What Causes Time Dilation in the Twin Paradox?

[Fredrik]

Do we? Or are you just talking about SR time dilation, not GR time dilation? It seems to me that if we're talking about an accelerated observer, we have to consider GR time dilation as well (equivalence principle).

Many of us (including me) consider that a part of SR, not GR. The special theory of relativity consists of a mathematical model (Minkowski space) and a set of postulates about identifications between the real world and the model (e.g. "what a clock measures is the proper time along the curve that represents the clock's motion"). It is possible to come up with a list of such postulates that make inertial frames the only valid coordinate systems, and you could (and apparently do) call that theory SR. I think of that theory as "partial SR", "1905 SR" or "crippled SR", and the theory you get with a more complete set of identifications as "SR".

 

[Fredrik]

But nothing is SR grants you permission to do that.
SR requires that you solve any problem like this wrt just one reference frame. Not two of your choice.

I know. If you had read enough of the discussion to see what it was about, you would have known that the result I was trying to obtain was the "paradox" part of the twin paradox. That's an incorrect result, and it obviously isn't possible to obtain an incorrect result without doing something wrong.

 

[Fredrik]

Don't you see? The fact that there is a bend in B's path is the reason why the other approach is wrong. In Minkowski geometry the longest timelike interval between two points is a straight line, so a path with a bend in it is always shorter than a straight path.

No, I don't see. That last sentence tells us that B must be younger when he meets A again because his world line is bent. No disagreement there. What I don't see is how that tells us what's wrong with the naive use of the time dilation formula that concludes that A is younger.

This is what's wrong with it: It neglects what happens when you switch from one inertial frame to another in the middle of a calculation. My approach explains what happens when you do. Your approach is coordinate independent, so it can't explain it.

Your approach is the best way to quickly find out which one of the twins is right, but I still don't consider it a complete resolution of the paradox. The paradox is a mistake in a coordinate dependent calculation, so no coordinate independent approach can tell us what the mistake is.

 

[neopolitan]

Fredrik,

I note that you never answered the question about a clock on "B"'s spaceship which is designed to give "B" the real universe ageing of "A".

Do you agree that the discontinuity from 7.2 to 32.8 years is part of the incorrect way of looking at the twin scenario which leads to it appearing to be a paradox, or are you giving it as the solution?

If you agree that there is no real need to advance such a clock from 7.2 to 32.8 years at the turnaround, and that the 7.2 and 32.8 year figures are representative of incorrectly using two inertial frames as if they were one then we are not in disagreement.

cheers,

neopolitan

BTW When I say real universe ageing of "A", I mean taking into account that "A" undergoes no acceleration - it is not meant to imply that there is some absolute ageing of "A".

 

[granpa]

the point of the twins paradox isn't that one twin ages less. we know why that is. it follows from time dilation. the question is why is it that the moving twin ages less yet from his point of view it is the other twin that is aging more slowly. the answer is that there is a shift that occurs when the moving twin changes speed.

the answer you are giving is simply the answer you would get if the moving twin were to completely stop. so the 2 really agree completely.

 

[matheinste]

Hello neopolitan.

The real time and ageing for B, and the real time and ageing for A are seen differently by each other.They are both equally real but not numerically equal.

Matheinste.

 

[neopolitan]

the point of the twins paradox isn't that one twin ages less. we know why that is. it follows from time dilation. the question is why is it that the moving twin ages less yet from his point of view it is the other twin that is aging more slowly. the answer is that there is a shift that occurs when the moving twin changes speed.

the answer you are giving is simply the answer you would get if the moving twin were to completely stop. so the 2 really agree completely.

No, granpa.

The reason the moving twin ages less is because the moving twin starts off stationary in "A"'s frame, changes inertial frame to one which is not stationary wrt to "A", changes to another inertial frame which is also not stationary wrt to "A" and ends up stationary again in "A"'s frame.

"A" remains in "A"'s frame the whole time.

There is no shift when the moving twin changes speed. If there were, can you at least answer why there is no corresponding shift during the accelerations that get "B" on the way and, at the end, bring "B" to an inertial frame which is stationary wrt "A". Of course there is a shift, from "being in one inertial frame to being in another inertial frame" obviously, but there is no jumping forward or backwards of the ageing clock. Why?

(BTW I think I can come up with the staff answer, I just want to check if you have it to hand. But, having the staff answer doesn't mean that I agree with the shift at turnaround.)

cheers,

neopolitan

 

[Dale]

Surely contracted meters per dilated seconds squared cannot be considered "absolute".

The term "absolute" means "frame invariant". Proper acceleration is the acceleration measured by an accelerometer, it's norm is the norm of the four-acceleration. Therefore proper acceleration is frame invariant aka absolute.

 

[Dale]

The paradox is a mistake in a coordinate dependent calculation, so no coordinate independent approach can tell us what the mistake is.

I disagree. The paradox is a mistake in the treatment of a non-inertial reference frame as an inertial reference frame. Students need to learn to identify and avoid non-inertial reference frames much more than they need to learn how to calculate simultaneity in an accelerating reference frame.

 

[RandallB]

I disagree. The paradox is a mistake in the treatment of a non-inertial reference frame as an inertial reference frame. Students need to learn to identify and avoid non-inertial reference frames much more than they need to learn how to calculate simultaneity in an accelerating reference frame.

I think (I hope) you meant to say;
“to learn how THEY CANNOT calculate simultaneity in an accelerating reference frame”.
Or Maybe
“to learn how to establish a framework of synchronized clocks in an accelerating reference frame”.

The rules drawn from simultaneity do not allow identifying spatially separated events as simultaneous in an accelerating reference frame (even if they are defined as carrying clocks synchronized in that frame), it merits no special or preferred consideration over an inertial frame in that respect.

If it did you could redefine the twin problem as B departing A at a high speed with a low fixed acceleration that will turn B around at some distant point and return to A with the same high speed vectored in the opposite direction.
It would still allow B time to run faster than A at the beginning of the trip, with the time rate of B at the return being much slower than both A and what B was at the beginning.

The crux of fully completing the Twin Problem analysis is when you confirm you cannot declare if time is passing the same for B in both frames it uses, or if one of those frames it may be running fast – even faster than A. Upon confirming that concept you have essentially established the essence of what is meant by Einstein Simultaneity. And using an accelerating reference frame does not avoid Simultaneity.

 

[Fredrik]

Fredrik,

I note that you never answered the question about a clock on "B"'s spaceship which is designed to give "B" the real universe ageing of "A".

If you agree that there is no real need to advance such a clock from 7.2 to 32.8 years at the turnaround, and that the 7.2 and 32.8 year figures are representative of incorrectly using two inertial frames as if they were one then we are not in disagreement.

There's no need to have a clock at all, and if we do put a clock on the ship, we can program it to display whatever we want. You can't say that there's one correct way to program the clock without first specifying exactly what it's supposed to display.

If my job is to program a clock on the ship to show A's age "now", in the inertial frame that's co-moving with B, I would make it get the ship's speed once a second or so, and use SR to calculate what time to display. This would make it jump from 7.2 to 32.8 years at the turnaround event. I would also make the clock display the ship's speed relative to Earth at all times, because the concept of "now" doesn't make sense without a coordinate system, and the speed is what you need to know to understand what coordinate system the clock is using.

BTW When I say real universe ageing of "A", I mean taking into account that "A" undergoes no acceleration - it is not meant to imply that there is some absolute ageing of "A".

Then what are you implying? Are you just saying that if we only consider A's point of view, there's no way to get a result that looks like a paradox? This is true, but it isn't a resolution of the paradox. It's just a way to ignore it.

Do you agree that the discontinuity from 7.2 to 32.8 years is part of the incorrect way of looking at the twin scenario which leads to it appearing to be a paradox, or are you giving it as the solution?

It's the resolution of the apparent paradox. It's what's missing in the naive and incorrect calculation that says that A will only age 14.4 years. It's what you have to add to the incorrect calculation to make it correct.

 

[Fredrik]

The rules drawn from simultaneity do not allow identifying spatially separated events as simultaneous in an accelerating reference frame

I had a discussion with DrGreg about that https://www.physicsforums.com/showthread.php?t=249815", and we agreed that the standard definition of simultaneity is sufficient to define a coordinate system on a region that contains the world line. It may not be well-defined very far from the world line, but at least it's well-defined in the immediate vicinity.

 

[RandallB]

I had a discussion with DrGreg about that https://www.physicsforums.com/showthread.php?t=249815", and we agreed that the standard definition of simultaneity is sufficient to define a coordinate system on a region that contains the world line. It may not be well-defined very far from the world line, but at least it's well-defined in the immediate vicinity.

I'm thinking NO.

Simultaneity does not IMO allow for a preferred observer and their world line any more than a preferred frame. That would be an assumption of simultaneous-ness inconsistent with simultaneity.

 

[Fredrik]

Huh? Who said anything about a preferred observer? I'm saying that given any world line, you can use the standard definition of simultaneity to associate a local coordinate system with it. Now, I could be wrong about that, but you'd need a mathematical argument to prove that. If you have one, post it in the other thread.

 

[Dale]

The rules drawn from simultaneity do not allow identifying spatially separated events as simultaneous in an accelerating reference frame (even if they are defined as carrying clocks synchronized in that frame)

I don't understand your comments. If you have a pair of synchronized clocks then two events are simultaneous if and only if they occur when their local clocks read the same. That's what it means to synchronize a pair of clocks.

 

[Al68]

There is no shift when the moving twin changes speed. If there were, can you at least answer why there is no corresponding shift during the accelerations that get "B" on the way and, at the end, bring "B" to an inertial frame which is stationary wrt "A". Of course there is a shift, from "being in one inertial frame to being in another inertial frame" obviously, but there is no jumping forward or backwards of the ageing clock. Why?

There is, but since it depends on the distance between the ship and earth, it's negligible when the distance is small, and goes away if we consider the distance to be zero.

 

[RandallB]

I don't understand your comments. If you have a pair of synchronized clocks then two events are simultaneous if and only if they occur when their local clocks read the same. That's what it means to synchronize a pair of clocks.

NO
Being synchronized does not mean the same times separated by distance are considered simultaneous. SR shows this with other frames all defining the frame you are using as having all its clocks out of synchronization. Unless you can demonstrate how a frame or item can declare it own system of synchronization correct over other frames you cannot assume it is the correct judge of when spatially separated events actually simultaneous.

Simultaneity does not mean you can pick any frame or world line and declare it preferred just because if you do use it as the only reference and ignore all others will give good results.
Simultaneity says that any other frame can do just as well using a different standard for synchronization.

That is the whole point made by Simultaneity no matter how much you love the frame you live in you can only know that events happening collocated in space and time are simultaneous. And that is why B can only know what time it is in the A frame at the turnaround and only at that place in the A frame. Because even the A’ observer waiting at the turnaround point cannot KNOW what is simultaneously being displayed on the clock back at A.

Does that not make commonsense? Well yah hey – that the point! the rules of SR boxes you into that result and it will take something outside of SR to get outside that box. A priori assumptions, like picking some timeline, won’t do.

 

[Dale]

Simultaneity says that any other frame can do just as well using a different standard for synchronization.

Yes, this is what is meant by the relativity of simultaneity.

Simultaneity is a frame-dependent concept. "Simultaneous" simply means that two events share the same time coordinate in the specified reference frame. The specified reference frame doesn't have to be inertial, but obviously the Einstein synchronization convention cannot be applied in non-inertial frames.

 

[Fredrik]

...obviously the Einstein synchronization convention cannot be applied in non-inertial frames.

You can apply it to the co-moving inertial frame at every point on the world line. This gives you a local definition of simultaneity. This defines the spatial coordinates of a coordinate system, and the proper time along the world line defines the time coordinate. So the result is a local coordinate system that's defined in a region that contains the world line.

Edit: I should mention that I'm not 100% sure that this procedure actually works. If the world line is curved, the simultaneity lines at two nearby points on the world line will intersect at some distance from the world line. If this distance goes to zero when we let the distance between the nearby points go to zero, the procedure doesn't work.

 

[granpa]

furthermore what you are wanting to do with the Earth frame is exactly what the people onboard the rocket will want to do with the rocket frame. they will consider the rocket to be stationary. to them it is the most convenient frame.

 

[atyy]

Do we? Or are you just talking about SR time dilation, not GR time dilation? It seems to me that if we're talking about an accelerated observer, we have to consider GR time dilation as well (equivalence principle).

Of course this would lead to crazy conclusions like Earth's clock running faster than the ship's clock (from the ship's POV) during the acceleration. Oh, wait...

And crazy conclusions like the ship's clock running slower than the Earth's clock (from the Earth's POV) during the acceleration, when a gravitational field suddenly springs up only within the ship...

 

[neopolitan]

furthermore what you are wanting to do with the Earth frame is exactly what the people onboard the rocket will want to do with the rocket frame. they will consider the rocket to be stationary. to them it is the most convenient frame.

I feel my face going metaphorically blue, those on the rocket will consider the rocket to be stationary if and only if they ignore the accelerations. Part of the scenario is that the twins are twins, which means they were born into the same inertial frame (we tend to ignore the orbital, rotational and gravitational complications of being born on a planet). Therefore at least one twin must undergo an acceleration to separate from the other. In the scenario we can call that the "travelling twin" or "B". "B" will experience an acceleration on leaving Earth, on slowing down near the turnaround point (and that could easily continue to effect the return velocity) and finally on return to Earth.

While inertial frames, note "frames", not "a frame", in which the rocket is at rest might be convenient, it is hard to credit that the crew of a spaceship will consider themselves to be stationary, contrary to the evidence provided by the receding Earth and the approach of the target star.

Why can't people try to think about this as if it were real? I mean, honestly, Christopher Columbus didn't pop on his ship, leave Spain behind (out of sight and out of mind) and then think that he was becalmed. There was plenty of evidence that he wasn't. There will be plenty of evidence available to "B" that there is some sort of motion going on and while "B" could consider that motion relative, just like Columbus could have done if an early version of Einstein was there to whisper in his ear, I strongly suspect that neither actually would.

I stress this, both would be entirely justified in considering themselves to be at rest, if they so wished, but for practical purposes, they just wouldn't.

cheers,

neopolitan

 

[Fredrik]

I stress this, both would be entirely justified in considering themselves to be at rest, if they so wished, but for practical purposes, they just wouldn't.

So your "resolution" of the twin paradox is that the apparent paradox is irrelevant because people would choose to only consider A's frame?

 

[neopolitan]

So your "resolution" of the twin paradox is that the apparent paradox is irrelevant because people would choose to only consider A's frame?

No, and I think you know that. I know you should know that.

I think that people in a spaceship which has, over a journey, a number of inertial frames, separated by periods of acceleration will not consider themselves to have been in one inertial frame for the entirety of that journey.

Which is what granpa said they would want to do in the post to which I was replying.

Did you miss that, or are you being cantankerous?

cheers,

neopolitan

PS Just for a laugh, let's take some words you posted out of context:

"resolution" of the twin paradox is is irrelevant because people only consider A's frame

All your words, in the correct order. I just removed some words which weren't convenient for making fun of you. I could then paraphrase this out of context sentence and say that you said that the twin paradox is irrelevant because people should only consider A's frame.

Get the point?

 

[JesseM]

While inertial frames, note "frames", not "a frame", in which the rocket is at rest might be convenient, it is hard to credit that the crew of a spaceship will consider themselves to be stationary, contrary to the evidence provided by the receding Earth and the approach of the target star.

What do you mean by "stationary"? It seems to me you don't have anything rigorous in mind, but just a vague notion of "at rest relative to some large landmarks". But what makes you think the Earth and the target star are themselves "stationary"? (this question is of course meaningless unless you can provide some definition of what it means to be stationary in an absolute, non-relative sense, and relativity says the fundamental laws of physics will appear exactly the same in all inertial frames so there can't be a procedure involving fundamental physics that will pick out one frame as a special 'stationary' frame).

Why can't people try to think about this as if it were real?

Because in "real life" we use all sorts of practical definitions that don't have much to do with fundamental physics. For instance, on Earth we may use "stationary" as a shorthand for "stationary relative to the Earth", which is not to imply we have any reason whatsoever to believe the Earth itself is "stationary" in any absolute sense (and if you really believe in absolute motion, then if the Earth was moving at 2,000 km/s in the direction of some star in an absolute sense, anyone traveling at 2,000 km/s relative to the Earth in the direction away from that star would have to be stationary in the absolute sense, even though they are clearly not stationary relative to the Earth).

 

[Fredrik]

No, and I think you know that. I know you should know that.

I think that people in a spaceship which has, over a journey, a number of inertial frames, separated by periods of acceleration will not consider themselves to have been in one inertial frame for the entirety of that journey.

I honestly don't know what you're thinking about this whole thing. I asked you a bunch of questions during our discussion that would have clarified a lot, but most of them were ignored.

What you're saying here (in the second paragraph of the quoted text above) is something we agree on completely. I find it puzzling that you agree about this, because you have consistently refused to move B's clock ahead by 25.6 years when the rocket turns around, even though that's exactly what you need to do to compensate for the fact that you're switching from the +0.8c inertial frame to the -0.8c inertial frame at a distance of 16 light-years from Earth. (Yes, these are the numbers A would use. In both of B's inertial frames, the distance is 9.6 light-years)

 

[granpa]

I think that people in a spaceship which has, over a journey, a number of inertial frames, separated by periods of acceleration will not consider themselves to have been in one inertial frame for the entirety of that journey.

Which is what granpa said they would want to do in the post to which I was replying.

that is not what I said. I said that during the part of their journey that they arent accelerating they will find it convenient to consider themselves stationary in exactly the same way that you find it convenient to consider the Earth to be stationary the whole time. yet you can't seem to see that the rocket frame is just as legitimate as any other.

 

[neopolitan]

What do you mean by "stationary"? It seems to me you don't have anything rigorous in mind, but just a vague notion of "at rest relative to some large landmarks". But what makes you think the Earth and the target star are themselves "stationary"? (this question is of course meaningless unless you can provide some definition of what it means to be stationary in an absolute, non-relative sense, and relativity says the fundamental laws of physics will appear exactly the same in all inertial frames so there can't be a procedure involving fundamental physics that will pick out one frame as a special 'stationary' frame).

Because in "real life" we use all sorts of practical definitions that don't have much to do with fundamental physics. For instance, on Earth we may use "stationary" as a shorthand for "stationary relative to the Earth", which is not to imply we have any reason whatsoever to believe the Earth itself is "stationary" in any absolute sense (and if you really believe in absolute motion, then if the Earth was moving at 2,000 km/s in the direction of some star in an absolute sense, anyone traveling at 2,000 km/s relative to the Earth in the direction away from that star would have to be stationary in the absolute sense, even though they are clearly not stationary relative to the Earth).

I am going to get around your whole post by pointing out that I was responding to granpa's post. He used the word "stationary".

In my last sentence in the post to which you are referring, I used the words "considering themselves to be at rest".

I refer you to the PS in my post to Fredrik about an out of context comment.

cheers,

neopolitan

 

[neopolitan]

that is not what I said. I said that during the part of their journey that they arent accelerating they will find it convenient to consider themselves stationary in exactly the same way that you find it convenient to consider the Earth to be stationary the whole time. yet you can't seem to see that the rocket frame is just as legitimate as any other.

Each of the rocket's frames are legitimate, just not particularly useful when considering the totality of the twin paradox scenario. I was objecting to your use of the singular when the plural is actually applicable. You still use the singular here which is odd since you seem to understand that the rocket has frames plural.

cheers,

neopolitan

 

[JesseM]

I am going to get around your whole post by pointing out that I was responding to granpa's post. He used the word "stationary".

How does that make a difference? You used it too, you must have meant something by it.

In my last sentence in the post to which you are referring, I used the words "considering themselves to be at rest".

And how does that square with the statement "it is hard to credit that the crew of a spaceship will consider themselves to be stationary, contrary to the evidence provided by the receding Earth and the approach of the target star." Again, this is totally meaningless unless you have some definition of "stationary" in mind, if not this has about as much sense as "it is hard to credit that the crew of a spaceship will consider themselves to be sludoolaxeriffic, contrary to the evidence provided by the fact that they ate peanut butter sandwiches for lunch".

 

[neopolitan]

What you're saying here (in the second paragraph of the quoted text above) is something we agree on completely. I find it puzzling that you agree about this, because you have consistently refused to move B's clock ahead by 25.6 years when the rocket turns around, even though that's exactly what you need to do to compensate for the fact that you're switching from the +0.8c inertial frame to the -0.8c inertial frame at a distance of 16 light-years from Earth. (Yes, these are the numbers A would use. In both of B's inertial frames, the distance is 9.6 light-years)

Probably because I feel that you have ignored the fact that "B" undergoes acceleration before separating from "A" but prior to that "B" and "A" shared the same (not quite) inertial frame.

You also ignored the signals which I talked about, and the reasoning which followed from considering them.

All you consider is "B"'s ongoing calculation of what events at "A" are momentarily simultaneous with events at "B", as if the prevailing frame was always in effect.

Of course, using this very narrow view you will end up with a strange result. Instantaneously after turnaround, according to you, "B" will now use the prevailing frame to calculate that the prevailing moment at "B" is simultaneous with an event at "A" which is 25.6 years after the event instantaneously before turnaround.

Ok, I can understand the calculations. And on an almost "pure mathematics" basis I can see why you come up with the result. But, and this is the bit which you seem not to accept, when you talk about the Earth, notionally real people, notionally real spaceships and notionally real trajectories through spacetime, you have to use "applied mathematics" and take into account a little more than you can get away with in "pure mathematics". You should take into account things that you can ignore with "pure mathematics", for example, you would have to take into account the flow of information from "A" to "B" (and even "B" to "A") and that would have to behave properly.

I used daily signals from "A" to "B", but there is a continuous flow of information from the Earth to "B", since "B" should be able to use a well positioned, high definition camera to look at the Earth.

Let's say that a part of the twin experiment is to create such a huge clock that it can be seen from distances of more than, just to be safe, 20 lightyears.

Do you agree that there will be no discontinuity in the image of the Earth clock?

cheers,

neopolitan

 

[JesseM]

Ok, I can understand the calculations. And on an almost "pure mathematics" basis I can see why you come up with the result. But, and this is the bit which you seem not to accept, when you talk about the Earth, notionally real people, notionally real spaceships and notionally real trajectories through spacetime, you have to use "applied mathematics" and take into account a little more than you can get away with in "pure mathematics". You should take into account things that you can ignore with "pure mathematics", for example, you would have to take into account the flow of information from "A" to "B" (and even "B" to "A") and that would have to behave properly.

I used daily signals from "A" to "B", but there is a continuous flow of information from the Earth to "B", since "B" should be able to use a well positioned, high definition camera to look at the Earth.

Let's say that a part of the twin experiment is to create such a huge clock that it can be seen from distances of more than, just to be safe, 20 lightyears.

Do you agree that there will be no discontinuity in the image of the Earth clock?

Do you understand that even if you and I are two non-accelerating inertial observers, the rate that I see your clock ticking visually will not be the same as the rate that your clock is ticking in my own inertial coordinate system, due to the Doppler effect? Because of the Doppler effect, if I am moving away from you I'll see your clock ticking at a rate that's even slower than the rate given by the time dilation equation, and if I'm moving towards you I'll see your clock ticking faster than my own, not slower (basically this is because if you're moving away, the light from each successive tick has a longer distance to travel to reach me than the previous one, while if you're coming towards me, the light from each successive tick has a shorter distance to travel than the previous one). If you want an analysis of what is seen in the twin paradox based on the relativistic Doppler effect, see The Doppler Shift Analysis from the twin paradox FAQ, along with the diagram (fig. 2) in the too many explanations section. You're right that there's no discontinuity here, each twin sees the other twin's clock ticking slower when they're moving apart and faster after the turnaround when they're approaching each other, but the accelerated twin sees the change happen midway through the trip while the inertial twin sees the other twin turnaround much closer to the time that they reunite than the time that they departed from one another.

 

[neopolitan]

And how does that square with the statement "it is hard to credit that the crew of a spaceship will consider themselves to be stationary, contrary to the evidence provided by the receding Earth and the approach of the target star." Again, this is totally meaningless unless you have some definition of "stationary" in mind, if not this has about as much sense as "it is hard to credit that the crew of a spaceship will consider themselves to be sludoolaxeriffic, contrary to the evidence provided by the fact that they ate peanut butter sandwiches for lunch".

Jesse,

You are a funny fellow.

Do you think that NASA astronauts consider themselves be stationary when they (apparently) zip around in the heavens? If "B" travels from Earth to a distant star, even a distant point in space, what do you think will be going on in their heads, using their definition of "in motion" and "stationary".

I guess I was happy to use these terms because we do have utility for them in the real world, even if in the strict physics world, we should use "in an inertial frame which is not at rest relative to (something)" and "at rest relative to (something)".

There is a type of dictionary called a corpus dictionary. What the creators of such a dictionary do is scan for the usage of words in context, and the meanings of words therefore become defined by usage, rather than by expert opinion. I used "stationary" in what is more likely the definition that arises from a corpus dictionary.

I found the word "stationary" in the http://www.askoxford.com/concise_oed/stationary?view=uk", noting that the Oxford has gone over to a corpus basis. The definition is not physics related (which means that we shouldn't be using it) and makes no reference to being "at rest", merely about something that is neither moving nor changing.

I did not find the word "sludoolaxeriffic". Therefore, I feel that it is unreasonable to state that your sentence made as much sense as mine. (To give you credit, peanut butter was in there.)

cheers,

neopolitan

 

[neopolitan]

Do you understand that even if you and I are two non-accelerating inertial observers, the rate that I see your clock ticking visually will not be the same as the rate that your clock is ticking in my own inertial coordinate system, due to the Doppler effect? Because of the Doppler effect, if I am moving away from you I'll see your clock ticking at a rate that's even slower than the rate given by the time dilation equation, and if I'm moving towards you I'll see your clock ticking faster than my own, not slower. If you want an analysis of what is seen in the twin paradox based on the relativistic Doppler effect, see The Doppler Shift Analysis from the twin paradox FAQ, along with the diagram (fig. 2) in the too many explanations section. You're right that there's no discontinuity here, each twin sees the other twin's clock ticking slower when they're moving apart and faster after the turnaround when they're approaching each other, but the accelerated twin sees the change happen midway through the trip while the inertial twin sees the other twin turnaround much closer to the time that they reunite than the time that they departed from one another.

If you are going to jump in late, you could at least scan the preceding posts.

I am not going to bother replying to you in depth, since you are not telling me anything that could not be worked out from what I have written previously. It is sad though, given that you are the only one to even take on the signals (clocks ticking in you instance, but they are equivalent).

If you scan the preceding posts, you will see that I referenced the very same site you referred me too.

Again, you are a funny fellow.

cheers,

neopolitan

 

[JesseM]

Do you think that NASA astronauts consider themselves be stationary when they (apparently) zip around in the heavens?

I think that this is meaningless unless you define what you mean by "consider themselves to be stationary". For example, right now I consider myself to be stationary in the ordinary intuitive sense where stationary is just defined relative to the surface of the Earth, but I don't consider myself to be stationary on the level of real physics because I know there is no way to define "stationary" in terms of the laws of physics.

If "B" travels from Earth to a distant star, even a distant point in space, what do you think will be going on in their heads, using their definition of "in motion" and "stationary".

What definition? That's exactly what I'm asking you for, the definition that your imaginary astronauts are using. If you can't provide one, your statements are meaningless.

I guess I was happy to use these terms because we do have utility for them in the real world

Yes, the commonsense definition is useful in the real world because we live on the surface of a large planet, but it's unclear how to generalize this commonsense definition to a situation in space where you have lots of large astrophysical bodies in motion relative to one another. Similary, the words "up" and "down" have utility on planet Earth, in space not so much.

I found the word "stationary" in the http://www.askoxford.com/concise_oed/stationary?view=uk", noting that the Oxford has gone over to a corpus basis. The definition is not physics related (which means that we shouldn't be using it) and makes no reference to being "at rest", merely about something that is neither moving nor changing.

And how do I know whether something in space is "moving" or "not moving"? Is the Earth moving, for example? Again, when used by us planetbound beings it's always implicit that "not moving" means at rest relative to the surface of the Earth.

I did not find the word "sludoolaxeriffic". Therefore, I feel that it is unreasonable to state that your sentence made as much sense as mine.

The point is that while the commonsense usage of "stationary" has a well-understood implicit meaning on Earth, I have no idea what you want it to mean for your hypothetical astronauts, and you seem unwilling to think about how you might define it in order to make sense of your statement.

 

[JesseM]

If you are going to jump in late, you could at least scan the preceding posts.

This is a 9-page thread, it's not really reasonable to expect anyone who jumps into a long thread to look through every prior post before saying anything. It's not like I made a definite accusation that you were ignorant of the Doppler effect, I asked you "Do you understand that even if you and I are two non-accelerating inertial observers..."? A polite "yes, I understand" would suffice (and giving me the post# where you discussed it previously would be helpful although not necessary), no need for the digs about me being a "funny fellow". I think my question was reasonable, since you specifically asked about what would be seen visually, and said there'd be no discontinuity, but you didn't mention the Doppler effect or indicate that you understood that there is absolutely no conflict between this lack of a visual discontinuity and the type of simultaneity discontinuity Fredrik was talking about when we switch from one coordinate system to another midway through a problem.

 

[neopolitan]

I think that this is meaningless unless you define what you mean by "consider themselves to be stationary". For example, right now I consider myself to be stationary in the ordinary intuitive sense where stationary is just defined relative to the surface of the Earth, but I don't consider myself to be stationary on the level of real physics because I know there is no way to define "stationary" in terms of the laws of physics.

What definition? That's exactly what I'm asking you for, the definition that your imaginary astronauts are using. If you can't provide one, your statements are meaningless.

Yes, the commonsense definition is useful in the real world because we live on the surface of a large planet, but it's unclear how to generalize this commonsense definition to a situation in space where you have lots of large astrophysical bodies in motion relative to one another. Similary, the words "up" and "down" have utility on planet Earth, in space not so much.

And how do I know whether something in space is "moving" or "not moving"? Is the Earth moving, for example? Again, when used by us planetbound beings it's always implicit that "not moving" means at rest relative to the surface of the Earth.

The point is that while the commonsense usage of "stationary" has a well-understood implicit meaning on Earth, I have no idea what you want it to mean for your hypothetical astronauts, and you seem unwilling to think about how you might define it in order to make sense of your statement.

Jesse,

You are making no attempt to be helpful or to make a useful contribution to the discussion. You are merely taking one word and blowing it's usage out of proportion.

When we travel around the world, we use at rest relative to the Earth to mean "stationary".

If we were to travel across the universe, we could use at rest relative to the spaceship to mean "stationary". But when it comes to the spaceship itself, we would normally use something else against which to define "stationary". I strongly believe in a common-sense sort of definition for a spaceship such motion and rest would defined relative to the destination and/or the port of origin.

I have lived and worked on a ship (a "seaship", not a "spaceship"). Yes, I tended to use terms like "the stern is 50m from me" as if it were stationary. But I was also able to think about the ship as a whole as being in motion away from one port and heading to another.

I think that a spaceship crew will have the same sort of notions.

If that doesn't sit well with your physics notions, well, perhaps that is indicative of my being an engineer and you being ... well, a cartoonist? Sorry, totally unfair ad hom there, what is it that you do again?

cheers,

neopolitan

 

[neopolitan]

I think my question was reasonable, since you specifically asked about what would be seen visually, and said there'd be no discontinuity, but you didn't mention the Doppler effect or indicate that you understood that there is absolutely no conflict between this lack of a visual discontinuity and the type of simultaneity discontinuity Fredrik was talking about when we switch from one coordinate system to another midway through a problem.

That's the thing you see, I was asking Fredrik, not you. I wouldn't ask you, since you don't know the context. And you apparently seem to think it is unreasonable of me to expect you to check to context if you wanted to jump in and ask a question.

Can I humbly suggest that in such a case you write something like "I don't know the full context since this is such a long thread, but have you taken into account ..."?

Then it won't come over as "I am here! I don't really know what you are talking about, so you must be wrong. You must be so happy that I turned up to explain stuff for you."

cheers,

neopolitan

 

[JesseM]

If we were to travel across the universe, we could use at rest relative to the spaceship to mean "stationary". But when it comes to the spaceship itself, we would normally use something else against which to define "stationary".

"We" would? In what context? In conversation around the dinner table? When making course calculations? In any situation where math was involved, we'd be using some definite coordinate system; in ordinary conversation, it would probably mean relative to stuff on the ship, and if the astronauts talked about the ship's speed at all, it would probably be an implicit reference to whatever coordinate system they were using when doing course calculations. In any case, if you admit this has no relevance to physics, this whole conversation is irrelevant to the purpose of this forum and I don't know why you felt the need to bring it up.

If that doesn't sit well with your physics notions, well, perhaps that is indicative of my being an engineer and you being ... well, a cartoonist?

Nope, just have some cartoons from college on my personal website, it's kind of creepy that you would go there and then bring it up in order to get in another little dig at me.

Sorry, totally unfair ad hom there

I don't think you're "sorry" at all, or you would have just edited the comment out.

 

[JesseM]

That's the thing you see, I was asking Fredrik, not you. I wouldn't ask you, since you don't know the context. And you apparently seem to think it is unreasonable of me to expect you to check to context if you wanted to jump in and ask a question.

When "checking the context" involves reading an entire 9-page thread, yes it is unreasonable. If you've spent any time on this forum you'll know it's extremely common for people to jump into respond to individual comments during the course of long discussions (as it is on every other discussion forum I've participated in).

Can I humbly suggest that in such a case you write something like "I don't know the full context since this is such a long thread, but have you taken into account ..."?

That wouldn't be a bad thing to write, but it's unreasonable of you to expect that anyone jumping into a discussion would always have to preface their questions with such comments, or to interpret such questions/comments in totally thin-skinned and defensive ways like your paraphrase "you must be wrong. You must be so happy that I turned up to explain stuff for you." The point of this forum is explaining physics concepts, if someone occasionally explains something you already know (as has happened to me plenty of times), a simple "yes, I already knew about that" is fine, no need to scold the person or treat it as a personal attack (especially since the explanation could still be helpful to others reading the thread).

 

[neopolitan]

When "checking the context" involves reading an entire 9-page thread, yes it is unreasonable. If you've spent any time on this forum you'll know it's extremely common for people to jump into respond to individual comments during the course of long discussions (as it is on every other discussion forum I've participated in).

That wouldn't be a bad thing to write, but it's unreasonable of you to expect that anyone jumping into a discussion would always have to preface their questions with such comments, or to interpret such questions/comments in totally thin-skinned and defensive ways like your paraphrase "you must be wrong. You must be so happy that I turned up to explain stuff for you." The point of this forum is explaining physics concepts, if someone occasionally explains something you already know (as has happened to me plenty of times), a simple "yes, I already knew about that" is fine, no need to scold the person or treat it as a personal attack (especially since the explanation could still be helpful to others reading the thread).

Maybe I have just been fortunate, but I have interacted with quite a number of people who are far more polite and self-aware (and by that I mean more polite and self-aware than both you and me). Clearly anyone who reads this exchange will realize that we have a history (one which included me being given your website address, by you).

How about you back out, let Fredrik answer the question I posed to him and I won't have the feathers on my thin skin ruffled unnecessarily? Is that possible?

As pro quid pro, I promise to not jump into any longer discussions that you are having in other threads.

cheers,

neopolitan

 

[Fredrik]

I am not totally convinced that you have to even consider simultaneity at all in order to prove that the twin paradox is a false paradox. The only reason I am bringing it up is because I disagree very strongly that "B" is forced to calculate that "A" ages 25.6 years during the turn around.

I'm embarrassed to say that I didn't even see post #79 until now. I guess I was too focused on the discussion with DaleSpam at that time. I should at least comment the statement that I just quoted.

You don't have to consider simultaneity to prove that it's a false paradox. We know that there can't be a paradox because the scenario that allegedly contains a paradox is just a triangle in Minkowski space. If three straight lines forming a triangle can cause a paradox, all of mathematics would fall with it.

We can also find out which one of the twins is younger simply by using the postulate that what a clock measures is the integral of \sqrt{g_{\mu\nu}dx^\mu dx^\nu}along the curve in Minkowski space that represents its motion. The result of the calculation is the same no matter what coordinate system we use, so we can choose one that's convenient. In any inertial frame, the expression above simplifies to \sqrt{dt^2-dx^2}. A's rest frame is an inertial frame, so let's use that. Now we can immediately see that the integral along A's world line is greater than the integral along B's world line, since dx=0 along A's world line, but not along B's world line.

So now we know that there's no paradox, and that B is younger when they meet again, and if we do the integrals (which is easy), we find the exact final ages of both twins. Simultaneity is clearly not needed for any of that.

What we need simultaneity for is to explain what's wrong with the calculation that says that A is younger.

 

[Fredrik]

How about you back out, let Fredrik answer the question I posed to him...

What question? Have I missed something again? This one?

Do you agree that there will be no discontinuity in the image of the Earth clock?

I assumed that was a rhetorical question or something. It's like asking if I agree that bears crap in the woods.

 

[neopolitan]

What question? Have I missed something again? This one?

I assumed that was a rhetorical question or something. It's like asking if I agree that bears crap in the woods.

Ok, we agree about bears, and about the paradox thing. I think it is just that you want to explain why bears don't use those japanese fish ponds full of koi, and I believe you really don't need to explain the wrong answer works once you can show how the right answer is generated. While I think that your approach can lead to some confusion, it is certainly not wrong.

So, nothing substantial to discuss here :)

cheers,

neopolitan

 

[phyti]

Jesse,


But when it comes to the spaceship itself, we would normally use something else against which to define "stationary".

cheers,

neopolitan

How about the distant star field, it works for inertial navigation.
It's the closest thing to fixed position we have.

 

[atyy]

How about the distant star field, it works for inertial navigation.
It's the closest thing to fixed position we have.

GR texts often acknowledge that such motion is absolute and "inertial" in some sense. In GR, an inertial frame is defined to be one in which the observer knows he is inertial using a purely local test, without looking out of the window, but by using an accelerometer.

I haven't seen this definition in SR texts, but even those define the test for non-inertiality using an accelerometer locally. So even if twin B starts off moving at a constant velocity relative to twin A, B will know at the turn-around that he has accelerated in an absolute sense, and will have enough knowledge not to apply the time dilation formula too naively.

 

[neopolitan]

How about the distant star field, it works for inertial navigation.
It's the closest thing to fixed position we have.

While I agree with using the distant star field to a certain extent (since it is sort of fixed as a whole, as it probably consists of an aggregate of all possible trajectories), I'll point out that astronavigation (or celestial navigation) carried out on Earth using the stars also makes use of the fact that the Earth is moving. I suspect that you probably knew that, but it is worth pointing out that there are three informal frames used in star based navigation - the vessel, usually a ship; the Earth, mostly the rotation but with some daily corrections to take into account the orbit), and the stars which are taken to be fixed (but, as physics boffs, we know to not be fixed at all).

I am pretty sure that is the sort of navigation you are talking about, since there is another sort using gyroscopes to track the motion of a vessel which doesn't rely on the distant star field

There was someone who came out recently reporting that the twin paradox was solved due to the fact that we should use the universe as a whole as what would amount to a preferred frame, and in that sort of preferred frame, the traveling twin can be shown to age less rapidly. This is, of course, probably a horrible misrepresentation of what he said.

cheers,

neopolitan

 

[Al68]

If you agree that there is no real need to advance such a clock from 7.2 to 32.8 years at the turnaround, and that the 7.2 and 32.8 year figures are representative of incorrectly using two inertial frames as if they were one then we are not in disagreement.

Of course there is no need to advance such a clock. The "SR simultaneity rule" is not a law of physics, it's just true by convention. Those figures are obtained simply by using the SR simultaneity convention (t'=t-vx/c^2).

But if there is a clock at rest with earth, synched with Earth's clock in Earth's frame, and local to the turnaround, all observers would agree that it reads ~ 20 yrs just before, during, and after the turnaround, in every frame. 20 yrs is the turnaround time in Earth's frame. If this is all you're saying, I think everyone would agree (maybe).

I would even agree that the 7.2 and 32.8 yr figures don't represent anything in reality in an absolute sense. After all, they represent when signals would be received (adjusted for lightspeed delay) by observers in frames at rest with the ship's frames, but not local to the ship itself.

Also, we are not forced to even consider what the Earth's clock reads in the ship's frame. We could just consider a series of clocks at rest with Earth all along the trip, and call those readings "local Earth frame time". Each one would read ship time/0.6, assuming they are synched in Earth's frame. Of course these clocks are out of synch with each other in the ship's frame by vx/c^2, but we could just as rightfully claim that they represent reality.

Al

 

[atyy]

Of course there is no need to advance such a clock. The "SR simultaneity rule" is not a law of physics, it's just true by convention.

Although the sudden jump simultaneity convention works in this particular version of the twin paradox, it's kinda weird. George Jones posted a paper with a nice simultaneity convention that's a lot smoother for B (surprisingly simple too): https://www.physicsforums.com/showthread.php?p=1893032&highlight=accelerated#post1893032

 

[granpa]

why not consider 3 grids of synchronized clocks. one for Earth frame. one for outbound rocket frame. and one for inbound rocket frame.