame than it is in the Earth frame. And the distance between atmosphere and ground really is shorter in the muon's frame.

 

[PeroK]

Interesting. So we believe the space contraction would appear very real to the voyager and distance would appear reduced, relative to the original (stationary - as viewed on earth) distance to the destination. So, acceleration to high velocity is perceived to actually warp space enough to bring distant objects physically closer?

Nothing happens to space because one observer accelerates. Instead, the measurements of time and distance carried out by that observer are different from those of an observer who remains in the original frame.

As pointed out above there is no FTL travel in either frame.

That said, although relativity forbids FTL travel, it does provide the possibility of long-distance space travel in a short time for the space traveller.

In other words, you could travel far across space in your lifetime, while your journey would take hundreds, thousands or millions of years as observed from Earth.

 

[Raymond Potvin]

Yes, this is shown by how many muons created in the upper atmosphere by cosmic rays reach the ground. Their half life is 2 microseconds. Almost none should reach the ground, yet most of them actually do. We, on the ground see them taking 10s of microseconds to reach the ground, but almost all arrive without decaying because for the muon much less than 2 microseconds elapsed.

Hi Allen,
The muon experiment looks like half a twins paradox experiment: we know which clock is traveling. It wouldn't be the case if the two twins would both be traveling, and if both could chose their own direction and speed: we could not know which one has traveled more than the other before having seen their respective clocks. If we could consider that the Earth could be traveling towards the muon at relativistic speed, I'm afraid that the constant result we get from the observation would be considered as paradoxical as if we could predict which one of my traveling twins would get younger.

 

[PeroK]

Hi Allen,
The muon experiment looks like half a twins paradox experiment: we know which clock is traveling. It wouldn't be the case if the two twins would both be traveling, and if both could chose their own direction and speed: we could not know which one has traveled more than the other before having seen their respective clocks. If we could consider that the Earth could be traveling towards the muon at relativistic speed, I'm afraid that the constant result we get from the observation would be considered as paradoxical as if we could predict which one of my traveling twins would get younger.

The laws of physics are the same in all inertial reference frames, including those where the Earth is moving towards a muon at relativistic speed. No paradoxes arise from analysing the problem from this reference frame.

 

[PAllen]

Hi Allen,
The muon experiment looks like half a twins paradox experiment: we know which clock is traveling. It wouldn't be the case if the two twins would both be traveling, and if both could chose their own direction and speed: we could not know which one has traveled more than the other before having seen their respective clocks. If we could consider that the Earth could be traveling towards the muon at relativistic speed, I'm afraid that the constant result we get from the observation would be considered as paradoxical as if we could predict which one of my traveling twins would get younger.

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

 

[Mister T]

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".

 

[Mister T]

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?

 

[Mister T]

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.