How does the Twins Paradox challenge our understanding of ageing?

[Evolver]

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

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

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

I fully understand and actually agree with everything you are saying. My question arises though out of the idea that inertial reference frames could theoretically be considered relative:

Take your example of the accelerometer. The traveler's will not read zero... if it is an accelerometer based on the Earthbound observer's reference frame. But if the accelerometer were calibrated to read zero as he "accelerated" from the Earthbound observer's perspective, you could say that he was at rest while the Earthbound person and the universe were rapidly accelerating away from him, and that would be the sudden jolt that he felt. And from the "traveler's" perspective the Earthbound person's accelerometer would not be reading zero.

And the reason the Earthbound observer didn't feel the jolt, was because he was traveling with the universe and therefore felt no discrepancy.

 

[Dale]

if the accelerometer were calibrated to read zero as he "accelerated" from the Earthbound observer's perspective

If you deliberately mis-calibrated it then it would certainly not be an ideal accelerometer. Similarly with ideal clocks and ideal rods.

 

[Evolver]

If you deliberately mis-calibrated it then it would certainly not be an ideal accelerometer. Similarly with ideal clocks and ideal rods.

I wouldn't consider that mis-calibrating it though. It would be calibrating it to the proper reference frame. Otherwise you assume there is only one reference frame with which to calibrate them? Then of course the readings are always going to be in favor of that selected reference frame.

Much like the way they have to re-calibrate the clocks in satellites to make sure the GPS is accurate for the reference frame on Earth. They are adapting the one reference frame to suit the needs of their own. But there is no universal reference frame.

 

[matheinste]

In the twins scenario, would not the traveller's accelerometer, calibrated to read zero in any particular reference frame, exhibit different readings during different phases of the journey while the earthbound accelerometer would exhibit a constant reading.

Matheinste.

 

[Dale]

I wouldn't consider that mis-calibrating it though. It would be calibrating it to the proper reference frame.

Of course you wouldn't call it mis-calibrating and would prefer a more obfuscating term. However, the fact remains that such clocks, rods, and accelerometers certainly don't qualify as ideal. This includes the GPS clocks which are deliberately and carefully non-ideal.

 

[Evolver]

In the twins scenario, would not the traveller's accelerometer, calibrated to read zero in any particular reference frame, exhibit different readings during different phases of the journey while the earthbound accelerometer would exhibit a constant reading.

Matheinste.

No, because think of this:

If they were both calibrated to read zero for their specific inertial frames, they would do just that. They are essentially calibrated at zero for their own frames, yet to the other twin they would appear to be accelerating at a constant rate.

Each twin would say the other is moving and that their accelerometer is merely inaccurate in showing that it reads zero. Also, there is some unique trait that the traveler exhibits in that he is not traveling with the universe as the Earthbound observer is. The Earthbound observer is embedded in the motion of the universe so notices no difference about its motion. The traveler has, in some way, utilized energy in a way that he broke free from the motion of the universe and watches as it accelerates away from him in his inertial frame.

 

[Evolver]

Of course you wouldn't call it mis-calibrating and would prefer a more obfuscating term. However, the fact remains that such clocks, rods, and accelerometers certainly don't qualify as ideal. This includes the GPS clocks which are deliberately and carefully non-ideal.

Don't qualify as ideal? For what, the sake of ease? The fact remains that if you choose to calibrate said clock, accelerator, whatever, with a certain frame of reference it will always produce inaccurate results when compared to a different frame of reference.

If you wish to get the true effect of every inertial frame you need instruments that function in, and are tuned to accurately display that frame of reference. You cannot assume there is a universal clock, rod, accelerator that should be taken as true for all inertial frames, it automatically makes the results biased to that frame.

 

[Dale]

A correctly calibrated (ideal) clock, rod, or accelerometer is not tuned to a specific frame. It will work correctly in any reference frame (inertial or non-inertial, SR or GR, accelerating or not).

This conversation is getting rather silly. If you take any physics experiment and use mis-calibrated equipment you should not be surprised to obtain non-physical and non-sensical results. Garbage in garbage out.

 

[Evolver]

A correctly calibrated (ideal) clock, rod, or accelerometer is not tuned to a specific frame. It will work correctly in any reference frame.

This conversation is getting rather silly. If you take any physics experiment and use mis-calibrated equipment you should not be surprised to obtain non-physical and non-sensical results. Garbage in garbage out.

Ok, we obviously have a base disagreement, which is perfectly fine and I respect your opinion. But what I'm saying is, the clocks and instruments you use to do your experiments on Earth, ARE garbage to other inertial reference frames.

The GPS satellite issue proves that. There can be no universally calibrated instrument, it's all subjective. The clocks on the satellite are perfectly functioning clocks... as are those on Earth. But, because of Relativity they must be adjusted for in order for the information passing between the two reference frames to be accurate. If not, the GPS data would be drastically off here on Earth.

 

[Dale]

But what I'm saying is, the clocks and instruments you use to do your experiments on Earth, ARE garbage to other inertial reference frames.

No, an ideal clock correctly measures proper time in all reference frames. It does not provide a garbage measurement in any frame.

This is not restricted to inertial reference frames nor is it restricted to inertially moving clocks. It applies for all reference frames and it applies to clocks undergoing any sort of motion.

Similarly with ideal accelerometers which measure proper acceleration in all reference frames.

 

[Evolver]

No, an ideal clock correctly measures proper time in all reference frames. It does not provide a garbage measurement in any frame.

This is not restricted to inertial reference frames nor is it restricted to inertially moving clocks. It applies for all reference frames and it applies to clocks undergoing any sort of motion.

Similarly with ideal accelerometers which measure proper acceleration in all reference frames.

I completely understand what you're saying, and I agree with it in theory. I guess what I'm not convinced of is that such a device can exist. How could anyone device be deemed reliable in a universe that is innately relative and probabilistic as opposed to objective and deterministic? If time, motion, mass, speed, etc can all be considered relative and subjective to the observer.. how could there be one device to accurately measure them all, and itself be the officiator of what is accurate and what is not?

The idea of an ideal anything seems to be a paradox unto itself.

 

[Dale]

Sure, an ideal anything is an idealization. There is a lot of very valuable effort which goes into characterizing how a given real measurement device deviates from ideal using only other real measuring devices. This kind of thing is essentially what what the BIPM has to do whenever it decides to change the standard for the second or the meter. Currently our clocks and rods are pretty close to ideal, but our accelerometers and our scales are not nearly so close.

 

[Evolver]

Sure, an ideal anything is an idealization. There is a lot of very valuable effort which goes into characterizing how a given real measurement device deviates from ideal using only other real measuring devices. This kind of thing is essentially what what the BIPM has to do whenever it desides to change the standard for the second or the meter.

Precisely. Well we do agree after all it seems ;)

As long as we are saying that we create an ideal something for our purposes, though it is not necessarily the de facto rule of the universe.

 

[russ_watters]

If time, motion, mass, speed, etc can all be considered relative and subjective to the observer.. how could there be one device to accurately measure them all...

The first postulate of SR is that the laws of physics are the same in all inertial reference frames, so experiments that verify SR verify that there is no difference and no reason for a clock to behave differently in different frames.

Or try the corollary: if clocks behaved differently in different inertial reference frames, you could use that difference in functionality to identify the Universal Reference Frame. Failure to find any difference in functionality (ie, with the Michelson Morley Experiment) means a failure of the theory/postulate that different reference frames have different rules and that there is a Universal Reference Frame.

Or a third way: What you are suggesting is testable and is found through experimentation to not be true.

Take your example of the accelerometer. The traveler's will not read zero... if it is an accelerometer based on the Earthbound observer's reference frame. But if the accelerometer were calibrated to read zero as he "accelerated" from the Earthbound observer's perspective, you could say that he was at rest while the Earthbound person and the universe were rapidly accelerating away from him, and that would be the sudden jolt that he felt. And from the "traveler's" perspective the Earthbound person's accelerometer would not be reading zero.

No. If you calibrate the traveling twin's accelerometer to show no acceleration during the acceleration phase of its voyage, then it has to show acceleration during the "coast" phase of its voyage and double acceleration during the "turnaround" phase of its voyage.

All you've done is add a constant to both sides of an equation that cancels out and reduces to the reality that is what has already been said: the acceleration is not relative.

For example:
Both twins standing still out in space (lets avoid gravity): -1g
Accelerating: 0g
Coasting: -1g

Or
Both twins standing still out in space: 0g
Accelerating: 1g
Coasting: 0g

So what hasn't changed is that the difference between the starting frame and accelerating frame is 1g:
0-(-1)=1
or
1-0=1

All you've done is this:
1(-1)-[0(-1)] = 1

So you see, your "calibration" hasn't actually changed the scenario at all. The acceleration is still +1g.

 

[Evolver]

The first postulate of SR is that the laws of physics are the same in all inertial reference frames, so experiments that verify SR verify that there is no difference and no reason for a clock to behave differently in different frames.

Or try the corollary: if clocks behaved differently in different inertial reference frames, you could use that difference in functionality to identify the Universal Reference Frame. Failure to find any difference in functionality (ie, with the Michelson Morley Experiment) means a failure of the theory/postulate that different reference frames have different rules and that there is a Universal Reference Frame.

Or a third way: What you are suggesting is testable and is found through experimentation to not be true.

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).

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. For the Earthbound, the traveler contracted and shot away at light speed... for the traveler the Earth contracted and shot away near the speed of light. The observer's intsruments and the Earthbound's would have very different results.

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. If this were not done then the GPS data would be compromised. 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?

 

[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".