How does the Twins Paradox challenge our understanding of ageing?

[matheinste]

Each twin's age and clock readings reflect actual time elapsed. The reason for the difference is that the actual time elapsed is different.

Acceleration affects the spacetime paths, which affects the proper time elapsed. The only reason SR predicts different clock readings for the twins is because it assumes that each clock accurately records the elapsed time for each twin.

The above really says it all.

When talking of timelike intervals, which are the only type which can be traversed by a clock, the time recorded by an ideal clock while traversing this interval is said to be proper time whatever its motion or path through that interval. It is a measure of spacetime path length.

In a frame in which it is at rest the proper time recorded by the clock is the same as the coordinate time, that is the projection of the interval onto the time axis of that frame.

Since the coordinates in any inertial frame can be Lorentz transformed into coordinates in any other relatively moving inertial frame, the coordinates of a clock in any infinitessimal region of its travels can be transformed into those of a frame at which it as at rest in that infinitessimal region.

Since all inertial frames are equivalent in SR, each infinitessimal amount of coordinate time, which in each comoving rest frame is equal to proper time, can be summed, and, in the limit, as these infinitessimal regions are allowed to become smaller and smalle, so apprroaching zero, integrated over the path (timelike) of the clock to give the exact proper time, as a sum of coordinate times, for this path.

So there is nothing in this derivation of proper time which gives any clock any preference over any other clock as all proper times can be made equivalent to the sum of coordinate times of a clock in frames in which it is at rest.

In other words the time recorded by a clock can be viewed as the sum of coordinate times in inertial frames in which it is (for an infinitessimally small region) at rest, and since the use of all inertial frames is equally valid, all times so recorded are equally valid or "correct". So for a clock, any clock, the time it records, proper time, is for that clock THE time.

Matheinste.

 

[Dale]

I don't think that this is nearly as complicated as many of the posters have made this out to be. The reason that light clocks exhibit time dilation is the second postulate. The reason that all other clocks exhibit the same time dilation is the first postulate.

There is no deeper reason than the postulates, they are fundamental. And the reason we accept the postulates is that they fit the data very well.

 

[matheinste]

I don't think that this is nearly as complicated as many of the posters have made this out to be. The reason that light clocks exhibit time dilation is the second postulate. The reason that all other clocks exhibit the same time dilation is the first postulate.

There is no deeper reason than the postulates, they are fundamental. And the reason we accept the postulates is that they fit the data very well.

What you say is true, but lots detailed explanation is often needed to explain something that may not be obvious to some. I have a little knowledge of SR now, but had I been given nothing more than the above in a textbook, although it is possible to derive all of SR from the postulates, I am one of the many who could not have done so without much help and detailed explanation.

Matheinste.

 

[edpell]

Each twin's age and clock readings reflect actual time elapsed. The reason for the difference is that the actual time elapsed is different.[/i]

I agree and add what makes this topic (movement at speeds comparable to c) counter-intuitive is that when you transform to any frame that is not your own local rest frame time and the spatial dimension (the one of three that is in the direction of travel) are not orthogonal any more.

 

[ThomasT]

Sure, but it's not like the traveler's clock counted 5 years while 20 years elapsed in that path. Only 5 years elapsed on that path.

Setting aside the spacetime interpretation for the moment, what's been altered is the traveller's clock and the traveller due to their accelerations. Nothing else in the scenario has been altered by their accelerations. The earth-sun system evolved 20 years, the earthbound twin aged 20 years and his clock ticked off 20 years, and every other observer inside or outside the solar system agrees that the trip took 20 years. The anomalies are the accelerated twin and his accelerated clock.

Each twin's age and clock readings reflect actual time elapsed. The reason for the difference is that the actual time elapsed is different.

I agree. The traveller's clock actually ticked off 5 years and the earthbound clock actually ticked off 20 years, and the traveller actually aged 5 years and the earthbound twin actually aged 20 years, and they and all other observers actually counted 20 years wrt the earth-sun system.

Acceleration affects the spacetime paths, which affects the proper time elapsed.

Yes, that's a valid statement. But to say something about the physical differences that are measured in the real world we can say: accelerations (velocity changes) change the periods of oscillators. Can't we?

Anyway, I think this is a better conceptual (as well as intuitive) path to follow toward a deeper physical understanding of differential aging than the spacetime geometry.

 

[Dale]

What you say is true, but lots detailed explanation is often needed to explain something that may not be obvious to some.

This is very true. But in this case the OP already understands how time dilation for a light clock follows from the 2nd postulate and just doesn't understand how we go from that to biological aging. And that is what follows directly from the 1st postulate.

 

[matheinste]

Yes, that's a valid statement. But to say something about the physical differences that are measured in the real world we can say: accelerations (velocity changes) change the periods of oscillators. Can't we?

Anyway, I think this is a better conceptual (as well as intuitive) path to follow toward a deeper physical understanding of differential aging than the spacetime geometry.

There's seems no point in repeating what others have said about acceleration not being the direct cause of differential ageing but it is worth pointing out that the invariance of the spacetime interval is fundamental to relativity.

Matheinste.

 

[matheinste]

This is very true. But in this case the OP already understands how time dilation for a light clock follows from the 2nd postulate and just doesn't understand how we go from that to biological aging. And that is what follows directly from the 1st postulate.

Point taken.

Matheinste.

 

[Al68]

Setting aside the spacetime interpretation for the moment, what's been altered is the traveller's clock and the traveller due to their accelerations. Nothing else in the scenario has been altered by their accelerations. The earth-sun system evolved 20 years, the earthbound twin aged 20 years and his clock ticked off 20 years, and every other observer inside or outside the solar system agrees that the trip took 20 years. The anomalies are the accelerated twin and his accelerated clock.

No they don't. They all agree that 20 years elapsed in Earth's path and 5 years elapsed in the ship's path.

I agree. The traveller's clock actually ticked off 5 years and the earthbound clock actually ticked off 20 years, and the traveller actually aged 5 years and the earthbound twin actually aged 20 years, and they and all other observers actually counted 20 years wrt the earth-sun system.

and they and all other observers actually counted 5 years elapsed wrt the ship's system. You only listed three of the four relevant facts.

Yes, that's a valid statement. But to say something about the physical differences that are measured in the real world we can say: accelerations (velocity changes) change the periods of oscillators. Can't we?

Not really, since the exact same change in the period of an oscillator is observed when the observer changes velocity instead of the oscillator. The change in the period of the oscillator occurs because of a change in relative velocity between oscillator and reference frame, whether or not the oscillator accelerates.

Anyway, I think this is a better conceptual (as well as intuitive) path to follow toward a deeper physical understanding of differential aging than the spacetime geometry.

It may be more intuitive, but it's conceptually wrong. Each twin ages 1 year per year of elapsed time. Again, it's time itself that "flows" differently in different frames, not a change in the operation of various devices used to measure it.

Conceptually, it's like saying that my bathroom scales read higher because I ate too much ice cream and cake last week. The scales read higher because I'm heavier, not because of any difference in the scales' operation. This is true of any measuring device: different results do not imply a difference in the measuring device itself.

 

[ThomasT]

No they don't. They all agree that 20 years elapsed in Earth's path and 5 years elapsed in the ship's path.

Sorry for the delay in replying.

We're setting aside the spacetime interpretation for the moment.

... and they and all other observers actually counted 5 years elapsed wrt the ship's system.

Right. The traveling clock actually recorded fewer ticks than the earthbound clock.

Not really, since the exact same change in the period of an oscillator is observed when the observer changes velocity instead of the oscillator.

No, the physical fact is that only one clock ran slow -- this is the point of including the visual tracking of the earth-sun system.

The change in the period of the oscillator occurs because of a change in relative velocity between oscillator and reference frame, whether or not the oscillator accelerates.

No, the change in the period of an oscillator is due to the acceleration of that oscillator. What you're saying applies to situations where we don't have sufficient info regarding the acceleration histories (or we simply disregard it) of the two clocks being compared. But in the usual earthbound-travelling twin scenario, we do.

 

[edpell]

The change in the period of the oscillator occurs because of a change in relative velocity between oscillator and reference frame, whether or not the oscillator accelerates.

We have to be careful on the word here. You can not get velocity without acceleration.

Is it the velocity that alters that state of the clock or is it the acceleration that alters the state of the clock? What experiment can we do to measure which is responsible? Two things happen and a third is found to be correlated. If you can never separate the two things how will you ever be able to call one the cause and the other not the cause?

 

[ThomasT]

It may be more intuitive, but it's conceptually wrong. Each twin ages 1 year per year of elapsed time. Again, it's time itself that "flows" differently in different frames, not a change in the operation of various devices used to measure it.

Time itself ... flows differently??

The traveller, and all other observers, watched the earth-sun system rotate 20 times during the trip. Yet the traveller and his clock only ticked off 5 years.

We agree that difference in tick rate is due to difference in velocity, don't we? It seems clear to me from experiments that it isn't intervals of constant, uniform velocity that exhibit tick rate changes, but intervals of acceleration.

... different results do not imply a difference in the measuring device itself.

In this case they do.

 

[croghan27]

We have to be careful on the word here. You can not get velocity without acceleration.

Is it the velocity that alters that state of the clock or is it the acceleration that alters the state of the clock? What experiment can we do to measure which is responsible? Two things happen and a third is found to be correlated. If you can never separate the two things how will you ever be able to call one the cause and the other not the cause?

This may have been gone over before ... but kindly humour me.

If there was a clock on the traveling ship and a similar clock at the stationary take off location - say they are old grandfather clocks .. with swinging pendulums as a driving force. (the sort of things that Galileo worked with). Let us suppose there is a way to track the swing of the pendulum in the ship, but at the point of origin.

Would the swing of the pendulum on the ship match that of the clock at the stationary place? OR If it moved one centimetre in its' swing would it take less time than for the stationary clock's pendulum to move the same distance?

I guess this is a classical physics question being applied to a quantum physics situation.

Oh - by the way: look for the Bengals to take less time to move the football over the Jets goal line and do it more often than the Jets can do the reverse this afternoon.

 

[edpell]

The traveller, and all other observers, watched the earth-sun system rotate 20 times during the trip. Yet the traveller and his clock only ticked off 5 years.

NO!

This case seems to have gamma of 4. So the traveler only saw 5 rotations of the Earth around the sun when he/she looked in their telescope. Due to the fact that the light from rotations 6-20 has not yet reached the traveler. The traveler will have to keep looking for another 15 years (after arrival) to see the light from rotations 6-20.

 

[Janus]

Time itself ... flows differently??

The traveller, and all other observers, watched the earth-sun system rotate 20 times during the trip. Yet the traveller and his clock only ticked off 5 years.

No, the traveler watched the Earth-Sun make .9 rotations during the trip. (Relativistic Doppler effect). From his reckoning, figuring in his relative velocity with respect to the Solar system, The Earth-Sun has made 0.635 rotations. He now stops at the destination (assume a short enough time of deceleration that he is, in all intents and purposes, stops dead. He is seeing the same light as he was before he decelerated, but his reckoning of how much time has passed on Earth changes. He is now 19.365 ly from Earth, which means that the information is 19.365 years old. Therefore, by his reckoning the Earth has aged 20 yrs since he left.

We agree that difference in tick rate is due to difference in velocity, don't we? It seems clear to me from experiments that it isn't intervals of constant, uniform velocity that exhibit tick rate changes, but intervals of acceleration.

Let's try to explain this by way of analogy:

You have two men(A&B) walking in the Same direction at the same speed on a featureless plain.
If you consider the direction they are walking as "time", this represents our twins At the starting point, at rest we each other. They each progress through time at the same rate and age at the same rate.

Now one man(B) turns and starts to walk in a new direction. As each walks in his own direction, they get further apart, or as each progresses through time, the distance increases between them. This represents one of the twins while traveling away from his other twin.

Now consider the perspective of man A. As he walks, B falls further behind with respect to the direction that A is walking. This represents B progressing through time more slowly or aging less than A.

But now consider man B. By his perspective, it is A that it falling behind. and he is just as entitled to claim that the direction that he is walking is the direction of time progression, and that it is A that is making slower progress/aging slower. This is the whole point behind the principle of Relativity. Each inertial frame judges other with respect to itself and there is no absolute reference. Each judges time progression as progress in the direction he is walking.

Now consider what happens when Man B turns to walk in the same direction as A again. This represents the traveling twin reaching his destination and stopping. The distance between them no longer changes, and they are again "at rest" with respect to each other.

From A's perspective, this just means that B stops losing ground, and starts to age at the same rate. He doesn't make up lost ground, however, and his total progression through time remains less. He remains younger.

From B's perspective, as he turns, A's position with respect to Him changes. He goes from being behind to being in front. (Stand in the middle of the room with an object to one side and slightly behind you. Now turn 45° in that direction. The object, from your perspective moves from behind you to in front of you.)

After B completes his turn, He finds that A is now ahead of him in time, and progressing at the same speed. His has made more progression through time. His has aged more and is older.

Both men agree in the final result, but have different views of how that result came to be. And this is the important part: Each man's view of what happened is just as valid at the others.

So when you ask what causes one twin to be older than the other at the end of the trip, the answer is: It depends on which twin you are.

Relativity makes us rethink how we measure time. To use the direction analogy again: Before Relativity, we could think of time as the direction North. No matter who you asked and what relative directions they where facing, they all agreed on what direction North was. Ask them to point North, and they all point the same direction. It is, in a sense an absolute direction.

Relativity tells us however that time is like the the direction Left. Ask a number of people to point left, and they will all point in different directions depending on the relative directions they are facing. There is no absolute "left". Left is determined by the individual and moves with him. And in Relativity, time measurement is determined by what frame you measure it from.

 

[vela]

NO!

This case seems to have gamma of 4. So the traveler only saw 5 rotations of the Earth around the sun when he/she looked in their telescope. Due to the fact that the light from rotations 6-20 has not yet reached the traveler. The traveler will have to keep looking for another 15 years (after arrival) to see the light from rotations 6-20.

The difference in time between the two frame has nothing to do with the light travel time. SR says that even after you take into account those effects, the time elapsed between two events is different in the two frames. Also, in the twin paradox problem, the traveller's twin aged twenty years, so the traveller would see the Earth going around the Sun twenty times during the trip. You're thinking of a different situation.

Wikipedia has a good explanation of the twin paradox from the traveling twin's point of view.

http://en.wikipedia.org/wiki/Twin_paradox#Resolution_of_the_paradox_in_special_relativity

 

[Dale]

the physical fact is that only one clock ran slow

If two surveyors were to measure the distance along routes from New York to Miami, and one surveyor's route went through Washington DC and the other surveyor's route went through Los Angeles, would you say "the physical fact is that only one surveyor's chain was shrunk" or would you say "the physical fact is that only one surveyor's route was longer"? In other words, would you attribute the difference in measurement to a difference in the thing being measured or to a difference in the thing doing the measuring?

 

[Dale]

We have to be careful on the word here. You can not get velocity without acceleration.

Is it the velocity that alters that state of the clock or is it the acceleration that alters the state of the clock? What experiment can we do to measure which is responsible? Two things happen and a third is found to be correlated. If you can never separate the two things how will you ever be able to call one the cause and the other not the cause?

Actually, it is neither velocity nor acceleration (both vector quantities), it is speed (a scalar quantity). Although you cannot have acceleration without a change in velocity you can have acceleration without a change in speed. This experiment has been done with accelerations on the order of 10¹⁸ g, and the results are that the time dilation is not a function of the acceleration.

 

[GRDixon]

Hi, I'm a Biology teacher, constantly getting into discussions with the physics teachers at my school regarding the effect of traveling at speed on ageing.

This isn't exactly chemistry, but the following fact may provide insight. Consider a macroscopic "Bohr Atom," consisting of a resting, massive, positively charged central body orbited at constant speed in a circle by an equal magnitude negatively charged particle. For a given satellite speed, mass and orbital radius, one can readily calculate what the common magnitude charge must be. This system can be viewed from an alternate inertial frame, relative to which the central body moves with a constant velocity. When the electron's motion is computed relative to this second frame (using the laws of Maxwell, Lorentz and Newton) then the motion is a quasi-cycloid that cuts "above" and "below" the central body at distance R, but "in front of" and "behind" the central body at distance R/gamma. The computed motion also gives the result that the cycloid cycle time is (T)(gamma), where T=(2)(pi)(r)/(v). The interesting thing is that this is true no matter what inertial frame we initially assume the "atom" to be "at rest" in. Indeed, thanks to the way the clocks in the inertial frames are synchronized, each frame measures a moving "atom" to be length contracted. etc.! A more detailed account can be viewed at www.maxwellsociety.net/LovingLorentz.html[/URL]

 

[Evolver]

Because one of them accelerated and the other didn't. That breaks the symmetry of relativity.

But doesn't that defeat the point of relativity? When you say one twin accelerated away, that's only relative to the other twin... but the exact opposite is true if you take the relative experience of the second twin. Relatively speaking, it's always the other twin that accelerated away.

 

[jtbell]

Accdeleration is not relative. One twin feels a kick in the seat of his pants as his spaceship engines fire, the other twin does not. The first twin knows, without having to look outside his spaceship at all, that he is not at rest (or moving at constant velocity) in an inertial reference frame.

 

[Evolver]

Accdeleration is not relative. One twin feels a kick in the seat of his pants as his spaceship engines fire, the other twin does not. The first twin knows, without having to look outside his spaceship at all, that he is not at rest (or moving at constant velocity) in an inertial reference frame.

To say acceleration is not relative means you have already decided that one frame of reference is more absolute than the other. Though one twin experiences the other twin AND the universe accelerating away from him (hence the kick in the pants), while the other twin only experiences the first twin accelerating away... both experience the opposite twin accelerating away from them.

Also, being at rest is completely relative as well. Would you consider yourself at rest when typing your response to this on your computer? Because in reality you are rocketing through space on the Earth, and the Earth is swirling about the Milky Way, and who knows what else motions the entire universe is actually performing. But, in your current reference frame you are at rest... Everything is relative.

 

[Dale]

Hi Evolver, did you miss this part of jtbell's response:

One twin feels a kick in the seat of his pants as his spaceship engines fire, the other twin does not. The first twin knows, without having to look outside his spaceship at all

Nothing has to be decided in advance or with reference to the rest of the universe. An onboard accelerometer will suffice.

 

[Evolver]

Hi Evolver, did you miss this part of jtbell's response:

Nothing has to be decided in advance or with reference to the rest of the universe. An onboard accelerometer will suffice.

I did not miss it, in fact I commented on it directly (please read above.) "The kick in the pants" you refer to is only unique to twin #1 because the entire universe around him is accelerating away from him (including twin #2). That is the only unique difference between twin #1 and twin #2, and that is what the on board meters are registering. Twin #2, nonetheless, still experiences twin #1 accelerating away from him... if this were not true twin #1 would never leave twin #2's reference frame.

 

[Mentz114]

I did not miss it, in fact I commented on it directly (please read above.) "The kick in the pants" you refer to is only unique to twin #1 because the entire universe around him is accelerating away from him (including twin #2). That is the only unique difference between twin #1 and twin #2, and that is what the on board meters are registering. Twin #2, nonetheless, still experiences twin #1 accelerating away from him... if this were not true twin #1 would never leave twin #2's reference frame.

That's a lot of rot. It's been explained to you that only one twin in this scenario accelerates so it is not symmetrical as you insist.

JTBell and DaleSpam are far too polite to tell you - but you're being really stupid and arrogant.

 

[Evolver]

That's a lot of rot. It's been explained to you that only one twin in this scenario accelerates so it is not symmetrical as you insist.

JTBell and DaleSpam are far too polite to tell you - but you're being really stupid and arrogant.

Actually this is a forum for discussion, so if you want to resort to name calling instead of discussing, perhaps this is not the place for you.

And as I have stated above, these are my ideas of the scenario... it is called the twin paradox for just that reason, it is a paradox... there is no cut and dry answer. So please stop assuming you have it. If anyone is being arrogant here it is you. There are multiple arguments for this paradox... for example Max von Laue argued that one twin was using two inertial frames and that switching inertial frames caused the difference, not acceleration at all. That is one of many many possibilities.

Science fails when ignorance dominates... and ignorance occurs when you have a closed mind. I never once said anybody was wrong or right, I was merely giving my thoughts on it. You on the other hand, assume to have the answer... and that makes you very dangerous for scientific discussion.

 

[matheinste]

Actually this is a forum for discussion, so if you want to resort to name calling instead of discussing, perhaps this is not the place for you.

And as I have stated above, these are my ideas of the scenario... it is called the twin paradox for just that reason, it is a paradox... there is no cut and dry answer. So please stop assuming you have it. If anyone is being arrogant here it is you.

It is not a paradox and its "resolution" is explained in most textbooks on relativity and countless times in this forum. There are plenty of people here who would be willing to provide the explanation but, perhaps like me, do not want to spend time trying to convince someone who has already decided that the "paradox" does not have a "resolution" easily explained within SR. If you cannot accept the universally accepted fact that acceleration is absolute, an important part of the explanation which shows that the scenario is not symmetrical as regards the twins, then there is no point in going any further.

Matheinste.

 

[Evolver]

It is not a paradox and its "resolution" is explained in most textbooks on relativity and countless times in this forum. There are plenty of people here who would be willing to provide the explanation but, perhaps like me, do not want to spend time trying to convince someone who has already decided that the "paradox" does not have a "resolution" easily explained within SR. If you cannot accept the universally accepted fact that acceleration is absolute, an important part of the explanation which shows that the scenario is not symmetrical as regards the twins, then there is no point in going any further.

Matheinste.

Once again, the paradox arises from the interpretation of what is occurring, not the final outcome. The outcome remains the same and asymmetrical. Some like Von Laue chose to explain it as using multiple inertial frames, Einstein chose gravitational time dilation, Langevin said it was absolute acceleration that changed the direction of the velocity... all are asymmetrical in nature.

What you don't seem to get about my idea is that it IS NOT symmetrical, why you keep labeling it as such is beyond me. I say that both twins experience the other accelerating away from the other, but only twin #1 experiences the universe around him accelerating away. THAT IS NOT SYMMETRY.

Again, this is a forum for discussion and open thought, yet some of you have proven you do not accept that. Please then, don't comment on my posts, just ignore me. But before you do, please attempt to understand what I am saying and don't mislabel it. And as for your "textbook" comment... just remember that if Einstein had never dared to think outside the contexts of the textbooks of his day, there wouldn't even be a twin's paradox for us to debate about in the first place.

 

[matheinste]

To say acceleration is not relative means you have already decided that one frame of reference is more absolute than the other. Though one twin experiences the other twin AND the universe accelerating away from him (hence the kick in the pants), while the other twin only experiences the first twin accelerating away... both experience the opposite twin accelerating away from them.

Also, being at rest is completely relative as well. Would you consider yourself at rest when typing your response to this on your computer? Because in reality you are rocketing through space on the Earth, and the Earth is swirling about the Milky Way, and who knows what else motions the entire universe is actually performing. But, in your current reference frame you are at rest... Everything is relative.

Although no one frame is any more absolute than any other, the stay at home twin, along with the rest of the universe, can be considered, for our purposes, to be at rest in the same inertial frame of reference. The traveling twin does not remian in any inertial frame. There is a difference but neither is preferred or absolute.

Any observer/object in any reference frame is at rest with respect to that reference frame. I am at rest relative to the earth. But being on Earth I am not permanently at rest in any inertial reference frame as the Earth is accelerating. The Earth can be considered to be instantaneously at rest in a series of co-moving reference frames. But for purposes of illustration, thought experiments, the twin "paradox" etc. it is often considered to be at rest.

Matheinste.

 

[Dale]

I want to go back to this previous comment, as I feel it is important to the discussion.

To say acceleration is not relative means you have already decided that one frame of reference is more absolute than the other.

In SR there is indeed a special class of reference frames. We call this special class of reference frames "inertial". There are many equivalent ways to determine if a given reference frame is inertial or not, my favorite is that a reference frame is inertial if an ideal accelerometer at rest anywhere in the reference frame will always read 0.

The postulates of SR apply only to inertial reference frames. The traveling twin's frame is non-inertial, so they simply don't apply. The home twin's frame is inertial, and there are an infinite number of other inertial frames. By applying the standard formulas in any of those inertial reference frames you obtain the clear and unambiguous result that the traveling twin experiences less proper time.