Time dilation but for who?

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Time dilation... but for who??

I was reading Einstein's postulate that if two bodies A and B are moving relative to one another it is impossible to truely discern whether one of the bodies is stationary and the other is moving (i.e. we can only speak of their relative motion).

However, special relativity claims that as a body approaches light speed, time (for that body) slows down. But this seems to contradict the postulate that motion is always relative. If motion can only be described in relative terms, then wouldn't time slow down for both bodies compared with the other?
 

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  • #2
jtbell
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Yes.
 
  • #3
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So if you were in a space craft flying away from the earth at near light speed and then you returned to earth would earth clocks be slow (compared to your clocks) or your would clocks be slow (compared to earth clocks)? or would both be slow (if so how can you compare)? Please explain
 
  • #4
sylas
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So if you were in a space craft flying away from the earth at near light speed and then you returned to earth would earth clocks be slow (compared to your clocks) or your would clocks be slow (compared to earth clocks)? or would both be slow (if so how can you compare)? Please explain
It's called the twin paradox. The twin that turns around at some point is the one that has aged less when they meet up again. There's no ambiguity as to which twin turns around.

It's not really a paradox at all, but it's a good exercise for calculating with relativity.

Cheers -- sylas
 
  • #5
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Hi Sylas. At what point is the fact that the "turn around twin ages less" decided? Before he turns around? At the point he turns around? Or when he finally arrives back? What is special about the act of "turning round" that causes this twin to age less?
 
  • #6
malawi_glenn
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the twin that is in the space craft have to accelerate, and that is breaking the symmetry of the situation. The twin is physically accelerating, and one can not say that the two twins are in two inertial frames which moves at constant velocity w.r.t each other (special relativity is not applicable to accelerating frames)
 
  • #7
sylas
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Hi Sylas. At what point is the fact that the "turn around twin ages less" decided? Before he turns around? At the point he turns around? Or when he finally arrives back? What is special about the act of "turning round" that causes this twin to age less?
The way the question is phrased is likely to get you into a mess. As soon as you say "at what point", this implicitly suggests some commonly agreed upon instant in time. There's no such thing.

It is when you turn around that you know you are not in an inertial frame; but that is not when you "age less". The amount you age is simply the accumulation of "proper time" along your world line, and special relativity lets you calculate that.

The "metric" used has the property that the "shortest line" has the longest proper time. The thing about turning around is that you have a world line extending out, and reversing itself, and coming back, and that gives less "proper time" accumulated along that path. You end up younger than someone who stayed home.

Suppose you have a whole heap of friends, all of whom set out on various journeys around the galaxy, agreeing to meet back at some previously agreed point in space and time. When they meet up again, they'll all be different ages.

The age depends on their world line. Also -- assuming they kept out of strong gravitational fields! -- you can do the whole analysis in special relativity.

Basically, the increment in proper time dτ is defined as dτ2 = dt2 - (dx/c)2, where x and t and space and time co-ordinates in ANY inertial frame. Integrate that along the world line, and you get how much the traveller ages.

If any of these friends remained inertial the whole time, they will be the oldest. You can see this, by using their location as the origin of an inertial frame. The age of the others will depends on their whole path through space time, and that can be calculated with special relativity, as long as they stayed out of strong gravitational fields.

Cheers -- sylas
 
  • #8
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I was reading Einstein's postulate that if two bodies A and B are moving relative to one another it is impossible to truely discern whether one of the bodies is stationary and the other is moving (i.e. we can only speak of their relative motion).

However, special relativity claims that as a body approaches light speed, time (for that body) slows down. But this seems to contradict the postulate that motion is always relative. If motion can only be described in relative terms, then wouldn't time slow down for both bodies compared with the other?
The amount of accumulated time on a clock depends on how fast it moves.
The clock that leaves the earth and returns, travels a greater distance than earth, and must travel faster between departure and arrival, thus accumulating less clock time.
If both clocks left earth simultaneously and returned simultaneously, after different trips, you obviously could make a direct comparison on return. If you knew the flight plan for both, you could calculate the times before return.
While separated, each clock will appear to run slower to the other observer.
 
  • #9
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Yes.
So twins/clocks that travel apart and back together again would remain exactly the same age regardless of which twin/clock experienced acceleration changes?
 
  • #10
sylas
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So twins/clocks that travel apart and back together again would remain exactly the same age regardless of which twin/clock experienced acceleration changes?
No. (And the "Yes" for the other question is still correct.)
 
  • #11
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The amount of accumulated time on a clock depends on how fast it moves.
What determines how fast a clock moves? Or even that it moves?
The clock that leaves the earth and returns, travels a greater distance than earth, and must travel faster between departure and arrival, thus accumulating less clock time.
Given it can’t be determined that either clock is ever stationary or moving, surely the “earth clock” also leaves and returns to the “travelling clock“ and the clocks separate and rejoin at the same speed and over the same distance.
 
  • #12
sylas
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What determines how fast a clock moves? Or even that it moves?

Given it can’t be determined that either clock is ever stationary or moving, surely the “earth clock” also leaves and returns to the “travelling clock“ and the clocks separate and rejoin at the same speed and over the same distance.
Your "given" is incorrect.

In a situation of constant motion (an inertial frame) each clock is running slow relative to the other one. There's no contradiction here. The Lorentz transformations mean that distance, time and simultenaity all changes depending on what frame is being used.

With constant motion, the twins never get back together again, and so there's no paradox.

If one twin turns around to come back, then that twin adopts a new inertial frame; and in that new frame, simultenaity is different as well. Hence it is impossible for the twin who turns around to identify the turn around point as a particular instant simultaneous with the events at the other stay-at-home twin.

There's no ambiguity about which twin turns around, and you CAN determine whether you remain inertial or not.

There are heaps of different ways to look at this problem, and they all give the same answer. Anything different, and it's simply incorrect.

Cheers -- sylas
 
  • #13
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Your "given" is incorrect.
So “Einstein’s postulate” in the OP is wrong?

In a situation of constant motion (an inertial frame) each clock is running slow relative to the other one. There's no contradiction here. The Lorentz transformations mean that distance, time and simultenaity all changes depending on what frame is being used.

With constant motion, the twins never get back together again, and so there's no paradox.
What if the constant motion is circular and the twins do get back together again?
 
  • #14
sylas
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So “Einstein’s postulate” in the OP is wrong?
No; Einstein's postulate is correct.

Even with acceleration, there is no way to identify whether you are "stationary" or not at any point; and so the postulate is still true as expressed, even with accelerated motions. You can tell when you change velocity, from the acceleration you experience. You can never say that you are "stationary". That's an arbitrary choice.

What if the constant motion is circular and the twins do get back together again?
The twin travelling in a circle ages less. There's no ambiguity as to which twin is moving in circles ... that is an acceleration and the twin moving in circles can measure their own acceleration.

Cheers -- sylas
 
  • #15
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No; Einstein's postulate is correct.

Even with acceleration, there is no way to identify whether you are "stationary" or not at any point; and so the postulate is still true as expressed, even with accelerated motions. You can tell when you change velocity, from the acceleration you experience. You can never say that you are "stationary". That's an arbitrary choice.



The twin travelling in a circle ages less. There's no ambiguity as to which twin is moving in circles ... that is an acceleration and the twin moving in circles can measure their own acceleration.

Cheers -- sylas
If both twins are simultaneously travelling in mirror image circles that intersect are they the same age when they meet again?
 
  • #16
sylas
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If both twins are simultaneously travelling in mirror image circles that intersect are they the same age when they meet again?
Yes.
 
  • #17
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What determines how fast a clock moves? Or even that it moves?
.
The speed of the ship relative to earth.

Given it can’t be determined that either clock is ever stationary or moving, surely the “earth clock” also leaves and returns to the “travelling clock“ and the clocks separate and rejoin at the same speed and over the same distance
The ship must accelerate (change course) to leave and return. This is not the cause of time dilation but the asymmetrical feature that determines who moved. The earth does nothing.
The earth appears to leave and return to the ship passenger. This is a simple case, but if two travelers left and returned, you have to know the course each takes to predict any age difference before they return.
 
  • #18
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The speed of the ship relative to earth.


The ship must accelerate (change course) to leave and return. This is not the cause of time dilation but the asymmetrical feature that determines who moved. The earth does nothing.
The earth appears to leave and return to the ship passenger. This is a simple case, but if two travelers left and returned, you have to know the course each takes to predict any age difference before they return.
When did the Earth become the actual stationary position of the universe? Why is “The speed of the ship relative to earth” any more preferred or valid than the speed of the Earth relative to the ship?

Two people are on a conveyor belt. One person walks way from the other along the belt. An abstract conclusion is that the walking person is moving and the other is stationary. But say that the belt is moving at walking speed relative to what it’s sitting on and that the person walks against the movement of the belt. An abstract conclusion is that the walking person is stationary relative to the thing the belt is sitting on and the non-walking person is moving. Then say that the thing that the moving belt is sitting on is also moving . . . etc, etc. Thing is there is no actual stationary peg in the universe to hang your hat on. Acceleration doesn’t determine what moves per se it only determines what changes movement. A change in movement (acceleration) can never be determined as an actual increase or decreased in speed. I don’t see how the relative movement of things can be anything but symmetrically equal and opposite.
 
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  • #19
sylas
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When did the Earth become the actual stationary position of the universe? Why is “The speed of the ship relative to earth” any more preferred or valid than the speed of the Earth relative to the ship?
Because in the thought experiment, the twins compare their ages when they get back together at Earth.

You have completely ignored the fundamental point that one twin accelerates, and the other doesn't. To make your conveyor belt example relevant, you have to have someone walking along the belt, turning around, and coming back. That's two inertial frames, and it is NOT symmetric with a person walking on the belt at one consistent velocity, with a single inertial frame.

I don’t see how the relative movement of things can be anything but symmetrically equal and opposite.
As soon as you introduce the notion of turning around, it is no longer symmetric. One twin turns around, and the other doesn't. If you apply special relativity, then the twin who did the turn around is the one who ages less when they get back together and synchronize watches once more -- unambiguously.
 
  • #20
diazona
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I get the sense that what might not be clear here is that it is possible to tell if you're accelerating, but it is not possible to tell if you're moving at constant velocity.

Imagine if you were in a small box (or a small spaceship) that doesn't allow any sort of influence from outer space to come inside. So no windows, basically. The point is that anything you can tell about your motion must be based on the local observations, experiments you can run that are completely contained within the box (spaceship).

Now, what the principle of relativity says is that there's no possible way to figure out the relative velocity between you and, say, the Earth, without looking outside of the box. But you can tell whether you're accelerating or not: if you had an iPhone in your spaceship, you could just look at its accelerometer. And the iPhone would be able to sense this acceleration without receiving any sort of influence from outside the box. (You'd be able to feel it too, it'd feel kind of like gravity in fact) So, in a manner of speaking, there must be something fundamentally "special" about acceleration that allows you to define it absolutely, without reference to anything else. That is emphatically not true for velocity.

This applies to the twin paradox because each twin can independently determine his/her own acceleration (for instance, if they were both carrying iPhones). The twin who flies off, turns around, and comes back will notice a huge spike on her iPhone's accelerometer, but the twin who stays in place on Earth or wherever will not. And that means the situations of the two twins are not the same. The one who accelerates will be the one who ages less.

If you worked out some sort of flight plan in which both twins took voyages in which they both experienced identical accelerations, then they would be the same age when they returned. In that case, the twins could not distinguish which was which based on their accelerations (their iPhones would have exactly the same record of acceleration), so there's no way one could have aged more than the other.
 
  • #21
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Because in the thought experiment, the twins compare their ages when they get back together at Earth.

You have completely ignored the fundamental point that one twin accelerates, and the other doesn't. To make your conveyor belt example relevant, you have to have someone walking along the belt, turning around, and coming back. That's two inertial frames, and it is NOT symmetric with a person walking on the belt at one consistent velocity, with a single inertial frame.



As soon as you introduce the notion of turning around, it is no longer symmetric. One twin turns around, and the other doesn't. If you apply special relativity, then the twin who did the turn around is the one who ages less when they get back together and synchronize watches once more -- unambiguously.
I haven’t ignored the fact that one twin accelerates and the other doesn’t. I simply can’t see that acceleration is important to what we are discussing because it doesn’t define anything other than the fact that a thing is changing it’s motion (or is being subjected to gravity).

One twin accelerates and creates a seperation of the twins. That twin accelerates again to bring them back together. That the other twin doesn’t accelerate doesn’t that mean that it’s stationary. A third person observer that was some distance from the twins would simply see them separate and come back together again and wouldn’t know whether one or both had accelerated and both twins would appear to turn around. I can’t see any immediate significance in the “turn around” but I’m tired and have a headache so will give it more thought at a later time.
 
  • #22
sylas
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I haven’t ignored the fact that one twin accelerates and the other doesn’t. I simply can’t see that acceleration is important to what we are discussing because it doesn’t define anything other than the fact that a thing is changing it’s motion (or is being subjected to gravity).
It's not the acceleration as much as the change in inertial frame. You can do an analysis using SR only, and an instantaneous change in velocity. After the turn around, everything changes. The other twin appears red shifted. The angular size of the other twin in the sky is reduced. A laser range finder would indicate that the other twin has actually stopped moving. And so on. All of these things are natural consequences of a change in the inertial frame.

There is no ambiguity at all as to which twin actually does the turn around. You can tell with measurements before and after the turn, even if you sleep through the turn itself and don't notice the pilot of the ship screaming "Help; I've fallen down and I can't get up."

One twin accelerates and creates a seperation of the twins. That twin accelerates again to bring them back together. That the other twin doesn’t accelerate doesn’t that mean that it’s stationary.
It DOES, however, mean that the other twin is in the one inertial frame the whole time. There's no symmetry between the twins. The one who uses two different inertial frames ends up with the longer path in the spacetime metric ds^2 = dx^2 - dt^2, as measured by ANY inertial observer.

A third person observer that was some distance from the twins would simply see them separate and come back together again and wouldn’t know whether one or both had accelerated and both twins would appear to turn around. I can’t see any immediate significance in the “turn around” but I’m tired and have a headache so will give it more thought at a later time.
Of course the third observer will tell which one turns around. That's just silly!

Cheers -- sylas
 
  • #23
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The acceleration is very important as previously stated. It is the acceleration that breaks the symmetry in the situation. Say you were accelerating away from someone else. To an observer, the relative motion is the same from either perspective, but from your perspective you can feel acceleration and from theirs, they can't feel acceleration. As acceleration is the only difference, it is the acceleration that introduces time-dilation effects (otherwise yes, the symmetry of the situations would mean that there was no way of telling which entity should undergo time dilation wrt the other)
 
  • #24
sylas
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The acceleration is very important as previously stated. It is the acceleration that breaks the symmetry in the situation. Say you were accelerating away from someone else. To an observer, the relative motion is the same from either perspective, but from your perspective you can feel acceleration and from theirs, they can't feel acceleration. As acceleration is the only difference, it is the acceleration that introduces time-dilation effects (otherwise yes, the symmetry of the situations would mean that there was no way of telling which entity should undergo time dilation wrt the other)
Actually, the acceleration is useful as a convenient way to tell that you have shifted inertial frames.

It's not correct to say that acceleration "causes" time dilation. What causes time dilation, in special relativity, is the path through space time; ALL of it.

To see this, consider this thought experiment. You travel to another star. Along your journey, you accelerate four times. Once, up to 60% of the speed of light. Another time, up to 80% of the speed of light. Then again, to -60% of the speed of light (turn around). Then again, back to zero as you stop.

Does it make any difference WHEN you do these accelerations? Yes it does; and your eventual age at the end of the trip is calculated by integrating of proper time along the three intervals of constant velocity. The duration of each segment depends on when you do the accelerations. The calculation never even considers acceleration; it's enough to know the distances and velocities of the segments between accelerations.

Acceleration is one way to tell you are not inertial.

There are other ways to tell. Suppose you use a laser range finder, to keep track of how far away the other twin is. You send a message by laser to the other twin, containing your local time. The message is reflected, and when it gets back, you can tell how long the round trip of the laser light took. That lets you calculate how far away the twin WAS at the time of the reflection. Some time I may write all this up, but using laser range finding shows up clearly the asymmetry of the two twins, and the effects of a change in frame.

For the traveling twin... the one who exists in two different inertial frames, the data from their laser range finder will indicate that the stay-at-home twin is actually motionless, but blueshifted as if at the top of a large gravitational field, for most of the duration of the trip!

Such observations are sufficient to infer the change in inertial frame, even if you slept through the short acceleration at turn around without noticing. The ship-bound twin can also notice a sudden change in the apparent size of the stay-at-home twin. They suddenly shrink in size in the sky, at the time they go to blueshifted, as if suddenly transported far far away. But the laser range finder disagrees, and indicates that they merely stopped.

None of these things are seen by the stay-at-home twin.

The key, in all of this, is not acceleration per se, but being in a different inertial frame.

Cheers -- sylas
 
  • #25
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.Of course the third observer will tell which one turns around. That's just silly!
You are in total darkness. A great distance away there are two lights that are together and you are only able to see them as a single light dot. The lights move apart to the degree that you are able to see there are two and that they have moved apart. The lights move together again. The only things you are every able to see are the small light dots. Because of the distance and total lack of any other positioning reference you won’t be able to tell whether one or both of the lights underwent acceleration to create the away and back movements. You will only be able to tell that two dots of light have moved apart and back together.
 

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