Post by: Dimensional on 11/01/2023 18:46:12
Here is a link that Fermilab put out, . At 12:00, it explains that the reason for the time dilation of the twin is because of the change in direction and not acceleration (although he does say that acceleration plays a small part).
The other claim is made by Sabine Hossenfelder. She says in this video, , at 11:00, that it is the acceleration that causes the dilation.
There must be a simple formula to calculate the time dilation by the acceleration. This seems to be a way to know who is correct.
Any thoughts about this?
Post by: Halc on 11/01/2023 19:54:34
One of the best ways is simply to choose an inertial frame of reference and stick with it. Time dilation is a function of the speed of each twin in that frame. It's that simple.
it explains that the reason for the time dilation of the twin is because of the change in direction and not accelerationThis explains the asymmetry of the situation, but it is possible for both twins to change direction, and this explanation then falls apart.
Quote
The other claim is made by Sabine Hossenfelder. She says in this video,It is misleading to simplify it to this, totally out of context. I don't think Hossenfelder said this without qualifying context.
, at 11:00, that it is the acceleration that causes the dilation.
I can have two clocks, one accelerating at about 1/30th of a g for a year, and the other at thousands of g for a year. The clocks can be kept in sync. Or maybe the high-g one can be made to age faster or slower. Point is, it simply isn't a function of acceleration, but rather a function of speed relative to some given frame of reference. There's no way to fool that method.
Post by: alancalverd on 11/01/2023 22:28:45
Post by: Dimensional on 11/01/2023 23:19:56
So if the twin only accelerated instead of traveling at a velocity, there wouldn't be a difference in age? Consider the twin accelerates away for half the distance towards the turning point, and returns by accelerating towards the twin for the second half of the distance. Are you saying that their clocks would be equal upon return to the twin?
I can have two clocks, one accelerating at about 1/30th of a g for a year, and the other at thousands of g for a year. The clocks can be kept in sync. Or maybe the high-g one can be made to age faster or slower. Point is, it simply isn't a function of acceleration, but rather a function of speed relative to some given frame of reference. There's no way to fool that method.
At 12:05 in the video, she says, "the real time dilation comes from the acceleration".
And the other video tries to explain how no acceleration is needed for time dilation.
Post by: Dimensional on 12/01/2023 00:07:52
A change in direction is an acceleration.Yes, I meant to say that the video from Fermilab says that no acceleration is needed. While the other video claims that the acceleration caused the time dilation.
Post by: Dimensional on 12/01/2023 04:05:21
It's not a function of acceleration, so I cannot say from just that.
Then would you say that Sabine in the video is wrong?
The point of my thread is to try to figure out if there is actually a clear and definite understanding of the twin paradox.
Post by: Eternal Student on 12/01/2023 04:24:12
I've watched both videos sufficiently (I would think). Sabine's video is long and people could just jump in to it about one-third the way along and stop before she discusses general relativity (the last third). Meanwhile, the Fermilab video probably does need to be watched almost all the way through.
The videos aren't really contradictory, they are just emphasizing things in slightly different ways.
The common ground is:
They assume you are broadly familiar with the twin paradox and why it seems like a paradox (specifically they they can't both be older than the other).
They state the paradox is resolved because there is an asymmetry between the two twins.
They both state that Special Relativity is sufficient, you don't need General relativity.
The differences:
Sabine's video emphasizes that one twin can measure an acceleration with an accelerometer (she uses a spring balance). She spends some time imagining a realistic acceleration, i.e. where one twin is smoothly accelerated.
Don / Fermilab video tries to emphasize that acceleration isn't used much to determine the time dilation. Indeed, that much is true if you understand it a certain way: It hardly matters if the acceleration was smooth and steady or abrupt or, as Don tries to suggest if there was no acceleration at all. Notice that Don never really gets his space traveller back home in the second half of his video, he only gets some information about time clocks back. At best this scenario could be used to model a situation where the acceleration is abrupt, the space traveller is instantly thrown from one one rest frame into a different rest frame (i.e. the two rocket crews didn't just hold up their clocks as they passed each other, they threw the traveller out of the airlock of one ship and into the other ship, the other ship's crew presumably had a very good doctor who could put Ron back together again after their impact on the other ship at a speed close to c ).
The key element in the Fermilab video is where Don explains the resolution of the paradox at 12: 00 ~ 12: 30. He states "The moving observer existed in TWO different frames". He does then confound the issue at 12:30 ~12:40 by explaining that the acceleration wasn't important....
Summary:
Overall I can find more fault with the Don Lincoln's / Fermilab video. I can't help but mention one minor detail - the statement "the stationary observer only existed in one frame while the moving twin existed in two different frames" is just wrong. They existed in all valid frames of reference, all he means is that there was only ever one rest frame for the twin on Earth but two different rest frames for the traveller. People don't suddenly stop existing in any frame of reference, they just stop being being at rest in that frame.
The more important point is clearly where he implies that the change of rest frames is important but then states that acceleration is NOT important. You MUST read between the lines here..... The acceleration was obviously important because otherwise the space travelling twin wouldn't have had two different rest frames. However, it's just the way the acceleration was applied that doesn't matter and isn't used in the usual treatment of the twins paradox under Special relativity. I get the impression that Don Lincoln was just emphasizing that General relativity is not required. This, I think, is where some confusion has been left with the viewer ( @Dimensional ). Let's try and give a simple analogy:
Alice buys some strawberry milkshake that was in a glass bottle. She pours the milkshake into a cup and gives it to her son. We would say that it doesn't matter how she poured the milkshake or what the original glass bottle was like. She could have poured it slowly, quickly, in two separate goes with a break in between... it doesn't matter. What matters is that it's in the cup at the end. This is what Don Lincoln was stating. The nature of the acceleration is unimportant (the way she poured the milkshake is unimportant) BUT we know the travelling twin changed rest frames somehow (just as we understand that some milkshake pouring operation must have happened). So, we end up with a mathematical formula for the time dilation in the twins paradox which does not include the variable, a (the acceleration), it only involves quantities like L (the distance between Andromeda and Earth) and V (the constant speed of travel). In this sense, the time dilation is independent of the acceleration.
I hope that helps a bit.
Best Wishes.
Post by: Dimensional on 12/01/2023 05:56:20
Hi.But at 14:25 in the video, he definitely seems adamant that acceleration is not the cause of the time dilation of the classical twin paradox thought experiment. So if acceleration is not the cause, then what is?
I've watched both videos sufficiently (I would think). Sabine's video is long and people could just jump in to it about one-third the way along and stop before she discusses general relativity (the last third). Meanwhile, the Fermilab video probably does need to be watched almost all the way through.
The videos aren't really contradictory, they are just emphasizing things in slightly different ways.
The common ground is:
They assume you are broadly familiar with the twin paradox and why it seems like a paradox (specifically they they can't both be older than the other).
They state the paradox is resolved because there is an asymmetry between the two twins.
They both state that Special Relativity is sufficient, you don't need General relativity.
The differences:
Sabine's video emphasizes that one twin can measure an acceleration with an accelerometer (she uses a spring balance). She spends some time imagining a realistic acceleration, i.e. where one twin is smoothly accelerated.
Don / Fermilab video tries to emphasize that acceleration isn't used much to determine the time dilation. Indeed, that much is true if you understand it a certain way: It hardly matters if the acceleration was smooth and steady or abrupt or, as Don tries to suggest if there was no acceleration at all. Notice that Don never really gets his space traveller back home in the second half of his video, he only gets some information about time clocks back. At best this scenario could be used to model a situation where the acceleration is abrupt, the space traveller is instantly thrown from one one rest frame into a different rest frame (i.e. the two rocket crews didn't just hold up their clocks as they passed each other, they threw the traveller out of the airlock of one ship and into the other ship, the other ship's crew presumably had a very good doctor who could put Ron back together again after their impact on the other ship at a speed close to c ).
The key element in the Fermilab video is where Don explains the resolution of the paradox at 12: 00 ~ 12: 30. He states "The moving observer existed in TWO different frames". He does then confound the issue at 12:30 ~12:40 by explaining that the acceleration wasn't important....
Summary:
Overall I can find more fault with the Don Lincoln's / Fermilab video. I can't help but mention one minor detail - the statement "the stationary observer only existed in one frame while the moving twin existed in two different frames" is just wrong. They existed in all valid frames of reference, all he means is that there was only ever one rest frame for the twin on Earth but two different rest frames for the traveller. People don't suddenly stop existing in any frame of reference, they just stop being being at rest in that frame.
The more important point is clearly where he implies that the change of rest frames is important but then states that acceleration is NOT important. You MUST read between the lines here..... The acceleration was obviously important because otherwise the space travelling twin wouldn't have had two different rest frames. However, it's just the way the acceleration was applied that doesn't matter and isn't used in the usual treatment of the twins paradox under Special relativity. I get the impression that Don Lincoln was just emphasizing that General relativity is not required. This, I think, is where some confusion has been left with the viewer ( @Dimensional ). Let's try and give a simple analogy:
Alice buys some strawberry milkshake that was in a glass bottle. She pours the milkshake into a cup and gives it to her son. We would say that it doesn't matter how she poured the milkshake or what the original glass bottle was like. She could have poured it slowly, quickly, in two separate goes with a break in between... it doesn't matter. What matters is that it's in the cup at the end. This is what Don Lincoln was stating. The nature of the acceleration is unimportant (the way she poured the milkshake is unimportant) BUT we know the travelling twin changed rest frames somehow (just as we understand that some milkshake pouring operation must have happened). So, we end up with a mathematical formula for the time dilation in the twins paradox which does not include the variable, a (the acceleration), it only involves quantities like L (the distance between Andromeda and Earth) and V (the constant speed of travel). In this sense, the time dilation is independent of the acceleration.
I hope that helps a bit.
Best Wishes.
As you saw, he then goes on to try to "prove" in the video that acceleration is not necessary (like you say, there would have been at least some form of acceleration, but anyway), and then does not really explain what is the cause of the dilation if not acceleration.
Post by: alancalverd on 12/01/2023 08:48:18
Yes, I meant to say that the video from Fermilab says that no acceleration is needed.Then it's wrong! If there is no acceleration between the twins, there is no relative speed, therefore no time discrepancy. If they were always moving relative to one another, they aren't twins because there never was any synchronicity.
Post by: Eternal Student on 12/01/2023 13:19:46
But at 14:25 in the video, he definitely seems adamant that acceleration is not the cause....This might be an error. Don Lincoln's video ends at 13:20, there isn't anything at 14:25.
I would be willing to explain the difference in time that each twin experienced by using a hybrid of both videos: It is because the space traveller had two different rest frames (as per Don Lincoln's video). However, an acceleration was necessary for that happen (as per Sabines's video). The exact details of the acceleration aren't important only that it ultimately results in the traveller moving in the opposite direction as observed by the twin who remained on planet Earth.
It is then a bit arbitrary to say that the acceleration did or did not cause it. The acceleration had to be there but it only had to meet one condition (a reversal of the travelling twins velocity). Provided that condition is met, then the acceleration is arbitrary and does not change the difference in elapsed time that the twins would experience. Meanwhile, the distance between between Earth and Andromeda, L, along with the speed of travel of the travelling twin (V which is stated as 0.99 c in Don Lincoln's video) is very important. Change L or V and the time difference experienced by the two twins does change.
Best Wishes.
Post by: Eternal Student on 12/01/2023 13:37:37
Look, there's always a problem trying to summarise things, inevitably you leave something out. The difficulty here is that acceleration and speed are connected.
The nature of the acceleration does matter a little because it could prevent the assumption of a constant speed of travel being reasonable. The travelling twin is assumed to be moving at 0.99c almost all the time. They change their velocity from + 0.99c to -0.99c as far as the twin on earth is concerned and this must happen over a short amount of time, if it happened over a long period of time then their speed wasn't 0.99c for some of the journey.
Anyway, I could go on finding minor details and issues but it may not help. Overall, in the simple treatment of the twins paradox, the assumption is that the acceleration is so rapid that it can be ignored, it happens in approximately 0 seconds.
Best Wishes.
Post by: Dimensional on 12/01/2023 14:33:49
Hi again.Please excuse me if I am wrong, but this would seem to suggest that the minimum that is necessary for the classical twin paradox scenario to work (outside of any wormhole or crazy geometric possibilities for the twin to decrease in age relative to the other) is that acceleration is necessary.
Look, there's always a problem trying to summarise things, inevitably you leave something out. The difficulty here is that acceleration and speed are connected.
The nature of the acceleration does matter a little because it could prevent the assumption of a constant speed of travel being reasonable. The travelling twin is assumed to be moving at 0.99c almost all the time. They change their velocity from + 0.99c to -0.99c as far as the twin on earth is concerned and this must happen over a short amount of time, if it happened over a long period of time then their speed wasn't 0.99c for some of the journey.
Anyway, I could go on finding minor details and issues but it may not help. Overall, in the simple treatment of the twins paradox, the assumption is that the acceleration is so rapid that it can be ignored, it happens in approximately 0 seconds.
Best Wishes.
But Don says at 4:25 (not 14:25, sorry) that the acceleration (in the typical scenario or the twin paradox, not the "frame changing example") is not the reason for the dilation. While, Sabine gives an example using only acceleration.
I still can't help but see a distinct contradiction between Sabine and Don.
Post by: Dimensional on 12/01/2023 15:39:30
Yes accept that it haunts me that at 4:25 (not 14:25) he also says that many physicists who don't work with relativity a lot believe that time dilation occurs during the acceleration periods (in the classical twin paradox thought experiment).Yes, I meant to say that the video from Fermilab says that no acceleration is needed.Then it's wrong! If there is no acceleration between the twins, there is no relative speed, therefore no time discrepancy. If they were always moving relative to one another, they aren't twins because there never was any synchronicity.
And when I think about it, in his example in which he claims there is no acceleration, there is a way to look at it where there really isn't any change in direction either. None of the travelers change direction or accelerate, yet the result is the same as if the twin were thrown into the returning ship.
Post by: alancalverd on 12/01/2023 18:39:05
If both clocks have the same velocity, there is no discrepancy between them (observed fact!).
Post by: Dimensional on 12/01/2023 19:10:41
Thrown - acceleration. Change of velocity vector from one ship to another - acceleration. Acceleration is nothing more or less than a change of velocity: speed, direction or both.Then this would mean that acceleration played a role in the time dilation. Do you know any math formulas to see how acceleration and time dilation are related? A possible problem might be that acceleration is infinite using,
If both clocks have the same velocity, there is no discrepancy between them (observed fact!).
a = (vf - vi)/t
Post by: alancalverd on 12/01/2023 22:47:45
I had the odd experience of hearing Hermann Bondi explaining this to Shirley Williams on a broken-down train one morning when both were famous and trains usually worked.
Post by: Eternal Student on 13/01/2023 02:39:44
I'm concerned you might be adding a bit more confusion @Alanacalverd but there's every chance I'm also doing the same.
When @alancalverd says something like "there is no relative velocity", he means the velocity of one thing relative to the other thing was numerically 0. Don't assume there was no relative velocity in any other sense, there was one, there always is a velocity of one thing relative to another thing, it just is numerically 0 sometimes.
- - - - - - - - -
Do you know any math formulas to see how acceleration and time dilation are related?Yes. It's in most textbooks. Did you want to see it here?
Δt = time elapsed for the twin remaining on earth =
[Eqn 1]
where xA = x co-ordinate position of Andromeda and we have chosen the axis so that x=0 is where Earth is located; v(t) = velocity of the traveller at time t and we can assume the position x(t) of the traveller is an invertible function of time so that we can express the time t as a function of the position, t = t(x) because then v(t) = v(t(x)) can also be expressed as a function of x and then we can perform the integral appropriately. (If the traveller wasn't always travelling away from earth but spent some time moving to/from it like taking 2 steps forward with 1 step backward then we can't invert the function x(t) to find t(x) but we can still perform the calculation - we would just break the integral into a sum of smaller sections where the traveller was always travelling in one direction on each section. This is needlessly complicated, so in most simple treatments of the problem the traveller only ever moves in 1 direction along each leg of the journey and we only ever need to split it into two pieces, the outward journey and the return journey back to earth).
Meanwhile, the elapsed time for the travelling twin (who goes to Andromeda) is given by:
Δτ =
[Eqn 2]
That formula is based on using the proper time interval, dτ, which will be the identical to the time elapsed on a clock that was moving with the traveller.Now, when we assume the speed v(t) was constant, then the gamma factor γ(t) is also constant and can be taken outside the integral as a constant. Ultimately we then have Δτ = Δt / γ as usual.
If you want to know the difference between the elapsed times, then just subtract them. Also, we have deliberately only looked at the outward journey. The calculation for the return journey is much the same and indeed there is an obvious symmetry. We would just add the times for the two sections together. I'm sure you know that adding two things that are the same is equivalent to multiplying by 2. So you should multiply both Δt and Δτ by 2 if you want to consider the total elapsed time for the combined outward + return journey.
Now the point that Don Lincoln was trying to communicate is that only v(t) = velocity of the traveller and xA = distance to Andromeda appeared in the integrals and therefore influence the elapsed times, the acceleration does not directly appear. However, it's a superficial comment. v(t) is related to the acceleration, a(t) by the following:
v(t) = v0 +
[Eqn 3]
So the acceleration is there, it's just hidden in the assumptions about what v(t) is like. (In the simplest situation the velocity is always kept constant).So we would just substitute v(t) with that expression [Eqn 3] in the two formulae earlier [Eqn 1] and [Eqn 2]. It's obviously a bit messy but still useable.
For the purpose of getting the basic principles of physics across, it's easier to assume a(t) is constant and especially easy if a(t) = 0 everywhere (i.e. to assume the traveller maintains constant speed except for a negligible and completely ignorable amount of time at Andromeda where they turn around and possibly at planet Earth if you want them to start and stop there. So that is what is generally done. However, if you must have a varying acceleration, a = a(t), then you can.
Look, I don't know how to phrase this carefully: Don Lincoln was just saying that acceleration doesn't appear in the usual formula for the twin paradox, which is true. However, this is only because a simple pattern of movement is usually assumed, in particular the speed is constant everywhere except where the travelling twin is rapidly turned around at Andromeda, which is such a rapid turn around that it can be completely ignored. He was also boosting or reinforcing the claim that general relativity was never required, which is also true.
You ( @Dimensional ) are just taking some bits of the video too literally and out of context. Don Lincoln is not without fault here - he has promoted or up-sold his video with some short and snappy sounding phrases and it was too easy for a viewer to walk away with the wrong ideas.
Take the phrasing at 4:25 which you point to in the broader context it was intended: The time dilation isn't JUST happening at the time or place where the traveller experienced some acceleration (made the turn around Andromeda), it was happening somewhere or all the way through the journey. This is why the things that are important and will affect the total time elapsed are (i) the total distance travelled and (ii) the speed of travel during the whole journey. The dilation happens everywhere along the journey. Take a moment to let that sink in before you read the next paragraph.....
Now, the time dilation was happening everywhere along the journey, however, there is still some discrepancy, some reason to explain why it wasn't happening exactly the same way to the twin who remained on Earth. Recall that this is the fundamental issue in the twin paradox, why can't we consider the situation as being perfectly symmetric (the travelling twin stayed still while the earth twin appeared to move away and come back). Indeed, if you really do take the time and effort to study the paradox situation, then you will see that the travelling twin really does think that the clocks on planet Earth are ticking more slowly. If nothing else happened then the travelling twin should have found that LESS time had elapsed for his Earth twin and not the MORE time which we know is the correct result. There is a "discrepancy" of some sort. It is the discrepancy in the elapsed times for the two twins which is explained by the acceleration that only one of them experienced around Andromeda. When the travelling twin was abruptly shifted into a new rest frame, they "jumped tracks" or "skipped over some events for the earth twin". Some moments of time that the twin on Earth would have experienced were skipped over. Some events (which is a formal mathematical term, the nearest ordinary English language idea is to say those "moments of time at that place on earth") were in the travelling twins future (in the old rest frame) but they abruptly changed to being events that were in their past (in the new rest frame), they were never in their present or "now" , they were skipped over entirely. Where you don't assume an instantaneous acceleration but just a very rapid one, then those events aren't completely skipped they are just very tightly compressed, they all occur over a very small time interval for the travelling twin.
I know that the idea of skipping over or missing out some events is difficult to get your head around. LATE EDITING: I can show you the maths but I reckon this post is long enough already.
So I would say that Don Lincoln is mis-representing what many physicists think. Those who have spent some time studying the problem know that "the discrepancy" in elapsed time happens because of the acceleration at Andromeda but they are well aware that it's not as if the time dilation effect was only happening during the acceleration. It is impossible to say exactly "where" it was happening - some time dilation effect was happening everywhere along the journey but it wasn't a discrepancy in the right way (it would make the earth twin experience more time than the traveller), the major discrepancy (which does make the change in the right way) occurs at Andromeda where the traveller jumps rest frames with the result that some events the earth twin experiences are abruptly shifted from the travellers future into their past (skipped over). That "discrepancy" is obviously due to the abrupt shift in rest frames, which is a consequence of an abrupt acceleration (no matter how hard Don Lincoln protests about it). So, what I'm trying to say as politely as possible is that Don Lincoln has over-emphasised or over-sold something. Many of the statements you have highlighted are just wrong IF you insist on taking them on their own, out of the general context, or as being more than just an impression or summary using English that is accessible to the general public.
Best Wishes.
Post by: Dimensional on 13/01/2023 03:54:24
Time dilation requires (a) that two clocks were synchronised at some point and (b) that they are now moving relative to one another. Therefore one must have accelerated. Hence no paradox - you do something to a clock, and something changes. If you do nothing, they have no relative velocity and nothing changes. If they were "always" moving relative to one another, you had no means of synchronising them.Thanks, I think I get it now.
I had the odd experience of hearing Hermann Bondi explaining this to Shirley Williams on a broken-down train one morning when both were famous and trains usually worked.
Post by: Dimensional on 13/01/2023 03:55:11
Hi.Thank you very much, I think it makes sense now.
I'm concerned you might be adding a bit more confusion @Alanacalverd but there's every chance I'm also doing the same.
When @alancalverd says something like "there is no relative velocity", he means the velocity of one thing relative to the other thing was numerically 0. Don't assume there was no relative velocity in any other sense, there was one, there always is a velocity of one thing relative to another thing, it just is numerically 0 sometimes.
- - - - - - - - -Do you know any math formulas to see how acceleration and time dilation are related?Yes. It's in most textbooks. Did you want to see it here?
Δt = time elapsed for the twin remaining on earth =[Eqn 1]
where xA = x co-ordinate position of Andromeda and we have chosen the axis so that x=0 is where Earth is located; v(t) = velocity of the traveller at time t and we can assume the position x(t) of the traveller is an invertible function of time so that we can express the time t as a function of the position, t = t(x) because then v(t) = v(t(x)) can also be expressed as a function of x and then we can perform the integral appropriately. (If the traveller wasn't always travelling away from earth but spent some time moving to/from it like taking 2 steps forward with 1 step backward then we can't invert the function x(t) to find t(x) but we can still perform the calculation - we would just break the integral into a sum of smaller sections where the traveller was always travelling in one direction on each section. This is needlessly complicated, so in most simple treatments of the problem the traveller only ever moves in 1 direction along each leg of the journey and we only ever need to split it into two pieces, the outward journey and the return journey back to earth).
Meanwhile, the elapsed time for the travelling twin (who goes to Andromeda) is given by:
Δτ =[Eqn 2]That formula is based on using the proper time interval, dτ, which will be the identical to the time elapsed on a clock that was moving with the traveller.
Now, when we assume the speed v(t) was constant, then the gamma factor γ(t) is also constant and can be taken outside the integral as a constant. Ultimately we then have Δτ = Δt / γ as usual.
If you want to know the difference between the elapsed times, then just subtract them. Also, we have deliberately only looked at the outward journey. The calculation for the return journey is much the same and indeed there is an obvious symmetry. We would just add the times for the two sections together. I'm sure you know that adding two things that are the same is equivalent to multiplying by 2. So you should multiply both Δt and Δτ by 2 if you want to consider the total elapsed time for the combined outward + return journey.
Now the point that Don Lincoln was trying to communicate is that only v(t) = velocity of the traveller and xA = distance to Andromeda appeared in the integrals and therefore influence the elapsed times, the acceleration does not directly appear. However, it's a superficial comment. v(t) is related to the acceleration, a(t) by the following:
v(t) = v0 +[Eqn 3]So the acceleration is there, it's just hidden in the assumptions about what v(t) is like. (In the simplest situation the velocity is always kept constant).
So we would just substitute v(t) with that expression [Eqn 3] in the two formulae earlier [Eqn 1] and [Eqn 2]. It's obviously a bit messy but still useable.
For the purpose of getting the basic principles of physics across, it's easier to assume a(t) is constant and especially easy if a(t) = 0 everywhere (i.e. to assume the traveller maintains constant speed except for a negligible and completely ignorable amount of time at Andromeda where they turn around and possibly at planet Earth if you want them to start and stop there. So that is what is generally done. However, if you must have a varying acceleration, a = a(t), then you can.
Look, I don't know how to phrase this carefully: Don Lincoln was just saying that acceleration doesn't appear in the usual formula for the twin paradox, which is true. However, this is only because a simple pattern of movement is usually assumed, in particular the speed is constant everywhere except where the travelling twin is rapidly turned around at Andromeda, which is such a rapid turn around that it can be completely ignored. He was also boosting or reinforcing the claim that general relativity was never required, which is also true.
You ( @Dimensional ) are just taking some bits of the video too literally and out of context. Don Lincoln is not without fault here - he has promoted or up-sold his video with some short and snappy sounding phrases and it was too easy for a viewer to walk away with the wrong ideas.
Take the phrasing at 4:25 which you point to in the broader context it was intended: The time dilation isn't JUST happening at the time or place where the traveller experienced some acceleration (made the turn around Andromeda), it was happening somewhere or all the way through the journey. This is why the things that are important and will affect the total time elapsed are (i) the total distance travelled and (ii) the speed of travel during the whole journey. The dilation happens everywhere along the journey. Take a moment to let that sink in before you read the next paragraph.....
Now, the time dilation was happening everywhere along the journey, however, there is still some discrepancy, some reason to explain why it wasn't happening exactly the same way to the twin who remained on Earth. Recall that this is the fundamental issue in the twin paradox, why can't we consider the situation as being perfectly symmetric (the travelling twin stayed still while the earth twin appeared to move away and come back). Indeed, if you really do take the time and effort to study the paradox situation, then you will see that the travelling twin really does think that the clocks on planet Earth are ticking more slowly. If nothing else happened then the travelling twin should have found that LESS time had elapsed for his Earth twin and not the MORE time which we know is the correct result. There is a "discrepancy" of some sort. It is the discrepancy in the elapsed times for the two twins which is explained by the acceleration that only one of them experienced around Andromeda. When the travelling twin was abruptly shifted into a new rest frame, they "jumped tracks" or "skipped over some events for the earth twin". Some moments of time that the twin on Earth would have experienced were skipped over. Some events (which is a formal mathematical term, the nearest ordinary English language idea is to say those "moments of time at that place on earth") were in the travelling twins future (in the old rest frame) but they abruptly changed to being events that were in their past (in the new rest frame), they were never in their present or "now" , they were skipped over entirely. Where you don't assume an instantaneous acceleration but just a very rapid one, then those events aren't completely skipped they are just very tightly compressed, they all occur over a very small time interval for the travelling twin.
I know that the idea of skipping over or missing out some events is difficult to get your head around. LATE EDITING: I can show you the maths but I reckon this post is long enough already.
So I would say that Don Lincoln is mis-representing what many physicists think. Those who have spent some time studying the problem know that "the discrepancy" in elapsed time happens because of the acceleration at Andromeda but they are well aware that it's not as if the time dilation effect was only happening during the acceleration. It is impossible to say exactly "where" it was happening - some time dilation effect was happening everywhere along the journey but it wasn't a discrepancy in the right way (it would make the earth twin experience more time than the traveller), the major discrepancy (which does make the change in the right way) occurs at Andromeda where the traveller jumps rest frames with the result that some events the earth twin experiences are abruptly shifted from the travellers future into their past (skipped over). That "discrepancy" is obviously due to the abrupt shift in rest frames, which is a consequence of an abrupt acceleration (no matter how hard Don Lincoln protests about it). So, what I'm trying to say as politely as possible is that Don Lincoln has over-emphasised or over-sold something. Many of the statements you have highlighted are just wrong IF you insist on taking them on their own, out of the general context, or as being more than just an impression or summary using English that is accessible to the general public.
Best Wishes.
Post by: alancalverd on 13/01/2023 09:02:31
Don't assume there was no relative velocity in any other sense, there was one, there always is a velocity of one thing relative to another thing, it just is numerically 0 sometimes.
And they call me pedantic! ;)
I didn't watch the video, but life is too short to attend lectures by physicists who ignore Newton's basic principles.
Post by: Halc on 15/01/2023 16:19:16
I am actually going to go so far as to say exactly that. I caution against taking a simple comment out of context, and I'm not much on clicking videos and actually watching them (21 minutes to wade through), and it's Sabine, so I presumed the content is accurate. Well it isn't, which is a shame.It's not a function of acceleration, so I cannot say from just that.Then would you say that Sabine in the video is wrong?
At 0:40 she complains about trying to learn relativity from pop-science sources and failing or finding them incorrect. Many are. Here she is creating her own pop-science tutorial and she does the same thing: get it wrong.
At 1:45 she gets into the length of the path between two sets of coordinates, correctly pointing out that different paths are different lengths despite the beginning and end of the paths being the same, as it is in the twins scenario.
At 6:50 she shows how the calculation of the temporal length of an arbitrary path can be done by breaking the path into pieces and integrating over the length of the path. This is what Eternal Student has done in post 16:
The computation above is completely scalar. Note the complete lack of acceleration reference in the formula. I see time and speed (v) and that's it. It isn't a function of acceleration, as I said above. The formula above is from special relativity, so it only applies to the special case where gravity is not involved. Hossenfelder's video is entitled "Special Relativity: This Is Why You Misunderstand It", which means the content should stay away from gravity, or the video is mistitled.Do you know any math formulas to see how acceleration and time dilation are related?
the elapsed time for the travelling twin (who goes to Andromeda) is given by:
Δτ =[Eqn 2]
And what's with Andromeda? Sure, with enough acceleration, Bob can get there and back before he dies, but Alice (and the whole human race for that matter) isn't going to be there upon his return. Sabine should pick a closer target.
Back to the video:
At 11:00 we get into the twins thing and she correctly says that at least one of the twins needs to accelerate to turn around. That's a biased way of putting it, but true. More correctly, at least one of them needs to accelerate in order for their paths to diverge but meet up a second time. Without acceleration, any relative velocity will just have them meet once at best and forever diverge after that. But it isn't the acceleration that causes the dilation, it is the relative temporal lengths of the paths they take, as computed by the above formula.
11:25 She says acceleration is absolute. She means proper acceleration (the kind you feel with an accelerometer) is absolute. Coordinate acceleration is relative to some coordinate system and is thus not absolute. So sitting at your computer reading this, your coordinate acceleration (relative to your house maybe) is stationary, but your proper acceleration is 1g upward because that's how hard the chair under you is accelerating you.
12:52 She correctly points out that the twins scenario has nothing to do with gravity.
13:39 She correctly points out that the twins starting and ending with the same velocity is not necessary (except to explain that they're twins and presumably had reasonably identical velocity at birth. They merely have to meet twice.
15:30 We start getting into gravity, which is out of scope for a video entitled "Special relativity". She starts with pointing out that under Einstein, gravity is not a force. It is in fact spacetime which has a geometery other than flat Minkowskian spacetime. So anything not accelerating (has no force acting on it) follows a geodesic along the local spacetime.
16:55 She first says acceleration causes time dilation. This is blatantly wrong. Contradictions follow.
17:50 Things really start falling apart. The time runs slower at sea level than on a mountain due to greater acceleration at sea level. This is completely wrong. If true, clocks would run fastest at the center of Earth where acceleration would be zero, but they in fact run slowest there than anywhere else on Earth. The acceleration on the surface of Mercury is under 40% of that on Earth, but time on Mercury runs slower, directly contradicting what Sabine is saying.
19:25 She asks if her video was any better than those incomprehensible books from way back? Well it would be if she hadn't mucked it up.
Back to Special relativity, since I want to disassemble her treatment of that as well and not just her botching the gravity bit. A couple examples contradicting her assertions:
Example 1) Alice, Bob and Chuck are triplets and age 20. Alice stays home. Bob and Check set out on a trip and accelerate identically (10g say) for a month and then coast, riding side by side for a while. After a year on his own clock, Bob accelerates towards Earth at 10g for 2 months, going back towards home at the same speed he went out. He coasts for another year and takes a month to stop. He's aged 2 years coasting and 4 months acceleration and is age 22y4m now and finds Alice at age 23y2m, or 10 months older. They wait together for Chuck to come back.
Chuck coasts twice as long and turns back. So he ages 4 years coasting and the 4 months accelerating and comes home at age 24y4m finding Alice to be 25y5.7m and Bob to be 24y7.7m.
This contradicts what Hossenfelder says since both Bob and Chuck have experienced identical accelerations, just at different times. They should be aged identically per Hossenfelder's words, but they're not. This is one trouble with doing physics in the language of laymen instead of the language of physcs. Time dilation is not a function of acceleration and there's no mathematical formula expressing it in terms of acceleration.
Example 2)
I have a pair of wheels or gears. One wheel is 1000 times the radius of the other, and they meet at one point and move at the same velocity there. I put a clock on each wheel at the point at which they meet. The wheels get turned with the small one going around at 1000 times the RPM and hence 1000 times the centripetal acceleration. Both clocks are moving at the same speed relative to the inertial frame of the setup. The two clocks will stay in sync indefinitely despite the one acceleration being a thousand times the other. This also contradicts what Hossenfelder says in the video, but is entirely consistent with the formula that ES provided.
Post by: alancalverd on 15/01/2023 23:25:11
The two clocks will stay in sync indefinitely despite the one acceleration being a thousand times the other.Not if they were in sync before you started the second one moving. The twin "paradox" is about two clocks initially at rest and synced with respect to one another but subsequently acquiring a relative velocity, therefore one must have accelerated.
Post by: Halc on 15/01/2023 23:48:36
Incorrect. If you read my post, they're both moving relative to Earth, and always at the exact same speed (~460 m/sec). The difference is in magnitude of acceleration, 1g (away from the axis) vs 1000g (towards the axis).The two clocks will stay in sync indefinitely despite the one acceleration being a thousand times the other.Not if they were in sync before you started the second one moving.
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The twin "paradox" is about two clocks initially at rest and synced with respect to one another but subsequently acquiring a relative velocity, therefore one must have accelerated.In the example above, both accelerate, but one far more than the other. The point (unlike the twin scenario) is to illustrate that differential aging is not a function of magnitude of acceleration, as the video mistakenly suggests. Neither clock will run faster than the other.
Since you're on the horn:
If they were "always" moving relative to one another, you had no means of synchronising them.This is incorrect. Clocks in each other's presence can be objectively synchronised or compared to each other. They can either both be zeroed (such as at the departure event) or the either observer can note the time on the other clock as it passes by (such as at the return event). Physical events such as this are objective and not frame dependent. If Bob reads a certain value at some event, that value measured is the same regardless of frame choice.
Post by: alancalverd on 16/01/2023 08:57:52
Incorrect. If you read my post, they're both moving relative to Earth, and always at the exact same speed (~460 m/sec). The difference is in magnitude of acceleration, 1g (away from the axis) vs 1000g (towards the axis).But the "polar" clock P started at rest relative to the earth's surface and was therefore travelling 460m/s slower than the "equatorial" clock E. So if you synchronised them (to make twins) and then accelerated P to 460 m/s you will have altered its tick rate as seen from E. Alternatively you could wait until their relative speed is zero and then synchronise them, in which case they will indeed remain in step.
Post by: alancalverd on 16/01/2023 09:00:08
either observer can note the time on the other clock as it passes byThat isn't the point. Time dilation concerns the tick rate of A as observed at B.
Post by: alancalverd on 22/01/2023 13:15:40
It is caused by the change in velocity of the traveling twin (he), when he is separated from the home twin (she).And apropos another thread. when did "change in velocity" cease to mean "acceleration"?
Also important to note that "twins" implies identity, such that when the relative velocity is zero, both clocks (physical or biological) remain in sync. Thus "instantaneous synchronisation" on a fly-by is not permitted.
Post by: Petrochemicals on 23/05/2023 15:19:33
Post by: hamdani yusuf on 18/06/2023 02:49:07
Post by: varsigma on 20/06/2023 23:54:51
A change in direction is an acceleration.It's also a coordinate change, which is of course, relative to the other twin.
The other key thing is the difference between comparing clocks locally (being able to synchronize clocks), and comparing them over a distance because--the speed of light is finite (!).
Post by: Gilyermo on 11/08/2023 09:16:51
Post by: hamdani yusuf on 01/09/2023 12:39:49
Robert L. Shuler Jr.*
NASA Johnson Space Center, Houston, TX, USA.
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AbstractI guess the article here can be considered mainstream.
The twins or clock paradox has been a subject of lively discussion and occasional disagreement among both relativists and the public for over 100 years, and continues to attract physicists who write papers giving new analyses or defending old ones, even though many physicists now consider the matter only of educational interest. This paper investigates the number of papers, which is increasing, and trends in explanations, some of which are now targeted at professional physicists and other of which are targeted at optical or radar visualization rather than problem solving. Observations of students indicate that the latest techniques help but only somewhat. An analysis is made of 21 previous treatments appearing in the education related American Journal of Physics, Einstein?s discussions and several other pedagogical papers. A new memory aid for simultaneity transformation is given that puts it on a par with ?time dilation? and ?length contraction? for quick and easy problem visualization. The point of view of a trailing twin is introduced to show how simultaneity changes account for missing time in the turnaround. Length contraction is treated on equal footing with time dilation, and Swann?s insight into clocks is extended to lengths. Treatments using the conventionality of simultaneity are seen as equivalent to choice of co-moving frames. Responses to difficult questions are suggested which avoid being dismissive, and engage students? critical thinking.
https://www.scirp.org/journal/paperinformation.aspx?paperid=47747
Post by: yor_on on 05/09/2023 08:46:36
http://hyperphysics.phy-astr.gsu.edu/hbase/Relativ/muon.html
you can also take a look at this one. https://physics.stackexchange.com/questions/165179/does-light-itself-experience-time-dilation
Post by: yor_on on 05/09/2023 08:55:49
=
Gravity is an example of an equivalence to mass or if you like, 'acceleration', in relativity, So is gravity time dilated? And photons, or light, is defined as a speed, a 'constant' speed. so when that 'photon' follows its geodesic, gravity 'bending the path' as defined by us?
Another example: Think of that twin traveling, as defined by you and your common 'origin'. His time, and everything being in a same reference, 'slows down' relative your own clock. Aka becoming younger than you once back. So what happens to that rockets 'velocity', as defined by you?
So no, it's not only about accelerations, although they definitely play a big role. But it also depends on your definitions. For example, if one agree on that accelerations, gravity and mass are equivalences, describing the same thing from although from different angles? Blue & red shifts being massless equivalences to different 'speeds' (including accelerations) described in a 'proper mass reference frame'?
that whole thing becomes a question
=
The funny thing, accepting the above, is that you might be able to reach a conclusion much like Newton did about 'time'. An locally 'absolute time' of no variance intrinsically, with other permutations of it described through 'frames of reference', 'masking' that invariance.
Post by: hamdani yusuf on 05/09/2023 11:55:19
It's about being in different frames of reference to me.Let's start with the simplest frame of reference first, which is the midway observer. What will he observe when he meet both travelling twins? At that moment, what's shown by his own clock, and the clocks brought by the travelling twins?
Before these questions are answered, it's useless to switch to other frames of reference and pursue more complex questions.
Post by: yor_on on 05/09/2023 16:06:03
Post by: yor_on on 05/09/2023 16:24:19
=
The only thing that twin experiment brings with it is the idea of time being malleable. But to do it right you will need to create a 'global' frame of reference for it. An unyielding time and space with the eye of a God watching it / ours. Somewhat like Newton. And Einstein himself defined it as no such frame can exist. So it's still 'observer dependent' that twin experiment
That's actually one of the trickiest parts of relativity. That no frame of reference can be a more 'privileged frame' than any other, no matter what I may think of the universe I observe. Which actually, turned around, and in a very backhanded fashion means that all frames of reference 'intrinsically' or 'locally' could be seen as equivalent
Post by: Eternal Student on 06/01/2024 17:53:36
I've only skim read some of the later posts but was here at the beginning, there may be some bits in the middle I have overlooked. So I apologise if much of this has already been said.
The reply here https://www.thenakedscientists.com/forum/index.php?topic=86675.msg719270#msg719270 by @Halc looks good.
There are several places where people have raised the question about whether General relativity is needed in the Twin paradox and not just Special relativity. This is presumably because one twin has to be accelerated while the other doesn't have to be. Some people wanted experimental results to back up the notion that SR is sufficient and GR is not required.
It is indeed difficult to do the experiment where the travelling twin was never accelerated, we can't easily just take all the acceleration away. However, we can add extra acceleration and that doesn't seem to affect the result, it remains consistent with the application of just SR.
The travelling object (maybe the travelling twin) doesn't have to take a straight line path out to some place and abruptly reverse direction. The result still holds if the travelling object moved in a circular path and that can obviously still bring them back to the original starting location. The obvious example of a suitable experiment is putting a clock into an aeroplane, flying it around the world and comparing with a clock that remained on the surface of the earth. Since the travelling object is undergoing circular motion, it is experiencing a centripetal accelertion that is not present if the object had moved in straight paths out to their turn-around point and then back home.
Experiments like this have been done. See https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment
If you do spend a moment looking at the Hafele?Keating experiment (the clock in an aeroplane), you'll notice that they didn't consider the clock on earth as being in an inertial frame (because planet earth rotates). Instead they assumed only that a clock at rest at the centre of the earth would be in frame that could be considered to be inertial. Indeed, the clock on the plane actually runs faster than the clock staying on the surface of the earth when they fly westward. Only the eastward flight resulted in the aeroplane clock running more slowly than the earth-bound clock. If the clock staying on earth had been at rest in an inertial frame, then a clock moving either way relative to the earth bound clock should have ticked more slowly.
Analysing the situation in the same reference frame they used, we see that the eastward and westward travelling plane actually required different centripetal accelerations. They did not (and seemingly did not need to) consider this difference in acceleration when predicting the difference displayed on the clocks. The only use of results from GR involved making an adjustment for the different altitudes of the planes - since there would be some gravitational time dilation.
That's enough for this post and the question being asked here. For a side-line people may wish to spend a moment considering whether a centripetal acceleration is indistinguishable from acceleration due to a gravitational field. That's a separate issue that may only confuse or confound the point being made. It is recognised that gravitational time dilation is dependant on the difference in gravitational potential of two clocks and not on the actual accelerations those two clocks may experience. In essence then, using GR to correct for gravitational time dilation did not accidentally (or intentionally) take account of the different centripetal accelerations of the clocks.
A more modern version of the experiment can allow for a greater variation of accelerations, speeds and total distance travelled. Here's an outline of an experiment you could do, although I do not have the equipment and I can't find any internet reference to something like this.
Since centripetal acceleration a = v2 / r, we can control the acceleration by altering the radius of a circular path while holding the speed constant. A radioactive substance has a half-life and this can act as a clock that travels with our object. So we can put a charged radioactive particle into a cyclotron and control its path by altering the magnetic field in the cyclotron. The average decay time of the particle as measured in the lab frame should be longer than if the particle had been kept at rest in the lab frame. We can try various combinations of speed, total distance travelled and centripetal acceleration experienced. Assuming SR is sufficient, then only the speed and total distance travelled matters (acceleration doesn't).
Best Wishes.
Post by: Jaaanosik on 11/01/2024 20:00:02
at 10:36
C's perspective and event I
(x,t)I,C=(0,0)
This is wrong.
The event I does not start at xC=0.
This is not the origin of the C perspective if C position is chosen as the origin of C reference frame.
Regardless, xI,C=xIII,C has to be true.
If it is not true then the analysis is wrong.
Clearly, the video shows different x values so it is wrong.
That guy made a mistake!
Post by: Eternal Student on 11/01/2024 21:38:23
if C position is chosen as the origin of C reference frame.Don (the presenter) didn't make it clear where the origin for the reference frame of C would be. If it had been centred on C then you'd be absolutely right. However, in this video he didn't have that frame centred on C. All frames (A, B, or C) were set up to have the origin (0,0) identify event I (in words, the origin of all the reference frames was planet earth at the moment when A started to travel away from it). So only observers A and B have the origin of their reference frame centred around themselves.
This wasn't made clear by the presenter and isn't a very conventional choice but it isn't necessarily wrong. Since it can cause confusion it's a fault in the video of one sort. The "confusion" isn't just something you had, it took me quite a bit of time and re-playing the video to see what had happened.
Best Wishes.
Post by: Jaaanosik on 12/01/2024 03:45:58
Hi.Then it comes back to clock synchronization and simultaneity.if C position is chosen as the origin of C reference frame.Don (the presenter) didn't make it clear where the origin for the reference frame of C would be. If it had been centred on C then you'd be absolutely right. However, in this video he didn't have that frame centred on C. All frames (A, B, or C) were set up to have the origin (0,0) identify event I (in words, the origin of all the reference frames was planet earth at the moment when A started to travel away from it). So only observers A and B have the origin of their reference frame centred around themselves.
This wasn't made clear by the presenter and isn't a very conventional choice but it isn't necessarily wrong. Since it can cause confusion it's a fault in the video of one sort. The "confusion" isn't just something you had, it took me quite a bit of time and re-playing the video to see what had happened.
Best Wishes.
The inertial frames do not agree on the simultaneity.
The time on the C spaceship is wrong.
Edit:
A question.
How do we call 'jumping' from one inertial frame to another?
Changing an inertial reference frame?
...
Answer: acceleration, momentarily comoving inertial reference frames explain it.
Post by: Halc on 20/01/2024 17:14:53
Clearly, the video shows different x values so it is wrong.You're right. From C's perspective, no matter where the origin of that frame is placed, C should be at the same X coordinate at both the II and III events since he's present at both of these, but he's not.
That guy made a mistake!
There are errors in both videos in the OP.
A question.I think the latter phrase says it well.
How do we call 'jumping' from one inertial frame to another?
Changing an inertial reference frame?
It correctly doesn't imply that one is exiting some frame, or that one is necessarily accelerating. A frame change simply needs a Lorentz transform.
Here is a demonstration of what went wrong in the OP video.The discussion of the train/platform setup seems to have little to do with the video. I didn't watch it all, so maybe it comes up elsewhere.
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It is impossible to align the following 4 events due to disagreement on the simultaneity between the inertial frames.It would help if you said what speed one was going relative to the other. The pictures don't say, but I see proper lengths of 3.46 platform and twice that for the train car, so I'm guessing train speed of .+.866c to the right.
Imaging a 'space train car' and a 'space platform'.
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The events F', B', P, B cannot be aligned though.'Aligned' isn't really a physics term. You mean they are not the same events? At time zero, apparently F' and P are the same event, and B' and B are not.
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Then the invariance of the space-time intervals of a light round-trip defines stationary preferred frame with the slowest time.This comment would be false if it made any sense, but it's not even wrong. The spacetime interval of light is always zero. That fact does not in any way define a preferred reference frame.
Post by: Eternal Student on 20/01/2024 20:27:16
I would concur, this bit looks an error...
From C's perspective, ...., C should be at the same X coordinate at both the II and III events...
Assuming Don (the presenter) establishes the frame C so that event I is the origin, then he should have listed the x co-ordinate for event II as 2γL and not γL. That does seem to be at least a typing error.
Fortunately, he didn't need the x co-ordinates for the subsequent calculations.
Crumbs, Halc, how many times have you watched this video to spot that error?
There are errors in both videos in the OP.Both videos were basically Pop Sci videos or at best what is sometimes called "edu-tainment". I think both presenters up-sold their videos and made fairly grand claims about how their video fixed some mis-understanding. Neither of them stayed around or did some after-market research to investigate any new mis-understanding that may have arisen in people after they watched the videos - and there are some: See the contents of this thread and the various people who have been involved.
I have more of an axe to grind for Don's video. You can legitimately argue that he hasn't got any one person to make the round trip and was therefore never really answering the main issue. There was only an exchange of information at event II between two people when they flew past each other.
Some of the people in this thread (including some that have now been split into a second related thread) have interpreted the video as if it resolves the twin paradox without assuming any acceleration of a twin - but it doesn't.
It's apparent the calculation you can perform to determine the total elapsed times would be independant of the acceleration at event II. That is not in dispute, there are numerous videos and textbooks that will show that result. Don's method is an accpetable one you could use to calculate the total elapsed times for various people. However, Don's method does not magically prevent a twin from needing an acceleration to change their motion at event II if, in fact, one person really was making the round trip.
A major mis-conception that has arisen in some people after Don's video is that the acceleration (the change in motion) that occurred at the turn-around point isn't important at all. This is a serious problem when people start asking questions like exactly where, when or as a result of which things, some discrepancy in allocation of times start to appear between the twins. If you start trying to consider how the different twins would allocate co-ordinates to events, there is an abrupt shift in the allocation of co-ordinates for one of the twins at the turn around point. It's not that the time dilation was only happening during the acceleration (that would also be a mis-conception) - but just that a change in the alllocation of co-ordinates for events at the turn-around is a contributing issue which cannot be ignored.
Best Wishes.
Post by: Halc on 21/01/2024 18:43:37
Assuming Don (the presenter) establishes the frame C so that event I is the origin, then he should have listed the x co-ordinate for event II as 2γL and not γL. That does seem to be at least a typing error.Yes, x = 2γL for both events II and III if the origin of the C frame is event I.
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Crumbs, Halc, how many times have you watched this video to spot that error?That was actually the first time for me, and then only from minutes 8 to 11. I don't watch most videos just because somebody posts them. I would have thought that a video endorsed by Fermilab would be at least peer reviewed, but apparently neither video in the OP was.
As for how I spotted that, Jano gave the exact timestamp (10:36) with the errors. I had to backtrack a bit from there to get the context, where I spotted at least one more.
8:23 shows a picture identifying the entire system as a space-like state being identified as events I through III which is just wrong. They treated as events (with an x coordinate) later on, but that picture is beyond wrong. The events should have an arrow pointing to the actual events, which is the left of the top line, but Don says that event I is "when they all start" instead of the event where A and B part company. C is not present at event I, but the picture tells a different story.
The title of the video identified it as crank from the start, since it claims to be "the real explanation" like the other valid ones are wrong. That's a big reason why I didn't bother to watch it. Somebody who knows their physics wouldn't insist on just one way being the only correct way. Of course that might be just self-promotional hype, but then at least get it right.
His story also doesn't involve twins, which arguably disqualifies it as an explanation of the twins paradox. He's trying to show how acceleration isn't necessarily involved, but as Alan points out, if twins never accelerate, then they can never be at different locations. You noticed this as well.
Both videos were basically Pop Sci videos or at best what is sometimes called "edu-tainment"Yes, but a video put out by something like Fermilab or somebody with a reputation to protect (Hossenfelder, college physics professors) shouldn't be putting out stuff that is blatantly wrong, and so many of them do.
I kind of expect it from all the uncredentialed yahoos making you-tubes from their mom's basement, but sometimes those guys actually hit the mark and put out something quality.
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It's apparent the calculation you can perform to determine the total elapsed times would be independant of the acceleration at event II.It shows that you can do the computation without knowing the acceleration at any time, anywhere. You just have to know the speed of everybody, or if you're going to complicate your process with coordinate changes, you need to know the velocity of everybody at all times. If the velocity is known, then the accelerations can be deduced, but since the result can be computed from just speeds, it isn't a function of accelerations.
My simple method (which does not worry about acceleration) was posted in the first reply.
My most general explanation (which works in all cases, not just the twins scenario) involved summing up intervals, and also wasn't a function of accelerations. It was posted in one of the other threads that I can no longer find.
Post by: paul cotter on 21/01/2024 19:02:02
Post by: alancalverd on 21/01/2024 23:05:36
Identical clocks are seen as ticking at different rates if they are moving relative to one another. So their initial relative velocity must have been zero in order to establish synchrony, demonstrate identity, be born as twins, or whatever initial condition you choose to make the subsequent observation paradoxical. So at least one of them must have accelerated to produce a relative velocity.
Post by: Eternal Student on 22/01/2024 02:38:02
We had blackboards, they were awesome. A wall of blackboards and you could slide one up and another down. It meant the lecturer could write half-a-dozen formulae and draw a diagram and then slide them up while continuing on another board. Awesome.
So when the lecturer continued for another half-a-dozen lines and said "we can see from the definition of Z that....", you actually could gaze upwards and see the definition of Z. You don't realise how good something is until it's gone.
That's all I wanted to say, thank you for your time and have a good day.
Best Wishes.
(There is some relevance: By comparison, You Tube videos don't have anything slide up the wall. Formulae and diagrams are gone and you can never fiddle with the time slider adequately to get them back. If they say "You can see from the definition of Z", I'm just going to go with it. I also don't recall people coming into the lecture hall and advertising stuff but I suppose that's a separate issue and a moan for another day).
Post by: hamdani yusuf on 23/01/2024 13:41:59
Emphasising yet again the hazards of pop science education by youtube.It's not specifically YouTube's fault. Any other media can be used to produce misleading or incomplete information. That's including textbooks, websites, podcast, tiktok, and live lectures.
Post by: alancalverd on 23/01/2024 16:13:19
Live lectures are subject to all sorts of heckling and barracking (unless you are talking absolute bollocks from a pulpit, in which case the audience will swallow anything with utter reverence).
Peer review isn't perfect, but it's better than the nothing you get from online media.
Post by: paul cotter on 02/10/2024 16:00:48
Post by: Halc on 02/10/2024 16:50:54
Oh dear, here we go, again. Word salad.Indeed. The prior posts have been removed for several reasons.
1) Nonsense in the main sections of the forum
2) Contained personal information
3) Had nothing to do with the topic title, hence is a hijack of a topic
4) Contained a bibliography which was nowhere referenced
5) Contained no content from any of said bibliography
6) Word salad as Paul points out
7) Duplicate posts
At least the first three of those violate forum rules.
Post by: paul cotter on 02/10/2024 20:40:03
Post by: varsigma on 13/10/2024 04:29:56
The twin paradox is a problem--a physics problem. But apply a bit of logic and it's obvious that the acceleration/continuous coordinate change is over a distance which is much shorter than the distances covered at constant velocity.
Hence the distance for acceleration(s) is negligible, hence ignoring that part of the journey has a negligible effect. Logic.
Post by: alancalverd on 13/10/2024 09:56:03
Hence the distance for acceleration(s) is negligible, hence ignoring that part of the journey has a negligible effect. Logic.
Brilliant!
The time spent accelerating a bullet in a gun barrel is negligible compared with the time it spends in flight at constant velocity, so it doesn't matter whether you fire the gun or just send the bullet by post, the lethal effect is for all practical purposes identical.
Post by: hamdani yusuf on 13/10/2024 10:13:44
The twin paradox is a problem--a physics problem. But apply a bit of logic and it's obvious that the acceleration/continuous coordinate change is over a distance which is much shorter than the distances covered at constant velocity.Some people said that acceleration is relative, thus it's undefined without a frame of reference. Some others said that it's absolute, thus acceleration of an object can be determined without a frame of reference. This difference showed up in many YouTube videos trying to solve the twin paradox. What do you think is the correct one?
Post by: paul cotter on 13/10/2024 11:16:51
Post by: alancalverd on 13/10/2024 14:59:25
Some people said that acceleration is relative
An accelerometer consists of a mass attached to one end of some kind of spring, the other end of which is attached to the object being accelerated. An observer within any accelerating object will see a deflection on his accelerometer. Acceleration is therefore absolute.
Post by: varsigma on 13/10/2024 18:12:06
Brilliant!Aw shucks. Not really.
Quote
The time spent accelerating a bullet in a gun barrel is negligible compared with the time it spends in flight at constant velocity, so it doesn't matter whether you fire the gun or just send the bullet by post, the lethal effect is for all practical purposes identical.To be physically pedantic, that ignores the atmosphere and the earth's gravity; and that it's rotating. But as they say, your solution is accurate over small enough distances. "lethal effect" isn't really physics, though. There will be a transfer of momentum, I think.
And so we see that firing the gun will result in a larger transfer of momentum to the bullet, over small enough distances, than posting it in a letter. You could ask the postie to throw it, perhaps.
Post by: alancalverd on 13/10/2024 22:15:25
"lethal effect" isn't really physics, though.It is mostly physics, with a bit of anatomy, followed by physiology.
Post by: alancalverd on 13/10/2024 22:20:35
The twin paradox is a problem--a physics problem.It isn't a paradox at all. It is a measurable effect, fully explained by relativity, which is of little significance in most people's lives. Unless they use GPS navigation, of course.
As for "problem", it's simply a question of solving a slightly more complicated equation involving v/c if v is not zero.
Post by: alancalverd on 13/10/2024 22:42:52
A and B set their clocks to zero as they whizz past each other - i.e. as their position vectors diverge. Some time later, they pass again and compare their clocks.
For simplicity, let A remain at rest or travelling in a straight line at constant velocity. He knows this because his accelerometer reads zero throughout the experiment.
How, then, can B fly past him again? Not if he is travelling at a constant velocity because their position vectors would continue to diverge. So he must....accelerate.
Post by: varsigma on 14/10/2024 00:49:26
It isn't a paradox at all. It is a measurable effect,Maybe it isn't a paradox, but that's how it was initially introduced in a thought experiment.
It is measurable, and of course, observation isn't a paradox; the paradox arises when dummies like us try to explain it.
Post by: Halc on 14/10/2024 02:57:06
Einstein's special theory is really like the law of thermodynamics: if your theory denies the reality of SR, there is no hope for it.If the theory is valid, then there is hope for it. There are valid theories which deny relativity and use completely different premises. But indeed, none of the speculations posted in any forum is one of those. It's just not how valid theories get submitted.
Quote
The twin paradox is a problem--a physics problem.It isn't a problem since relativity (and the valid alternatives) all explain it without paradox. It only seems paradoxical when one tries to drag in premises of non-relativistic theories like Newtonian assumptions.
Quote
Hence the distance for acceleration(s) is negligible, hence ignoring that part of the journey has a negligible effect. Logic.The distance of acceleration is whatever the scenario specifies. Most realistic descriptions of space travel involve acceleration during the majority of the journey, so that portion of the journey cannot be negligible.
Some people said that acceleration is relative, thus it's undefined without a frame of reference. Some others said that it's absolute, thus acceleration of an object can be determined without a frame of reference.Proper acceleration (that which an accelerometer measures) is absolute. Coordinate acceleration is frame dependent. 'acceleration' without adjective is ambiguous.
Proper acceleration can continue indefinitely, so a proper acceleration of 1G for 2 proper years will get you going a proper speed of about 2c, meaning you're traveling 2 light years (as measured in the inertial frame where you were originally at rest) for every year you age. Constant coordinate acceleration cannot continue indefinitely (unbounded coordinate time) since it would result in a speed greater than light speed.
A and B set their clocks to zero as they whizz past each otherIt is good to see you supporting the possibility of doing this. In prior times, you had asserted that the two must become relatively stationary in each other's presence in order to set their clocks to the same value. Indeed, it can be done in passing, as is done in several scenarios found on the web.
For simplicity, let A remain at rest or travelling in a straight line at constant velocity. He knows this because his accelerometer reads zero throughout the experiment.True in flat (Minkowskian) spacetime. In curved spacetime, as in non-Euclidean spacetime, two straight lines (no proper acceleration) can meet in more than one place, and with differing lengths between the meetings.
How, then, can B fly past him again? Not if he is travelling at a constant velocity because their position vectors would continue to diverge. So he must....accelerate.
This is seen in simple eccentric orbits. The perigee of one orbit (of just a clock say) might be the same event as the apogee of another. The latter might have an orbital period of twice the former, so the two objects meet regularly, and show different elapsed times between these meetings, all without registering any proper acceleration at all.
Post by: varsigma on 14/10/2024 18:13:54
The distance of acceleration is whatever the scenario specifies. Most realistic descriptions of space travel involve acceleration during the majority of the journey, so that portion of the journey cannot be negligible.Ok. But the twin (non)paradox doesn't have that description. Instead, it describes a journey then a return at constant velocity, usually the same velocity. It restricts the problem (it is a problem, even if it has a solution) to constant velocities and accelerations can be ignored. It isn't mysterious or a way to somehow cheat. It makes perfect sense to simply apply a single change of coordinates--the turnaround, rather than the continuous change that accelerations require.
I see this problem as a good way to investigate the significance of the Lorentz factor.
Post by: alancalverd on 14/10/2024 19:12:53
Instead, it describes a journey then a return at constant velocity, usually the same velocity. It restricts the problem (it is a problem, even if it has a solution) to constant velocities and accelerations can be ignored.You can't ignore acceleration - regardless of the speed profile, the journey won't begin without an acceleration.
Post by: alancalverd on 14/10/2024 19:19:37
It is good to see you supporting the possibility of doing this. In prior times, you had asserted that the two must become relatively stationary in each other's presence in order to set their clocks to the same value.There is no problem setting clocks to the same instantaneous value, but that isn't synchronisation - they could be running at widely different speeds before and after the "reset". Huge difference between reset (instantaneous push on the zero button) and synchronise (check they still read the same value a minute later).
I actually encountered this as a problem when dealing with a famous precision watchmaker back in the days of mechanical watches. He insisted that his master clock was correct because it reset to zero on the midnight GMT transmission. Problem was that by 4 pm it was a minute slow, and so his very expensive chronographs couldn't be used for navigation.!
Post by: paul cotter on 14/10/2024 20:08:03
Post by: alancalverd on 14/10/2024 22:34:16
Post by: varsigma on 15/10/2024 04:26:32
You can't ignore acceleration - regardless of the speed profile, the journey won't begin without an acceleration.Sure. Ok.
What you can do instead is say that, as long as accelerations are limited to distances much shorter than the total distance in the journey, there and back, they can be left out of the equations of motion. The result will be approximate, but you can still estimate this.
Why do artillery shells have a muzzle velocity? Why isn't the acceleration of an artillery shell in the barrel of a field gun part of the firing solution, when the approximate shell speed after it leaves the barrel is known?
Post by: alancalverd on 15/10/2024 08:48:18
.
Post by: hamdani yusuf on 15/10/2024 13:48:58
ISS is orbiting the earth, thus it's accelerating. But your accelerometer won't show the correct value of acceleration there. It will show something close to zero g.Some people said that acceleration is relative
An accelerometer consists of a mass attached to one end of some kind of spring, the other end of which is attached to the object being accelerated. An observer within any accelerating object will see a deflection on his accelerometer. Acceleration is therefore absolute.
Post by: hamdani yusuf on 15/10/2024 14:04:43
Proper acceleration can continue indefinitely, so a proper acceleration of 1G for 2 proper years will get you going a proper speed of about 2c, meaning you're traveling 2 light years (as measured in the inertial frame where you were originally at rest) for every year you age.Does it mean I will see the earth recedes with speed 2c? What happens to the cosmic speed limit?
Post by: hamdani yusuf on 15/10/2024 14:16:20
I actually encountered this as a problem when dealing with a famous precision watchmaker back in the days of mechanical watches. He insisted that his master clock was correct because it reset to zero on the midnight GMT transmission. Problem was that by 4 pm it was a minute slow, and so his very expensive chronographs couldn't be used for navigation.!https://control.com/textbook/instrument-calibration/zero-and-span-adjustments-analog-instruments/
Some instruments that we use have 1 point calibration. Some have 2 points of calibration. Some have a few more points of calibration.
Post by: alancalverd on 15/10/2024 15:15:29
Accelerating a clock alters its tick rate, so when the traveller returns, the discrepancy between the elapsed times of the erstwhile twins depends on how long he has been away and what accelerations he has experienced in the trip.
Post by: alancalverd on 15/10/2024 15:17:57
ISS is orbiting the earth, thus it's accelerating. But your accelerometer won't show the correct value of acceleration there. It will show something close to zero g.Only if it read +1g before launch. The difference is the centripetal acceleration.
Post by: paul cotter on 15/10/2024 17:24:28
Post by: Janus on 15/10/2024 17:58:34
You have put your finger on the misunderstanding that pervades much of this discussion!No, it does not effect it's tick rate, it alters how it would consider other clock's tick rates compared to it own. Clocks in the direction of the acceleration would be ticking faster compared to his own, and those in the opposite direction slower ( this is in addition to any Doppler shift due to relative velocity). The difference in tick rate increases with distance in these directions.
Accelerating a clock alters its tick rate, so when the traveller returns, the discrepancy between the elapsed times of the erstwhile twins depends on how long he has been away and what accelerations he has experienced in the trip.
Post by: varsigma on 15/10/2024 22:09:10
The relativistic correction to the age of an artillery shell is irrelevant since it is not normally returned to its twin.Relativity is irrelevant if the topic is just acceleration. That is, how relevant is it, and to what.
Post by: Halc on 15/10/2024 22:26:22
ISS is orbiting the earth, thus it's accelerating. But your accelerometer won't show the correct value of acceleration there. It will show something close to zero g.Read my post. Any accelerometer shows proper acceleration and an orbiting satellite will undergo no proper acceleration. The acceleration you speak of is coordinate acceleration, and even that might be zero. I mean, in the coordinate frame of my house, my orbiting sat-TV satellite is stationary (no coordinate acceleration) which is why I can point my dish at it and not have to move the dish.
Does it mean I will see the earth recedes with speed 2c? What happens to the cosmic speed limit?
With respect to #70: yes the earth will appear to recede at 2c because your rapidity will be 2c. From the earth you will be seen to be travelling at <c.There's no direct appearance to a recession speed. It is very frame dependent.
Relative to the inertial frame in which the ship is momentarily stationary, the Earth will be receding at around 0.964c. Nothing can exceed c relative to an inertial frame. But if there was a tape measure glued to Earth that goes all the way along your journey, with a tick mark every light second, you'd see two of those tick marks go by your ship every second. That's what it means to be moving at a proper velocity of 2c relative to Earth.
Relative to the ship's accelerating frame, Earth will be seen receding almost not at all, and will never reach a light year away even after indefinite ship time, all very much like dropping a clock into a black hole.
Celerity (and not rapidity) is another word for proper velocity, at least they're the same in Minkowskian spaceitme. One must be careful to use the correct term in other contexts. And yes, the >c recession of galaxies relative to the expanding cosmic frame (not an inertial frame) is like a celerity of sorts. The proper distance between us and the distant thing (measured along a line of constant cosmologtical time) grows at a rate of >c. Inertial frames are not even relevant at such distances, but if you remove all energy, the distant galaxy would not be moving faster than c relative to any inertial frame since the distance would not be along a line of constant cosmological time. It would be far closer, and its velocity in that frame would be sub-luminal. It would still be moving at well over c in the non-inertial expanding frame, but that's a coordinate difference, not a physical one.
Accelerating a clock alters its tick rateNot true. I gave examples early in this topic that demonstrates otherwise, bottom of post 20.
Post by: paul cotter on 16/10/2024 08:22:16
Post by: hamdani yusuf on 16/10/2024 12:24:46
I gave examples early in this topic that demonstrates otherwise, bottom of post 20.
Example 2)Is the bold statement backed up by experimental evidence?
I have a pair of wheels or gears. One wheel is 1000 times the radius of the other, and they meet at one point and move at the same velocity there. I put a clock on each wheel at the point at which they meet. The wheels get turned with the small one going around at 1000 times the RPM and hence 1000 times the centripetal acceleration. Both clocks are moving at the same speed relative to the inertial frame of the setup. The two clocks will stay in sync indefinitely despite the one acceleration being a thousand times the other. This also contradicts what Hossenfelder says in the video, but is entirely consistent with the formula that ES provided.
Post by: hamdani yusuf on 17/10/2024 04:44:19
Relative to the inertial frame in which the ship is momentarily stationary, the Earth will be receding at around 0.964c. Nothing can exceed c relative to an inertial frame. But if there was a tape measure glued to Earth that goes all the way along your journey, with a tick mark every light second, you'd see two of those tick marks go by your ship every second. That's what it means to be moving at a proper velocity of 2c relative to Earth.If an identical measuring tape is glued to the ship, will the earth observer see two of those tick marks go by every second?
Post by: paul cotter on 17/10/2024 09:12:06
Post by: Halc on 17/10/2024 14:10:29
Is the bold statement backed up by experimental evidence?I don't think they've ever made a set of gears with a 1000-1 size ratio, let alone turn any reasonably rigid object at significant relativistic speeds. The bolded statement is backed by the very simple mathematics of γ=1/√(1-v2) which is identical on both sides since the sole variable v is identical on both sides.
If an identical measuring tape is glued to the ship, will the earth observer see two of those tick marks go by every second?The situation is not symmetrical since the ship is accelerating and the Earth is not. Earth can have a tape measure of indefinite length attached to it, one that the ship can read forever. The ship (at proper acceleration of 1G) can trail not even a light year of tape behind it. The tape cannot extend beyond the ship's event horizon without breaking.
How many ticks per second the Earth observer sees depends on when he looks. At some point, the ticks go by infinitely fast just before the tape ends, and then they see no more.
There was that ship event where the ship guy sees 2 ticks/sec go by. In Earth frame, the event there that is simultaneous with that ship event, the tape will already have been exhausted.
I made the mistake of trying to apply SR to a scenario where some of the frames of reference were not inertial and were thus in need of GR for solution.GR is only needed for situations involving gravity (which I suppose my black hole mention does). But the accelerating frame of the ship is a straight SR exercise. You might want to look up Rindler frame or Rindler coordinates for info on how SR treats an accelerating frame like this.
SR handles accelerating frames just fine, as it does rotating frames. It handles normal expanding frames as well, but not accelerating expansion frames which involves dark energy and puts things into GR territory.
Post by: paul cotter on 17/10/2024 16:22:50
Post by: Bored chemist on 17/10/2024 16:38:07
"What is the exact cause of the time dilation of the twin?"
The same thing that causes time.
And I'm not sure we actually know what that is.
Post by: Halc on 17/10/2024 17:00:23
I had been told years ago by a theoretical physicist(who now holds a distinguished position at an American university but who will remain nameless) that GR was needed for accelerated frames of reference.That's actually pretty sad for somebody claiming those credentials. I googled "is GR needed for accelerated reference frames" and got correct replies from several sources with poorer credentials, but one from a university site.
AI overview: "No, general relativity (GR) is not required for accelerated reference frames:
Special relativity (SR) is sufficient
SR can handle accelerated frames and objects, and is sufficient to explain the Twin Paradox. SR is valid in the presence of accelerations because it describes flat Minkowski spacetime"
That is a very poor reference (as is any LLM), but it's correct. The twin paradox bit is barely relevant since discussion of it is rarely described via changing accelerated reference frames. That quote seems to answer more "Is GR needed to describe acceleration" rather than to describe accelerated frames, but accelerating objects are perfectly well described in inertial, accelerating, expanding, rotating, and other kinds of frames.
The next hit is better, from University of California, Riverside
"It's a common misconception that special relativity cannot handle accelerating objects or accelerating reference frames. Sometimes it's claimed that general relativity is required for these situations, the reason being given that special relativity only applies to inertial frames. This is not true."
I got no immediate hits that said that GR was required, but I'm sure they're out there. Bottom line is, GR is needed for curved spacetime, which only comes into play with gravity and dark energy, and none of the discussion here has been about those things. I do not know my GR well enough to say do the tensor calculus required to generate numeric answers. Tensor mathematics is not required for anything in SR, including Rindler frames.
"What is the exact cause of the time dilation of the twin?"I don't think time is something that is caused. It is exactly like asking what causes distance, which seems to be an ill-posed question. I do agree that most of the recent discussion has digressed from the immediate topic title, but since it is mostly framed as questions about relativity and not assertions of speculations, I've not moved any of it to the lighter side.
The same thing that causes time.
And I'm not sure we actually know what that is.
Post by: hamdani yusuf on 18/10/2024 11:49:02
Quote
ChatGPT:
Yes, General Relativity (GR) is necessary when dealing with accelerated frames of reference, especially when the acceleration is significant or when gravitational effects are involved. While Special Relativity (SR) handles inertial frames (non-accelerating), GR extends the theory to include non-inertial frames, such as those that are accelerating or influenced by gravity.
In GR, gravity is not seen as a force but rather as the curvature of spacetime, and this curvature affects how objects move, including those in accelerated reference frames. So, for understanding the full effects of acceleration, particularly in the presence of strong gravitational fields, GR is required.
Post by: hamdani yusuf on 18/10/2024 11:50:14
Quote
Yes, General Relativity (GR) is crucial for understanding accelerated frames of reference. Here's why:
* Equivalence Principle: GR postulates that gravity and acceleration are equivalent. This means that an observer in a uniformly accelerating spaceship cannot distinguish between the force of acceleration and the force of gravity. This principle forms the foundation of GR.
* Curvature of Spacetime: In GR, gravity is described as a curvature of spacetime. This curvature is caused by the presence of mass or energy. In an accelerated frame of reference, the spacetime is curved due to the acceleration.
* Time Dilation and Length Contraction: GR predicts that time runs slower in a gravitational field or an accelerated frame of reference. This is known as gravitational time dilation. Additionally, objects appear shorter in the direction of motion in an accelerated frame, a phenomenon called length contraction.
* Global Positioning System (GPS): GR is essential for the accurate functioning of GPS satellites. The satellites are moving at high speeds and are at a different gravitational potential compared to Earth's surface. Without accounting for GR, the GPS system would be significantly inaccurate.
In summary, GR provides a comprehensive framework for understanding the physics of accelerated frames of reference. It is a fundamental theory that has been experimentally verified and is essential for many modern technologies.
Post by: Halc on 27/11/2024 19:09:27
I can highlight the wrong and particularly correct and really wrong answers.
Is GR needed for accelerated frames of reference?
Quote from: ChatGPT
Yes, General Relativity (GR) is necessary when dealing with accelerated frames of reference, especially when the acceleration is significant or when gravitational effects are involved. While Special Relativity (SR) handles inertial frames (non-accelerating), GR extends the theory to include non-inertial frames, such as those that are accelerating or influenced by gravity.
In GR, gravity is not seen as a force but rather as the curvature of spacetime, and this curvature affects how objects move, including those in accelerated reference frames. So, for understanding the full effects of acceleration, particularly in the presence of strong gravitational fields, GR is required.
ChatGPT tries to sneak in gravity since yes, GR is needed to deal with gravity. But acceleration does not produce gravity at it implies. It seems to just repeat this comment a number of times.
At least ChatGPT doesn't attempt to leverage the equivalence principle, which I cannot say for the other examples. Gemini is definitely the worst of the bunch.
The same question for Gemini,
Quote from: Gemini
Yes, General Relativity (GR) is crucial for understanding accelerated frames of reference. Here's why:
* Equivalence Principle: GR postulates that gravity and acceleration are equivalent. This means that an observer in a uniformly accelerating spaceship cannot distinguish between the force of acceleration and the force of gravity. This principle forms the foundation of GR.
* Curvature of Spacetime: In GR, gravity is described as a curvature of spacetime. This curvature is caused by the presence of mass or energy. In an accelerated frame of reference the spacetime is curved due to the acceleration.
* Time Dilation and Length Contraction: GR predicts that time runs slower in a gravitational field or an accelerated frame of reference. This is known as gravitational time dilation. Additionally, objects appear shorter in the direction of motion in an accelerated frame, a phenomenon called length contraction.
* Global Positioning System (GPS): GR is essential for the accurate functioning of GPS satellites. The satellites are moving at high speeds and are at a different gravitational potential compared to Earth's surface. Without accounting for GR, the GPS system would be significantly inaccurate.
In summary, GR provides a comprehensive framework for understanding the physics of accelerated frames of reference. It is a fundamental theory that has been experimentally verified and is essential for many modern technologies.
That was horrible. I would love to have questioned Gemini after that comment and show how it directly contradicts itself. I tried to do it with copilot, getting this conversation, not as bad as the two above. This is actually my first intentional interaction with any LLM ever.
Quote from: Halc
Is GR needed for accelerated frames of reference?
Quote from: copilot
In some ways, yes. Accelerated frames of reference are closely tied to the principles of General Relativity (GR). Unlike Special Relativity, which deals with constant velocities and inertial frames, General Relativity accounts for acceleration and gravity.
Einstein's theory of General Relativity generalizes the idea of relativity to include non-inertial (accelerated) frames of reference. It essentially states that the presence of mass and energy curves spacetime, which in turn affects the motion of objects. In this context, acceleration can be considered equivalent to gravitational effects?a principle known as the equivalence principle.
So, while you might not need all the complexities of GR for simple cases of acceleration, understanding the full implications of accelerated frames and gravityindeed requires the framework provided by General Relativity. If you're diving deeper into areas like gravitational waves, black holes, or cosmology, GR becomes essential.
Try as I might, I cannot get copilot to mention accelerated frames without dragging gravity into it as well, making the comments ambiguous.
Quote from: Halc
But there is no curve spacetime under special relativity. Are you saying that acceleration creates spacetime curvature?
Quote from: copilot
You're correct that Special Relativity (SR) doesn't involve curved spacetime. SR deals with inertial frames of reference?those moving at constant speeds relative to each other?and doesn?t account for acceleration or gravitational effects.Note the evasion of actually answering the question.
Quote from: copilot
In General Relativity (GR), however, acceleration and gravity are indeed linked to the curvature of spacetime. The equivalence principle in GR states that locally (in a small region of spacetime), the effects of acceleration are indistinguishable from the effects of gravity. This means that in an accelerated frame of reference, the spacetime can be thought of as curved. So, yes, acceleration is related to spacetime curvature in the context of GR.
Think of it this way: in an accelerating elevator, you feel a force pushing you down, similar to gravity. GR explains this by suggesting that the acceleration causes a curvature in spacetime, akin to how a massive object like Earth curves spacetime, creating what we perceive as gravity.
Quote from: Halc
What do you mean by acceleration being linked to curved spacetime? Does it curve spacetime or not? The equivalence principle indeed says that locally, the effects of acceleration are indistinguishable from gravity, but locally, spacetime is not curved, gravity or otherwise. You seem to imply otherwise when saying "This means that in an accelerated frame of reference, the spacetime can be thought of as curved" when the opposite is true, that locally, even under gravity, spacetime can be thought of (and is) flat.
Quote from: copilot
You bring up an excellent point. You're right?locally, spacetime is considered flat, even in the presence of gravity. Let's clear up the confusion.
The equivalence principle states that within a sufficiently small region of spacetime, the effects of acceleration are indistinguishable from the effects of gravity. In this local sense, spacetime can be approximated as flat, which aligns with your statement that locally spacetime is not curved.
To clarify: acceleration itself does not directly cause spacetime curvature. Instead, in GR, acceleration and gravity are related through the equivalence principle. When we consider larger scales or longer durations, gravity (or the presence of mass and energy) causes spacetime to curve. This curvature affects how objects move, leading to what we perceive as gravitational effects.
So, while an accelerated frame of reference might feel similar to experiencing gravity, this does not imply that acceleration curves spacetime in the same way mass and energy do. Locally, spacetime remains flat, and the equivalence principle helps us understand why the effects of acceleration can mimic gravitational effects in small regions.
There was more, but you get the idea
Post by: paul cotter on 27/11/2024 21:39:15
Post by: Eternal Student on 28/11/2024 00:54:42
...This is actually my first intentional interaction with any LLM ever....
They're actually awesome aren't they? Just how they seem to understand what you're asking is amazing. Getting a perfect answer is probably still a few years away but we should see the glass as half full.
We may not need forum moderators in the future, an LLM can analyse and critque the work produced by the forum users LLM well enough.
My input: Please criticise this work: (I copied and pasted the reply @Halc obtained from Gemini).....
Output from Chat GPT: ..... (loads of stuff but I'm just picking out the most relevant bit)....
Areas for Improvement:
You say that "spacetime is curved due to the acceleration" in an accelerated frame..... It would be better to mention that acceleration causes the perception of curvature, or locally mimics gravitational effects due to the equivalence principle. In an accelerating reference frame, spacetime itself doesn?t curve in the same way as it would near a massive object (like Earth), but an observer would perceive certain effects similar to those in a gravitational field.....
------------
Overall, the LLM generated critique did catch many of the errors in the original LLM generated response.
Maybe the trick is to make two passes, get your article written by one LLM and then get it criticised by a different one.
After all, that's probably how many online courses will go in a few years.... students using LLM to write the essays and someone else using a LLM to mark and grade them.
So at the moment the way to stay ahead in the game is for the student to make these two-passes themselves at home and refine the essay until the critique comes out quite positively. Then they would deliberately put in a few spelling errors here and there to dodge the AI detection software that the establishment may run on the work submitted by the students.
I think I've mumbled stuff about this in another thread some time ago but it's really about always trying to look at the glass as being half full. The new graduates in Physics may know nothing about Physics but they are are going to be very highly skilled and competent in using LLM and AI software. This is going to be a valuable skill for their future jobs: Writing to others, maybe some other company, in a way that the recipients LLM software will understand and regard as being of very high quality. This is precisely what a future employer will be needing from their graduate employees in a few years.
Best Wishes.
Post by: alancalverd on 28/11/2024 11:09:40
Teaching science, particularly physics, is about teaching people to think, not to regurgitate facts or "facts".
Post by: paul cotter on 28/11/2024 13:47:51
Post by: Halc on 29/11/2024 00:26:06
. Having never used supposed "AI"(no intention of doing so-you can't teach an old dog new tricks!), I am in a weak position to criticise. I have seen some atrocious rubbish in replies to questions posed by others and a high degree of suggestibility. In response to a question that requires a blunt "NO", answers will often digress into unsubstantiated speculation with the seeming aim of perpetuating the discourse rather than delivering a straightforward answer.This is very perceptive. Yes, the answers always seem agreeable, and if you protest a correct answer by asserting your own sufficiently plausible rubbish, none of the LLMs seem capable of telling you that it's still rubbish. It might seem a bit skeptical, but it will encourage you to explore your line of thinking rather than point out where it contradicts evidence or contradicts itself.
I didn't want to tell copilot that its answers were rubbish. I had hoped that it would figure it out itself after I pointed out inconsistencies in its replies.
We may not need forum moderators in the future, an LLM can analyse and critque the work produced by the forum users LLM well enough.Moderators are needed to moderate, to recognize and deal with posts not complying with the rules. Being correct is more of a job for site experts, be they moderators or not.
I'm no expert in pretty much any subject, but I know enough to take apart a lot of answers I see from AI.
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(I copied and pasted the reply @Halc obtained from Gemini).....Actually, Hamdani provided replies from both chatGPT and gemini. I just copied his quotes so I could color them
My replies below are replies to chatGPT apparently agreeing with much of what gemini had to say..
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You say that "spacetime is curved due to the acceleration" in an accelerated frame..... It would be better to mention that acceleration causes the perception of curvature, or locally mimics gravitational effects due to the equivalence principle.But that isn't right. There is no curvature locally, so there cannot be any local perception of it. In the non-local case, most of the effects are due to the accelerated frame. it is quite hard to distinguish curved spacetime from flat since all the effects are present in both, but differently.
For instance, I am under proper acceleration of 1g and dangle a clock on a long rope. In both cases the clock on the rope will run objectively slower, so that effect is not due to curved spacetime. But the two cases differ a bit for how much slower since they differ. Nearby, it differs but a little, but for a gravitational field of a small mass, it can differ a lot over not that much distance.
The equivalence principle does not suggest any of this
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In an accelerating reference frame, spacetime itself doesn?t curve in the same way...It doesn't curve at all. Spacetime curvature is objective, not a coordinate effect, and an accelerated frame is just a coordinate choice. I would have immediately grilled gemini on this point, but I have no access to it.
Quote from: Eternal Student
students using LLM to write the essays and someone else using a LLM to mark and grade them.They get what they deserve if they commit the same sins. Education should devolve into GIGO. Nobody should pay for any pseudo-education implemented in this manner.
I talked to my AI about black holes and got Newtonian answers in response. It had no clue.
Thought of another one: Sagnac effect is a favorite empirical disproof of anything Einstein. Let me have a go:
Does light travel west faster than it does east?
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Light travels at a constant speed in a vacuum, ... This speed remains the same regardless of the direction in which the light is traveling, be it west, east, or any other direction.
The notion that light could travel faster in one direction over another doesn't hold up according to our current understanding of physics. The speed of light is influenced by the medium through which it travels (such as air, water, or glass), but not by the direction.
So if I create a vacuum tunnel and some mirrors around the world and shine a pulse in both directions, both pulses will return to the origin spot at the same time?
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Yes, exactly! In your vacuum tunnel setup, if you shine a pulse of light in both the west and east directions simultaneously, both pulses would return to the origin at the same time. The speed of light in a vacuum is constant and does not depend on the direction of travel.
This constancy of the speed of light is a cornerstone of Einstein's theory of relativity and is true regardless of the motion of the source or the observer. It?s one of the fascinating and sometimes counterintuitive aspects of the way our universe works.
So the Sagnac effect disproves relativity then? It predicts that west and east light go different speeds and measurement of this difference is used to detect absolute rotation. Sure, most Sagnac devices have a far smaller circumference than a planet, but the principle is the same
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...The Sagnac effect occurs in rotating reference frames, such as a rotating disk or the surface of a spinning planet like Earth. In these scenarios, if you send two beams of light in opposite directions around a loop, they will take different amounts of time to complete the loop.Not in the context of Sagnac. In the context of what actually happensQuoteSo the two pulses do take different times to come back to the emitter then?Yes, in the context of the Sagnac effect within a rotating reference frame, the two pulses of light would indeed take different amounts of time to return to the emitter.
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Let's break this down in the context of what actually happens with light pulses and rotation.
If you set up a vacuum tunnel with mirrors and shine a pulse of light in both the westward and eastward directions, the two pulses would indeed take different amounts of time to return to the origin if the system is rotating.
So I didn't color anything, but it didn't take much to get it to contradict itself. The LLM did not take into account the rotating frame of reference in the first reply because despite the real-Earth scenario, I didn't word the question in a way that drew attention to the fact that we're working with a rotating frame, despite the fact that west and east are not even defined on a planet that doesn't rotate.
I did word the one query as an attempt to discredit relativity like so much training material attempts to do, and it at least didn't take that bait. I partly wanted to see if I could lead it down a false path if it looked like it was my purpose to do so.
The copilot replies were edited heavily, cutting it down to actual replies, and cutting out all the educational stuff it tried to add on, and of course all the congratulatory stuff at the end about how perceptive my questions are. It tacks that on to ever single reply in some form or other.
Post by: hamdani yusuf on 29/11/2024 06:53:03
But acceleration does not produce gravity at it impliesI think it's the implication from equivalence principle.
Post by: hamdani yusuf on 29/11/2024 06:55:51
The essence of AI is faith in the published word.Only LLM. There are other types of AI trained using different sets of data types, such as CCTV cameras, industrial sensors and actuators, financial transactions, self playing games, etc.
Post by: alancalverd on 29/11/2024 11:02:42
The passenger in an accelerating rocket may read 1 g on his accelerometer because he is being pushed from behind. Having landed on Earth his instrument will read 1 g because he is being pulled from below.
Continuous acceleration requires the expenditure of energy. No energy is expended by standing on the surface of a planet.
Post by: paul cotter on 29/11/2024 16:04:50
Post by: hamdani yusuf on 29/11/2024 16:59:19
Continuous acceleration requires the expenditure of energy. No energy is expended by standing on the surface of a planet.Two balls are connected by a string, floating freely in outer space. They are spun until having a constant angular speed. No energy is expended afterwards, even though the balls are continuously accelerated.
Post by: alancalverd on 29/11/2024 18:32:08
Consider one ball moving in a straight line at constant speed. If we want to change its direction we need to exert a force perpendicular to the track, so work is done.
I await your analysis of two balls on a string, with eager anticipation!
Post by: Halc on 29/11/2024 19:12:02
The passenger in an accelerating rocket may read 1 g on his accelerometer because he is being pushed from behind. Having landed on Earth his instrument will read 1 g because he is being pulled from below.No, both cases are due to being pushed from below. Were it not for this push, both cases would locally experience no proper acceleration. The two cases being locally indistinguishable is the essence of the equivalence principle, and not the below suggestion:
You show signs of not having read the critique at all, since it is that assertion that was colored red every time it was made. The equivalence principle is not in any way applicable to the mathematics of an accelerating frame, either locally or not. It makes it sound like the mathematics of special relativity was derived from general relativity and not the other way around.But acceleration does not produce gravity as [chatGTP] impliesI think it's the implication from equivalence principle.
Two balls are connected by a string, floating freely in outer space. They are spun until having a constant angular speed. No energy is expended afterwards, even though the balls are continuously accelerated.Excellent counterexample.
Consider one ball moving in a straight line at constant speed. If we want to change its direction we need to exert a force perpendicular to the track, so work is done.A force perpendicular to motion does no work, which is why the 2 balls on a string don't slow in their rotation over time.
Post by: alancalverd on 01/12/2024 16:10:52
No, both cases are due to being pushed from below.In my universe, gravity sucks. If I let go of the accelerometer, it flies towards the ground, not away from it.
Post by: varsigma on 06/12/2024 00:59:59
No, it is not a true explanation of a theory, which is why such assertions should not be posted in the main sections of the forum. That area is reserved for questions and answers to them.I apologise for what I'm about to post then.
Einstein, and Feynman have both said that relativity says we move in the time direction. Time isn't really a thing with extent, but it is a direction. We move at the speed of light in that direction.
John Baez, Roger Penrose, say it too.
Post by: Halc on 06/12/2024 01:43:43
Einstein, and Feynman have both said that relativity says we move in the time direction. Time isn't really a thing with extent, but it is a direction. We move at the speed of light in that direction.Actual quotes (and context) would really help. Are these statements in peer reviewed publications or are they casual comments or from pop articles?
John Baez, Roger Penrose, say it too.
What they are trying to say is that time and space are the same thing, meaning time and length can be used interchangably. So for instance, a worldline segment one second long (the worldline of any clock over one second measured by it) is exactly one light-second in length. The statement is one to define this ratio of translating space to time. But to call it 'speed' totally contradicts the definition of speed, as Paul has correctly pointed out. There is no meaningful motion through spacetime except for the one example I posted in the other topic, and that motion is completely undetectable, given that the interpretation posits a completely undetectable thing.
In particular, with motion, when the object gets to the destination, it is no longer at the former location. With a worldline, the object is present at every event along the line. It doesn't move from one event to another, leaving the former event 'vacant' so to speak.
It is also a common shorthand to identify a frame by an observer stationary in it, but it must be made clear at some point that frame selection is an arbitrary abstract choice, not a physical property of an object or observer. If Penrose did not make that clear in his book, then he's not doing a very good job of explaining relativity.
The vast majority of human observers choose a different frame than the inertial one in which they are stationary. It is far more pragmatic to use say the accelerating rotating frame of the surface of Earth when walking past another person.
Post by: varsigma on 06/12/2024 02:08:32
That's because a space-time distance that is zero for one observer is zero for all observers. This is also the case in Euclidean space, but in Euclidean space, this just means zero in each of the directions of space. But what does a zero distance mean in space-time? Well, let's find out. For simplicity, let us look at only one dimension of space. So if the distance in space-time is zero, this means that the distance in space divided by the distance in time equals plus or minus c. And that?s the same for all observers. So this speed, c, is an invariant speed.
But, well, we are not light, so we do not travel with the speed of light through space, and we do actually cover a distance in space-time. So let us look at this equation for the space-time distance again. Now let us divide this by the time difference. Now what you have on the left side is the space-time distance per time. And under the square root you have roughly something like the squares of the velocities in each of the directions of space. Plus c2.
And there you have it. Relative to yourself, you do not move through space, so these velocities are zero. You then only move into the time-like direction, and in this direction, you move with the speed of light. So, we indeed all travel through time with the speed of light."--from a Ph.D blog
Post by: varsigma on 06/12/2024 03:35:44
In Minkowski spacetime you have a relativistic 4-velocity. It cannot be zero or, well, lots of things just don't happen.
Post by: Halc on 06/12/2024 15:25:33
"Einstein based special relativity on the idea that the speed of light is the same for all observers.That it is the same relative to any inertial frame. It is not true relative to non-inertial frames, and there is no mention of observers in the premises.
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That's because a space-time distance that is zero for one observer is zero for all observers.It's called an interval, not a distance, and any interval (zero or otherwise) between two events or along any worldline is frame independent. Again, observers play no role in this.
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So this speed, c, is an invariant speed.You make it sound like frame invariant light speed is derived from this zero interval, rather than the frame invariant interval (of any value) being derived from the fixed light speed postulate.
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You then only move into the time-like direction, and in this direction, you move with the speed of light.That's like saying that a school bus is parked in my driveway (our reference frame), front bumper against my garage door. 20 ns later the rear bumper is 10 meters away at the street? Did the bus move at faster than c? No. It's just a different part of an extended object and the thing isn't moving at all. Likewise, you are a worldline, an extended object that is present at both events delimiting the measurement. You don't move from one event to the other, it's just different parts of you that are present at each event, just like the bumpers being different parts of one bus. It isn't motion.
All that said, yes, different definitions are used, and it is commonplace to express motion through spacetime as taking place at c, expressed as a four-velocity, not a normal velocity.
Post by: varsigma on 07/12/2024 02:07:24
All that said, yes, different definitions are used, and it is commonplace to express motion through spacetime as taking place at c, expressed as a four-velocity, not a normal velocity.I'm trying to figure out a response to the phrase "normal velocity"; if you mean the Euclidean part of the spacetime metric, I guess. But in the case of non-Euclidean solutions, I don't know what to say about it.
If you accept that "normal" is restricted to a locally defined region of the universe, the only thing moving at c is light, and the universal expansion is effectively zero; I would say that then, the universe is indeed "normal". But I know enough about the equations that I can say, that is a trivial solution. I was hoping we could lean towards what an exact reason for the different ages of twins is. Part of the reason is the exact speed of light, of course. Another part is the relativistic 4-velocity any object with mass "inherits" from the ah, causal structure.
Post by: paul cotter on 07/12/2024 11:33:53
Post by: Halc on 07/12/2024 18:53:02
I was hoping we could lean towards what an exact reason for the different ages of twins is.
Am I missing something? I was of the opinion that this question was comprehensively answered at an early stage in this query.That was indeed done in the very first reply, the important part being this:
There are many ways to explain the difference, so there is no one correct way.That means that anything claiming or asking for 'the correct way' is already presuming something wrong.
The rest of the post lists only one of the ways to explain it, and also provides counterexamples to every one of the 'explanations' mentioned in the videos, both of which were shown to be mistaken in subsequent posts. Takeaway is to use a peer reviewed text to get your information, not pop videos, even those put out by supposedly knowledgeable celebrities. An arm-chair amateur like me should not so easily be able to find the mistakes in them.
If you want another explanation, it can be something as simple as "That's the nature of Minkowskian geometry". A straight (timelike) path between two spacetime points (events) is longer in length than one that isn't straight. This is unintuitive since in Euclidean geometry, the opposite is true.
Post by: varsigma on 07/12/2024 20:50:59
I have to bear in mind I suppose, that this pattern emerged as soon as Einstein published his general theory. The idea that a spacetime existed in which the notions of fixed time and space were only relative, weren't met with enthusiasm.
Post by: A-wal on 02/07/2025 16:30:50
There must be a simple formula to calculate the time dilation by the acceleration. This seems to be a way to know who is correct.Of course there is, T = (2(√(c^2/(c^2−v^2))))((vx)/c^2) where x is space applies a non‐reciprocal time dilation in the form of a time jump on the inertial frame from the perspective of the accelerating frame that's proportional to distance. It simplifies to this because we're using constant relative velocities and instantaneous accelerations.
This overcooks the time difference so that despite the Earth twin's clocks slowing during the inertial phases of the journey from the perspective of the accelerating twin both twins will agree on the time difference once the traveling twin returns because the time jump is proportional to distance, this is a simultaneity shift.
A simpler way to look at it, if the turnaround point is at rest relative to Earth then the distance is shortened by the square root of ((c^2−v^2)/c^2) for an observer that is in motion relative to that frame, so the time that it takes to travel that shortened distance is reduced by the same amount, so the shortened time for the traveling twin is simply T = t(√((c^2−v^2)/c^2)).
Post by: A-wal on 02/07/2025 22:02:07
If you had a smooth acceleration profile or an acceleration profile that kept accelerating in the opposite direction to slow its velocity relative to some other reference frame the second profile would have a great deal more acceleration than the first smoother acceleration profile but the simultaneity shift would be identical. So in that way it's not acceleration directly that causes the twin's age different, it's the change in velocity relative to another frame scaled by distance.In the topic where this comment originated, I gave several examples of constant acceleration with negligible dilation, and examples of different accelerations that gave identical dilation.There must be a simple formula to calculate the time dilation by the acceleration. This seems to be a way to know who is correct.Of course there is, T = (2(√(c^2/(c^2−v^2))))((vx)/c^2)
Meanwhile, the formula posted makes no mention at all of acceleration, only speed, making it a function of speed, not of acceleration at all.