Twins flying at the speed of light in opposite directions

[kinimod]

If two guys, each sitting on a different Earth-like habitable planet, fly in the opposite directions, each at the speed of light, which guy would age slower? And slower compared to what?

My own understanding is that they both age normally. Because Special Relativity doesn't describe physiological processes, but only hints at visual disparity of the spacetime (photons can't travel fast enough to observe the reality from any given reference frame).

If this is true then the whole twin paradox is a very unfortunate way of teaching kids, just creates confusion...

 

[Dale]

If two guys, each sitting on a different Earth-like habitable planet, fly in the opposite directions, each at the speed of light, which guy would age slower? And slower compared to what?

Hi kninimod, welcome to PF!

Of course, since they have mass they cannot travel at the speed of light, so I will assume that you mean just under the speed of light. If they are each traveling at the same speed in opposite directions then they would both age equally slowly compared to clocks at rest in the reference frame where they are moving equally fast.

My own understanding is that they both age normally.

They do each age normally in their own reference frame. They each age slowly in the other's reference frame.

Because Special Relativity doesn't describe physiological processes, but only hints at visual disparity of the spacetime (photons can't travel fast enough to observe the reality from any given reference frame).

Special relativity is not about visual effects. The standard relativistic effects are about things that remain after the optical delays are correctly accounted for.

 

[Herman Trivilino]

If this is true then the whole twin paradox is a very unfortunate way of teaching kids, just creates confusion...

Things like the twin paradox must be introduced carefully, not just thrown at students in a way that leaves them confused. Time dilation is a fact of life.

 

[kinimod]

Thanks for a warm welcome.

If we take humans out of this example, and suppose we only have two equivalent rocks, what does "aging" mean for a rock? How can a rock "age", slower or faster? I'm trying to understand what is fundamentally happening to particles at speeds close to speed of light that we define it as "aging".

 

[russ_watters]

If we take humans out of this example, and suppose we only have two equivalent rocks, what does "aging" mean for a rock? How can a rock "age", slower or faster? I'm trying to understand what is fundamentally happening to particles at speeds close to speed of light that we define it as "aging".

Depends on the rock. Most rocks found on Earth contain radioactive isotopes, which can be used to measure their age. The longer they age, the more the isotopes decay.

The particulars of the processes are not really all that relevant here though and tell me you are resisting accepting the idea of time dilation.

 

[Herman Trivilino]

I'm trying to understand what is fundamentally happening to particles at speeds close to speed of light that we define it as "aging".

I think aging is just a way of measuring time. Time on a clock is known to pass at slower rates when measured by people moving relative to it.

If you have a muon that takes 2.2 μs to decay, you might say that when the muon's age reaches 2.2 μs it decays. Move muons at a fast speed relative to you and when you measure their age you get a number bigger than 2.2 μs.

 

[kinimod]

Does then the same decay model apply to a human body? I.e. if you patiently keep accelerating a human body to almost the speed of light, then decelerate back and return it to Earth, will the person live much longer compared to other folks on Earth, or about the same?

 

[Nugatory]

Does then the same decay model apply to a human body? I.e. if you patiently keep accelerating a human body to almost the speed of light, then decelerate back and return it to Earth, will the person live much longer compared to other folks on Earth, or about the same?

The traveler will return to Earth less aged than if he had remained on earth. However, he won't exactly be "living longer",in the sense of having a longer life to enjoy - he doesn't get any more heartbeats between birth and death, and doesn't get any more time between heartbeats. Instead, the traveler will say that while he was gone time passed more quickly on earth, so when he returned everyone else was older than he was.

 

[kinimod]

The traveler will return to Earth less aged than if he had remained on earth. However, he won't exactly be "living longer",in the sense of having a longer life to enjoy - he doesn't get any more heartbeats between birth and death, and doesn't get any more time between heartbeats. Instead, the traveler will say that while he was gone time passed more quickly on earth, so when he returned everyone else was older than he was.

Why does a human body situated on Earth show signs of wear, aging, decay at a different rate than to a human body traveling (accelerating, decelerating) around the speed of light? How is Time Dilation related to biological processes?

 

[Orodruin]

Time dilation is not related to biological processes, it is related to what time actually is. Your underlying assumption seems to be that there is a universal "master time" which tells you how old things are. This is false in relativity and it is the first misconception you need to dispell if you want to understand further.

 

[kinimod]

Time dilation is not related to biological processes, it is related to what time actually is. Your underlying assumption seems to be that there is a universal "master time" which tells you how old things are. This is false in relativity and it is the first misconception you need to dispell if you want to understand further.

So you mean a human body situated on Earth does not show any signs of wear, aging, decay any differently (at a different rate) than a human body traveling (accelerating, decelerating) around the speed of light, then returning to Earth... We just use this human aging example in textbooks when covering Time Dilation to confuse students with some bogus, fictional stories because we can not explain it better?

 

[Orodruin]

So you mean a human body situated on Earth does not show any signs of wear, aging, decay any differently (at a different rate) than a human body traveling (accelerating, decelerating) around the speed of light, then returning to Earth...

Your big problem is how you define rate. The human body will experience processes at exactly the same rate regardless of the state of motion, but it is a rate relative to its proper time, not relative to the time coordinate of some arbitrarily defined coordinate system. The proper time for two observers between separating and reuniting may very well be different and they will therefore have aged by different amounts. The bottom line is that there does not exist any universal time which is the same for everyone. You can use the time coordinate of some inertial frame as a substitute, but it is not equivalent to the time elapsed for observers other than those who are at rest in that particular frame.

If I draw two curves which intersect at two points, you will likely be able to tell which is the longest. This will be completely independent of what coordinates you chose to describe the curves. Proper time works in an exactly analogous manner, but in space-time. It is the length of a curve is space time and so is independent of which inertial frame you use to describe it - and, by extension, of the time coordinate used in that particular frame.

 

[Smattering]

Why does a human body situated on Earth show signs of wear, aging, decay at a different rate than to a human body traveling (accelerating, decelerating) around the speed of light?

It's not about staying on earth. Rather, it ís about changing the inertial frame of reference opposed to staying within the same inertial frame of reference.
If person A stays within the same inertial frame all the time, while person B changes his inertial frame, then person B will have aged slower when they reunite.
If both persons stay within the same inertial frame or they change their inertial frames symmetrically, then they will have aged at the same rate,when they reunite.

How is Time Dilation related to biological processes?

Time dilation "slows down" all physical processes. As biological processes are just a special case of physical processes, they are "slowed down" as well from the perspective of an unaffected observer. THe same is true for any clock-like device that can exist. Because clock-like devices are based on physical processes as well. Actually, measuring time with a clock is like measuring mass with a beam balance. As the beam balance needs some reference weights, the clock needs a reference process. And this reference process that is used for time measurements will be "slowed down" in the same way as any other process.

 

[Orodruin]

It's not about staying on earth. Rather, it ís about changing the inertial frame of reference opposed to staying within the same inertial frame of reference.

This is a common misconception. An observer does not "belong" to an inertial frame. All observers exist in all inertial frames and may be described using either. What is happening is that just trying to apply the time dilation formula to the traveling twin, you are using different inertial frames to describe different parts of the journey. This is perfectly fine as long as you remember to take the relativity of simultaneity into account.

 

[Smattering]

This is a common misconception. An observer does not "belong" to an inertial frame.

I did not use the term "belong".

All observers exist in all inertial frames and may be described using either.

O.k., I see that this is a terminological minefield. So let's leave away all frames and express it in terms of acceleration.

What is happening is that just trying to apply the time dilation formula to the traveling twin, you are using different inertial frames to describe different parts of the journey. This is perfectly fine as long as you remember to take the relativity of simultaneity into account.

Nevertheless, there is a pretty simple heuristic to tell which of the twins will have aged at slower rate when they reunite: It is the one who accelerated. Also, when both of the twins accelerate symmetrically, they will have aged at the same rate when they renuite.

 

[Orodruin]

Nevertheless, there is a pretty simple heuristic to tell which of the twins will have aged at slower rate when they reunite: It is the one who accelerated. Also, when both of the twins accelerate symmetrically, they will have aged at the same rate when they renuite.

While this is true, it gives the impression that acceleration plays a central role, which it does not. Any effects from the accelerating parts of the journey can be made completely negligible simply by extending the constant velocity parts. The twin "paradox" comes about simply from missing out on the relativity of simultaneity and blindly applying the time dilation formula.

Regarding the acceleration, it is relatively simple to show that the straight, unaccelerated path in Minkowski space between two events will maximise the proper time between them. This is no stranger than a straight line minimising the length of a curve between two points in Euclidean geometry.

 

[Herman Trivilino]

So you mean a human body situated on Earth does not show any signs of wear, aging, decay any differently (at a different rate) than a human body traveling (accelerating, decelerating) around the speed of light, then returning to Earth...

They experience different amounts of proper time. Proper time is the time on your wrist watch. Say you spend a decade traveling at high speeds along a path that returns you home. Your wrist watch will confirm that a decade of time has passed. You are 10 years older than you were when you left.

You compare the readings on your wrist watch to the clock you left behind in your kitchen and you find a discrepancy. Clocks and calendars on Earth indicate a proper time of 100 years have passed. You visit the grave of your twin brother who died of old age while you were gone. You find that you had grandchildren, not yet born when you left, who are now dead of old age after having lived long lives and raising children of their own. You visit those great grand children and they have family albums and remember stories their grandfather told them about his father who left on a trip 100 years ago. That person is you.

We just use this human aging example in textbooks when covering Time Dilation to confuse students with some bogus, fictional stories because we can not explain it better?

Do you suppose this is done on purpose with malice, or do you think it's something that people are doing because they misunderstand?

Time dilation is a scientific fact. It follows from logic based on sound principles. It's been verified in countless ways by countless experiments.

When the idea was introduced just over 100 years ago it was met with doubts of the type you have about its veracity. These doubts likely contributed to the overwhelming number of experimental verifications carried out. It is now a fact of life for scientists and engineers who use it every day. If, for example, they have it wrong, your GPS wouldn't be able to tell you what street you're driving on. The best it could do is tell you what state you're in, something you already know, rendering the device useless.

 

[Smattering]

Regarding the acceleration, it is relatively simple to show that the straight, unaccelerated path in Minkowski space between two events will maximise the proper time between them. This is no stranger than a straight line minimising the length of a curve between two points in Euclidean geometry.

Yes, exactly *this*. And I guess that the OP will be completely satisfied as soon as he comes to this conclusion.

While this is true, it gives the impression that acceleration plays a central role, which it does not.

I am not sure whether I can agree here. If the unaccelerated path maximizes proper time, then to say that acceleration does not play a role, seems a bit exaggerated to me. It might not be the root cause, but it certainly plays a role.

Any effects from the accelerating parts of the journey can be made completely negligible simply by extending the constant velocity parts.

You can also make the steering parts of a car journey completely negligible simply by extending the constant direction parts. Still that "negligible steering" might have a huge impact on the result.

 

[PAllen]

Smattering,

Acceleration of either or both observers is necessary to have them co-located at two events (in SR, which is all we are considering here). That is the only role it plays in differential aging along different world lines. Ascribing more to it leads to difficulties with scenarios where both observer's have identical acceleration experiences, yet age differently between meetings. For example, let B recede from A inertially at .8c in A's rest frame. After 1 year on B's clock, B applies an acceleration profile such as to reverse direction and speed very quickly (per A's initial rest frame). After 3 years on A's clock, A applies the identical acceleration profile toward B. If you draw the spacetime diagram, you will see that this is all possible. Then, at meeting, A will have obviously aged over 3 years, while B will have aged less than 2 years.

 

[Smattering]

For example, let B recede from A inertially at .8c in A's rest frame. After 1 year on B's clock, B applies an acceleration profile such as to reverse direction and speed very quickly (per A's initial rest frame). After 3 years on A's clock, A applies the identical acceleration profile toward B. If you draw the spacetime diagram, you will see that this is all possible. Then, at meeting, A will have obviously aged over 3 years, while B will have aged less than 2 years.

Yes, I am aware of this. That's why I wrote that they have to accelerate *symmetrically* in order to have aged at the same rate when they reunite. The spacetime diagram will certainly reveal that the example you mentioned is not symmetrical.

 

[PAllen]

Yes, I am aware of this. That's why I wrote that they have to accelerate *symmetrically* in order to have aged at the same rate when they reunite. The spacetime diagram will certainly reveal that the example you mentioned is not symmetrical.

It is true there is an asymmetry, but it is not in the acceleration, per se. By construction, the readings on a recording accelerometer during acceleration period will be identical for A and B. The asymmetry is, of course, when, on their own clocks, they choose to accelerate.

 

[Nugatory]

Nevertheless, there is a pretty simple heuristic to tell which of the twins will have aged at slower rate when they reunite: It is the one who accelerated. Also, when both of the twins accelerate symmetrically, they will have aged at the same rate when they renuite.

It gets trickier with more complicated acceleration profiles, and there is also a variant of the twin paradox in which both twins are in freefall (except for symmetrical accelerations at the two ends of the journey so that they can start and finish at rest relative to one another) throughout their journeys; all that's required is that they freefall in different trajectories around a gravitating body.

It's for this reason that we try to stress that the essence of the twin paradox is that the two different paths through spacetime have different lengths, and that the acceleration is just one of the means by which we might set the twins on their different paths.

This doesn't make what you're saying wrong, just that there is another way of thinking about it.

 

[Smattering]

there is also a variant of the twin paradox in which both twins are in freefall (except for symmetrical accelerations at the two ends of the journey so that they can start and finish at rest relative to one another) throughout their journeys; all that's required is that they freefall in different trajectories around a gravitating body.

Agreed, but as the OP referred to SR I excluded such cases.

It's for this reason that we try to stress that the essence of the twin paradox is that the two different paths through spacetime have different lengths, and that the acceleration is just one of the means by which we might set the twins on their different paths.

O.k., I can completely agree with this wording. But of course, only someone who is familiar with spacetime diagrams can follow those arguments.

This doesn't make what you're saying wrong, just that there is another way of thinking about it.

As I said before, I was only trying to give some simple heuristics for those that are not familiar with spacetime diagrams.

 

[russ_watters]

Can we try not to drag it too far from the op's question...?

So you mean a human body situated on Earth does not show any signs of wear, aging, decay any differently (at a different rate) than a human body traveling (accelerating, decelerating) around the speed of light, then returning to Earth...

As seen by who's clock? By his own clock, nothing seems to change about how fast he's aging. By a clock on Earth, it looks very different.

We just use this human aging example in textbooks when covering Time Dilation to confuse students with some bogus, fictional stories because we can not explain it better?

It's used (and you apparently asked about it) because if people only talk about clocks, many people will come away believing it only applies to clocks (due to some unknown error). Talking about human aging (standing next to your twin, who is *magically* much older than you) helps convince people it is real and what it really means for the concept of time.

 

[Smattering]

It's used (and you apparently asked about it) because if people only talk about clocks, many people will come away believing it only applies to clocks (due to some unknown error). Talking about human aging (standing next to your twin, who is *magically* much older than you) helps convince people it is real and what it really means for the concept of time.

Because people do not seem to understand that biological processes are just a special case of physical processes.

And also people do not seem to understand that we measure time by observing the progress of physical processes that we are using as a reference. There is just no way to measure time "directly".

 

[kinimod]

Thanks everybody. I still can't comprehend it on human aging though.

In my mind, if you take 1 million teenagers today on planet Earth and shoot them into space for exploration around the entire galaxy, they can make stops on planets, change directions, accelerate and decelerate as they wish to any speed.

Once they at some point simultaneously reunite anywhere in the universe (might as well be planet Earth), regardless of how each was managing his/her particular motion, speed or stopovers, they will all see each other aged just like if they all remained on Earth the whole time. The net effect would be that nobody would notice any strange discrepancy in the age of others, e.g. in form of someone appearing unexplainably young.

If I am wrong, then by definition it means that particular accelerations, cruising, decelerations and gravity have very specific and lab-reproducible effects on human/organic biology (physics in general in fact), and with the right mix of speed variation and gravities, you can force some human to decay slower compared to the rest of civilization just by flying him around the Solar System for a while. He comes back and everybody is dead, while he's still a handsomely fresh guy.

What am I missing?

 

[Smattering]

Thanks everybody. I still can't comprehend it on human aging though.

What makes you think that biological processes like human aging might behave any different from physical processes like radioactive decay?

If I am wrong, then by definition it means that particular accelerations, cruising, decelerations and gravity have very specific and lab-reproducible effects on human/organic biology (physics in general in fact),

Yes.

and with the right mix of speed variation and gravities, you can force some human to decay slower compared to the rest of civilization just by flying him around the Solar System for a while.

Yes.

He comes back and everybody is dead, while he's still a handsomely fresh guy.

With the velocities that our current technology allows us to reach, it would rather be a fraction of a second. But with a sufficiently precise clock, it can still be measured, and this has already been done.

What am I missing?

This:

http://home.earthlink.net/~owl232/twinparadox.pdf

 

[russ_watters]

If I am wrong, then by definition it means that particular accelerations, cruising, decelerations and gravity have very specific and lab-reproducible effects on human/organic biology...

What am I missing?

The mechanism(s). Or, rather, the need for them.

For example, a pendulum clock has a specific reaction to acceleration, which alters it's tick rate vs other processes in a predictable way. See, it is YOUR idea that requires individual mechanisms to describe how different processes are affected differently (or not, which is what is observed).

There simply is no mechanism or collection of many different mechanisms that coincidentally all vary at the same rate which could explain what has been observed. There is no evidence that time dilation is anything but really, truly, no fooling, different rates of the passage of time between different observers.

 

[Orodruin]

What am I missing?

You are missing that the only time which is of actual physical relevance in relativity is the proper time, which describes the time elapsed for an observer following a particular world line. Observers following different world lines will experience different proper times. The time coordinate $t$ which appears in special relativity is just that, a coordinate without actual physical significance in itself. There is no universal time which everybody can use as a reference. In fact, you cannot say that the teenagers have been away for T years, where T is some fixed number, without specifying for whom T years have passed.

 

[kinimod]

Thanks all again. I really appreciate it and I think I'm making progress in visualizing and comprehending the concept.

I am now understanding the following: In non-inertial reference frame the laws of physics vary depending on the acceleration of that frame (with respect to some inertial frame).

I am imagining an accelerating atom in which electrons have to "compensate" and behave differently to remain in an atom structure -- compared to electrons in another hypothetical atom not undergoing acceleration.

Consequence of that is e.g. muons decaying differently, or e.g. humans showing signs that we perceive as being further away from death (I'm careful to not use words like "faster" or "age" here).

Is this correct? If laws of physics vary as described above (and solely depending on acceleration), then the question is "well how exactly do they vary?". Is there non-mathematical way of explaining the variation?