Exploring the Paradox of Time Dilation: Who Experiences Slower Time?

[swerdna]

It was sylas that claimed it could be determined if a thing was accelerating by purely visual means not me. I didn’t remove the ability to view.

Is there anything incorrect with the following statements? (written in layman‘s-speak) . . .

(1) There is no point in the universe that is known to be actually stationary, therefore nothing can be correctly assumed to be either moving or stationary.

(2) Because of (1) - A thing doesn’t move relative to itself or any actual stationary point and therefore only moves relative to other things.

(3) Because of (1) and (2) - Any measurements of relative motion cannot be correctly attributed solely or partially to a single thing and all that can be correctly measured is the speed at which the things move relative to each other (the speed of moving apart or together).

 

[diazona]

I don't believe sylas ever claimed that it's possible to determine if a thing was accelerating by purely visual means.

A third observer CAN tell who is changing velocity, with nothing more than line of sight to the two twins, and working within their own local reference frame.

(emphasis added) The third observer's knowledge of his/her own local reference frame (basically, whether it's inertial or not) is cruicial.

Regarding your three statements, what's wrong with them is that they are written in layman-speak ;-p Unless one is being very precise about the wording it's easy to misinterpret statements like these.

(1) There is no point in the universe that is known to be actually stationary, therefore nothing can be correctly assumed to be either moving or stationary.

I think you may have an issue right there. Yes, it's true that you cannot ever identify a particular point or object and say "that is absolutely not moving." Nothing can be assumed to be stationary in an absolute sense. But something can be assumed to be moving in an absolute sense, if it is accelerating. An accelerating object cannot be stationary. (Forget about gravity for now)

 

[sylas]

It was sylas that claimed it could be determined if a thing was accelerating by purely visual means not me. I didn’t remove the ability to view.

Sylas is correct that you can tell something is accelerating by watching. You were trying to deny that, saying that a third observer would NOT be able to tell. You were wrong, and you responded to all attempts to show how it is done by removing the ability view the direction in which something is moving relative to you.

(1) There is no point in the universe that is known to be actually stationary, therefore nothing can be correctly assumed to be either moving or stationary.

It's poorly worded. There's no such thing as an absolute reference frame, but there are plenty of inertial frames, any of which will work perfectly well as a basis for calculations. Things most definitely can be "actually stationary" in your chosen reference frame.

So it's not a problem with being "actually" stationary, but being "absolutely" stationary, in a way that all observers can identify and agree upon.

(2) Because of (1) - A thing doesn’t move relative to itself or any actual stationary point and therefore only moves relative to other things.

That's a better way to express it. Motion is always in relation to something else.

(3) Because of (1) and (2) - Any measurements of relative motion cannot be correctly attributed solely or partially to a single thing and all that can be correctly measured is the speed at which the things move relative to each other.

The first part of this is difficult to parse, but if you simply mean that speed, or velocity is given in relation to something else, then that's okay.

Here's a thing, though. When you CHANGE your velocity, you can give the new velocity in relation to your previous self. This is acceleration, and it can be identified without reference to any other particles.

What this means is that you CAN be "absolutely inertial", even though there's no notion of "absolutely stationary". If you are holding a fixed velocity, then EVERYONE will agree that you are holding a fixed velocity.

In the extension to general relativity, substitute "in freefall" for "fixed velocity".

 

[sylas]

I don't believe sylas ever claimed that it's possible to determine if a thing was accelerating by purely visual means.

I did claim that. Purely visual means allow detection of acceleration quite easily. There may be some special cases where you are located in just the wrong position to detect an acceleration, but this is far and away the exception. A deceptive spaceship could possibly follow a course cunningly devised to appear that it is not accelerating, for one particular observer they want to deceive. But I think even this would be difficult when you consider information from redshift and angular size, as well as direction. In general, nearly all observers will note the acceleration easily.

If a particle is NOT accelerating, there are strict regularities in what can be observed. Violate any of those, and you must be accelerating.

Purely visual means allow you to know direction in the sky, angular size, red shift; and anyone of these can reveal a discontinuity that implies acceleration.

Cheers -- sylas

 

[Carid]

While separated, each clock will appear to run slower to the other observer.

So two of the triplets head off in their space ships in opposite directions. After accelerating to a reasonable fraction of the speed of light they both loop around some handy local star and both head back to base arriving at the same time. They find their third triplet looking somewhat aged up. They also agree that their own spaceship clocks show the same time.

During the journey each space-faring triplet kept an eye on the clock of the other. Both observed that the other was running slower. But on the return journey wouldn't they notice that the clock of the other had speeded up, otherwise how would they show the same time when they got back?

BTW ENGLISH GRAMMAR NITPICK : the title should be "Time dilation...but for whom?"

 

[JesseM]

So two of the triplets head off in their space ships in opposite directions. After accelerating to a reasonable fraction of the speed of light they both loop around some handy local star and both head back to base arriving at the same time. They find their third triplet looking somewhat aged up. They also agree that their own spaceship clocks show the same time.

During the journey each space-faring triplet kept an eye on the clock of the other. Both observed that the other was running slower. But on the return journey wouldn't they notice that the clock of the other had speeded up, otherwise how would they show the same time when they got back?

Visually yes, each one sees the other one's clock speed up when they are moving towards each other, because of the Doppler effect--this is also true in the standard twin paradox where one twin moves inertially the whole time, although in this case the inertial twin sees the non-inertial twin moving towards him for a smaller fraction of the trip than the non-inertial twin sees the inertial twin moving towards him (see the second diagram in this section of the twin paradox page). On the other hand, in the inertial frame where one of the twins is at rest during the return phase (his own inertial rest frame during that phase, although he wasn't at rest in this frame before turning around), the other twin's clock is ticking slow relative to the time coordinates of that frame, even though his clock will look like it's ticking fast to the first twin due to the Doppler effect.

 

[diazona]

I did claim that. Purely visual means allow detection of acceleration quite easily.

Sorry if I misinterpreted you... I wanted to point out what appeared to be a fallacy in swerdna's "distant lights in total darkness" idea.

 

[swerdna]

Sorry I should have made it clear that by “moving/motion” I was only meaning non-accelerating linear motion. I thought of making that clear but then forgot to do it. I have the flu (not swine thank dog) so the brain is even more of a mush than usual.

 

[sylas]

Sorry I should have made it clear that by “moving/motion” I was only meaning non-accelerating linear motion. I thought of making that clear but then forgot to do it. I have the flu (not swine thank dog) so the brain is even more of a mush than usual.

The whole idea of the dark room bit you introduced in [post=2183780]msg #25[/post] was a case of two twins moving apart and together again, and having a third observer trying to figure out which one turned around.

We've all been talking about accelerated motions -- you also -- for some time.

Cheers -- sylas

 

[squarkman]

What is the significance of turning around, to the relative ages of the twins?

If twin A remains on Earth and twin B gets in a spaceship and travels at .8 C, he should be younger when he returns. But is it a moot point if he is younger BEFORE he turns around since comparison is impossible?

So to compare the ages, he has to return which implies acceleration. But of course, just to get to .8 C you must also accelerate.

And when he turns around and comes back, that's doubling the amount of time he's accelerating, with respect to his twin B. Just making him younger still?

 

[JesseM]

What is the significance of turning around, to the relative ages of the twins?

If twin A remains on Earth and twin B gets in a spaceship and travels at .8 C, he should be younger when he returns. But is it a moot point if he is younger BEFORE he turns around since comparison is impossible?

So to compare the ages, he has to return which implies acceleration. But of course, just to get to .8 C you must also accelerate.

And when he turns around and comes back, that's doubling the amount of time he's accelerating, with respect to his twin B. Just making him younger still?

Initial and final accelerations don't have any significant effect on his age, assuming acceleration is brief. You could imagine that the guy who turns around had been moving inertially forever before that, and simply compared clocks with the guy on Earth when the passed by each other, and later compared clocks again after the turnaround when he passed the Earth in the opposite direction, so that the only acceleration on his worldline is during the turnaround itself--the difference in aging would be almost exactly the same. It's not that acceleration itself causes a difference in age to accumulate during the accelerated phase, it's more about the geometry of the two paths through spacetime, and how a turn implies a very differently-shaped path. There's a direct analogy between paths through spacetime and paths through a flat 2D surface. Suppose you mark two points on level ground, A and B; then two cars travel from A to B by different routes, one going on a straight path and one going on a path that has a bend in in it somewhere. If both cars have odometers that measure how much distance they've traveled along their paths (analogous to clocks measuring time elapsed on paths through spacetime), we know that since a straight line is always the shortest distance between points on a plane, the car that traveled on the straight path must have accumulated less distance than the car that traveled on the bent path. But the bent path might consist of two long straight segments at different angles, connected by only a very short non-straight segment, like the bend in a straw--did all its extra distance accumulate on that little curved segment? The answer is no, even if the odometer was turned off during the curved segment, the distance it accumulated on the two straight segments would be greater than the distance along the straight-line from A to B, because these two segments were at different angles rather than pointing directly along the axis from A to B.

The math with accumulated clock time on paths through spacetime is very similar, except that here a "straight" path through spacetime is the one with the greatest proper time, unlike in 2D space where a straight path is the one with the shortest distance. This has to do with the fact that if you have two points in a 2D spatial coordinate system (x1,y1) and (x2,y2), the distance along a straight line between them is given by the pythagorean theorem sqrt[(x2-x1)^2 + (y2-y1)^2], whereas in spacetime if you have two points (x1,t1) and (x2,t2), when calculating the time on a clock that travels a straight path between them you actually subtract (x2-x1) rather than add it, i.e. sqrt[(t2-t1)^2 - (x2-x1)^2/c^2]. But aside from that one difference the two situations are identical mathematically, so intuitions about paths through space are helpful when understanding paths through spacetime.

 

[squarkman]

Hmm, so it's all about how you traverse space-time. not about your rate of change of velocity...Although you do have to approach the speed of light for significant effect. Yes?

I'm just really thrown by the turning around 180 degrees thing.

Regarding your 2D analogy...let's say twin 1 stays at point A and twin 2 travels to point B (all on 2D flat geometry). He could go straight to B from A but then take any of an infinite alternative routes back, not straight.

How would doing this in space-time affect the relative clocks?

Let's say he did the 4D analogy of traversing the perimeter of a square. A to B is the first lap of his journey. Then coming home, he goes from B to C, C to D and finally D to A again. How would this affect time for the twin 2?

In this case, he rather takes three 90 degree turns instead of one 180 degree turn. This implies a great difference in his path home.

In the original case he went from A to B turned around 180 degrees and came back. In the latter. he does a squarish route in space-time. No difference, great difference or incalculable difference?
Thx

 

[swerdna]

The whole idea of the dark room bit you introduced in [post=2183780]msg #25[/post] was a case of two twins moving apart and together again, and having a third observer trying to figure out which one turned around.

We've all been talking about accelerated motions -- you also -- for some time.

Cheers -- sylas

My post #36 was to find out if my current understanding of non-accelerated linear motion is correct or not.

I agree that my statement (1) of post #36 is incorrect and as diazona (and others) correctly pointed out “Something can be assumed to be moving in an absolute sense if it is accelerating.” I already knew this and am puzzled and disappointed that I wrote what I did.

As I understand it acceleration itself doesn’t cause time dilation but apparently is somehow important because it establishes that a thing has changed its direction or speed and therefore experiences different “frames“. Unless things retain some form of memory of acceleration I can‘t see that which thing accelerates to cause it to move relative to something else is important. I can’t see how relative movement is anything but symmetrical regardless of which thing accelerates. I guess what I find hard to accept about relativity is that it seems to consider things from abstract partial views (frames) and doesn’t consider a universal or omnipresent view. I know that an omnipresent view of the universe isn’t possible but that doesn’t mean that the universe doesn’t have an omnipresent existence. The limitations of observation affect the perception of existence but I can’t see that they can change the actual reality of existence.

 

[JesseM]

Hmm, so it's all about how you traverse space-time. not about your rate of change of velocity...Although you do have to approach the speed of light for significant effect. Yes?

I'm just really thrown by the turning around 180 degrees thing.

Regarding your 2D analogy...let's say twin 1 stays at point A and twin 2 travels to point B (all on 2D flat geometry). He could go straight to B from A but then take any of an infinite alternative routes back, not straight.

How would doing this in space-time affect the relative clocks?

Let's say he did the 4D analogy of traversing the perimeter of a square. A to B is the first lap of his journey. Then coming home, he goes from B to C, C to D and finally D to A again. How would this affect time for the twin 2?

In this case, he rather takes three 90 degree turns instead of one 180 degree turn. This implies a great difference in his path home.

In the original case he went from A to B turned around 180 degrees and came back. In the latter. he does a squarish route in space-time. No difference, great difference or incalculable difference?
Thx

Well, in a spacetime diagram you can't make a square path because if time is the vertical axis, then a horizontal path would mean you were covering a finite distance in zero time, implying infinite velocity. The slope of any traveler would have to be closer to vertical than the slope of a light ray, which if you use units where c=1 (like light-years on the space axis and years on the time axis) looks like a 45 degree angle on a spacetime diagram.

You can talk about a path consisting of a bunch of constant-velocity segments joined by instantaneous acceleration, though. In this case, from the perspective of an inertial coordinate system, if you know the coordinate time delta-t between the beginning of a given segment and the end of it, and the velocity the ship was moving during that segment, then the time elapsed on the ship's clock during that segment will just be delta-t times the time dilation factor of sqrt(1 - v^2/c^2). Then you can just do the same thing for all the segments and add up the results to find the total time elapsed on the ship's path over the entire trip. The neat thing about this is it doesn't matter what inertial frame you use to calculate the time elapsed on a given segment--different frames will disagree about the value of delta-t on that segment, and also disagree about the value of v, but they always agree on the time elapsed on the ship's clock. For example, suppose in Earth's frame the first segment consists of the ship moving away from the Earth at 0.8c until it reaches a star 16 light-years away in the Earth frame, at which point it accelerates. At 0.8c it'll take 16/0.8 = 20 years in the Earth frame for it to get to that star, but the ship's clock is calculated to be slowed down by a factor of sqrt(1 - 0.8^2) = 0.6 in this frame, so the ship's clock is only predicted to tick forward by 20*0.6 = 12 years. Now switch to a frame where the ship is at rest during this segment--in this frame the distance between the Earth and the star is shrunk to 16*0.6 = 9.6 light-years due to length contraction, and the star is approaching the ship at 0.8c, so it'll take 9.6/0.8 = 12 years for the star to reach the ship, and of course in this ship the ship has a velocity of zero so the time dilation factor is sqrt(1 - 0^2) = 1, meaning this frame also predicts the ship's clock ticks forward by 12 years during this segment.

 

[swerdna]

A thought experiment - There are four clocks. Two are conventional clocks that are self-powered and two that are powered by pulses of light from a distant source. All clocks are synchronised. A conventional and a pulse powered clock travel away from the other two along a curved path that keeps all clocks always the same distance from the source of the light pulse. When the “travelling” clocks return to the others, how would all clocks compare? (time to take some more medication).

 

[JesseM]

A thought experiment - There are four clocks. Two are conventional clocks that are self-powered and two that are powered by pulses of light from a distant source.

When you say "powered", do you mean something like the idea that the clock will tick once each time it receives a light pulse from the source, and the source is sending out pulses once a second in its own rest frame?

All clocks are synchronised. A conventional and a pulse powered clock travel away from the other two along a curved path that keeps all clocks always the same distance from the source of the light pulse. When the “travelling” clocks return to the others, how would all clocks compare? (time to take some more medication).

If my understanding above is right, then the "powered" clock will naturally have ticked forward by the number of pulses the source has sent out since it left, which is the same as the number of ticks or a normal clock that's been sitting next to the source the whole time (since the source sent out one pulse each time the normal clock next to it ticked). So, the only clock that will show a different time is the normal clock that took the curved path away from and back to the other two that are next to the source, whereas the clock powered by light that took the curved path will read exactly the same as the other two when it returns to them.

 

[swerdna]

When you say "powered", do you mean something like the idea that the clock will tick once each time it receives a light pulse from the source, and the source is sending out pulses once a second in its own rest frame?

Yes. Sorry I wasn’t more specific.

If my understanding above is right, then the "powered" clock will naturally have ticked forward by the number of pulses the source has sent out since it left, which is the same as the number of ticks or a normal clock that's been sitting next to the source the whole time (since the source sent out one pulse each time the normal clock next to it ticked). So, the only clock that will show a different time is the normal clock that took the curved path away from and back to the other two that are next to the source, whereas the clock powered by light that took the curved path will read exactly the same as the other two when it returns to them.

If one clock orbits another is there any time dilation of the orbiting clock compared to the orbited clock? If so shouldn’t the frequency of the pulses of light effectively have sped up for the traveling pulse clock as it would have been time dilated compared to the pulse source?

 

[JesseM]

If one clock orbits another is there any time dilation of the orbiting clock compared to the orbited clock? If so shouldn’t the pulses of light effectively have sped up for the traveling pulse clock as it would have been time dilated compared to the pulse source?

They would be "sped up" relative to the normal clock next to it, but obviously the externally powered clock would say they were coming in at one pulse per second, since it's designed to tick forward by one second every time it receives a pulse.

 

[swerdna]

They would be "sped up" relative to the normal clock next to it, but obviously the externally powered clock would say they were coming in at one pulse per second, since it's designed to tick forward by one second every time it receives a pulse.

Isn’t the pulse emitter essentially a fifth clock being observed from a different frame by the traveling pulse clock? Wouldn’t that mean that it runs faster (hope that's correct) compared to the traveling pulse clock? In other words, how can clocks in different frames run at the same speed if one is time dilated compared to the other?

 

[JesseM]

Isn’t the pulse emitter essentially a fifth clock being observed from a different frame by the traveling pulse clock?

But the traveling pulse clock is receiving its pulses from the same emitter, right? If so, in what sense is it "observing" it? It has no independent basis for judging how fast the pulses are coming in, since again it's designed so that by definition the pulses come in at one tick per second.

Wouldn’t that mean that it runs faster (hope that's correct) compared to the traveling pulse clock? In other words, how can clocks in different frames run at the same speed if one is time dilated compared to the other?

The time dilation formula is designed to work for clocks that tick at the "correct" rate in their own rest frame, it doesn't tell you anything about incorrectly designed clocks like a clock that ticks based on external pulses. I could design a clock that went forward at 1 tick ever 3 seconds on Mondays, 1 tick every 12 seconds on Tuesdays, 1 tick ever 0.0001 seconds on Wednesdays, etc., presumably you see why it's obvious the time dilation formula isn't meant to apply to the ticks of this clock, the same is true for the "externally powered" clock.

 

[swerdna]

But the traveling pulse clock is receiving its pulses from the same emitter, right? If so, in what sense is it "observing" it? It has no independent basis for judging how fast the pulses are coming in, since again it's designed so that by definition the pulses come in at one tick per second.

The time dilation formula is designed to work for clocks that tick at the "correct" rate in their own rest frame, it doesn't tell you anything about incorrectly designed clocks like a clock that ticks based on external pulses. I could design a clock that went forward at 1 tick ever 3 seconds on Mondays, 1 tick every 12 seconds on Tuesdays, 1 tick ever 0.0001 seconds on Wednesdays, etc., presumably you see why it's obvious the time dilation formula isn't meant to apply to the ticks of this clock, the same is true for the "externally powered" clock.

Can’t quite follow your logic so will need to give it some thought - Thanks.

ETA - But a “correct” second for the traveling clocks is not the same as a “correct” second for the emitter and stationary clocks. Wouldn’t this mean that the frequency between pulses would effectively speed up for the traveling clocks? (or is that slow down?) Didn't know that it was possible to incorrectly design a clock that works.

 

[sylas]

I agree that my statement (1) of post #36 is incorrect and as diazona (and others) correctly pointed out “Something can be assumed to be moving in an absolute sense if it is accelerating.” I already knew this and am puzzled and disappointed that I wrote what I did.

No problem... thanks for clarifying, and glad to be back on the same page.

As I understand it acceleration itself doesn’t cause time dilation but apparently is somehow important because it establishes that a thing has changed its direction or speed and therefore experiences different “frames“. Unless things retain some form of memory of acceleration I can‘t see that which thing accelerates to cause it to move relative to something else is important.

The first sentence is, IMHO, an excellent description of the role of acceleration in special relativity. It's not the acceleration, per se, but the change in perspective.

There's no need of "memory". When you move frames, everything changes. If you "remember" what you were observing in the past, then you'll be able to infer that you've shifted into a new frame. But if you don't remember, then you can still just use current observations to infer your current circumstance, and draw the appropriate conclusions.

Specifically. In the case of traveling twins. Suppose that twin A remains at home, while twin B moves at 60% light speed for 8 years (by their own ship-clock) and then reverses to come back at 60% the speed of light.

Observations of twin A

Twin A infers that twin B has a clock running 80% slow. Hence, the 8 years ship time will be 10 years elapsed time by A's own clock, and the turn around occurs at a distance of 6 light years, 10 years after B left. Twin A actually sees this turn around 6 years after it occurs, because the light takes that long to get back from the turn around point. Hence, 16 years after B left, A will observe that B has turned around. The angular size of B in the sky indicates that the turn around occurred at 6 light years distance.

Everything makes sense to A, and they infer that B traveled for 10 years outbound, and 10 years back, or 20 years in total. With the 80% time dilation, twin A infers, correctly, that twin B will be 16 years older on return.


Observations of twin B

Twin B also observes twin A receding at first, at 60% light speed.

Just before the turn around at 8 years into the trip, twin B can see twin A in the far distance. They can tell, by red shift and the Doppler effect, that twin A is still receding at 60% light speed. They can tell, by the angular size of A in the sky, or the luminosity, that the light they are receiving is coming from 3 light years distance, and hence represents where A was three years previously.

Just after the turn around, twin B can see twin A in the far distance. They can tell, by blue shift and the Doppler effect, that twin A is approaching at 60% light speed. They can tell, by the angular size of A in the sky, or the luminosity, that the light they are receiving is coming from 12 light years distance, and hence represents where A was twelve years previously.

This is not a contradiction; it is simply a different frame of view. If twin B actually remembers what they had been observing just previously, then they could infer that they must have moved into a new reference frame -- even if this shift occurred with no acceleration, as if by a strange warp in space that simply turns the ship to a new direction without altering the time or place.

But suppose twin B merely notes down the expected age of A at the point where A apparently started to approach again.

Twin B can figure out that just before the shift in perspective 8 years into their journey, that they are seeing twin A as they were after 5 years. Hence, from time dilation, twin A will have aged 4 years.

On the second 8 years ship-time, twin B sees twin A approaching from a distance of 12 light years. The elapsed time of the trip for A, at 60% light speed, is 20 years, but with time dilation A is expected to age 80% of 20, or 16 years.

Total expected age of A, based on the observations of B, is 20 years. And that is just what they see when the twins are reunited.

I can’t see how relative movement is anything but symmetrical regardless of which thing accelerates. I guess what I find hard to accept about relativity is that it seems to consider things from abstract partial views (frames) and doesn’t consider a universal or omnipresent view.

You are not alone in finding it hard to understand.

However, it is definitely the case that the situations of the two twins are not symmetric at all. They observe very different things in what they actually see by looking at the other twin. Furthermore, a third observer will in general have no trouble seeing which twin was the one that reversed their direction of travel.

The whole point of relativity is that there ISN'T a universal view. There is no such thing as absolute motion: a velocity is always with respect to some observer.

Once you actually get this with all its logical implications, all the paradox evaporates. The whole situation is consistent, and both twins can calculate correctly the amount that the other one is expected to have aged, based on their own observations of the other twin during the trip.

Cheers -- sylas

 

[JesseM]

ETA - But a “correct” second for the traveling clocks is not the same as a “correct” second for the emitter and stationary clocks.

By "correct" I just mean it ticks at the same rate as any other correct clock that's right next to it and at rest relative to it throughout its trip. For example, one type of correct clock would be an atomic clock, which ticks based on the regular oscillations of certain types of cesium atoms. The pulse-powered clock isn't ticking at the same rate as the (presumably correct) self-powered clock, so the pulse-powered clock's time doesn't correctly match what relativity would say about the proper time along its worldline.

Wouldn’t this mean that the frequency between pulses would effectively speed up for the traveling clocks? (or is that slow down?)

Speed up or slow down relative to what? And when you say "travelling clocks", are you still talking about the clock whose rate of ticking is based on external light pulses, or are you talking about normal clocks?

 

[swerdna]

The whole point of relativity is that there ISN'T a universal view. There is no such thing as absolute motion: a velocity is always with respect to some observer.

I would say that there is potentially or theoretically a universal view but it not possible to achieve it by anything other than perhaps the universe itself. A limitation of observation isn’t a limitation of existence. I would also say that a velocity is always with respect to some other thing rather than observer. I‘ve never been able to see any significance in whether a thing is observed or not. Things exist and do things regardless of whether they are observed or not. A tree that falls in a forest makes a noise regardless of whether there is a listener or not. If A has a velocity compared to B then B has the exact same velocity compared to A. I guess I’m saying that I believe velocity should be attributed to the relative movement of things and not the actual things.

Here’s mud in your eye (aka cheers ;-)

 

[swerdna]

By "correct" I just mean it ticks at the same rate as any other correct clock that's right next to it and at rest relative to it throughout its trip. For example, one type of correct clock would be an atomic clock, which ticks based on the regular oscillations of certain types of cesium atoms. The pulse-powered clock isn't ticking at the same rate as the (presumably correct) self-powered clock, so the pulse-powered clock's time doesn't correctly match what relativity would say about the proper time along its worldline.

Speed up or slow down relative to what? And when you say "travelling clocks", are you still talking about the clock whose rate of ticking is based on external light pulses, or are you talking about normal clocks?

“Travelling” clocks are the two (one conventional and one pulse) that accelerated to a different frame from the other two (one conventional and one pulse) and the pulse emitter that are all “stationary“. Sorry but I have no more time to continue right now.

 

[swerdna]

Speed up or slow down relative to what?

Relative to a second in the frame of the traveling clocks which is dilated relative to a second in the frame of the light emitter and the stationary clocks. Each frame has different “proper” times. I realize that relativity says that light travels at c regardless of which frame it travels through but I’m talking about the periods between the light pulses. Essentially the period between the pulses is what time is isn’t it? Rather than faster or slower perhaps dilated would be more correct.

 

[JesseM]

Relative to a second in the frame of the traveling clocks which is dilated relative to a second in the frame of the light emitter and the stationary clocks.

But do you understand that the clock powered by external pulses will also be dilated relative to coordinate time in its own rest frame? (and relative to the normal clock traveling along with it, which is running at the same rate as coordinate time in their rest frame) The notion of coordinate time in a "frame" is assumed to match that of what I have called "correct" clocks that are at rest in that frame.

Each frame has different “proper” times.

"Proper time" is not frame-dependent, the term refers to the time along a particular worldline (between one specified point on the worldline and another), as measured by a (correct) clock moving along that worldline. All frames agree in their predictions about the proper time along a worldline.

I realize that relativity says that light travels at c regardless of which frame it travels through but I’m talking about the periods between the light pulses. Essentially the period between the pulses is what time is isn’t it?

No, time is what is measured by a correct clock that agrees with other correct clocks. You can build a "light clock" based on the period of light, but this is based on having the clock tick each time the light travels a certain distance along the clock itself, not on ticking every time it receives a pulse from some external source. You can also build clocks whose time isn't based on light at all, like atomic clocks or clocks whose ticking is based on springs. I'll repost I said about the notion of time in an older thread:

Well, I'd say time is an abstraction based on the fact that we see various physical objects which exhibit regular cycles (like the atomic oscillations that atomic clocks are based on) such that when the objects are next to each other the ratio of their cycles remains constant. For example, if I have an atomic clock based on oscillations of cesium 133 atoms, and a spring clock which ticks in the units we label as "seconds", then if you place them next to each other on Earth you'll find the atomic clock always registers around 9,193 billion ticks between each tick of the spring clock (it will depend on how good the spring clock is of course, nowadays a second is supposed to correspond to exactly 9192631770 oscillations of such a cesium 133 clock). If you take a second atomic clock/spring clock pair which is physically identical to the first and take them on a relativistic journey through space and then return them to Earth, the pair that took the journey will have registered less ticks than the pair that remained on Earth, but the ratio between the number of ticks registered on the atomic clock that took the journey and the number of ticks registered on the spring clock that took the journey should still be about 9,193:1, assuming both clocks were next to each other as they traveled so their velocity at each moment (in whatever frame we choose) would have been the same. From this you can abstract that all paths through spacetime have a certain "proper time" along them, different clocks will divide the proper time into different increments but the ratio between ticks of different clocks should stay the same as long as they take the same path through spacetime.

 

[swerdna]

Another check to see if I understand things correctly (once again in layman-speak)

(1) A thing that is not accelerating can’t correctly be defined as being either moving or stationary.

(2) A thing that is accelerating can be correctly defined to be moving.

(3) After a thing has been through a period of acceleration (and is no longer accelerating) it can’t correctly be defined as being either moving or stationary.

 

[swerdna]

But do you understand that the clock powered by external pulses will also be dilated relative to coordinate time in its own rest frame? (and relative to the normal clock traveling along with it, which is running at the same rate as coordinate time in their rest frame) The notion of coordinate time in a "frame" is assumed to match that of what I have called "correct" clocks that are at rest in that frame.

"Proper time" is not frame-dependent, the term refers to the time along a particular worldline (between one specified point on the worldline and another), as measured by a (correct) clock moving along that worldline. All frames agree in their predictions about the proper time along a worldline.

No, time is what is measured by a correct clock that agrees with other correct clocks. You can build a "light clock" based on the period of light, but this is based on having the clock tick each time the light travels a certain distance along the clock itself, not on ticking every time it receives a pulse from some external source. You can also build clocks whose time isn't based on light at all, like atomic clocks or clocks whose ticking is based on springs. I'll repost I said about the notion of time in an older thread:

Thanks - That will take some time to read and digest.

 

[JesseM]

Another check to see if I understand things correctly (once again in layman-speak)

(1) If a thing is not accelerating it can’t correctly be defined as being either moving or stationary.

Not in any absolute sense, no, although it can be defined as moving or stationary relative to a particular choice of inertial reference frame.

(2) A thing that is accelerating can be correctly defined to be moving.

You can't say it's moving at any given instant even if you stick to inertial frames, since at any instant there will be some inertial frame where it's instantaneously at rest. You can say that its velocity is changing in every inertial frame though. It's also possible to use non-inertial coordinate systems in which even an accelerating object (in the sense of an object experiencing G-forces) is at rest, but the laws of physics don't take the same form in such a coordinate system that they take in inertial frames (for example, the speed of light is not necessarily constant in non-inertial frames like it is in inertial frames).

(3) After a thing has been through a period of acceleration (and is no longer accelerating) it can’t correctly be defined as being either moving or stationary.

Again, not in any absolute, frame-independent sense.

 

[JM]

To p.tryon and swerdna: Keep questioning, you have much correct.
To all: The discussion on the thread 'In twin paradox, please help' in relavent here, the twins were diiscussed at length there.

 

[JM]

To Sylas: I like your idea of treating each twin separately.
Re twin B: Toward the end you say '...A is expected to age 80% of 20 years, or 16 years.' Doesn't this mean that twin B calculates A to be younger when they reunite? If so then each thinks the other is younger when they reunite.

 

[JM]

Again re post #57: The view of twin B can be found as follows. On his outbound segment he is inertial, and so is entitled to consider himself to be at rest and to use the usual formula to calculate the time dilation of A's clock. The time on the clocks is not affected by the turnaround if it is quick enough. After turnaroound B is inertial again and can calculate A's dilation as before. B's view of A's motions is the same as A's view of B's motions, so each will calculate the same dilation, and each will calculate the other to be younger when they reunite.

 

[sylas]

I am the author of message [post=2185614]msg #57[/post] to which JM refers.

Again re post #57: The view of twin B can be found as follows. On his outbound segment he is inertial, and so is entitled to consider himself to be at rest and to use the usual formula to calculate the time dilation of A's clock. The time on the clocks is not affected by the turnaround if it is quick enough. After turnaroound B is inertial again and can calculate A's dilation as before. B's view of A's motions is the same as A's view of B's motions, so each will calculate the same dilation, and each will calculate the other to be younger when they reunite.

That is incorrect.

The fundamental error is this statement: The time on the clocks is not affected by the turnaround if it is quick enough.

That's incorrect, because in fact, time and distance all depend on an observer. When you turn around, there is a shift of the observer into a new inertial frame, in which everything is different. That's a bedrock fact about physics that you have failed to take into account.

Note that the twins are not together to compare their clocks directly at the turn around point. All they can actually see is light that left the other clock a long time ago. Conclusions about what is happening at that "same time" (from their perspective) are inferences, not observations.

I described a case in which twin A stays at home, while twin B sets out at 60% of the speed of light, for 8 years according to their own spaceship clock.

In this case, A observes B for 16 years with a redshift, and 4 years with a blue shift. At 60% light speed, the clock is viewed running slow, or fast, by a factor of 2. This factor includes both the time dilation and also the effects of approach or recession on the light travel time. A thus calculates B ages 16/2 + 4*2 = 16 years.

On the other hand B observes A for 8 years with a redshift, and 8 years with a blue shift. B thus calculates A has aged 8/2 + 8*2 = 20 years.

Each twin makes different observations, and is able to correctly calculate the elapsed age of the other. The twin who turned around aged 16 years. The one who stayed home aged 20 years.

If you calculate anything different, you aren't using relativity, and you are calculating incorrectly.

Cheers -- sylas

 

[JesseM]

Again re post #57: The view of twin B can be found as follows. On his outbound segment he is inertial, and so is entitled to consider himself to be at rest and to use the usual formula to calculate the time dilation of A's clock. The time on the clocks is not affected by the turnaround if it is quick enough.

You are ignoring the relativity of simultaneity! Even if the turnaround is instantaneously brief, the time on twin A's clock at the moment of the turnaround in the inertial frame where B was at rest during the outbound phase of the journey is very different from the time on A's clock at the moment of the turnaround in the inertial frame where B was at rest during the inbound phase of the journey, you can't combine results from two frames that way without considering simultaneity issues. Did you read my post #112 in response to you on this thread? I gave a numerical example there which illustrates this point. You might also look at my discussion with otg about the issue of simultaneity and the twin paradox in this thread.