How are the twins distinguished?

[narps]

If it is impossible to distinguish rest from motion, how is it that one of the twins' clock is slower than the other twins'? Shouldn't each twin appear to be the one moving with respect to the other, so both of their clocks run slow compared to the other's (even though this is impossible)? How do you get around this?

 

[novop]

One of them undergoes acceleration, one doesn't.

 

[phyzguy]

Here's a nice animation that shows how the apparent paradox is resolved:

http://math.ucr.edu/~jdp/Relativity/TwinParadox.html

 

[LBrandt]

I understand that one of them undergoes acceleration and the other doesn't, but what I've never been able to understand is this: Once the accelerating twin has stopped accelerating and is moving at uniform velocity relative to the other twin, why does time dilation CONTINUE to operate while he is at uniform velocity relative to the stay-at-home-twin? I've read what I consider to be conflicting answers to the twin paradox. In some of them, I'm told that time dilation operates BECAUSE of the acceleration, and in others, I'm told that time dilation operates even at uniform velocity. I thought that special relativity states that there is no preferred frame of reference for objects moving at uniform velocity relative to each other.

 

[Fredrik]

If it is impossible to distinguish rest from motion, how is it that one of the twins' clock is slower than the other twins'? Shouldn't each twin appear to be the one moving with respect to the other, so both of their clocks run slow compared to the other's (even though this is impossible)?

It isn't impossible, and is in fact what happens. The claim that clock B "runs slow" relative clock A really means that in the coordinate system that we associate with the motion of clock A, clock B isn't keeping up with the time coordinates. (Swap A and B, and that sentence is still true). Note that this means that the two "obviously" contradictory statements are actually statements about two different coordinate systems, so it's certainly not obvious that they contradict each other. A closer inspection reveals that they don't.

I understand that one of them undergoes acceleration and the other doesn't, but what I've never been able to understand is this: Once the accelerating twin has stopped accelerating and is moving at uniform velocity relative to the other twin, why does time dilation CONTINUE to operate while he is at uniform velocity relative to the stay-at-home-twin? I've read what I consider to be conflicting answers to the twin paradox. In some of them, I'm told that time dilation operates BECAUSE of the acceleration, and in others, I'm told that time dilation operates even at uniform velocity. I thought that special relativity states that there is no preferred frame of reference for objects moving at uniform velocity relative to each other.

Time dilation doesn't "continue to operate" after he has landed on Earth, because now their aging rates are the same. He is younger because he took a path through spacetime that had a shorter proper time. The ticking rate of a moving clock in an inertial coordinate system depends only on its velocity, not on its acceleration. Note that the fact that one of the twins is accelerating means that we can't associate an inertial coordinate system with his motion.

By the way, there's a ridiculous number of threads about the twin paradox already. This is one of them.

 

[jcsd]

I understand that one of them undergoes acceleration and the other doesn't, but what I've never been able to understand is this: Once the accelerating twin has stopped accelerating and is moving at uniform velocity relative to the other twin, why does time dilation CONTINUE to operate while he is at uniform velocity relative to the stay-at-home-twin? I've read what I consider to be conflicting answers to the twin paradox. In some of them, I'm told that time dilation operates BECAUSE of the acceleration, and in others, I'm told that time dilation operates even at uniform velocity. I thought that special relativity states that there is no preferred frame of reference for objects moving at uniform velocity relative to each other.

When the twins are both in uniform motion, the time dialtion is symmetric i.e. both twins perceive the other's clock to be ticking at the same slower rate. I.e. if you were to ask either twin who's clock is running slower they would both say the other.

To work out the time elapsed between the spacebound twin leaving and returning you must consider the motion as a whole, you cannot ignore the acceleration even if it is instantaneous (instantaneous acceleration is unphysical, but including it in the twin paradox doesn't qualitively affect the result). The acceleration breaks the symmetry between the twins. The spacebound twin undergoes acceleration they would calulate this effect as the other twin's clock speeding up in the time it took them (the spacebound twin) to accelerate, if the acceleration was instantaneous they would calculate that the other twins clock had jumped forward instantaneously.

 

[MikeLizzi]

When the twins are both in uniform motion, the time dialtion is symmetric i.e. both twins perceive the other's clock to be ticking at the same slower rate. I.e. if you were to ask either twin who's clock is running slower they would both say the other.

To work out the time elapsed between the spacebound twin leaving and returning you must consider the motion as a whole, you cannot ignore the acceleration even if it is instantaneous (instantaneous acceleration is unphysical, but including it in the twin paradox doesn't qualitively affect the result). The acceleration breaks the symmetry between the twins. The spacebound twin undergoes acceleration they would calulate this effect as the other twin's clock speeding up in the time it took them (the spacebound twin) to accelerate, if the acceleration was instantaneous they would calculate that the other twins clock had jumped forward instantaneously.

Excellent response. There are mebers of this forum who insist that an explanation can be constructed without considering acceleration. I am not one of them.

 

[yuiop]

Excellent response. There are mebers of this forum who insist that an explanation can be constructed without considering acceleration. I am not one of them.

There are a number of philosophical problems with acceleration explanation.

Problem 1: The "Hidden variable" problem.

The amount the stay Earth twins' clock leaps forward during the turn around acceleration of the traveling twin is proportional to the acceleration and the distance of the turn around point from the Earth. If the relative change in the clock rates is a function of the distance between the clocks then the clocks must somehow be keeping track of how far they are apart in some "hidden" variable.

Problem 2: The superluminal signalling problem.

Let us say the traveling twin is 8 light years from Earth when he turns around. At the instant the traveling twin turns around, the Earth twins clock leaps forward, but it would take 8 years for the information to reach the Earth and let it know the it is time to leap forward. Spooky action at a distance or non locality as Einstein would say.

Problem 3: The duality problem.

Let us say we triplets. One stays on Earth and the other two head off in the same direction. After 10 years one of the traveling triplets get home sick and turns around but the other traveling triplet is more adventurous and continues on with constant velocity. Now the Earth clock has to "leap forward" relative to the clock of the triplet that turns around, but not leap forward relative to the triplet that continues. Obviously the Earth clock can not physically leap forward and not leap forward at the same time so any physical changes must happen with the triplets clocks as they undergo acceleration. Now if the jump in time happens with the triplets clock during the acceleration, it would have to leap backwards, (i.e time reversal). Does rapid acceleration really cause time to go backwards?

Problem 4: The non self synchronization problem.

When a set of mutually at rest clocks with inertial motion accelerate to change velocity and return to inertial motion again, the clocks are no longer synchronised. They have to be manually resynchronised using the Einstein clock synchronisation procedure. If we had a very long ship, say 10 light years long proper length, such that when the nose was at the turn around point, the tail was level with the Earth, then when the nose turns around it would take over 10 years to resynchronise the clocks manually using the Einstein method by sending light signals back and forth. The "instant leap forward" of the Earth clock is an artifact of the manual synchronisation of the traveling clocks when changing inertial reference frames.

Problem 5: The equal acceleration, unequal time dilation problem.

It can and has been shown that two rockets starting at the same point and undergoing exactly the same acceleration patterns can end up with different elapsed proper times when they return to the same location.

Problem 6: The experimental evidence problem.

Real life experiments with muons in synchrotron storage rings have shown that the time dilation is exactly what would you would expect from the tangential velocity of the muons, despite the fact they are subjected to centripetal forces of 1000g or more. Now while you could ignore the velocity of the muons and consider all the time dilation of the muons to be due to the acceleration they experience, this contradicts the acceleration explanation of the twins paradox, because in the paradox, both velocity related time dilation and pseudo gravitational time dilation are taken into account. On the outward journey the Earth clock is ticking slower according to the traveling twin due to velocity time dilation, but during the turn around the time lost by the Earth clock is regained with interest when the Earth clock speeds up significantly during the turn around.

Problem 7: The feasibility problem.

The acceleration explanation is equivalent to a gravitational field instantaneously appearing and accelerating the Earth and the entire universe at the instant the twin applies thrust to turn around. Now while it is not possible to prove that this does no actually occur, it is highly unlikely that this is what actually happens as a physical explanation.


Hmmm.. I'm sure there are some more counter arguments.

 

[jcsd]

Hello Kev, did you notice in my post I used the word 'calculate', rather than observe. The distinction is important. Clocks jumping forward etc, are all just conceits of allowing the spacebound twin a spatially extended frame of reference.

Some of your objections are, sorry, a little bizarre. How does the clock know how to jump forward? The same way the moon knows to orbit my head when I spin it (my head) around.

 

[yuiop]

Hello Kev, did you notice in my post I used the word 'calculate', rather than observe. The distinction is important. Clocks jumping forward etc, are all just conceits of allowing the spacebound twin a spatially extended frame of reference.

Some of your objections are, sorry, a little bizarre.

I was just making clear that distinction, in a slightly tongue in cheek way. It was meant to demonstrate just how "bizarre" it would be if anyone actually believed acceleration caused clocks to jump forward, and because acceleration is the not physical cause of differential ageing of the twins, saying the twins paradox is explained by acceleration is slightly misleading.

Allowing the spacebound twin with varying acceleration, a spatially extended frame of reference, is problematic and poorly defined, as discussed in these recent threads:

https://www.physicsforums.com/showthread.php?t=422350

https://www.physicsforums.com/showthread.php?t=420634

One of the problems is that if you extend the frame of reference of the accelerating twin in both directions, then points further away from the Earth go backwards in time. You also construct acceleration patterns where of the twin, where events on the Earth do not have a unique one to one relationship with events in the accelerating twins frame leading to ambiguities and contradictions, which makes spatially separated events, distances and velocities in an accelerating frame poorly defined, especially when the rate of acceleration is varying.

Despite the tongue in cheek nature of my last post, there are some serious points in there worth considering

 

[jcsd]

Hi Kev,

I thinm you're tongue was a bit too far in your cheek

I think the correct phrase for the naive accelerated frame a 'bad' coordinate system. I.e. one in which points are mapped to multiple coordinates.

You don't need to construct a spatially extended frame of reference to resolve the 'paradox'. It's just when you do don't expect everything in your spatially extended frame of reference to be sensible. However acceleration is still the obvious cause of the assymetry between the twins.

 

[starthaus]

because acceleration is the not physical cause of differential ageing of the twins,

You sure about this? Because correct calculations show exactly the opposite, the difference in elapsed proper time is a function of acceleration. This is true whether you make the calculations from the perspective of the inertial twin or the accelerated twin.

 

[jcsd]

You sure about this? Because correct calculations show exactly the opposite, the difference in elapsed proper time is a function of acceleration. This is true whether you make the calculations from the perspective of the inertial twin or the accelerated twin.

Whether he's sure or not he's wrong.

The acceleration introduces the assymetry which is evident in the proper times experinced by both twins from the 'setting off' and 'returning home' events.

The difference in elapsed proper time is a function of the twins' journeys considered as a whole, you can't ignore any part or non-trivial aspect (e.g. acceleration) of their journeys.

 

[starthaus]

Whether he's sure or not he's wrong.

The acceleration introduces the assymetry which is evident in the proper times experinced by both twins from the 'setting off' and 'returning home' events.

The difference in elapsed proper time is a function of the twins' journeys considered as a whole, you can't ignore any part or non-trivial aspect (e.g. acceleration) of their journeys.

I agree with you on all accounts.

 

[MikeLizzi]

I was just making clear that distinction, in a slightly tongue in cheek way. It was meant to demonstrate just how "bizarre" it would be if anyone actually believed acceleration caused clocks to jump forward, and because acceleration is the not physical cause of differential ageing of the twins, saying the twins paradox is explained by acceleration is slightly misleading.


Despite the tongue in cheek nature of my last post, there are some serious points in there worth considering

Very serious indeed. And very sad that a person who obviously knows the details of SR can't put them together.

Analyzing the differential aging of the twins from the point of view of the astronaut, without taking acceleration into account will give you the paradox, the thing you are trying to resolve. Throwing in a clock jump for the Earth twin’s clock will resolve that paradox.

But clocks don’t jump. Both space and time are continuums in Relativistic Physics (and Newtonian Physics too). You know that. When you add in the clock jump for the Earth twin what you are really doing is approximating the aging differences that happen during the astronaut’s period of acceleration.

So, if you are in the habit of adding in a clock jump in your calculations to resolve the Twins Paradox, you are taking acceleration into account, whether you realize it or not.

 

[yuiop]

You sure about this? Because correct calculations show exactly the opposite, the difference in elapsed proper time is a function of acceleration. This is true whether you make the calculations from the perspective of the inertial twin or the accelerated twin.

The differential ageing is a function of acceleration and distance apart at the time of the acceleration. We could informally say that in the classic twins paradox setup, that the twin that experiences proper acceleration is the one that ages the least, but this could be confusing to beginners because we can set up a scenario where both twins experience the same proper acceleration yet they age differently. See this diagram by DrGreg:

It is clear from the diagram that both twins experience equal proper acceleration in the depicted scenario. The differential ageing comes about because they accelerated at different times and places. I.e. it is better to say that the differential ageing is due to different paths through spacetime.

Whether he's sure or not he's wrong.

The acceleration introduces the asymmetry which is evident in the proper times experienced by both twins from the 'setting off' and 'returning home' events.

Sure the acceleration introduces the asymmetry, but the differential ageing is still only a function of the instantaneous velocity. This is a quote from the Physicforums FAQ:

The clock hypothesis states that the tick rate of a clock when measured in an inertial frame depends only upon its velocity relative to that frame, and is independent of its acceleration or higher derivatives. The experiment of Bailey et al. referenced above stored muons in a magnetic storage ring and measured their lifetime. While being stored in the ring they were subject to a proper acceleration of approximately 1,000,000,000,000,000,000 g (1 g = 9.8 m/s2). The observed agreement between the lifetime of the stored muons with that of muons with the same energy moving inertially confirms the clock hypothesis for accelerations of that magnitude.
--------------------------------------------------------------------------------------
Sherwin, “Some Recent Experimental Tests of the 'Clock Paradox'”, Phys. Rev. 129 no. 1 (1960), pg 17.
--------------------------------------------------------------------------------------
He discusses some Mössbauer experiments that show that the rate of a clock is independent of acceleration (~10,000,000,000,000,000 g) and depends only upon velocity.

The difference in elapsed proper time is a function of the twins' journeys considered as a whole, you can't ignore any part or non-trivial aspect (e.g. acceleration) of their journeys.

In another thread, I have analysed the exact differential ageing of the twins experiment including the time dilation that happens during the acceleration in a non-zero time interval to within a second in an experiment lasting years. I have not ignored the acceleration and calculated the contribution exactly, and it can be shown that that if the acceleration phase is limited to seconds in an experiment lasting years, the maximum error that can be introduced by ignoring the acceleration is of the order of seconds, while the differential ageing due to different spacetime paths is of the order of years. See #24 of this thread: https://www.physicsforums.com/showthread.php?t=422350&page=2

While you might understand the limitations of saying the twins paradox is explained by acceleration, it is confusing to beginners, because as it says in the PF FAQ, the clock hypothesis states that "the tick rate of a clock when measured in an inertial frame... is independent of its acceleration"

 

[Fredrik]

This is funny. I was just about to post the reply you can see below when I saw kev's post. I even thought I had discovered a new trick by img-tagging a previously uploaded image, but apparently kev already knew that trick. I was somewhat confused when I previewed and saw the image twice.

__________________

I agree with kev about the specific statement "acceleration is not the physical cause of differential ageing of the twins". It would be silly to say that it is the cause, since they can accelerate the same and have different ages at the end:

<the exact same image that kev just linked to>

This scenario was described by Kev in a post he made in 2008, which inspired DrGreg to draw this diagram.

 

[yuiop]

But clocks don’t jump. Both space and time are continuums in Relativistic Physics (and Newtonian Physics too). You know that. When you add in the clock jump for the Earth twin what you are really doing is approximating the aging differences that happen during the astronaut’s period of acceleration.

So, if you are in the habit of adding in a clock jump in your calculations to resolve the Twins Paradox, you are taking acceleration into account, whether you realize it or not.

I understand the rational behind the "clock jumping" method and I understand the equivalence and that you can obtain correct numerical results by using this method, but physically it is unsatisfactory as an "explanation" of the twins paradox and as I said before it can also predict that events on the other side of the twin jump backwards in time, which does not actually happen and can be confusing for beginners. When you add in a clock jump to resolve the twins paradox, you are taking acceleration into account, but you you should make it clear that you are also taking spatial separation into account to.

 

[jcsd]

I think it's a semantical disagreement, certainly kev what you've said is correct, on the other hand I would say the two observers (in your diagram) don't have the same pattern of acceleration which is the assymetry between them. This again though more a point of semantics.

 

[starthaus]

The differential ageing is a function of acceleration and distance apart at the time of the acceleration.

So, you no longer deny that the time differential is a function of acceleration? This is good.

While you might understand the limitations of saying the twins paradox is explained by acceleration, it is confusing to beginners,

We are not talking about beginners, we are talking about basic misconceptions that need to be cleared.

 

[Fredrik]

So, you no longer deny that the time differential is a function of acceleration? This is good.

I'm pretty sure that he has never denied that at least one of them must accelerate.

Are you saying that the time differential is a function of acceleration? This would be very misleading, in my opinion.

 

[Fredrik]

I think it's a semantical disagreement, certainly kev what you've said is correct, on the other hand I would say the two observers (in your diagram) don't have the same pattern of acceleration which is the assymetry between them. This again though more a point of semantics.

I agree that it is an issue of semantics, but note that the red parts of the left curve are identical to the red parts of the right curve. The only difference between the two curves is the times at which they initiate their scheduled velocity changes. (It's "the only difference" in the sense that if those times had been the same, the curves would have been identical). This causes them to spend different amounts of time at the two different constant speeds, and this alone accounts for the age difference.

 

[starthaus]

Are you saying that the time differential is a function of acceleration? This would be very misleading, in my opinion.

But it is true. As a mathematician, I am sure that you would appreciate the fact.

 

[jcsd]

I agree that it is an issue of semantics, but note that the red parts of the left curve are identical to the red parts of the right curve. The only difference between the two curves is the times at which they initiate their scheduled velocity changes. (This causes them to spend different amounts of time at the two different constant speeds, and this alone accounts for the age difference).

Yep, but I would still say they don't have the same pattern of acceleration as the amount of proper time they spend at zero acceleration for each period of zero acceleration is not the same. But as we both agree it's semantics, entirely dependent on the way I've choosen to define the concept of 'pattern of acceleration'.

 

[starthaus]

In another thread, I have analysed the exact differential ageing of the twins experiment including the time dilation that happens during the acceleration in a non-zero time interval to within a second in an experiment lasting years. I have not ignored the acceleration and calculated the contribution exactly, and it can be shown that that if the acceleration phase is limited to seconds in an experiment lasting years, the maximum error that can be introduced by ignoring the acceleration is of the order of seconds, while the differential ageing due to different spacetime paths is of the order of years. See #24 of this thread: https://www.physicsforums.com/showthread.php?t=422350&page=2

True, yet if the acceleration period is not neglible wrt the cruising period, you would get huge errors from your method. I included the exact formulas in order to prove that, see here. Note that, contrary to your beliefs, acceleration plays a key role in both the speed up/down time and (surprisingly) in the cruising time.

 

[Austin0]

The differential ageing is a function of acceleration and distance apart at the time of the acceleration. We could informally say that in the classic twins paradox setup, that the twin that experiences proper acceleration is the one that ages the least, but this could be confusing to beginners because we can set up a scenario where both twins experience the same proper acceleration yet they age differently.

It is clear from the diagram that both twins experience equal proper acceleration in the depicted scenario. The differential ageing comes about because they accelerated at different times and places. I.e. it is better to say that the differential ageing is due to different paths through spacetime.

Sure the acceleration introduces the asymmetr

While you might understand the limitations of saying the twins paradox is explained by acceleration, it is confusing to beginners, because as it says in the PF FAQ, the clock hypothesis states that "the tick rate of a clock when measured in an inertial frame... is independent of its acceleration"

I think a lot of the confusion stems from the convention of considering frames at rest.
In the end I think Fredriks approach is the most applicable.
If we just forget acceleration, simultaneity and relative velocity, you can consider the Earth or any other point traveling at any velocity whatever and then the simple logic and geometry makes it an absolute certainty that traveling to any other point and then returning must inevitably cover more spacetime.
Whatever spacetime traveled by the initial point, in whatever directionm, the second system has to have traveled that same spacetime distance to catch up, plus the distance to get to the turnaround point.
Self evidently, this in all cases must include acceleration phases, but they have no direct effect other than changing direction and faciilitating the return.
Without the return, even with acceleration , with two systems in space with no other referent , there is no basis to calculate or determine relative time.
It seems to me that as soon as you hypothetically add a spatial reference point , whichever frame you use to place that point becomes it and is destined to live faster and die earlier.
Maybe?

 

[Fredrik]

But it is true.

We could define an age difference function as a function that takes two timelike curves with the same endpoints to a real number. If we specify both twins' accelerations at all proper times, and also specify that their world lines must have the same endpoints, we can determine their world lines from that. So the claim is true in that sense, but I don't think many people who hear the exact words "the time differential is a function of acceleration" would think of all that. When I hear the word "acceleration", I think of a number, or a vector, so I think your choice of words suggests a function that takes a number or a vector to a real number. That's why I think it's misleading.

 

[Mentz114]

Yep, but I would still say they don't have the same pattern of acceleration as the amount of proper time they spend at zero acceleration for each period of zero acceleration is not the same. But as we both agree it's semantics, entirely dependent on the way I've choosen to define the concept of 'pattern of acceleration'.

Isn't what you're talking about here just the proper interval. The Lorentzian length of a curve whose 'shape' takes into account all the periods of acceleration/deceleration/coasting etc. ? All these things contribute to changes in the interval so arguing that anyone of them is a fundamental cause is a waste of time.

 

[jcsd]

Isn't what you're talking about here just the proper interval. The Lorentzian length of a curve whose 'shape' takes into account all the periods of acceleration/deceleration/coasting etc. ? All these things contribute to changes in the interval so arguing that anyone of them is a fundamental cause is a waste of time.

I'm not arguing about the 'fundamental cause', like I said it's purely a matter of semantics.

What we're actually doing is comparing two curves, comapring their patterns of acceleration is one way to compare them.

 

[starthaus]

We could define an age difference function as a function that takes two timelike curves with the same endpoints to a real number. If we specify both twins' accelerations at all proper times, and also specify that their world lines must have the same endpoints, we can determine their world lines from that. So the claim is true in that sense,

This is precisely how the twins time differential is calculated..

but I don't think many people who hear the exact words "the time differential is a function of acceleration" would think of all that.

This is why the language of physics is math, because it is non-ambigous. I am quite sure that you, being a mathematician, appreciates this.