Undergrad How does the Twins Paradox challenge our understanding of ageing?

[edpell]

croghan27, yes I agree the English language is based on Newtonian time and has no direct words to deal with my time versus your time versus their time. In Newtonian English when we say the Earth observer goes 20 years in time and the ship observer goes 2 years in time and they both meet at 2030 (say it starts in the year 2010 and gamma is 10). This does not make any sense in Newtonian English. I have no disagreement with SR or the results I just think we have to come up with a better vocabulary for SR time.

 

[Al68]

I disagree with this. Acceleration affects the periods of oscillators.

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.

If the twins refer to a common third clock (say, revolutions of the Earth around the sun), then they will both note the same elapsed time for the traveling twin's trip. But, the traveller will have aged less, and the traveller's clock will have counted fewer oscillations than his earthbound twin's 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.

 

[edpell]

If the twins refer to a common third clock

What velocity does the third clock have with respect to the Earth clock? What velocity with respect to the ship clock?

 

[croghan27]

Somewhere between:

"Acceleration affects the periods of oscillators."
and
"What velocity does the third clock have with respect to the Earth clock? What velocity with respect to the ship clock?"

I have become lost again. While velocity and acceleration are connected, they are not, in my philosophy, Horatio, the same thing. One involves achieving and is a change of velocity; while the other is a constant.

One must accelerate to achieve a certain velocity, or conversely decelerate, but the latter is the result of the former. What is the connection here and which results in the ageing or less ageing of the twins?

(At the risk of being a drag, there is another question in the background of this.)

 

[Al68]

Somewhere between:

"Acceleration affects the periods of oscillators."
and
"What velocity does the third clock have with respect to the Earth clock? What velocity with respect to the ship clock?"

I have become lost again. While velocity and acceleration are connected, they are not, in my philosophy, Horatio, the same thing. One involves achieving and is a change of velocity; while the other is a constant.

One must accelerate to achieve a certain velocity, or conversely decelerate, but the latter is the result of the former. What is the connection here and which results in the ageing or less ageing of the twins?

(At the risk of being a drag, there is another question in the background of this.)

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.

 

[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.