How does the Twins Paradox challenge our understanding of ageing?

[ThomasT]

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.

He went somewhere and came back, all the while keeping visual contact with the earth-sun system.

Why wouldn't the light from rotations 6-20 reach him on the turnaround and return trip?

 

[DrGreg]

There's a simple way to tell if you're undergoing proper acceleration or not (i.e. moving inertially). Hold a golf ball stationary in front of you and then gently let go of it. If the ball continues to remain exactly where it was, you are not accelerating. If the ball moves, you are accelerating. You don't need to calibrate anything. Either the ball moves or it doesn't.

All this assumes no gravity. In the presence of a gravitational tide, you'd need to hold an infinitesimally small ball infinitesimally close to your infinitesimal self. Oh, and gravity or not, do it in a vacuum so the ball can't be blown by wind. And I'm assuming the ball isn't charged, or magnetic, or any other reason for it accelerate.

 

[ThomasT]

No, the traveler watched the Earth-Sun make .9 rotations during the trip ...

Thanks for the lengthy explanation. I don't thing that SR requires the interpretation of TIME that most here seem to associate with it.

I'm not convinced that the traveller wouldn't see 20 earth-sun rotations -- even though they'll accumulate somewhat more erratically for the traveller.

I have to go but will return to nitpick when the vacation permits.

 

[Evolver]

There's a simple way to tell if you're undergoing proper acceleration or not (i.e. moving inertially). Hold a golf ball stationary in front of you and then gently let go of it. If the ball continues to remain exactly where it was, you are not accelerating. If the ball moves, you are accelerating. You don't need to calibrate anything. Either the ball moves or it doesn't.

All this assumes no gravity. In the presence of a gravitational tide, you'd need to hold an infinitesimally small ball infinitesimally close to your infinitesimal self. Oh, and gravity or not, do it in a vacuum so the ball can't be blown by wind. And I'm assuming the ball isn't charged, or magnetic, or any other reason for it accelerate.

That doesn't account for frames of reference... because like was stated before... the ball actually is constantly changing velocity if looked at from the Earth's frame of reference as it zooms through space... or it is stationary per your frame of reference as you are planted on the Earth. The whole point of the frames of reference is that they are subjective to the observer.

Or if you don't want to be on the Earth like you said, you could seem still relatively to your frame, but the entire galaxy you are in is spinning about at high speeds... or if you are outside the galaxy where gravity is weak, then the entire universe is expanding at an accelerated rate with you in it. There is always motion in some frame of reference it would seem.

 

[Mentz114]

Why wouldn't the light from rotations 6-20 reach him on the turnaround and return trip?

In my opinion they would. Possibly the poster who implied they would not meant something else. Both frames must agree on the number of rotations or else there would be a serious paradox.

 

[Dale]

That doesn't account for frames of reference... because like was stated before... the ball actually is constantly changing velocity if looked at from the Earth's frame of reference as it zooms through space... or it is stationary per your frame of reference as you are planted on the Earth

That is coordinate acceleration, and different reference frames disagree. Accelerometers measure proper acceleration in all reference frames, and all reference frames agree. I think you are confusing the two. Dr Greg's comments were correct.

 

[matheinste]

That doesn't account for frames of reference... because like was stated before... the ball actually is accelerating if looked at from the Earth's frame of reference as it zooms through space... or it is stationary per your frame of reference as you are planted on the Earth. The whole point of the frames of reference is that they are subjective to the observer.

Or if you don't want to be on the Earth like you said, you could seem still relatively to your frame, but the entire galaxy you are in is spinning about at high speeds... or if you are outside the galaxy where gravity is weak, then the entire universe is expanding with you in it. There is always motion in some frame of reference it would seem.

There are an infinite number of frames of reference, inertial and accelerating. They are not physical realities but coordinate systems defined by us. Given an observer or object we can of course define a frame in which the observer or object is at rest. We do not accelerate reference frames but we can attach reference frames to an accelerating object so that this object at rest in that frame. If this object is an accelerometer it will detect an applied force by showing an acceleration whatever frame of reference you consider it to be in. So we can define a frame in which it may be permanently at rest but show acceleration if there is a force applied to it, the accelerometer.

Take accelerometers and place one in each of this infinite number of frames and note the reading on each. Take anyone of these accelerometers and note the reading on it and apply a force to it, and not to the others, so that its reading changes. Now, observers at rest in all the other frames will see this object, to which the force was applied, accelerate, and to observers at rest in the accelerated objects frame, the accelerometers in all the other frames will also appear to accelerate. But then check the readings on all the other accelerometers, their readings will not have changed after the application of the force to the accelerometer originally chosen. So the accelerometer to which a force was applied shows a change in reading, all others do not.

Matheinste.

 

[russ_watters]

Special relativity is formulated so as to not assume that any particular frame of reference is special. Yes they share the same physics, but that does not mean they are perceived the same (besides the speed of light which is the only constant).

They are perceived the same by experiments performed in their frames - just not experiments performed between the frames. That's the whole point of the postulate.

For instance the contraction of bodies approaching light speed and the increase of their mass is solely dependent on which observer you ask to find out who's mass increased.

True, but I don't see what that has to do with the above point...

As far as clocks behaving differently in different frames, this can be witnessed in satellites. GPS satellite clocks must be adjusted for because they run at a different rate than Earthbound clocks. They, in effect, experience different time.[emphasis added]

No, that's not what it means and it directly contradicts your previous quote. Time dilation is only measurable between two frames, it is not something you can measure in your own frame.

The only reason we prefer one to the other is because we happen to live in one of them. There is no absolute reference frame.

Is that not true?

That part is correct, but you seem to be jumping around here a bit. Maybe it is that you don't see the difference between things being frame dependent and things being different in different frames. No experiment in a particular frame can tell you what frame you are in - only when you conduct an experiment between two frames can you quantify the difference. That's the point of the principle of relativity.

...you also seem to be jumping back and forth between saying there is and isn't an absolute reference frame.

 

[Evolver]

That part is correct, but you seem to be jumping around here a bit. Maybe it is that you don't see the difference between things being frame dependent and things being different in different frames. No experiment in a particular frame can tell you what frame you are in - only when you conduct an experiment between two frames can you quantify the difference. That's the point of the principle of relativity.

Ok, then I guess this is where my confusion is rooted. In the the twin paradox of one twin zooming away from the other... how is there not an observable difference between these two frames based on subjectivity of some observer measuring the experiment. (say either one of the twins, or perhaps a 3rd observer witnessing the action from afar, perhaps in a passing spaceship of his own?)

And as such, if performing a measurement between the two frames to determine said difference, how would you know which instruments are ideal for performing the functions? Because though I understand that the physics are always the same in the inertial frames, would not your subjective viewpoint interpret those physics differently? (Let's say not an accelerometer, but a clock for example.)

No, that's not what it means and it directly contradicts your previous quote. time dilation is only measurable between two frames, it is not something you can measure in your own frame.

I am also confused on this. How is the satellite's trajectory around the Earth not one frame of reference and the Earthbound human's another? And why is the adjusting of the difference in their clocks not a measurement between frames? This seems to be an element of my misunderstanding of what you are saying.

It is articles like this one that are abundantly found that really propel my confusion, perhaps you can help clarify:

"For GPS satellites, General Relativity predicts that the atomic clocks at GPS orbital altitudes will tick faster by about 45,900 ns/day because they are in a weaker gravitational field than atomic clocks on Earth's surface. Special Relativity (SR) predicts that atomic clocks moving at GPS orbital speeds will tick slower by about 7,200 ns/day than stationary ground clocks. Rather than have clocks with such large rate differences, the satellite clocks are reset in rate before launch to compensate for these predicted effects. In practice, simply changing the international definition of the number of atomic transitions that constitute a one-second interval accomplishes this goal. Therefore, we observe the clocks running at their offset rates before launch. Then we observe the clocks running after launch and compare their rates with the predictions of relativity, both GR and SR combined. If the predictions are right, we should see the clocks run again at nearly the same rates as ground clocks, despite using an offset definition for the length of one second."

 

[Dale]

Perhaps I can help wrt the GPS issue which you have mentioned a few times. As I said earlier an ideal clock measures proper time. This is independent of reference frame or state of motion of the clock, the clock and/or the reference frame may be at rest, or moving inertially or moving non-inertially.

The GPS clocks are not ideal clocks. By design they do not measure proper time in any reference frame. The GPS clocks are designed instead to measure coordinate time in the earth-centered inertial frame (ECIF). SR and GR predict a fairly simple relationship between proper time along their orbits and the coordinate time in the ECIF, this is the essence of the compensation. Due to this compensation, the GPS clocks do not measure proper time in any reference frame, instead they measure coordinate time and that only in the ECIF.

 

[ThomasT]

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?

Wrt the surveyors, we would attribute the difference in measurment to the thing being measured.

Wrt the twins, it has to do with the thing doing the measuring.

All observers will see the earth-sun system age 20 years between takeoff and landing.
The traveller saw the earth-sun system evolve 20 years between takeoff and landing, but his shipboard clock only ticked off 5 years and he only aged 5 years during the trip.

From this, I think one must conclude that the traveling clock's tick rate changed during the trip.

And, since constant velocity = constant tick rate, then I think one must conclude that the traveling clock's tick rate changed during its intervals of acceleration.

So, the statement that accelerations affect the periods of oscillators seems ok.

 

[matheinste]

From this, I think one must conclude that the traveling clock's tick rate changed during the trip.

And, since constant velocity = constant tick rate, then I think one must conclude that the traveling clock's tick rate changed during its intervals of acceleration.

So, the statement that accelerations affect the periods of oscillators seems ok.

The clock hypothesis says that clocks considered ideal in SR are not affected by acceleration. This has been experimentally verified for some types of real clock to very high accuracy for accelerations up $$10^{18}g$$.

Matheinste.

 

[ThomasT]

The clock hypothesis says that clocks considered ideal in SR are not affected by acceleration. This has been experimentally verified for some types of real clock to very high accuracy for accelerations up $$10^{18}g$$.

Matheinste.

Is it possible that the clock hypothesis is rather more a calculational convention than a statement about what's actually happening with our accelerated clock?

We just want to be able to say something about the physical cause(s) of differential aging.

SR has presented us with one of the deepest physical mysteries:

Two identical clocks, with identical tick rates sit side by side. As long as they're left that way there won't be any difference in accumulated time.

But accelerate one clock or the other and then bring them together again, and they'll show a difference in accumulated time.

The PHYSICAL reason for this difference is one of physics' open questions.

 

[matheinste]

But accelerate one clock or the other and then bring them together again, and they'll show a difference in accumulated time.

The PHYSICAL reason for this difference is one of physics' open questions.

The question has been answered many times. They record different proper times because they have experienced different proper times because they have traveled different spcetime paths.

Matheinste.

 

[Dmitry67]

There is no mystery. It is a trivial property of pseudoeuclidean spacetime

Regarding word 'PHYSICAL' in bold:

http://math.ucr.edu/home/baez/crackpot.html
Crackpot index #17

10 points for arguing that while a current well-established theory predicts phenomena correctly, it doesn't explain "why" they occur, or fails to provide a "mechanism".

 

[Evolver]

Perhaps I can help wrt the GPS issue which you have mentioned a few times. As I said earlier an ideal clock measures proper time. This is independent of reference frame or state of motion of the clock, the clock and/or the reference frame may be at rest, or moving inertially or moving non-inertially.

The GPS clocks are not ideal clocks. By design they do not measure proper time in any reference frame. The GPS clocks are designed instead to measure coordinate time in the earth-centered inertial frame (ECIF). SR and GR predict a fairly simple relationship between proper time along their orbits and the coordinate time in the ECIF, this is the essence of the compensation. Due to this compensation, the GPS clocks do not measure proper time in any reference frame, instead they measure coordinate time and that only in the ECIF.

I guess my confusion then stems from the idea of how an ideal clock can exist. Because if SR says there is no absolute reference frame, then how can their be one clock to measure absolutely?

I understand that they may exist, but my confusion is concerning how is that possible? And perhaps you could give me an example as simply saying that an ideal clock measures time for all reference frames does not help my confusion about what you're saying.

 

[ThomasT]

There is no mystery. It is a trivial property of pseudoeuclidean spacetime

Oh, ok.

Regarding word 'PHYSICAL' in bold:

http://math.ucr.edu/home/baez/crackpot.html
Crackpot index #17

The original poster asked for a physical explanation of differential aging. There isn't one -- and, as at least one poster was honest enough to acknowledge, SR isn't designed to provide one.

I think it's a mistake to take the "paths in spacetime geometries" explanation(s) as physical explanations. These are interpretations of SR developed for calculational purposes which provide accurate predictions. Their status as descriptions of the real world is unknown.

For those who want to take the "different paths in spacetime geometry" as the final word on differential aging, then fine, you don't have to ponder it any more. However, I would conjecture that a significant number of working physicists think there is a deep physical mystery wrt differential aging that has yet to be solved.

 

[ThomasT]

The question has been answered many times. They record different proper times because they have experienced different proper times because they have traveled different spacetime paths.

Recall that we've set aside this interpretation of SR for the moment. In which case, the "different spacetime paths" explanation of differential aging is unacceptable.

 

[Dmitry67]

You can use as an example of a clock a system of 2 ideal mirrors and light bouncing back and forth. The number of bounces counts the number ot fixed time interval.

You can check that the number is proportional to the proper time. So nothing 'deep'. Just pure 'shut up and calculate'.

You should probably be more specific, what puzzles you
1. The fact that different clocks, no matter how they are made are slowed down at the same ratio?
2. That aging of biological beings is proportional to the amount of proper time they are experiencing?
3. Something else?

 

[ThomasT]

You can use as an example of a clock a system of 2 ideal mirrors and light bouncing back and forth. The number of bounces counts the number ot fixed time interval.

You can check that the number is proportional to the proper time. So nothing 'deep'. Just pure 'shut up and calculate'.

You should probably be more specific, what puzzles you
1. The fact that different clocks, no matter how they are made are slowed down at the same ratio?
2. That aging of biological beings is proportional to the amount of proper time they are experiencing?
3. Something else?

The tick rates of clocks (the periods of oscillators) are altered by acceleration. How would you begin to explain this (without spacetime geometry)?

 

[Evolver]

You can use as an example of a clock a system of 2 ideal mirrors and light bouncing back and forth. The number of bounces counts the number ot fixed time interval.

You can check that the number is proportional to the proper time. So nothing 'deep'. Just pure 'shut up and calculate'.

You should probably be more specific, what puzzles you
1. The fact that different clocks, no matter how they are made are slowed down at the same ratio?
2. That aging of biological beings is proportional to the amount of proper time they are experiencing?
3. Something else?

You are using ideal mirrors to describe my confusion about ideal clocks... and that is the very nature of my confusion of how something can even be considered ideal, assuming there is no absolute reference frame. Would not the idea of an ideal anything imply that there is an ideal reference frame?

I think that falls into category number 3 that you listed.

 

[Dmitry67]

I called mirrors 'ideal' to assume that 100% of light is reflected.
You can replace that system with 2 lasers, detector, so when one side detects a signal it sends a light splash back. In such case no ideal mirros are required. But for the discussion it is irrelevant.

 

[Dmitry67]

The tick rates of clocks (the periods of oscillators) are altered by acceleration. How would you begin to explain this (without spacetime geometry)?

As you know, Einstein had derived all SR formulas without knowing the Minkowsy metrics, just using his 2 axioms.

 

[ThomasT]

As you know, Einstein had derived all SR formulas without knowing the Minkowsy metrics, just using his 2 axioms.

What's your point?

 

[matheinste]

Oh, ok.

The original poster asked for a physical explanation of differential aging. There isn't one -- and, as at least one poster was honest enough to acknowledge, SR isn't designed to provide one.

I think it's a mistake to take the "paths in spacetime geometries" explanation(s) as physical explanations. These are interpretations of SR developed for calculational purposes which provide accurate predictions. Their status as descriptions of the real world is unknown.

For those who want to take the "different paths in spacetime geometry" as the final word on differential aging, then fine, you don't have to ponder it any more. However, I would conjecture that a significant number of working physicists think there is a deep physical mystery wrt differential aging that has yet to be solved.

I do not know about the deeper mysteries underlying the workings of the world. Nor do physicists or philosophers. If they did, I am sure they would have shared this knowledge with us. My problem is that in an earlier response you said it was not unreasonable to infer that clock rates are affected by acceleration. Physicists do know something about the clock hypothesis and it has been tested experimentally to a high degree of accuracy. So your statement is untrue by definition for an ideal clock and untrue to a great experimental accuracy for some real clocks.

Hopefully someday we will have a deeper understanding of the workings of nature and then we will again be looking for a deeper one still.

Matheinste.

 

[ThomasT]

I do not know about the deeper mysteries underlying the workings of the world. Nor do physicists or philosophers. If they did, I am sure they would have shared this knowledge with us.

Physicists do have many ideas, make many inferences about deep(er) reality, based on their experience. Many have been published, and some seem better than others.

My problem is that in an earlier response you said it was not unreasonable to infer that clock rates are affected by acceleration. Physicists do know something about the clock hypothesis and it has been tested experimentally to a high degree of accuracy. So your statement is untrue by definition for an ideal clock and untrue to a great experimental accuracy for some real clocks.

I'll ask again, is it possible that the clock hypothesis is rather more a calculational convention than a statement about what's actually happening with our accelerated clock?

Remember, we're not using the spacetime geometric interpretation.

In fact, you don't have to do any calculations at all to see the logic involved.

In the experiment where you have two identical clocks, with identical tick rates sitting side by side, and you accelerate one to wherever, then bring it back to rest beside the unmoved clock, it's obvious that the tick rate of the traveling clock has been altered during the trip. It follows that the tick rate of the traveling clock was altered due to velocity changes (during intervals of acceleration) during its round trip.

And of course it follows that accelerations affect the periods of oscillators. This is all I want to say ... really.

This simple experimental scenario seems to falsify the clock hypothesis. You can show again and again that the accumulated times will be the same if no acceleration is involved (that is, if neither clock is moved), and they will be different if one clock or the other is accelerated.

Or maybe the clock hypothesis isn't a hypothesis, per se.

 

[Dmitry67]

What's your point?

It was an answer to your question

How would you begin to explain this (without spacetime geometry)?

So Einstein did it without spacetime geometry

SR (Einstein): 1905
Minkowsky: 1908

SR developed his theory without using the Mikowsky metrics.

 

[Dmitry67]

In the experiment where you have two identical clocks, with identical tick rates sitting side by side, and you accelerate one to wherever, then bring it back to rest beside the unmoved clock, it's obvious that the tick rate of one clock or the other has been altered during the trip. Since the acceleratedn traveling clock is the anomaly, then it follows that the tick rate of the traveling clock was altered due to accelerations during its round trip.

You can make the acceleration very small (g, for example) but you still have the same effect.

 

[ThomasT]

It was an answer to your question

So Einstein did it without spacetime geometry

SR (Einstein): 1905
Minkowsky: 1908

SR developed his theory without using the Mikowsky metrics.

I'm aware that Einstein predicted differential aging in 1905, but how did he explain it without spacetime geometry?

 

[ThomasT]

You can make the acceleration very small (g, for example) but you still have the same effect.

Ok, so we agree that there is an alteration in tick rate due to acceleration?

 

[Dmitry67]

http://en.wikipedia.org/wiki/Time_d...nce_of_time_dilation_due_to_relative_velocity

Check 2 pictures on the right.

 

[matheinste]

Physicists do have many ideas, make many inferences about deep(er) reality, based on their experience. Many have been published, and some seem better than others.

I'll ask again, is it possible that the clock hypothesis is rather more a calculational convention than a statement about what's actually happening with our accelerated clock?

The clock hypothesis has been tested experimentally. It is not an calculational convention. Are you perhaps mixing up the clock hypothesis with the clock paradox?

Matheinste.

 

[Dmitry67]

Ok, so we agree that there is an alteration in tick rate due to acceleration?

No, of course.

Say, you have a stationary twin. The second one is
1. Accelerating distance L with acceleration a;
2. Then moving distance B without any acceleration;
3. breaks with the same acceleration (-a) the same distance B
4. accelerates back (B)
5. Moves distance B back without an acceleration
6. Breaks

Total distance traveled (in a frame of stationary observer) is 2*(L+B+L)=4L+2B
Now you repeat the experiment keeping the same a and L but varying B
If it was the acceleration which caused the time dilation then the effect would not depend on B which is wrong

 

[matheinste]

Ok, so we agree that there is an alteration in tick rate due to acceleration?

The tick rate does not alter with acceleration. The minimizing of acceleration periods is to counter any such claims of clock rates changeing by making the effects approach zero IF they existed.

Matheinste.

 

[ThomasT]

The clock hypothesis has been tested experimentally. It is not an calculational convention. Are you perhaps mixing up the clock hypothesis with the clock paradox?

No, we're talking about the same thing.

The net effect of the clock hypothesis is that you disregard accelerations and calculate in terms of instantaneous velocities.

But just consider the simple two-clock scenario I outlined a few posts ago. From it, we can deduce that it's during intervals of acceleration that changes in the tick rate of the accelerated clock are occurring.