How does the Twins Paradox challenge our understanding of ageing?

[croghan27]

The differential aging is the result of less elapsed time for the ship's twin, which is a function of velocity. Acceleration is relevant as the time derivative of velocity.

Thanks for that ... both terms seemed to be used interchangeably and I was being led astray.

The other question I have may be somewhat off the wall ... but as we sit on Earth we are busy whurrling about in the motion that makes days, on top of that we are circulating about the sun, in the circuit that defines years. The sun is just one of the stars in a very mobile galaxy grandly twisting in 'space'. So we are moving in all direction at once when compared to just about any reference point.

What effect does all this motion have upon us relative to ...er...er.. relativity?

 

[Al68]

Thanks for that ... both terms seemed to be used interchangeably and I was being led astray.

The other question I have may be somewhat off the wall ... but as we sit on Earth we are busy whurrling about in the motion that makes days, on top of that we are circulating about the sun, in the circuit that defines years. The sun is just one of the stars in a very mobile galaxy grandly twisting in 'space'. So we are moving in all direction at once when compared to just about any reference point.

What effect does all this motion have upon us relative to ...er...er.. relativity?

All motion is relative to a defined reference frame or "reference point", like you say, so the effect of our motion relative to a particular reference frame would depend on the reference frame chosen.

 

[ThomasT]

If a clock is affected by acceleration, then it is simply not a valid clock in SR. This is the "clock hypothesis", that a clock's rate is unaffected by acceleration. Of course a real clock may be affected by acceleration, but the predictions of SR are not valid for such a clock.

I think you must have misread my post. My point was that the traveler's clock is predicted to show a lower reading and the ship twin is predicted to age less for a common underlying reason: Less elapsed time passes.

I don't think this addressed the OP's concern: adwuk wrote, "What I can't get my head around is how in the twins paradox one twin has physically aged more than the other. How does traveling at the speed of light affect the chemical reactions involved in the ageing of (biological) cells?"

SR can't answer the question of the deep physical cause(s) for differential aging.

Relative position in gravitational field is also connected to differential aging.

Atoms, quartz clocks, humans, etc., all material objects are bounded, standing wave structures, ie., oscillators, of lesser or greater complexity.

One take on differential aging is that acceleration affects the periods of oscillators.

 

[matheinste]

One take on differential aging is that acceleration affects the periods of oscillators.

While real clocks, that is periodic effects may well be affected mechanically by acceleration, the clock hypothesis assumes that for ideal clocks this is not the case. Differential ageing assumes the clock hypothesis and so definitely precludes the varying periodicity of clocks as a cause for the effect.

Differential aging is a logical consequence of clocks following different spacetime paths. This requires acceleration on the part of one or both of the clocks but the acceleration is not the direct cause of the effect. Remember we are using ideal clocks that satisfy the clock hypothesis.

Matheinste.

 

[Al68]

SR can't answer the question of the deep physical cause(s) for differential aging.

It's not supposed to. SR isn't biology. SR only answers the question of how much time elapses. Common sense says more elapsed time equals more aging.

Relative position in gravitational field is also connected to differential aging.

Atoms, quartz clocks, humans, etc., all material objects are bounded, standing wave structures, ie., oscillators, of lesser or greater complexity.

One take on differential aging is that acceleration affects the periods of oscillators.

SR predicts what a hypothetical clock will read if it is not unaffected by acceleration.

Clocks which are unaffected by acceleration will show that the ship twin has less elapsed time.

 

[ThomasT]

Thanks for the input(s). My concern is that in calculating in terms of instantaneous velocities (vis clock postulate), and visualizing in terms of paths in spacetime geometry, then maybe some important physical considerations get glossed over.

We agree that relativity theory is not designed to provide an answer to the OP's question about deeper physical cause(s) of differential aging. A more fundamental (wave?) theory is required.

The physical evidence does suggest that modifications of oscillatory periods happen during intervals of acceleration.

 

[matheinste]

The physical evidence does suggest that modifications of oscillatory periods happen during intervals of acceleration.

What evidence are we talking about. I thought that the clock hypothesis had been confirmed to a high very high degree for atomic clocks.

Matheinste.

 

[ThomasT]

What evidence are we talking about. I thought that the clock hypothesis had been confirmed to a high very high degree for atomic clocks.

Matheinste.

The most compelling evidence is that you can feel when you're accelerating. It seems logical to assume that it's during these intervals that changes in oscillatory periods are occurring.

I'm not familiar with the experiments you're talking about. I'd be interested to see an experiment that shows that acceleration has no effect on clocks.

 

[matheinste]

The most compelling evidence is that you can feel when you're accelerating. It seems logical to assume that it's during these intervals that changes in oscillatory periods are occurring.

I'm not familiar with the experiments you're talking about. I'd be interested to see an experiment that shows that acceleration has no effect on clocks.

Look at the FAQ at the top of the forum entitled Experimental Basis for Special Relativity and follow the links. The hypothesis has been confirmed up to $$10^{18}g$$

Matheinste.

 

[croghan27]

All motion is relative to a defined reference frame or "reference point", like you say, so the effect of our motion relative to a particular reference frame would depend on the reference frame chosen.

I guess I am going to have to accept there is no such thing as a stationary object - it is always relative. Motion seems to be something that was/is and forever shall be present.

Now we are speaking of a innate characteristic of the universe - is there something that is responsible for this? CERN is busy spending billions to find a particle that may or may not hold the secret to mass - is there a chronological particle/wave/force?

 

[Al68]

The most compelling evidence is that you can feel when you're accelerating. It seems logical to assume that it's during these intervals that changes in oscillatory periods are occurring.

I'm not familiar with the experiments you're talking about. I'd be interested to see an experiment that shows that acceleration has no effect on clocks.

Some clocks might very well be affected by acceleration, they might break completely, but those clocks are not valid in SR. SR predicts only what a clock will read if the clock keeps proper time regardless of acceleration.

 

[ThomasT]

Look at the FAQ at the top of the forum entitled Experimental Basis for Special Relativity and follow the links. The hypothesis has been confirmed up to $$10^{18}g$$

Matheinste.

Thanks. Unfortunately, I checked out the link "bailey et al" from a couple of places and it doesn't lead to an article that I can read.

 

[Dale]

Here is a link to the abstract:
http://www.nature.com/nature/journal/v268/n5618/abs/268301a0.html

You can probably find it at a local library. Nature and Science are widely subscribed to. There also used to be a http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muonex.html"[/URL], but I couldn't connect to it today.

 

[ThomasT]

Some clocks might very well be affected by acceleration, they might break completely, but those clocks are not valid in SR. SR predicts only what a clock will read if the clock keeps proper time regardless of acceleration.

I'm not sure what you're saying. If you change a real clock's velocity, then won't it, at the different velocity, keep different time? This has been experimentally confirmed, hasn't it?

So, assuming that a clock's tick rate is proportional to the speed at which the clock is moving, the question I'm interested in is: when tick rates change -- during what are called acceleration intervals -- then what are the mechanics of the change?

 

[Janus]

Thanks. Unfortunately, I checked out the link "bailey et al" from a couple of places and it doesn't lead to an article that I can read.

Put simply, it works like this:

Put a clock at the end of a centrifuge. Spin up the centrifuge so that the clock is traveling in circle at a given speed while experiencing an acceleration. Compare the clock's rate with that expected just due to its velocity and see if it varies. (is the acceleration having an additional effect on the clock rate).

By varying the radius of the centrifuge and its rate of spin you can create situations where you have different accelerations but maintain the same speed for the clock or maintain the same acceleration for different speeds of the clock.

Th experiment has been done with high speed centrifuges and using samples of a radioisotope for the clock. To the accuracy already stated, it has been found that the measured decay rate of the sample is only determined by the speed at which it moves and that the acceleration has no effect.

 

[ThomasT]

Here is a link to the abstract:
http://www.nature.com/nature/journal/v268/n5618/abs/268301a0.html

You can probably find it at a local library. Nature and Science are widely subscribed to. There also used to be a http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/muonex.html"[/URL], but I couldn't connect to it today.[/QUOTE]Thanks. I'm in Fort Lauderdale. I'll try to get a copy within the next few days.

 

[ThomasT]

Put simply, it works like this:

Put a clock at the end of a centrifuge. Spin up the centrifuge so that the clock is traveling in circle at a given speed while experiencing an acceleration. Compare the clock's rate with that expected just due to its velocity and see if it varies. (is the acceleration having an additional effect on the clock rate).

By varying the radius of the centrifuge and its rate of spin you can create situations where you have different accelerations but maintain the same speed for the clock or maintain the same acceleration for different speeds of the clock.

Th experiment has been done with high speed centrifuges and using samples of a radioisotope for the clock. To the accuracy already stated, it has been found that the measured decay rate of the sample is only determined by the speed at which it moves and that the acceleration has no effect.

Thanks. Reference?

 

[Al68]

I'm not sure what you're saying. If you change a real clock's velocity, then won't it, at the different velocity, keep different time? This has been experimentally confirmed, hasn't it?

The clock will run slow relative to an observer's rest frame if the relative velocity between the clock and observer changes, but it makes no difference whether the clock or observer accelerated.

So, assuming that a clock's tick rate is proportional to the speed at which the clock is moving, the question I'm interested in is: when tick rates change -- during what are called acceleration intervals -- then what are the mechanics of the change?

It's not the clock that changed, it's the relative motion between the clock and reference frame that changed. A clock runs slow relative to a frame in which it is in motion whether the clock accelerated or not.

For example a clock on a "moving" spaceship will run at the same rate as the watch of a co-moving observer on the ship, both keeping proper time. But if that observer decides to leave the ship on a shuttle and decelerate to come to rest with earth, then the ship's clock will then run slow relative to him. Nothing happened to the clock at all. There are no "mechanics of the change" because there was no physical change of the clock.

Another analogy is kinetic energy. The kinetic energy of an object is different in different reference frames. Would you ask for the "mechanics of the change" to explain how the object gained or lost kinetic energy simply because we switched reference frames? Of course not, because, like the rate of a clock in SR, kinetic energy is frame dependent.

 

[edpell]

But if that observer decides to leave the ship on a shuttle and decelerate to come to rest with earth, then the ship's clock will then run slow relative to him.

A person on Earth "observes" the flashes [let us say the clock on the ship emits a light flash every one second ship time] at a lower frequency due to the, distortion caused by the, finite speed of propagation of light. Versus if we have [this is a thought experiment] a signal that propagates at say 10^100 times c would the observer on Earth see the flashes at a rate of one per Earth clock second?

 

[ThomasT]

The clock will run slow relative to an observer's rest frame if the relative velocity between the clock and observer changes, but it makes no difference whether the clock or observer accelerated.

Yes, but when we know which clock was accelerated, then doesn't that allow us to infer that its changes in velocity had a real, physical effect on its tick rate?

For example a clock on a "moving" spaceship will run at the same rate as the watch of a co-moving observer on the ship, both keeping proper time. But if that observer decides to leave the ship on a shuttle and decelerate to come to rest with earth, then the ship's clock will then run slow relative to him. Nothing happened to the clock at all. There are no "mechanics of the change" because there was no physical change of the clock.

What about the watch that went to the earth?

The way I interpret the experiments that I've read is that the tick rates of clocks (ie. the periods of oscillators) are affected by velocity changes. Do you think this is wrong?

 

[Al68]

Yes, but when we know which clock was accelerated, then doesn't that allow us to infer that its changes in velocity had a real, physical effect on its tick rate?

No, because the exact same effect occurs anytime there is a change in the relative velocity between clock and observer. An effect that occurs whether the clock accelerates or not can't be attributed to its acceleration.

What about the watch that went to the earth?

The way I interpret the experiments that I've read is that the tick rates of clocks (ie. the periods of oscillators) are affected by velocity changes. Do you think this is wrong?

They aren't "affected" by a change in velocity of the clock, they depend on the relative velocity between clock and reference frame. That's a subtle but crucial difference.

The tick rate of a valid clock is 1 sec per second of proper time in its rest frame, regardless of its motion or acceleration. It's the ratio between proper time in the rest frame of the clock and coordinate time in the observer's rest frame that "changes" with a change in the relative velocity between clock and observer, not anything physical about the clock itself.

 

[ThomasT]

No, because the exact same effect occurs anytime there is a change in the relative velocity between clock and observer. An effect that occurs whether the clock accelerates or not can't be attributed to its acceleration.

Keep two identical clocks side by side at a constant velocity and they display the same times.
Now accelerate one clock, then bring it back aside the other again and they display different times. Doesn't it make sense to attribute this difference to the acceleration?

They aren't "affected" by a change in velocity of the clock, they depend on the relative velocity between clock and reference frame. That's a subtle but crucial difference.

The tick rate of a valid clock is 1 sec per second of proper time in its rest frame, regardless of its motion or acceleration. It's the ratio between proper time in the rest frame of the clock and coordinate time in the observer's rest frame that "changes" with a change in the relative velocity between clock and observer, not anything physical about the clock itself.

And yet, when we reunite the clocks and compare their times, they're significantly (physically) different.

In light of the evidence, I don't understand how one can say that a different tick accumulation (associated with an acceleration) isn't "anything physical about the clock itself."

 

[Al68]

Keep two identical clocks side by side at a constant velocity and they display the same times.
Now accelerate one clock, then bring it back aside the other again and they display different times. Doesn't it make sense to attribute this difference to the acceleration?

Sure. But a difference in elapsed time between events is very different from the previous issue of a clock running slow relative to a different frame.

And yet, when we reunite the clocks and compare their times, they're significantly (physically) different.

In light of the evidence, I don't understand how one can say that a different tick accumulation (associated with an acceleration) isn't "anything physical about the clock itself."

It's physical in the sense that one clock physically had a path through specetime with less elapsed time than the other path. Each clock shows 1 second for each second of time elapsed along their path.

In other words, one path between two events has less elapsed proper time than the other path between those events. Each clock keeps good proper time. The difference in clock readings is due to a difference in elapsed proper time, not a difference in the clocks.

 

[ThomasT]

It's physical in the sense that one clock physically had a path through spacetime with less elapsed time than the other path.

This is one way of representing it. But I don't think that this is the sense in which it's physical.

We know that the two clocks have counted a different number of ticks, and that one clock was accelerated and the other not. So, we agree that we can attribute the difference to the acceleration intervals.

The difference in clock readings is due to a difference in elapsed proper time, not a difference in the clocks.

There's a difference in the clock readings of the twins, while there's no difference in the visual count of the number of years from takeoff to landing for any and all observers. So, we know that the trip took, say, 20 years, but the traveller's clock only counted, say, 5 years and he only aged 5 years.

Spacetime path(s) notwithstanding, I think we're forced to conclude that the periods of the oscillator(s) of the traveller's clock and the traveller himself have been temporarily, physically altered during their accelerations.

 

[Al68]

There's a difference in the clock readings of the twins, while there's no difference in the visual count of the number of years from takeoff to landing for any and all observers. So, we know that the trip took, say, 20 years, but the traveller's clock only counted, say, 5 years and he only aged 5 years.

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.

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.

 

[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.