How does the Twins Paradox challenge our understanding of ageing?

[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.

 

[Evolver]

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 mirrors are required. But for the discussion it is irrelevant.

Ok I understand this and agree with it... Now comes my confusion:

In the twin paradox, both twins would be using said ideal clock to measure their time... but as they separated away from one another near the speed of light, to the opposite twin the opposing twin's clock would read at a different rate, and each twin would say the others clock has changed. Each twin would experience a different rate of time relative to the others perspective.

 

[ThomasT]

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

? I didn't say that acceleration causes time dilation.

I said that acceleration alters the periods of oscillators.

 

[Dmitry67]

Period of oscilator IS proper time.
If you don't agree, then you are denying the axiom or special relativity: that speed of light is always c.

Of course you can deny it if you want, but then it must belong to some other thread.

 

[Mentz114]

ThomasT:

I said that acceleration alters the periods of oscillators.

maybe, but not clocks. For instance, a mechanical clock worn on the wrist undergoes lots of accelerations but still keeps time. The clocks used on spacecraft undergo great accelerations during launch but still keep time.

 

[matheinste]

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.

The clock rates of each clock do not change. Their perceived rate is different between frames. That is normal time dilation. During changes of velocity the accelerating body moves through a sequence of different instantaneous comoving frames and so its ideas of simultaneity alters sequentially and the other clock's rate is appears to run differently due to this, in addition to the time dilation effect.

Matheinste.

 

[ThomasT]

The tick rate does not alter with acceleration.

You believe that the tick rate of the traveling clock isn't altered. Right?

You believe this because the spacetime geometric interpretation of SR provides an explanation (altered spacetime path) which precludes the alteration of tick rates vis accelerations. Right?

But remember that we're not using this interpretation of SR, because we want to see if there might be a more physical (and, yes, intuitive) approach to actually understanding the deep physics of differential aging.

So, with that in mind, is it logical to conclude that tick rate changes are occurring during periods of acceleration?

 

[matheinste]

You believe that the tick rate of the traveling clock isn't altered. Right?

You believe this because the spacetime geometric interpretation of SR provides an explanation (altered spacetime path) which precludes the alteration of tick rates vis accelerations. Right?

No, I believe the click rates are not altered because there is experimental evidence that this is the case.

Matheinste.

 

[Dmitry67]

So, with that in mind, is it logical to conclude that tick rate changes are occurring during periods of acceleration?

No,
I showed the example which proves that this hypotesis is wrong few posts above

 

[tryceo]

First of all, all the chemical process and the brain activity and everything that is going on in a human body would slow down RELATIVE to the twin on earth. The twin traveling at the near speed of light would not notice this change. So what seem to be 1 second to the light-speed moving twin would be years for the non-moving twin on earth.

 

[Dale]

ThomasT, you have stated that acceleration causes a change in the tick rate of clocks. What is the equation describing this relationship between acceleration and tick rate?