Time Dilation and Differential Aging

[Sherlock]

I know very little about SR -- just the transformation equations I learned in high school.

I remember reading somewhere that time dilation is a symmetric artifact of the synchronization convention, and that, by itself, it isn't the reason for differential aging. The reason, if I'm remembering accurately, had to do with geometric interpretation and also the idea that 'empty space' isn't really emptly.

I'm sure you get naive questions all the time from laypersons (like me) who have difficulty getting wrapped around the idea that aging is a function of velocity (or is it a function of acceleration?) Anyway, I'm thinking, velocity wrt what?

Remembering that the transformations had to do with two observers, each with their own clock, moving relative to each other, I wondered if they would record the same time (for, say, a round trip by one of them from the Earth to the Andromeda galaxy and back) if they were both using the *same* clock (say, revolutions of the Earth around the Sun). Of course, the traveller would record fewer revolutions on his way to Andromeda than on his way back, and the rate at which he recorded them would be different than the rate at which the Earthbound observer recorded them. However, on landing back on Earth, wouldn't the traveller have recorded the same total number of revolutions for his trip as the Earthbound observer?

If not, why? If so, then what would it mean to say that they aged differently?

 

[jtbell]

The traveler agrees that the Earth has made the same number of orbits around ths sun during his trip, as are counted by the stay-at-home twin. The details of how he comes to that conclusion depend on exactly how he uses the Earth's orbits as a clock. If he does it by watching the Earth and Sun through a telescope as he travels out and back, then the situation is exactly like the one analyzed in posting #3 in this thread (click here).

But in this case, the traveler simply sees the Earth revolving at a different rate than it normally does. He experiences the actual passage of time (i.e. grows older) according to clocks that he carries along with him.

Note that the traveler actually sees the Earth revolving at different rates during the outbound and inbound halves of his trip. What he actually sees with his eyes depends not only on the Earth's rate of revolution in his reference frame (via time dilation), but also on the time it takes for light to travel from the solar system to his eyes, which continually changes as he travels (via the Doppler effect).

 

[JesseM]

I remember reading somewhere that time dilation is a symmetric artifact of the synchronization convention

It isn't. If you used the same type of synchronization convention in a Newtonian universe you wouldn't see any time dilation.

I'm sure you get naive questions all the time from laypersons (like me) who have difficulty getting wrapped around the idea that aging is a function of velocity (or is it a function of acceleration?) Anyway, I'm thinking, velocity wrt what?

Relative to any inertial frame--although of course, different frames will disagree on the rate that a given person is aging. But if two people separate, move apart for a while and then reunite, all frames will make the same prediction about what ages the people will be when they reunite, and they'll all agree that the one who moved inertially aged more than the one who didn't. You can think of this in analogy with picking two points on a piece of paper, then drawing two paths between them, one straight and one bendy--you could then draw different xy axes on the paper, and in each coordinate system see how x is changing as a function of y along each path and integrate it to find the total length of the path. Even though different coordinate systems would have different functions for how x changes as a function of y along a given path, they'd all get the same answer for the lengths of the two paths between the points, and the straight-line path would always be the shorter one no matter how the bendy path was drawn.

Remembering that the transformations had to do with two observers, each with their own clock, moving relative to each other, I wondered if they would record the same time (for, say, a round trip by one of them from the Earth to the Andromeda galaxy and back) if they were both using the *same* clock (say, revolutions of the Earth around the Sun). Of course, the traveller would record fewer revolutions on his way to Andromeda than on his way back, and the rate at which he recorded them would be different than the rate at which the Earthbound observer recorded them. However, on landing back on Earth, wouldn't the traveller have recorded the same total number of revolutions for his trip as the Earthbound observer?

Sure, otherwise the two observers would be making different predictions about actual physical events, which can't happen. If two clocks cross paths at a single point in spacetime, all frames have to agree about what each clock reads at that moment. And the Earth going around the sun can be thought of as a type of clock, you could imagine big numbers displayed on the Earth which increment each time it completes an orbit.

 

[Sherlock]

The traveler agrees that the Earth has made the same number of orbits around ths sun during his trip, as are counted by the stay-at-home twin.
...

He experiences the actual passage of time (i.e. grows older) according to clocks that he carries along with him.

The traveller isn't carrying a clock with him. The time convention that they're using is the Earth's revolutions around the sun. They count the same passage of time for the round trip. So, what does it mean to say that the traveller has aged differently?

Or, we could use the round-trip itself as the unit of time (their common clock), and during this unit of time they count the same number of earth-sun revolutions.

I'm thinking that maybe SR just doesn't apply here.

Maybe a better way of framing my question is to have the traveller simply fly around the Earth for, say, five years (five earth-sun revolutions). They would both count the same number of revolutions that the traveller has made around the Earth during this time.

I'm thinking of time-keeping as an arbitrary convention. As with all things, what is observed depends on the observational context. The earthbound observer and the traveller are always part of some encompassing motional system. In the last example, wrt the motion of the solar system in its local group, both observers have traveled the same distance in the same amount of time.

Anyway, the way I'm thinking about it, differential aging shouldn't really have anything to do with time dilation due to Lorentz transformations and Einstein's simultaneity convention, since this is applicable only to a certain, arbitrarily chosen, observational context.

 

[Sherlock]

It isn't. If you used the same type of synchronization convention in a Newtonian universe you wouldn't see any time dilation.

Yes, I remember now that it was the *transformations* and the simultaneity convention that produced the time dilation effects.

Relative to any inertial frame--although of course, different frames will disagree on the rate that a given person is aging. But if two people separate, move apart for a while and then reunite, all frames will make the same prediction about what ages the people will be when they reunite, and they'll all agree that the one who moved inertially aged more than the one who didn't.

If all frames agree that the trip took, say, five years (all observers counted the same number of earth-sun revolutions for the trip), then where's the differential aging?

 

[JesseM]

Yes, I remember now that it was the *transformations* and the simultaneity convention that produced the time dilation effects.

But even that's not quite enough--after all, you could use the same coordinate transformation in a Newtonian universe, but natural physical clocks would not tick at the same rate as the coordinate time in their rest frame. It's the fact that the laws of physics are Lorentz-invariant that produces differential aging, where "Lorentz-invariance" means the laws obey the same equations in all the different coordinate systems produced by the Lorentz transformation.

If all frames agree that the trip took, say, five years (all observers counted the same number of earth-sun revolutions for the trip), then where's the differential aging?

Because "differential aging" refers specifically to comparing clocks that move along with both travelers. Anyway, even if the space traveller doesn't carry a clock along with him, all the natural clocks in his body will have elapsed more time (this is why twins are usually used in the thought-experiment, so you can tell that one is visibly older than the other).

 

[jtbell]

So, what does it mean to say that the traveller has aged differently?

It means, for example, that if the trip is long enough, the stay-at-home twin's hair turns grey but the traveller's hair does not.

This particular effect hasn't been observed yet (differential hair-turning-grey), but a similar phenomenon is routinely observed in high-energy particle physics, where fast-moving particles decay more slowly than slow-moving ones.

 

[Janus]

If all frames agree that the trip took, say, five years (all observers counted the same number of earth-sun revolutions for the trip), then where's the differential aging?

That all depends on how you define a "year". If you define it as 31,558,464 sec, then the spaceship twin will say that the trip took fewer than 5 years while the Earth twin will say that it took 5 years.

If you define it by "one Earth-Sun revolution, then they will say the trip took the same number of "years', but the Spaceship twin will say that each year lasted for fewer seconds than the Earth will.

Example:
Assume that the relative velocity is 0.866c, and each twin has an average heart rate of 60 beats/min. Then, during five Earth-Sun revolutions, the Earth twin will have experienced 157,792,320 heartbeats, and the Spaceship twin will have experienced 78,896,160 heartbeats.

 

[Sherlock]

It's the fact that the laws of physics are Lorentz-invariant that produces differential aging, where "Lorentz-invariance" means the laws obey the same equations in all the different coordinate systems produced by the Lorentz transformation.

Effects produced by relative motion are symmetric, isn't this correct? Isn't that one of the reasons why SR was developed -- to deal with these effects symmetrically, rather than asymmetrically as had been done before?

So, I'm having a difficult time understanding how this applies to differential aging? I remember that the writer of the article that I'm trying to remember (I think it might have been Keating -- he's not some quack or something is he?) said something about time dilation and differential aging being due to different reasons (a different relative history of acceleration or something like that). And, as I was reflecting on this recently it seemed to make sense, sort of.

... "differential aging" refers specifically to comparing clocks that move along with both travelers.

That's what I thought. So, if they're using the same clock then there's no differential aging ... I thought. :-) However, the author of the paper said that there is differential aging, but that it was due to empty space having a metric structure, that empty space isn't really empty. If this is true, then does acceleration mean more, or less, interaction between the accelerating object and the structure of space?

Do you understand my confusion yet? Because I, obviously, don't? :-)

Anyway, even if the space traveller doesn't carry a clock along with him, all the natural clocks in his body will have elapsed more time (this is why twins are usually used in the thought-experiment, so you can tell that one is visibly older than the other).

Isn't the earth-sun system a natural clock?

 

[Sherlock]

This particular effect hasn't been observed yet (differential hair-turning-grey), but a similar phenomenon is routinely observed in high-energy particle physics, where fast-moving particles decay more slowly than slow-moving ones.

Could you give a brief summary of how those experiments work?

 

[Sherlock]

That all depends on how you define a "year". If you define it as 31,558,464 sec, then the spaceship twin will say that the trip took fewer than 5 years while the Earth twin will say that it took 5 years.

If you define it by "one Earth-Sun revolution, then they will say the trip took the same number of "years', but the Spaceship twin will say that each year lasted for fewer seconds than the Earth will.

Example:
Assume that the relative velocity is 0.866c, and each twin has an average heart rate of 60 beats/min. Then, during five Earth-Sun revolutions, the Earth twin will have experienced 157,792,320 heartbeats, and the Spaceship twin will have experienced 78,896,160 heartbeats.

Assuming that's true, then what physical-mechanical interaction is *causing* this differential aging -- or is it an open question?

For example, I have no doubt that gravitational fields affect the period of anything that one might want to use as a clock. But, with gravitational fields the reason for this is a bit easier for me to conceptualize/visualize than with an object simply accelerating from a previous state of motion.
Hmmm, is the answer to my question in there somewhere? Is differential aging connected to gravitational fields?

 

[JesseM]

Effects produced by relative motion are symmetric, isn't this correct?

Only if the motion is inertial. The laws of physics will look the same to an experimenter in any two windowless boxes that aren't accelerating, but in an accelerating box they'll look different.

That's what I thought. So, if they're using the same clock then there's no differential aging ... I thought. :-) However, the author of the paper said that there is differential aging, but that it was due to empty space having a metric structure, that empty space isn't really empty. If this is true, then does acceleration mean more, or less, interaction between the accelerating object and the structure of space?

I don't know what you mean by "interaction between the accelerating object and the structure of space". Again, you can think in terms of the analogy I made earlier with the distance between points on an ordinary 2D piece of paper--just as the "structure" of euclidean space is such that the shortest path between two points is a straight line, so it is that the "structure" of spacetime is such that the path between two points in spacetime with the greatest proper time (time as measured by a clock that follows that path) is an inertial one. Just as all non-straight paths between points in 2D space will have a greater length than the straight one, so all non-straight (accelerating) worldlines between two points in spacetime will have a shorter proper time than the straight one. And just as you could use different coordinate systems in a euclidean space which would give different functions y(x) for a given path, and thus different functions s(x)=dy/dx for the slope of the path as a function of x, yet no matter which coordinate system you used you'd get the same answer for the total length of the path when you integrate the appropriate function involving s(x) (I think you'd have to integrate $$\int \sqrt{1 + s(x)^2} \, dx$$, because if you have a right triangle with horizontal side x and vertical side y then the length of the hypotenuse is $$x \sqrt{1 + (y/x)^2}$$, but I could have that wrong), so it's analogously true that despite the fact that different coordinate systems have different functions x(t) for a path through spacetime, and thus different functions v(t) for the velocity as a function of time, when you integrate $$\int \sqrt{1 - v(t)^2/c^2} \, dv$$ in each coordinate system you'll get the same answer for the total amount of time ticked by a clock moving along that path (note that in any reference frame, a clock moving at velocity v will tick at $$\sqrt{1 - v^2/c^2}$$ the rate of a clock at rest in that reference frame).

Isn't the earth-sun system a natural clock?

Yes, but it isn't one moving along with the traveling twin. If the traveling twin took an exact copy of the earth-sun system along with him, his Earth #2 would make less orbits around sun #2 than the original Earth around the original sun. This is because the original sun is moving (approximately) inertially while the sun moving along with the traveling twin is not.

 

[Sherlock]

Only if the motion is inertial. The laws of physics will look the same to an experimenter in any two windowless boxes that aren't accelerating, but in an accelerating box they'll look different.

Isn't everything accelerating wrt, perhaps, many different gravitational hierarchies. That is, aren't gravitational fields more or less everywhere?

I don't know what you mean by "interaction between the accelerating object and the structure of space".

Neither do I at this point. Just some vague idea having to do with wave interactions.

... but it isn't one moving along with the traveling twin.

In the revised example I gave, the traveller remains, along with the earthbound observer, part of the earth-sun system. Of course, his trip still has him moving differently wrt the gravitational field than the earthbound observer. So, I'm thinking that it's this differential interaction with the gravitational field that has to do with any differential aging that might be observed.

 

[Sherlock]

If the traveling twin took an exact copy of the earth-sun system along with him ...

Isn't that, in effect, what he's doing by observing light from the earth-sun system during his trip?

 

[JesseM]

Isn't everything accelerating wrt, perhaps, many different gravitational hierarchies. That is, aren't gravitational fields more or less everywhere?

Special relativity doesn't deal with gravity, it just deals with flat spacetime, while general relativity treats gravity in terms of curved spacetime.

In the revised example I gave, the traveller remains, along with the earthbound observer, part of the earth-sun system.

What does "part of it" mean? The sole issue here is that the Earth twin is moving inertially, or close to it anyway, while the other twin is accelerating significantly.

Isn't that, in effect, what he's doing by observing light from the earth-sun system during his trip?

No, he is accelerating significantly relative to the sun. If he took a copy of the sun along with him, and he was at rest wrt this copy throughout his trip, and meanwhile the first twin was at rest with respect to the original sun, then the copy sun would undergo fewer orbits.

 

[Janus]

In the revised example I gave, the traveller remains, along with the earthbound observer, part of the earth-sun system. Of course, his trip still has him moving differently wrt the gravitational field than the earthbound observer. So, I'm thinking that it's this differential interaction with the gravitational field that has to do with any differential aging that might be observed.

No, there would be an age difference even if there were no gravitational fields present. In fact, Special Relativity only deals with situations where there are no gravitational fields. General Relativity is needed to deal with the addtional effects due to the presence of gravitational fields.

 

[Sherlock]

The sole issue here is that the Earth twin is moving inertially, or close to it anyway, while the other twin is accelerating significantly.

Ok, so my question becomes: what is it about this acceleration that is causing the traveller's natural periods to be altered? Is it in part due to a change in way he is interacting (due to the changes in his motion) with the gravitational fields that he is traveling through. Might it have anything to do with the expansion of the universe?

The thing is, it doesn't seem to me to be correct to say that the differential aging is caused by time dilation. I mean you can use the transformations to calculate the effect, but that doesn't tell you why it's happening -- does it?

 

[JesseM]

Ok, so my question becomes: what is it about this acceleration that is causing the traveller's natural periods to be altered?

I dunno, that's like asking what is it about curved paths between points in euclidean space that make them always be longer than a straight-line path between the same two points.

Is it in part due to a change in way he is interacting (due to the changes in his motion) with the gravitational fields that he is traveling through. Might it have anything to do with the expansion of the universe?

No. Both gravity and the expansion of space are part of GR and do not exist in flat spacetime, but the twin paradox certainly works in flat spacetime...SR is solely concerned with what happens in flat spacetime.

The thing is, it doesn't seem to me to be correct to say that the differential aging is caused by time dilation. I mean you can use the transformations to calculate the effect, but that doesn't tell you why it's happening -- does it?

Again, why is it that a curved path between two points in euclidean space is always longer than a straight path between the points? Do you need an explanation of "why" this is besides just noting that it's a consequence of how distance works in euclidean geometry?

 

[jtbell]

(about high-energy particle physics experiments where fast-moving particles decay more slowly than slow-moving ones)

Could you give a brief summary of how those experiments work?

As an example, one of my friends in graduate school was part of a group that studied sigma and xi hyperons. These particles decay with a very short lifetime that had been well-measured at low speeds (small energies). The apparatus produced a high-energy beam of these particles, traveling at a significant fraction of the speed of light. Despite their high speed, if the particles had had the same lifetime as at low speeds, the beam would have extended only a very short distance, maybe a few millimeters or centimeters. (This was 25 years ago, so I don't remember the specific numbers.) However, because of time dilation, these fast-moving particles lived long enough to produce a beam several meters long, which made it a lot easier to study them.

Note that time dilation was not the point of the experiment; rather, time dilation was simply used as a means of making the experiment feasible. If time dilation didn't work the way relativity predicts, this experiment would not have been possible. I've forgotten what the actual goal of the experiment was... something like measuring the particles' spin magnetic moments.

 

[Sherlock]

No, there would be an age difference even if there were no gravitational fields present.

How could we know for sure -- since there's always gravitational fields present?

 

[Sherlock]

I dunno, that's like asking what is it about curved paths between points in euclidean space that make them always be longer than a straight-line path between the same two points.

I think it's a bit different than asking that. :-)

 

[robphy]

The thing is, it doesn't seem to me to be correct to say that the differential aging is caused by time dilation. I mean you can use the transformations to calculate the effect, but that doesn't tell you why it's happening -- does it?

Try this:
http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/ , which puts more emphasis on the operational physics and less emphasis on the mathematics of the transformation. It provides a visualization of the Clock Effect.

 

[JesseM]

I think it's a bit different than asking that. :-)

Why do you think it's different? The analogy is pretty good, as I tried to make clear in earlier posts. A geodesic in 2D space is the path between two points with the shortest length, and a geodesic in spacetime is the path between two events with the greatest proper time (this is true in the curved spacetime of GR as well, but in flat spacetime the geodesic will always be the straight worldline). Where do you think the analogy breaks down?

 

[JesseM]

How could we know for sure -- since there's always gravitational fields present?

Because that's what SR predicts, and GR reduces to SR in the case of flat spacetime. So unless both GR and SR are wrong, differential aging has nothing to do with gravity.

 

[Janus]

How could we know for sure -- since there's always gravitational fields present?

Because then the results one would get would differ from those predicted by Relativity, and all the experimental results we have agree with Relativity.

 

[Sherlock]

Try this:
http://physics.syr.edu/courses/modules/LIGHTCONE/LightClock/ , which puts more emphasis on the operational physics and less emphasis on the mathematics of the transformation. It provides a visualization of the Clock Effect.

Thanks, that's a great page. I've downloaded it and some of the cool animations. However, I'm not really having any difficulty visualizing time dilation. My consideration has more to do with the physical cause(s) of differential aging.

Since I started this thread, I found the article that I was trying to remember. The author (Keating) says that in modern relativity "empty space is an existing reality with physical content and is the immediate physical cause of twin clock effects". Put this way, accumulated time dilation effects due to relative velocity and acceleration don't seem so counter-intuitive.

I also wondered about the physical connection between acceleration and gravity. Thinking in terms of intensity and complexity (density?) of wave-system interactions, the connection seems a bit clearer to me now.

 

[Sherlock]

Why do you think it's different? The analogy is pretty good, as I tried to make clear in earlier posts. A geodesic in 2D space is the path between two points with the shortest length, and a geodesic in spacetime is the path between two events with the greatest proper time (this is true in the curved spacetime of GR as well, but in flat spacetime the geodesic will always be the straight worldline). Where do you think the analogy breaks down?

There's nothing wrong with it, afaik. It's just that I wasn't looking for a geometrization of the kinematics.

Thanks for your replies, I'm going to stop thinking about this now. It makes my head hurt. :=)

 

[Sherlock]

... both GR and SR are wrong, differential aging has nothing to do with gravity.

My current conception is that the physical nature of differential aging has to do with wave-system interactions. This has everything to do with gravity, acceleration, or any motion for that matter. A comprehensive qualitative picture of the interactions has yet to be developed of course.

 

[Sherlock]

Because then the results one would get would differ from those predicted by Relativity, and all the experimental results we have agree with Relativity.

Gravitational fields are everywhere, aren't they? Maybe these fields are the 'stuff' of empty space. Anyway, no matter where an object moves -- even in the emptiest of empty spaces -- it's always, I'm assuming, interacting with something. And this interaction (however vague a notion this might currently be) is what I take to be the physical nature of differential aging as well as any other effects produced by motion of any sort.

SR and GR provide accurate descriptions at a certain level. I was just looking for something (maybe some 'intuitive' speculation from those here who are well-versed in the theories) a bit deeper than that. Differential aging seems to be a fact of nature. But to say that it's *caused* by time dilation might be a bit misleading I think.

Thanks for your replies (and to anyone else who contributed).

 

[Sam Woole]

... The sole issue here is that the Earth twin is moving inertially, or close to it anyway, while the other twin is accelerating significantly. No, he is accelerating significantly relative to the sun. If he took a copy of the sun along with him, and he was at rest wrt this copy throughout his trip, and meanwhile the first twin was at rest with respect to the original sun, then the copy sun would undergo fewer orbits.

When Einstein demonstrated how time dilation happened, he always said it was "uniform motion v". Here as if you were saying, only accelerating SIGNIFICANTLY would produce the effect of time dilation while uniform motion would not. Why?

 

[Doc Al]

When Einstein demonstrated how time dilation happened, he always said it was "uniform motion v". Here as if you were saying, only accelerating SIGNIFICANTLY would produce the effect of time dilation while uniform motion would not. Why?

For two frames in relative motion, the time dilation "effect" is completely symmetric. Each measures the other's clocks as running slow (and being out of synch). In order for the twin to return to return to earth, so that his age can be directly compared to his brother's, he must accelerate. That breaks the symmetry, since the traveling twin cannot remain in a single inertial frame. But it's the relative speed, not the acceleration, that produces the differential aging.

 

[JesseM]

When Einstein demonstrated how time dilation happened, he always said it was "uniform motion v". Here as if you were saying, only accelerating SIGNIFICANTLY would produce the effect of time dilation while uniform motion would not. Why?

Only when acceleration is involved can they move apart and then reunite at a single spot to see whose clock is behind. As Doc Al said, if they are not in a single spot, then because they disagree about simultaneity, they can disagree about what their clocks read "at the same moment", so they can disagree about whose clock is behind. Take a look at my thread An illustration of relativity with rulers and clocks to see how two frames moving inertially can each say the other frame's clocks are running slow, but they'll never disagree about what two clocks passing next to each other at a single location in space read at the moment they pass.