Who Truly Experiences Slower Time in the Paradox of Time Dilation?

[p.tryon]

Time dilation... but for who??

I was reading Einstein's postulate that if two bodies A and B are moving relative to one another it is impossible to truly discern whether one of the bodies is stationary and the other is moving (i.e. we can only speak of their relative motion).

However, special relativity claims that as a body approaches light speed, time (for that body) slows down. But this seems to contradict the postulate that motion is always relative. If motion can only be described in relative terms, then wouldn't time slow down for both bodies compared with the other?

 

[jtbell]

Yes.

 

[p.tryon]

So if you were in a spacecraft flying away from the Earth at near light speed and then you returned to Earth would Earth clocks be slow (compared to your clocks) or your would clocks be slow (compared to Earth clocks)? or would both be slow (if so how can you compare)? Please explain

 

[sylas]

So if you were in a spacecraft flying away from the Earth at near light speed and then you returned to Earth would Earth clocks be slow (compared to your clocks) or your would clocks be slow (compared to Earth clocks)? or would both be slow (if so how can you compare)? Please explain

It's called the twin paradox. The twin that turns around at some point is the one that has aged less when they meet up again. There's no ambiguity as to which twin turns around.

It's not really a paradox at all, but it's a good exercise for calculating with relativity.

Cheers -- sylas

 

[p.tryon]

Hi Sylas. At what point is the fact that the "turn around twin ages less" decided? Before he turns around? At the point he turns around? Or when he finally arrives back? What is special about the act of "turning round" that causes this twin to age less?

 

[malawi_glenn]

the twin that is in the spacecraft have to accelerate, and that is breaking the symmetry of the situation. The twin is physically accelerating, and one can not say that the two twins are in two inertial frames which moves at constant velocity w.r.t each other (special relativity is not applicable to accelerating frames)

 

[sylas]

Hi Sylas. At what point is the fact that the "turn around twin ages less" decided? Before he turns around? At the point he turns around? Or when he finally arrives back? What is special about the act of "turning round" that causes this twin to age less?

The way the question is phrased is likely to get you into a mess. As soon as you say "at what point", this implicitly suggests some commonly agreed upon instant in time. There's no such thing.

It is when you turn around that you know you are not in an inertial frame; but that is not when you "age less". The amount you age is simply the accumulation of "proper time" along your world line, and special relativity let's you calculate that.

The "metric" used has the property that the "shortest line" has the longest proper time. The thing about turning around is that you have a world line extending out, and reversing itself, and coming back, and that gives less "proper time" accumulated along that path. You end up younger than someone who stayed home.

Suppose you have a whole heap of friends, all of whom set out on various journeys around the galaxy, agreeing to meet back at some previously agreed point in space and time. When they meet up again, they'll all be different ages.

The age depends on their world line. Also -- assuming they kept out of strong gravitational fields! -- you can do the whole analysis in special relativity.

Basically, the increment in proper time dτ is defined as dτ² = dt² - (dx/c)², where x and t and space and time co-ordinates in ANY inertial frame. Integrate that along the world line, and you get how much the traveller ages.

If any of these friends remained inertial the whole time, they will be the oldest. You can see this, by using their location as the origin of an inertial frame. The age of the others will depends on their whole path through space time, and that can be calculated with special relativity, as long as they stayed out of strong gravitational fields.

Cheers -- sylas

 

[phyti]

I was reading Einstein's postulate that if two bodies A and B are moving relative to one another it is impossible to truly discern whether one of the bodies is stationary and the other is moving (i.e. we can only speak of their relative motion).

However, special relativity claims that as a body approaches light speed, time (for that body) slows down. But this seems to contradict the postulate that motion is always relative. If motion can only be described in relative terms, then wouldn't time slow down for both bodies compared with the other?

The amount of accumulated time on a clock depends on how fast it moves.
The clock that leaves the Earth and returns, travels a greater distance than earth, and must travel faster between departure and arrival, thus accumulating less clock time.
If both clocks left Earth simultaneously and returned simultaneously, after different trips, you obviously could make a direct comparison on return. If you knew the flight plan for both, you could calculate the times before return.
While separated, each clock will appear to run slower to the other observer.

 

[swerdna]

Yes.

So twins/clocks that travel apart and back together again would remain exactly the same age regardless of which twin/clock experienced acceleration changes?

 

[sylas]

So twins/clocks that travel apart and back together again would remain exactly the same age regardless of which twin/clock experienced acceleration changes?

No. (And the "Yes" for the other question is still correct.)

 

[swerdna]

The amount of accumulated time on a clock depends on how fast it moves.

What determines how fast a clock moves? Or even that it moves?

The clock that leaves the Earth and returns, travels a greater distance than earth, and must travel faster between departure and arrival, thus accumulating less clock time.

Given it can’t be determined that either clock is ever stationary or moving, surely the “earth clock” also leaves and returns to the “travelling clock“ and the clocks separate and rejoin at the same speed and over the same distance.

 

[sylas]

What determines how fast a clock moves? Or even that it moves?

Given it can’t be determined that either clock is ever stationary or moving, surely the “earth clock” also leaves and returns to the “travelling clock“ and the clocks separate and rejoin at the same speed and over the same distance.

Your "given" is incorrect.

In a situation of constant motion (an inertial frame) each clock is running slow relative to the other one. There's no contradiction here. The Lorentz transformations mean that distance, time and simultenaity all changes depending on what frame is being used.

With constant motion, the twins never get back together again, and so there's no paradox.

If one twin turns around to come back, then that twin adopts a new inertial frame; and in that new frame, simultenaity is different as well. Hence it is impossible for the twin who turns around to identify the turn around point as a particular instant simultaneous with the events at the other stay-at-home twin.

There's no ambiguity about which twin turns around, and you CAN determine whether you remain inertial or not.

There are heaps of different ways to look at this problem, and they all give the same answer. Anything different, and it's simply incorrect.

Cheers -- sylas

 

[swerdna]

Your "given" is incorrect.

So “Einstein’s postulate” in the OP is wrong?

In a situation of constant motion (an inertial frame) each clock is running slow relative to the other one. There's no contradiction here. The Lorentz transformations mean that distance, time and simultenaity all changes depending on what frame is being used.

With constant motion, the twins never get back together again, and so there's no paradox.

What if the constant motion is circular and the twins do get back together again?

 

[sylas]

So “Einstein’s postulate” in the OP is wrong?

No; Einstein's postulate is correct.

Even with acceleration, there is no way to identify whether you are "stationary" or not at any point; and so the postulate is still true as expressed, even with accelerated motions. You can tell when you change velocity, from the acceleration you experience. You can never say that you are "stationary". That's an arbitrary choice.

What if the constant motion is circular and the twins do get back together again?

The twin traveling in a circle ages less. There's no ambiguity as to which twin is moving in circles ... that is an acceleration and the twin moving in circles can measure their own acceleration.

Cheers -- sylas

 

[swerdna]

No; Einstein's postulate is correct.

Even with acceleration, there is no way to identify whether you are "stationary" or not at any point; and so the postulate is still true as expressed, even with accelerated motions. You can tell when you change velocity, from the acceleration you experience. You can never say that you are "stationary". That's an arbitrary choice.



The twin traveling in a circle ages less. There's no ambiguity as to which twin is moving in circles ... that is an acceleration and the twin moving in circles can measure their own acceleration.

Cheers -- sylas

If both twins are simultaneously traveling in mirror image circles that intersect are they the same age when they meet again?

 

[sylas]

If both twins are simultaneously traveling in mirror image circles that intersect are they the same age when they meet again?

Yes.

 

[phyti]

What determines how fast a clock moves? Or even that it moves?
.

The speed of the ship relative to earth.

Given it can’t be determined that either clock is ever stationary or moving, surely the “earth clock” also leaves and returns to the “travelling clock“ and the clocks separate and rejoin at the same speed and over the same distance

The ship must accelerate (change course) to leave and return. This is not the cause of time dilation but the asymmetrical feature that determines who moved. The Earth does nothing.
The Earth appears to leave and return to the ship passenger. This is a simple case, but if two travelers left and returned, you have to know the course each takes to predict any age difference before they return.

 

[swerdna]

The speed of the ship relative to earth.


The ship must accelerate (change course) to leave and return. This is not the cause of time dilation but the asymmetrical feature that determines who moved. The Earth does nothing.
The Earth appears to leave and return to the ship passenger. This is a simple case, but if two travelers left and returned, you have to know the course each takes to predict any age difference before they return.

When did the Earth become the actual stationary position of the universe? Why is “The speed of the ship relative to earth” any more preferred or valid than the speed of the Earth relative to the ship?

Two people are on a conveyor belt. One person walks way from the other along the belt. An abstract conclusion is that the walking person is moving and the other is stationary. But say that the belt is moving at walking speed relative to what it’s sitting on and that the person walks against the movement of the belt. An abstract conclusion is that the walking person is stationary relative to the thing the belt is sitting on and the non-walking person is moving. Then say that the thing that the moving belt is sitting on is also moving . . . etc, etc. Thing is there is no actual stationary peg in the universe to hang your hat on. Acceleration doesn’t determine what moves per se it only determines what changes movement. A change in movement (acceleration) can never be determined as an actual increase or decreased in speed. I don’t see how the relative movement of things can be anything but symmetrically equal and opposite.

 

[sylas]

When did the Earth become the actual stationary position of the universe? Why is “The speed of the ship relative to earth” any more preferred or valid than the speed of the Earth relative to the ship?

Because in the thought experiment, the twins compare their ages when they get back together at Earth.

You have completely ignored the fundamental point that one twin accelerates, and the other doesn't. To make your conveyor belt example relevant, you have to have someone walking along the belt, turning around, and coming back. That's two inertial frames, and it is NOT symmetric with a person walking on the belt at one consistent velocity, with a single inertial frame.

I don’t see how the relative movement of things can be anything but symmetrically equal and opposite.

As soon as you introduce the notion of turning around, it is no longer symmetric. One twin turns around, and the other doesn't. If you apply special relativity, then the twin who did the turn around is the one who ages less when they get back together and synchronize watches once more -- unambiguously.

 

[diazona]

I get the sense that what might not be clear here is that it is possible to tell if you're accelerating, but it is not possible to tell if you're moving at constant velocity.

Imagine if you were in a small box (or a small spaceship) that doesn't allow any sort of influence from outer space to come inside. So no windows, basically. The point is that anything you can tell about your motion must be based on the local observations, experiments you can run that are completely contained within the box (spaceship).

Now, what the principle of relativity says is that there's no possible way to figure out the relative velocity between you and, say, the Earth, without looking outside of the box. But you can tell whether you're accelerating or not: if you had an iPhone in your spaceship, you could just look at its accelerometer. And the iPhone would be able to sense this acceleration without receiving any sort of influence from outside the box. (You'd be able to feel it too, it'd feel kind of like gravity in fact) So, in a manner of speaking, there must be something fundamentally "special" about acceleration that allows you to define it absolutely, without reference to anything else. That is emphatically not true for velocity.

This applies to the twin paradox because each twin can independently determine his/her own acceleration (for instance, if they were both carrying iPhones). The twin who flies off, turns around, and comes back will notice a huge spike on her iPhone's accelerometer, but the twin who stays in place on Earth or wherever will not. And that means the situations of the two twins are not the same. The one who accelerates will be the one who ages less.

If you worked out some sort of flight plan in which both twins took voyages in which they both experienced identical accelerations, then they would be the same age when they returned. In that case, the twins could not distinguish which was which based on their accelerations (their iPhones would have exactly the same record of acceleration), so there's no way one could have aged more than the other.

 

[swerdna]

Because in the thought experiment, the twins compare their ages when they get back together at Earth.

You have completely ignored the fundamental point that one twin accelerates, and the other doesn't. To make your conveyor belt example relevant, you have to have someone walking along the belt, turning around, and coming back. That's two inertial frames, and it is NOT symmetric with a person walking on the belt at one consistent velocity, with a single inertial frame.



As soon as you introduce the notion of turning around, it is no longer symmetric. One twin turns around, and the other doesn't. If you apply special relativity, then the twin who did the turn around is the one who ages less when they get back together and synchronize watches once more -- unambiguously.

I haven’t ignored the fact that one twin accelerates and the other doesn’t. I simply can’t see that acceleration is important to what we are discussing because it doesn’t define anything other than the fact that a thing is changing it’s motion (or is being subjected to gravity).

One twin accelerates and creates a separation of the twins. That twin accelerates again to bring them back together. That the other twin doesn’t accelerate doesn’t that mean that it’s stationary. A third person observer that was some distance from the twins would simply see them separate and come back together again and wouldn’t know whether one or both had accelerated and both twins would appear to turn around. I can’t see any immediate significance in the “turn around” but I’m tired and have a headache so will give it more thought at a later time.

 

[sylas]

I haven’t ignored the fact that one twin accelerates and the other doesn’t. I simply can’t see that acceleration is important to what we are discussing because it doesn’t define anything other than the fact that a thing is changing it’s motion (or is being subjected to gravity).

It's not the acceleration as much as the change in inertial frame. You can do an analysis using SR only, and an instantaneous change in velocity. After the turn around, everything changes. The other twin appears red shifted. The angular size of the other twin in the sky is reduced. A laser range finder would indicate that the other twin has actually stopped moving. And so on. All of these things are natural consequences of a change in the inertial frame.

There is no ambiguity at all as to which twin actually does the turn around. You can tell with measurements before and after the turn, even if you sleep through the turn itself and don't notice the pilot of the ship screaming "Help; I've fallen down and I can't get up."

One twin accelerates and creates a separation of the twins. That twin accelerates again to bring them back together. That the other twin doesn’t accelerate doesn’t that mean that it’s stationary.

It DOES, however, mean that the other twin is in the one inertial frame the whole time. There's no symmetry between the twins. The one who uses two different inertial frames ends up with the longer path in the spacetime metric ds^2 = dx^2 - dt^2, as measured by ANY inertial observer.

A third person observer that was some distance from the twins would simply see them separate and come back together again and wouldn’t know whether one or both had accelerated and both twins would appear to turn around. I can’t see any immediate significance in the “turn around” but I’m tired and have a headache so will give it more thought at a later time.

Of course the third observer will tell which one turns around. That's just silly!

Cheers -- sylas

 

[workmad3]

The acceleration is very important as previously stated. It is the acceleration that breaks the symmetry in the situation. Say you were accelerating away from someone else. To an observer, the relative motion is the same from either perspective, but from your perspective you can feel acceleration and from theirs, they can't feel acceleration. As acceleration is the only difference, it is the acceleration that introduces time-dilation effects (otherwise yes, the symmetry of the situations would mean that there was no way of telling which entity should undergo time dilation wrt the other)

 

[sylas]

The acceleration is very important as previously stated. It is the acceleration that breaks the symmetry in the situation. Say you were accelerating away from someone else. To an observer, the relative motion is the same from either perspective, but from your perspective you can feel acceleration and from theirs, they can't feel acceleration. As acceleration is the only difference, it is the acceleration that introduces time-dilation effects (otherwise yes, the symmetry of the situations would mean that there was no way of telling which entity should undergo time dilation wrt the other)

Actually, the acceleration is useful as a convenient way to tell that you have shifted inertial frames.

It's not correct to say that acceleration "causes" time dilation. What causes time dilation, in special relativity, is the path through space time; ALL of it.

To see this, consider this thought experiment. You travel to another star. Along your journey, you accelerate four times. Once, up to 60% of the speed of light. Another time, up to 80% of the speed of light. Then again, to -60% of the speed of light (turn around). Then again, back to zero as you stop.

Does it make any difference WHEN you do these accelerations? Yes it does; and your eventual age at the end of the trip is calculated by integrating of proper time along the three intervals of constant velocity. The duration of each segment depends on when you do the accelerations. The calculation never even considers acceleration; it's enough to know the distances and velocities of the segments between accelerations.

Acceleration is one way to tell you are not inertial.

There are other ways to tell. Suppose you use a laser range finder, to keep track of how far away the other twin is. You send a message by laser to the other twin, containing your local time. The message is reflected, and when it gets back, you can tell how long the round trip of the laser light took. That let's you calculate how far away the twin WAS at the time of the reflection. Some time I may write all this up, but using laser range finding shows up clearly the asymmetry of the two twins, and the effects of a change in frame.

For the traveling twin... the one who exists in two different inertial frames, the data from their laser range finder will indicate that the stay-at-home twin is actually motionless, but blueshifted as if at the top of a large gravitational field, for most of the duration of the trip!

Such observations are sufficient to infer the change in inertial frame, even if you slept through the short acceleration at turn around without noticing. The ship-bound twin can also notice a sudden change in the apparent size of the stay-at-home twin. They suddenly shrink in size in the sky, at the time they go to blueshifted, as if suddenly transported far far away. But the laser range finder disagrees, and indicates that they merely stopped.

None of these things are seen by the stay-at-home twin.

The key, in all of this, is not acceleration per se, but being in a different inertial frame.

Cheers -- sylas

 

[swerdna]

.Of course the third observer will tell which one turns around. That's just silly!

You are in total darkness. A great distance away there are two lights that are together and you are only able to see them as a single light dot. The lights move apart to the degree that you are able to see there are two and that they have moved apart. The lights move together again. The only things you are every able to see are the small light dots. Because of the distance and total lack of any other positioning reference you won’t be able to tell whether one or both of the lights underwent acceleration to create the away and back movements. You will only be able to tell that two dots of light have moved apart and back together.

 

[NWH]

You are in total darkness. A great distance away there are two lights that are together and you are only able to see them as a single light dot. The lights move apart to the degree that you are able to see there are two and that they have moved apart. The lights move together again. The only things you are every able to see are the small light dots. Because of the distance and total lack of any other positioning reference you won’t be able to tell whether one or both of the lights underwent acceleration to create the away and back movements. You will only be able to tell that two dots of light have moved apart and back together.

Wait... So what if we were observing these dots from a fixed position, say from a telescope on Earth. Couldn't you determine which object did what by using the perimiter edge of your field of vision as a reference point? Granted, doing such a thing with human eyes (and brain) would be an incredibly complex task, but I don't get why an engineered optical observer wouldn't be able to detect this...

 

[Mentz114]

You are in total darkness. A great distance away there are two lights that are together and you are only able to see them as a single light dot. The lights move apart to the degree that you are able to see there are two and that they have moved apart. The lights move together again. The only things you are every able to see are the small light dots. Because of the distance and total lack of any other positioning reference you won’t be able to tell whether one or both of the lights underwent acceleration to create the away and back movements. You will only be able to tell that two dots of light have moved apart and back together.

So what ? It's got nothing to do with the case in point. You've been told in plain language by sylas and others that the elapsed time on a clock depends on the details of the journey through space-time. There's no paradox or mystery to be explained. Do you have a problem with this ?

 

[sylas]

You are in total darkness. A great distance away there are two lights that are together and you are only able to see them as a single light dot. The lights move apart to the degree that you are able to see there are two and that they have moved apart. The lights move together again. The only things you are every able to see are the small light dots. Because of the distance and total lack of any other positioning reference you won’t be able to tell whether one or both of the lights underwent acceleration to create the away and back movements. You will only be able to tell that two dots of light have moved apart and back together.

You use a gyroscope to fix your observation to a point in the sky. The apparent motions of an object you can observe are projections onto a sphere. The projected motion of a constant velocity motion are different from projected motions with a change in velocity.

You appear to be thinking that you must use one of the objects as a reference point, and only measure the other wrt to that. This is false. Your reference point is fixed in the sky with a gyroscope, and BOTH objects more wrt to that.

 

[swerdna]

I was merely responding to the “silly” claim, that’s “so what”.

You can’t use the “the perimeter edge of your field of vision” if you are in total darkness and all you can see are the two light dots.

 

[swerdna]

You use a gyroscope to fix your observation to a point in the sky. The apparent motions of an object you can observe are projections onto a sphere. The projected motion of a constant velocity motion are different from projected motions with a change in velocity.

You appear to be thinking that you must use one of the objects as a reference point, and only measure the other wrt to that. This is false. Your reference point is fixed in the sky with a gyroscope, and BOTH objects more wrt to that.

You are in total darkness so you can't see a gyroscope. What point in the sky when you can only see two light dots?

I'm happy to forget all this and call it silly if you like.

 

[sylas]

You are in total darkness so you can't see a gyroscope. What point in the sky when you can only see two light dots?

I'm happy to forget all this and call it silly if you like.

I can see why you'd like to forget it. Much better would be to actually remember and learn from it.

Your "total darkness" comment is beyond being merely silly; it amounts to a head in the sand refusal to deal with your error. 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. The two twins are not symmetrical.

Cheers -- sylas

 

[swerdna]

I can see why you'd like to forget it. Much better would be to actually remember and learn from it.

Your "total darkness" comment is beyond being merely silly; it amounts to a head in the sand refusal to deal with your error. 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. The two twins are not symmetrical.

Cheers -- sylas

You’re happy to use mythical light clock and 2D flatland scenarios but not distant lights in total darkness? Would it help if I called it an anology?

Suppose I make a video of two objects moving apart and together in which one object appears to be moving (accelerating) and the other appears to remain stationary. Would you be willing to bet any money that the object that appears to be accelerating is in fact doing so? Before you risk your money let me point out that I could be moving (accelerating) the camera back and forth in sync with the object that appears to be stationary but is actually accelerating. Everything else in the shot would move back and forth in sync with the camera as well to strengthen the illusion.

Without an actual stationary reference point (which doesn’t exist) you can't tell what is actually moving and what isn’t. You can only tell that a thing is moving relative to something else. Effects of acceleration can tell you that a thing is changing it’s movement but if you are an observer that has no way of detecting that acceleration how can you tell it is accelerating?

Unless you are able to detect what is actually accelerating when you see an object appear to accelerate away from another it could be that the other object and everything else in your field of vision is actually undergoing acceleration in the other direction.

 

[sylas]

You’re happy to use mythical light clock and 2D flatland scenarios but not distant lights in total darkness? Would it help if I called it an anology?

No, it wouldn't, and the main person not being helped is YOU.

Light clocks are not mythical; that's the basis of an atomic clock, in fact. We aren't using 2d flatland. We are using co-ordinates oriented to the direction of motion, in conventional 3d space which is what you need to solve the problem in reality.

The fundamental point is about inertial observers. One twin is inertial. The other isn't. There are all kinds of observations that the twins can use to recognize whether they are the one who is moving into a new inertial frame... acceleration is a local effect that any twin can use. There are also observations of the other twin that can be distinguished.

For example, the stay-at-home twin will observe the traveling twin suddenly switch from red shift to blue shift. The intensity of light from the twin will increase as well. That can occur as a result of the remote turn suddenly changing direction.

The twin who does the turning around sees something very different. They observe the stay-at-home go from red shift to blue shift, but at the same time they will see the intensity of light from the other twin DROP. That can't happen for an inertial observer. If you are watching a remote object become blue shifted and also drop in apparent magnitude, then you know that YOU are the one who has just changed your inertial frame.

You've tried to introduce a third observer. If that observer is inertial, then they are not rotating. That's the point about the gyroscope. If they ARE rotating, they can tell that they are not a simple inertial observer.

Suppose I make a video of two objects moving apart and together in which one object appears to be moving (accelerating) and the other appears to remain stationary. Would you be willing to bet any money that the object that appears to be accelerating is in fact doing so? Before you risk your money let me point out that I could be moving (accelerating) the camera back and forth in sync with the object that appears to be stationary but is actually accelerating. Everything else in the shot would move back and forth in sync with the camera as well to strengthen the illusion.

You've gone from silly to stupid. This is a red herring. Is it that important to you to avoid learning anything?

Sure, if you make videos you can artificially limit yourself so that you can't tell what's going on from the video. Not only will you have to suddenly accelerate the panning of your video; you will also need to use black and white video, with no color or grey scale. You might let in information about red shifts and intensities -- which would ALSO be enough for a third observer to tell unambiguously which of the two twins is shifting from one inertial frame to another.

sylas

 

[matheinste]

Quote:-
--Effects of acceleration can tell you that a thing is changing it’s movement but if you are an observer that has no way of detecting that acceleration how can you tell it is accelerating? ----

Your argument can be applied to anything. If you remove all means of detecting something then of course it is undetectable. I think it is more than a little unfair to artificially remove all means of detecting acceleration and then asking how you can then detect acceleration.

Matheinste.

 

[diazona]

Suppose I make a video of two objects moving apart and together in which one object appears to be moving (accelerating) and the other appears to remain stationary. Would you be willing to bet any money that the object that appears to be accelerating is in fact doing so? Before you risk your money let me point out that I could be moving (accelerating) the camera back and forth in sync with the object that appears to be stationary but is actually accelerating. Everything else in the shot would move back and forth in sync with the camera as well to strengthen the illusion.

The camera operator could tell whether the camera is accelerating or not.

The "third-party observer" everyone's talking about would be the camera operator. Not the person viewing the video later.

 

[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).