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.