Post by: Dimensional on 19/01/2023 03:53:23
In the image below from the website http://www.mysearch.org.uk/website1/html/250.Twins.html , they try to explain why the two situations are not symmetric, but I don't understand their approach. Even if the website is not giving a sufficient explanation, I would still like to know why the two diagrams are not symmetric.
(https://www.thenakedscientists.com/forum/proxy.php?request=http%3A%2F%2Fwww.mysearch.org.uk%2Fwebsite1%2Fimages%2Fpictures%2F250.1.jpg&hash=e4051dedfff4b8b8a906f19e781e8faf)
Post by: alancalverd on 19/01/2023 10:20:21
Einstein did not overturn Newtonian physics, but built on it.
Post by: Origin on 19/01/2023 13:33:26
Post by: Janus on 19/01/2023 16:46:33
The Earth twin never changes inertial frames, while the space twin has to transition between Outbound and Return frames. So the Earth twin can lay claim to having never changed velocity, while the Space twin cannot.
During this transition, the Space twin will be in a non-inertial, or accelerating frame. And time dilation measurements made in an accelerating frame follow different rules.
For such an observer, clocks in the direction of the acceleration run fast by a rate determined by their distance in that direction, and the magnitude of the acceleration. (keeping in mind the braking while heading away from the Earth is an acceleration towards the Earth.)*
It is this acceleration period at the turn-around point that breaks symmetry, and why the Space twin cannot assume to be the one who was stationary during the trip.
* conversely, clocks in the opposite direction will be measured as running slow.
Post by: Dimensional on 19/01/2023 20:08:00
However, I am currently discussing the same topic on another website with many verified educated people. They don't seem to think that acceleration is the reason.
Here is the website in case you want to discuss this with them, https://www.physicsforums.com/forums/special-and-general-relativity.70/ , and the thread is called "Please help with another twin paradox situation (sorry)" my name is student34 there in case you want to know.
Post by: Origin on 20/01/2023 16:57:44
However, I am currently discussing the same topic on another website with many verified educated people. They don't seem to think that acceleration is the reason.The problem is you do not understand what they are saying.
Post by: alancalverd on 20/01/2023 18:41:09
If you start with two synchronised clocks (or twins), they must be at rest with respect to one another for the duration of at least one tick. So the only way you can acquire a relative velocity is to accelerate one of them.
The trouble is that this is too bloody obvious for most clever people to recognise!
Post by: Origin on 20/01/2023 19:08:28
Or maybe they don't!No, it's Dimensional's problem. Everyone agrees that one twin must accelerate to a different reference frame.
Post by: alancalverd on 20/01/2023 23:08:31
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many verified educated people......don't seem to think that acceleration is the reason.
It is true that the basic dilation equation for moving clocks only uses a constant relative velocity v, but that ignores the underlying fact that twins or clocks can only be synchronised when v = 0, as is obvious from the dilation equation itself! Therefore in order to induce dilation, you have to introduce acceleration so that v > 0.
Post by: Dimensional on 20/01/2023 23:50:53
Then you must not have seen what they said.However, I am currently discussing the same topic on another website with many verified educated people. They don't seem to think that acceleration is the reason.The problem is you do not understand what they are saying.
Post by: Dimensional on 20/01/2023 23:54:32
But he said thatNot necessarily, I am pretty sure they can synchronize clocks as one twin passes by the other.Quotemany verified educated people......don't seem to think that acceleration is the reason.
It is true that the basic dilation equation for moving clocks only uses a constant relative velocity v, but that ignores the underlying fact that twins or clocks can only be synchronised when v = 0, as is obvious from the dilation equation itself! Therefore in order to induce dilation, you have to introduce acceleration so that v > 0.
Post by: alancalverd on 21/01/2023 11:07:56
I am pretty sure they can synchronize clocks as one twin passes by the other.
Not possible!
The colloquial use of "gentlemen, synchronise your watches, it will be 0100 in 5,4,3,2,1,now" assumes that once zeroed, all the watches will run at the same rate, so if we aim to arrive over the target at 0500 we will crash into one another.
The statement Δt' = Δt/√ (1 - v²/c²) clearly shows that if the watches are identical, Δt' = Δt only if v = 0, that is that identical watches will not run at the same rate from each other's viewpoint if they are moving with respect to one another.
Not a problem when we are all flying from Scampton to Edersee because our accelerations will be pretty much the same, but there have been enough experiments that demonstrate the effect of one aircraft accelerating and the other staying on the ground.
Post by: Halc on 21/01/2023 13:36:13
Not necessarily, I am pretty sure they can synchronize clocks as one twin passes by the other.You are correct on this. It is a common method of setting one clock to the time of another, or of comparing times, in various scenarios, almost all of them thought-experiments.
Of course, twins, pretty much by definition, are born effectively stationary relative to each other, so by that practicality, at least one of them is going to need to accelerate in order for them to part company.
Most of the posters on physicsforums are very knowledgeable, especially the ones with 'insights author' tag on their posts.
In short, acceleration does not cause time dilation nor does it cause differential aging. I gave a post in your prior thread illustrating cases where clocks stayed in sync despite vastly different accelerations (no dilation despite acceleration) and one where differential aging occurs without acceleration at all. I can also think of one where the accelerating one is the one that ages more that the one that is stationary the whole time.
https://www.thenakedscientists.com/forum/index.php?topic=86033.msg697485#msg697485
Read that post in your other topic. Time dilation is a coordinate effect due to speed relative to the coordinate system. Time dilation is a function of speed, as is stated in Eternal Student's equation posted in that topic. Differential aging (which is what the twin paradox illustrates) is the result of different path lengths through spacetime, just like you car driving more if you take the scenic route through space.
The top of the post refutes Sabine's assertion that time dilation is due to acceleration. I have all the respect for Sabine, but she messed up on this one, which is especially bad when she opens the discussion with complaints about things being poorly explained, and then she adds another bad explanation to the list. This assessment of that video is also shared at physicsforums.
Acceleration causes the asymmetry, but not the differential aging. This was very well pointed out in the physicsforum thread. To quote Ibix:
"If the list of specifications is different then you have your asymmetry. If the list of specifications is the same then you don't have two scenarios, you have one"
The other takeaway is the site in the OP, which is a site whose goal seems to be to obfuscate and cast doubt. The language on the home page makes it pretty clear it's not there to explain physics correctly, but it won't say exactly what the real goal is. The picture you posted is deliberately wrong, as admitted by the site when they put a big red X on the right side. There's no outright denialism, but it's still a crank website. Learn your relativity from a better source, and not from that site or from alancalverd who has trolled many a valid relativity discussion. (sorry Al, but you do)
The colloquial use of "gentlemen, synchronise your watches, it will be 0100 in 5,4,3,2,1,now" assumes that once zeroed, all the watches will run at the same rateThat assumption (that the watches will subsequently run at the same rate) is based on Newtonian physics, and the sync procedure does not require all the watches to be stationary relative to each other, only that they're all in proximity when 'now' happens.
The clocks running at the same rate is not a valid assumption in relativity experiments where it is well known that clocks synced in each other's presence won't stay synced if they're moving relative to each other.
Post by: alancalverd on 21/01/2023 15:51:29
Quote from: Dimensional on Yesterday at 23:54:32Setting one to the time of the other is irrelevant. You can do that any time you wish because there is no universal zero nor any requirement for classical simultaneity. What we mean by time dilation is that one second later, the two clocks will not show the same number as viewed from each other's position.
Not necessarily, I am pretty sure they can synchronize clocks as one twin passes by the other.
You are correct on this. It is a common method of setting one clock to the time of another, or of comparing times, in various scenarios, almost all of them thought-experiments.
In other words Δt' = Δt/√ (1 - v²/c²) means that Δt' ≠ Δt if v ≠ 0, so you can only synchronise clocks (i.e. ensure that they will both show the same time one second later) if they are not moving relative to one another.
It is the failure to understand this that turns the observed twins phenomenon into a "paradox".
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Acceleration causes the asymmetry, but not the differential aging.Wrong, for the same reason. Relativity does not depend on the nature of the clock. It doesn't matter (in principle) whether you use a cesium fountain, radioactive decay, a pendulum or a biological process to measure time. Ageing is the consequence of biological processes with their own time constants - except that we can't really call them constants in this context! The use of "twins"is to underline the fact that two identical processes begin with v = 0, then you accelerate one of them so v > 0.
Post by: Janus on 21/01/2023 17:20:59
The first is the comparison of clock rates as made from one frame of reference at any particular point.
So for example, during the outbound leg of the trip, both the Earth observer and Ship observer would rightfully claim that the other clock is time dilated.
The second is the end result of a all relativistic effects in play during the trip.
For example: Twin 1 stays at home, while Twin flies off to a planet 10 ly away at 0.8c. and then returns at the same speed.
For Twin 1, the round trip take 20/0.8 = 25 yrs, while Twin 2 undergoes twin dilation aging 0.6 *25 = 15 yrs upon return.
For Twin 1, the distance between the planet and Earth is length contracted to 6 ly, making the round trip 12 ly in length, which by his clock take 12/.8 = 15 yrs. So he agrees with twin 1 that he aged 15 yrs during the trip, but for different a different reason.
So the question is why does he agree that twin 1 aged 25 years between his leaving and returning, given that during the outbound and return legs he would conclude that Twin 1 was time dilated, and during the combined length of those legs would have aged only 9 years? How do we account for the additional 16 yrs?
For that we go back to what I said earlier about observers in accelerated frames. When twin 1 reaches the planet, and reverses direction, he accelerates towards Twin 1. And while this does not effect his own clock in any way, it does change what he would conclude is happening to Twin 1's clock, And that would be that Twin 1's clock would be running fast compared to his own. It would be during this period that, by his measurements, Twin 1 ages an additional 16 yrs.
Twin 1 on the other hand measures nothing additional happening to Twin 2 during this period other than that caused by the changing relative speed of Twin 2.
So what about the acceleration Twin 2 undergoes at the start and end of the trip?
If you remember, from my earlier post, the distance between Twin 1 and any clock he measures is a factor in determining how he measures that clocks tick rate. The greater the distance ( along the line of acceleration), the greater the tick rate difference.
When Twin 1 leaves Twin 2 and again, when he returns. They are essentially in the same place. The distance between them is 0. If we assume that Twin 2 undergoes an extremely high acceleration for a brief period of time to get up to speed, then he will have barely moved away from Twin 1. So while while the effect he see this having on Twin won't be 0, it will be negligible, and can safely be ignored for this scenario.
So, for Twin 1, the acceleration by Twin 2 has no additional effect on the end results , and for Twin 2, only the acceleration during turn-around has any significant bearing on the final results.
Post by: MikeFontenot on 21/01/2023 18:06:20
The key here is that symmetric time dilation is only valid between inertial frames of reference. And there are three inertial reference frames in the diagram: 1. Earth frame 2. Outbound leg frame. 3 Return leg frame.
The Earth twin never changes inertial frames, while the space twin has to transition between Outbound and Return frames. So the Earth twin can lay claim to having never changed velocity, while the Space twin cannot.
During this transition, the Space twin will be in a non-inertial, or accelerating frame. And time dilation measurements made in an accelerating frame follow different rules.
For such an observer, clocks in the direction of the acceleration run fast by a rate determined by their distance in that direction, and the magnitude of the acceleration. (keeping in mind the braking while heading away from the Earth is an acceleration towards the Earth.)*
It is this acceleration period at the turn-around point that breaks symmetry, and why the Space twin cannot assume to be the one who was stationary during the trip.
* conversely, clocks in the opposite direction will be measured as running slow.
Right on! You said everything that needed saying, and nothing that didn't need saying.
Post by: Halc on 21/01/2023 21:55:27
It is important not to conflate "time dilation" with " The difference in accrued time"Yes! And the second (also known as 'differential aging') is objective comparison of the clocks upon their reunion. This comparison, unlike dilation, is objective and yields the same value regardless of frame.
The first is the comparison of clock rates as made from one frame of reference at any particular point.
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For example: Twin 1 stays at home, while Twin flies off to a planet 10 ly away at 0.8c. and then returns at the same speed.This is the typo. Twin 1 is Earth frame, the frame in which the other planet is 10 LY away, so the distance is contracted in Twin2's frame where Earth is moving away at 0.8c and the other planet approaching at 0.8c from 6 LY away.
For Twin 1, the round trip take 20/0.8 = 25 yrs, while Twin 2 undergoes twin dilation aging 0.6 *25 = 15 yrs upon return.
For Twin 1, the distance between the planet and Earth is length contracted to 6 ly
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making the round trip 12 ly in length, which by his clock take 12/.8 = 15 yrs.There is no round trip from twin2's perspective. He's always stationary and Earth moves away at 0.8c to 6 LY away, and then after his own proper acceleration, Earth comes back at the same pace. So it's Earth that takes a 12 LY round trip of sorts, but twin2 is stationary from his own point of view, so he just sits there for 12 years with a serious acceleration after half of that. This is all just nits. You know all this, but I'm trying to clarify for the general audience.
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So he agrees with twin 1 that he aged 15 yrs during the trip, but for different a different reason.One of the points of this thread was to emphasize that acceleration itself has nothing to do with the differential aging. It has only to do with the asymmetry of the situtaion. I posted examples in the other topic (linked in my previous post) where one twin can (properly) accelerate thousands of times more than the other, and yet their ages remain the same. This directly contradicts what Sabine Hossenfelder says in her video (linked in the other topic) where she implies that clocks at the center of Earth run faster than on the surface because there is neither coordinate nor proper acceleration going on there. Time on Mercury should be slower according to what she states.
My first example in that post had triplets doing identical acceleration but turning around at different distances. Their ages were all different, but should be the same according to Sabine's video. I'd appreciate it if you critiqued that post since nobody who knows their stuff has commented on it.
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So the question is why does he agree that twin 1 aged 25 years between his leaving and returning, given that during the outbound and return legs he would conclude that Twin 1 was time dilated, and during the combined length of those legs would have aged only 9 years? How do we account for the additional 16 yrs?The official answer is the different temporal lengths of their respective worldlines. This is an objective explanation and is true regardless of frame (inertial or accelerating) chosen. This seems an unsatisfactory answer to the naive beginner since it isn't obvious why one worldline should have a shorter temporal length if it had a longer spatial length, but that is a direct consequence of Minkowskian geometry measuring intervals as s² = ct² - x² - y² - z² as opposed to the more intuitive Euclidean geometry where s² = ct² + x² + y² + z².
Anyway, wanted to say that. Not saying your answer is wrong because of it.
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The greater the distance ( along the line of acceleration), the greater the tick rate difference.This is also known as 'moment of acceleration' since it's magnitude is proportional to the distance (as measured by twin 1) between them. This is why the initial and final acceleration have no effect. No distance, so no moment. I hardly ever see this term used anymore, so I suspect it is falling out of general use.
Post by: Dimensional on 22/01/2023 16:41:40
Thanks, this is all very clear. However, I am still not completely convinced for the following reason.Not necessarily, I am pretty sure they can synchronize clocks as one twin passes by the other.You are correct on this. It is a common method of setting one clock to the time of another, or of comparing times, in various scenarios, almost all of them thought-experiments.
Of course, twins, pretty much by definition, are born effectively stationary relative to each other, so by that practicality, at least one of them is going to need to accelerate in order for them to part company.
Most of the posters on physicsforums are very knowledgeable, especially the ones with 'insights author' tag on their posts.
In short, acceleration does not cause time dilation nor does it cause differential aging. I gave a post in your prior thread illustrating cases where clocks stayed in sync despite vastly different accelerations (no dilation despite acceleration) and one where differential aging occurs without acceleration at all. I can also think of one where the accelerating one is the one that ages more that the one that is stationary the whole time.
https://www.thenakedscientists.com/forum/index.php?topic=86033.msg697485#msg697485
Read that post in your other topic. Time dilation is a coordinate effect due to speed relative to the coordinate system. Time dilation is a function of speed, as is stated in Eternal Student's equation posted in that topic. Differential aging (which is what the twin paradox illustrates) is the result of different path lengths through spacetime, just like you car driving more if you take the scenic route through space.
The top of the post refutes Sabine's assertion that time dilation is due to acceleration. I have all the respect for Sabine, but she messed up on this one, which is especially bad when she opens the discussion with complaints about things being poorly explained, and then she adds another bad explanation to the list. This assessment of that video is also shared at physicsforums.
Acceleration causes the asymmetry, but not the differential aging. This was very well pointed out in the physicsforum thread. To quote Ibix:
"If the list of specifications is different then you have your asymmetry. If the list of specifications is the same then you don't have two scenarios, you have one"
The other takeaway is the site in the OP, which is a site whose goal seems to be to obfuscate and cast doubt. The language on the home page makes it pretty clear it's not there to explain physics correctly, but it won't say exactly what the real goal is. The picture you posted is deliberately wrong, as admitted by the site when they put a big red X on the right side. There's no outright denialism, but it's still a crank website. Learn your relativity from a better source, and not from that site or from alancalverd who has trolled many a valid relativity discussion. (sorry Al, but you do)
Imagine a simple case where the twin only accelerates for the entire trip. Twin brothers start from rest with each other, and the travelling twin accelerates, say halfway to a certain distance away from the stationary twin, then decelerates so that he reaches the final distance, then he accelerates to nullify the deceleration until he come to a complete stop with his brother.
Now if it is fair to say that the only difference between the 2 twins was acceleration, how does your claim deal with this? At best, it would seem to have to be something that implies acceleration. In that case I would agree, but what is it exactly that would imply acceleration (would be in the group of "acceleration")?
Post by: Halc on 22/01/2023 18:46:36
Twin brothers start from rest with each other, and the travelling twin accelerates, say halfway to a certain distance away from the stationary twin, then decelerates so that he reaches the final distance, then he accelerates to nullify the deceleration until he come to a complete stop with his brother.You seem to be using the dictionary definition of 'accelerate' which means an increase of speed, with 'decelerate' being its opposite. In physics, acceleration is a vector and means a change in velocity, so it is acceleration all the way, just in different directions. This is a terminology thing, not something wrong with your scenario. I get what you're describing.
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Now if it is fair to say that the only difference between the 2 twins was acceleration, how does your claim deal with this?Well it isn't fair to say that. Worded that way, they put a clock on a jet and left the other one at the lab. They flew the jet around the world to the west back to the parked clock and it was the parked clock that accrued less time (it was younger).
In your scenario, there is plenty that is different. In the frame in which the two comparison events are at the same spatial location, the travelling twin is moving at a higher velocity than the Earth twin. The velocity relative to a given inertial frame is what defines the dilation in this case. Eternal Student's formula integrates this velocity, not the acceleration.
And most importantly, the temporal length of his worldline between those two events is shorter than that of the Earth twin. That worldline length defines the differential aging they experience.
So there are several things different, not just acceleration. I can have one twin accelerating and not the other, and either one might be older at the reunion. It isn't about speed. I can have one twin always moving faster than the other, and yet the slower one ages less. So given all cases, neither acceleration nor speed can account for differential aging.
But the worldline thing cannot lie. If the temporal length of one path between two events is longer than that of a different path between the same two events, more time will be measured on the longer path. This is true regardless of coordinate system chosen, special relativity, general relativity, with or without gravity.
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At best, it would seem to have to be something that implies acceleration.It isn't about acceleration, even though there happens to be acceleration involved in the twins scenario just because that's how the story is described. Differential aging can occur without any proper acceleration at all. It can also be done without any speed at all. You don't accept or even seem to acknowledge these counterexamples.
Differential aging cannot be done with two worldlines that don't differ in temporal length, so if there must be a 'cause', it's that.
The twins scenario can also be described (explained?) just by what each observer sees. The each see the clock of the other run slow as he recedes, but see it run faster as the approach each other. The symmetry is very nice in that instance, except the times of each phase are different, which explains the differential aging. But again, what anybody measures has nothing to do with causing something observed to age.
It seems that you will not accept any answers, correct or otherwise. You find a website that deliberately goes out of its way to be very confusing if not outright wrong. I cannot help you further. We're all just repeating the same answers.
Post by: Dimensional on 22/01/2023 20:41:43
In your scenario, there is plenty that is different. In the frame in which the two comparison events are at the same spatial location, the travelling twin is moving at a higher velocity than the Earth twin. The velocity relative to a given inertial frame is what defines the dilation in this case. Eternal Student's formula integrates this velocity, not the acceleration.
So in other layman words, is it integrating all the moments of its velocities throughout the acceleration (please excuse my layman wording, I hope the point of my question comes across.)?
One other question, when you said, "In the frame in which the two comparison events are at the same spatial location, the travelling twin is moving at a higher velocity than the Earth twin" do you mean at the moment he starts? I ask because I wanted them both to start at rest and end at rest in the thought experiment.
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And most importantly, the temporal length of his worldline between those two events is shorter than that of the Earth twin. That worldline length defines the differential aging they experience.
Yes, I agree. I am not arguing that the worldline should be longer than the Earth twin. My argument is how did it become longer; acceleration, something else?
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It can also be done without any speed at all. You don't accept or even seem to acknowledge these counterexamples.
Sorry, I must have missed them, or answered them in my head and forgot to post them.
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The twins scenario can also be described (explained?) just by what each observer sees. The each see the clock of the other run slow as he recedes, but see it run faster as the approach each other. The symmetry is very nice in that instance, except the times of each phase are different, which explains the differential aging. But again, what anybody measures has nothing to do with causing something observed to age.
This is confusing to me when there is no acceleration. Let's say 2 clocks have always been moving at a constant velocity with respect to one another. Each clock sees the other clock run faster as they approach each other. When they meet, there will be no time dilation. How can this be time dilation without acceleration?
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It seems that you will not accept any answers, correct or otherwise. You find a website that deliberately goes out of its way to be very confusing if not outright wrong.
Yes, I should be more careful with my references.
Post by: Halc on 22/01/2023 21:43:44
So in other layman words, is it integrating all the moments of its velocities throughout the acceleration (please excuse my layman wording, I hope the point of my question comes across.)?Integrating the speeds, but yes. The direction doesn't matter when doing it this way, only the magnitude. Magnitude of velocity is speed.
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One other question, when you said, "In the frame in which the two comparison events are at the same spatial location, the travelling twin is moving at a higher velocity than the Earth twin" do you mean at the moment he starts?A frame is not a moment, it is (in this case) an inertial coordinate system that assigns spatial and temporal coordinates to all events in spacetime.
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I ask because I wanted them both to start at rest and end at rest in the thought experiment.At rest is relative to a frame. Yes, they're both at rest relative to each other at the the start, end, and also the middle of your new scenario. At all other times, they're not.
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And most importantly, the temporal length of his worldline between those two events is shorter than that of the Earth twin. That worldline length defines the differential aging they experience.
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Yes, I agree. I am not arguing that the worldline should be longer than the Earth twin.Shorter. There is less time along that path.
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My argument is how did it become longer; acceleration, something else?It's a path, a time-like line of adjacent events (points) in spacetime. It has an intrinsic geometric length, just like a space-like worldline line has an intrinsic spatial length. The path doesn't ever become anything since it is always there. The one twin just happens to follow this particular path.
So it's like asking why a curved line on paper between two points is longer than the straight one. It never became longer, but one might choose the longer path rather than the shorter one. Paper is Euclidean geometry where the shortest path is a straight line. You find the length of the hypotenuse of a triangle (x/y axis) by L=√(y²+x²). Minkowskian spacetime isn't Euclidean like that. The length of the hypotenuse of a timelike worldline is L=√(ct²-x²). Notice the minus sign in there, which means if you move through space in your coordinate system (wander away from the straight line), the length of the line gets shorter, not longer like it does on Euclidean paper.
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There is acceleration in this case. It is the standard twins scenario, same story, different way of looking at it.QuoteThe twins scenario can also be described (explained?) just by what each observer sees. The each see the clock of the other run slow as he recedes, but see it run faster as the approach each other. The symmetry is very nice in that instance, except the times of each phase are different, which explains the differential aging. But again, what anybody measures has nothing to do with causing something observed to age.This is confusing to me when there is no acceleration.
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Let's say 2 clocks have always been moving at a constant velocity with respect to one another. Each clock sees the other clock run faster as they approach each other. When they meet, there will be no time dilation.There is always dilation because each clock is moving in the inertial frame of the other. That's pretty much one of the three ways to define dilation (inertial frames, accelerating frames, and curved frames: gravity). So each clock will run slower relative to the frame of the other, but an observer watching the incoming clock will see it running faster, mostly due to Doppler effect, just like the siren of an approaching ambulance.
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How can this be time dilation without acceleration?Inertial dilation is all about speed and is not a function of acceleration at all. In the twins scenario, the acceleration is necessary for the twins to meet twice in Minkowskian (flat) spacetime. It can be done without acceleration, but doing so requires curved space, meaning it involves gravity.
For example, take two satellites in very eccentric orbits about Earth. Sans engines, both follow a geodesic (a straight line) through curved spacetime. They meet at apogee of one satelite and perigee of the other, meaning one has a shorter orbit and one much larger, such that the period of one is exactly twice the other so they meet repeatedly where clocks can be compared. The clock on the inner satellite will record less time than the outer one at each comparison event. Everything is weightless (not accelerating) the whole time, so no proper acceleration. Everything traces straight lines through curved spacetime, but the path lengths between successive intersection events are not the same.
Post by: MikeFontenot on 22/01/2023 22:44:31
This is confusing to me when there is no acceleration. Let's say 2 clocks have always been moving at a constant velocity with respect to one another. Each clock sees the other clock run faster as they approach each other.
In the above, I think you are describing what the home twin (she) looks like to the traveling twin (him) if she has been transmitting a TV image of herself for a long time. He WILL see her ageing faster than himself on his TV monitor as he moves toward her. But that is entirely different from the question: "How old is she right now", which is the really important question. He knows that her image on his TV is out of date ... it doesn't show her age "NOW".
Post by: Dimensional on 22/01/2023 23:30:03
So in other layman words, is it integrating all the moments of its velocities throughout the acceleration (please excuse my layman wording, I hope the point of my question comes across.)?Integrating the speeds, but yes. The direction doesn't matter when doing it this way, only the magnitude. Magnitude of velocity is speed.
Okay, thanks, I did not know this.
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QuoteMy argument is how did it become longer; acceleration, something else?It's a path, a time-like line of adjacent events (points) in spacetime. It has an intrinsic geometric length, just like a space-like worldline line has an intrinsic spatial length. The path doesn't ever become anything since it is always there. The one twin just happens to follow this particular path.
So it's like asking why a curved line on paper between two points is longer than the straight one. It never became longer, but one might choose the longer path rather than the shorter one. Paper is Euclidean geometry where the shortest path is a straight line. You find the length of the hypotenuse of a triangle (x/y axis) by L=√(y²+x²). Minkowskian spacetime isn't Euclidean like that. The length of the hypotenuse of a timelike worldline is L=√(ct²-x²). Notice the minus sign in there, which means if you move through space in your coordinate system (wander away from the straight line), the length of the line gets shorter, not longer like it does on Euclidean paper.
Ok, that's a good point. I have already learnt about Minkowski metric vs Euclidean metric, as well as how to make basic spacetime diagrams. But I am definitely fuzzy about accelerated worldlines vs nonaccelerated worldlines and using the Minkowski metric to show the difference, and then what that would mean for time dilation.
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There is acceleration in this case. It is the standard twins scenario, same story, different way of looking at it.[/quote]QuoteThe twins scenario can also be described (explained?) just by what each observer sees. The each see the clock of the other run slow as he recedes, but see it run faster as the approach each other. The symmetry is very nice in that instance, except the times of each phase are different, which explains the differential aging. But again, what anybody measures has nothing to do with causing something observed to age.This is confusing to me when there is no acceleration.
I meant that for other examples when acceleration does not happen I get confused as to how time dilation makes sense. Then I started with an example that does not have acceleration.
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QuoteLet's say 2 clocks have always been moving at a constant velocity with respect to one another. Each clock sees the other clock run faster as they approach each other. When they meet, there will be no time dilation.There is always dilation because each clock is moving in the inertial frame of the other. That's pretty much one of the three ways to define dilation (inertial frames, accelerating frames, and curved frames: gravity). So each clock will run slower relative to the frame of the other, but an observer watching the incoming clock will see it running faster, mostly due to Doppler effect, just like the siren of an approaching ambulance.
I am not sure I understand exactly what you are saying about scenarios without acceleration (and gravity for this matter). Are you saying that there is time dilation for each clock relative to the other in my example with the clocks?
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QuoteHow can this be time dilation without acceleration?Inertial dilation is all about speed and is not a function of acceleration at all. In the twins scenario, the acceleration is necessary for the twins to meet twice in Minkowskian (flat) spacetime. It can be done without acceleration, but doing so requires curved space, meaning it involves gravity.
I meant for my example with the two clocks.
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For example, take two satellites in very eccentric orbits about Earth. Sans engines, both follow a geodesic (a straight line) through curved spacetime. They meet at apogee of one satelite and perigee of the other, meaning one has a shorter orbit and one much larger, such that the period of one is exactly twice the other so they meet repeatedly where clocks can be compared. The clock on the inner satellite will record less time than the outer one at each comparison event. Everything is weightless (not accelerating) the whole time, so no proper acceleration. Everything traces straight lines through curved spacetime, but the path lengths between successive intersection events are not the same.Yes, I know a little about this and that time dilation also comes from gravitational potential. So I am saying that acceleration is the only reason for time dilation. I am more interested in what exactly causes time dilation without gravity, and without acceleration for this matter.
Post by: alancalverd on 22/01/2023 23:44:26
I am more interested in what exactly causes time dilation without gravity, and without acceleration for this matter.It is not possible to experience time dilation without an energy change. Gravitational potential offers one form, acceleration another.
If A is moving relative to B, their identical clocks cannot synchronise, due to time dilation.
If A and B are synchronised they can only acquire a relative velocity if one of them accelerates.
Einstein recognised that a change in gravitational potential is equivalent to an acceleration. This makes cosmology rather more interesting as it implies that two widely separated clocks might appear to a third party to be synchronised and fixed in space, but one could then drift if it was approached by a large mass.
It is important to approach physics from the standpoint of relativistic mechanics rather than simple newtonian analysis. The relativistic equations neatly degenerate to classical mechanics whenever v<<c but you can't generate relativistic corrections if you begin with the degenerate form. And the relativistic results are confirmed by experiment.
Post by: Dimensional on 22/01/2023 23:52:43
I was just trying to think of an example without acceleration. But I just realized that my example does not make any sense because the clocks were never synchronized in the first place.
This is confusing to me when there is no acceleration. Let's say 2 clocks have always been moving at a constant velocity with respect to one another. Each clock sees the other clock run faster as they approach each other.
In the above, I think you are describing what the home twin (she) looks like to the traveling twin (him) if she has been transmitting a TV image of herself for a long time. He WILL see her ageing faster than himself on his TV monitor as he moves toward her. But that is entirely different from the question: "How old is she right now", which is the really important question. He knows that her image on his TV is out of date ... it doesn't show her age "NOW".
So the new example is just 2 clocks, no twins, that have always been travelling toward each other since infinity. When they meet they synchronize, and then continue along their paths in opposite directions. I believe one will "see" (let's leave doppler effects and photons out of it if we can) the other clock as running slower. I don't know if that counts as time dilation.
Post by: alancalverd on 23/01/2023 00:44:11
Be careful not to misuse "synchronise". As I pointed out in reply #11, the colloquial use of the word means to set them to both read t = zero right now, on the presumption that v<<c so for all practical purposes you can guarantee simultaneity when t = x, the time you want something to happen. Perfectly adequate for making a rendezvous by ship or car, and indeed the basis of timekeeping for trade ever since Stonehenge was built. But not for satellite navigation or cosmic red shift.
The whole point of specifying twins (or other identical clocks) is that initially each sees the other as having the same tick rate, so they have to observe one another for a finite elapsed time (at least one tick) to establish true synchronicity. But if they have a nonzero relative velocity, they cannot see each other as having the same tick rate.
Post by: Dimensional on 23/01/2023 01:44:13
I think the light is beginning to dawn!Yeah, good point!
Be careful not to misuse "synchronise". As I pointed out in reply #11, the colloquial use of the word means to set them to both read t = zero right now, on the presumption that v<<c so for all practical purposes you can guarantee simultaneity when t = x, the time you want something to happen. Perfectly adequate for making a rendezvous by ship or car, and indeed the basis of timekeeping for trade ever since Stonehenge was built. But not for satellite navigation or cosmic red shift.
The whole point of specifying twins (or other identical clocks) is that initially each sees the other as having the same tick rate, so they have to observe one another for a finite elapsed time (at least one tick) to establish true synchronicity. But if they have a nonzero relative velocity, they cannot see each other as having the same tick rate.
Post by: Halc on 23/01/2023 03:10:46
I meant that for other examples when acceleration does not happen I get confused as to how time dilation makes sense. Then I started with an example that does not have acceleration.It was a good example, one that illustrated dilation without the differential aging. Dilation from inertial motion is a function of speed. Differential aging (from any kind of situation) is a function of path lengths. The twin paradox is meant to illustrate the latter.
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I am not sure I understand exactly what you are saying about scenarios without acceleration (and gravity for this matter). Are you saying that there is time dilation for each clock relative to the other in my example with the clocks?Relative to the various inertial frames, yes. In one frame, the first clock runs faster and relative to another frame the second clock runs faster. Relative to some select frames, both tick at the same rate. It's all an abstract consequence of frame choice.
Differential aging is not a function of frame choice since the same answer is found regardless of choice of coordinate system with which to describe the situation.
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How can this be time dilation without acceleration?
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I meant for my example with the two clocks.Your example was a perfect one of dilation. Relative a frame where one of the clocks is stationary, the other clock is dilated (runs slower).
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Yes, I know a little about this and that time dilation also comes from gravitational potential.Yes, because curved spacetime alters path lengths, and sometimes allows multiple straight lines to meet more than once just like straight train tracks will cross in two places on Earth. The surface of Earth is 2D but positively curved so parallel lines meet after a while.
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So I am saying that acceleration is the only reason for time dilation.Then you're not getting it. I gave several examples of the dilated clock being the non-accelerated one, or the less accelerated one. Without gravity, clocks can have dilation without acceleration (such as in your example of passing clocks) but since they never meet more than once, there is no pair of paths between the same two events that can be compared. Without resorting to gravity there is no way to make the clocks meet twice without one or both of them accelerating (or by staying in each other's presence the entire way).
It is not possible to experience time dilation without an energy change.Time dilation, like length contraction, isn't something that is experienced. They are coordinate effects, and per the first postulate (Galilean relativity), physics is the same relative to any inertial frame, so by that postulate, dilation is not something that can be measured or felt.
Change of potential also cannot be felt, but proper acceleration very much can.
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If A is moving relative to B, their identical clocks cannot synchronise, due to time dilation.In standard physics texts, there is frequent mention of syncing passing clocks. Any clock can be zeroed or set to the reading of the other when in its presence, and it is not a misuse of the term 'synchronise' to do this. It does not require v<<c. There's no need for a tick to pass in order to set a clock to a specific time. With the twins, it's a calendar, hardly a stopwatch. Yes, if they're moving relative to each other, they cannot stay in sync except in some select frames in which they have the same speed.
This kind of sync just means the two clocks read the same value at that event. There's no implication that they're expected to subsequently tick at the same rate. The operation doesn't require a selection of frame
The other kind of sync is for clocks that are stationary relative to each other and not in each other's presence. This requires a selection of frame and a sync convention to get them to read the same value relative to the selected frame. You seem to only be aware of this sort of sync and not the other.
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Einstein recognised that a change in gravitational potential is equivalent to an acceleration.Actually, it was the lack of change of gravitational potential that is equivalent to acceleration. For instance, I cannot locally tell if I'm accelerating in a box in space or if the box is sitting on Earth at constant potential. Satellites on the other hand are often continuously changing potential with eccentric orbits, and yet they're in freefall, not accelerating. It is equivalent to no acceleration in flat spacetime.
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This makes cosmology rather more interesting as it implies that two widely separated clocks might appear to a third party to be synchronised and fixed in space, but one could then drift if it was approached by a large mass.Yes, and if this happens, the clocks will acquire a velocity relative to each other, further mucking up the sync well after the big object has gone by.
I was just trying to think of an example without acceleration. But I just realized that my example does not make any sense because the clocks were never synchronized in the first place.No, they were probably never synchronized in the first place, but they have calculators and could have computed when they'll pass and set the clocks to happen to read the same value when they do. One way to do this is to sync them to a frame in which the clocks tick at the same rate. No need to wait for them to meet. It can be done well ahead of time.
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I believe one will "see" (let's leave doppler effects and photons out of it if we can) the other clock as running slower.Scare quotes are appropriate here. They don't actually see this, but they compute it relative to their choice of frame. Remember, dilation is mostly abstract, not physical. Differential aging is physical, but there is none of that in this example.
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I don't know if that counts as time dilation.It exactly counts as dilation.
Post by: alancalverd on 23/01/2023 09:23:17
Time dilation, like length contraction, isn't something that is experienced.https://en.wikipedia.org/wiki/Hafele%E2%80%93Keating_experiment suggests otherwise.
There's no need for a tick to pass in order to set a clock to a specific time.Indeed, but that isn't what is implied by "synchronicity" when considering time dilation. It's all about tick rate, and consequently elapsed time as measured by two clocks moving relative to one another.
Post by: Dimensional on 23/01/2023 16:38:11
I meant that for other examples when acceleration does not happen I get confused as to how time dilation makes sense. Then I started with an example that does not have acceleration.It was a good example, one that illustrated dilation without the differential aging. Dilation from inertial motion is a function of speed. Differential aging (from any kind of situation) is a function of path lengths. The twin paradox is meant to illustrate the latter.
Here is an example of how my brain gets scrambled when thinking about this scenario.
Imagine that someone was watching the clocks come together. It is a perfectly symmetrical situation. The observer is between the clocks at their meeting point. The clocks are on a collision course as they have the same velocity relative to the observer in the middle. The clocks are synchronized.
If I am correct, each clock will see the other ticking more slowly. How does this get resolved as they come together?
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QuoteI am not sure I understand exactly what you are saying about scenarios without acceleration (and gravity for this matter). Are you saying that there is time dilation for each clock relative to the other in my example with the clocks?Relative to the various inertial frames, yes. In one frame, the first clock runs faster and relative to another frame the second clock runs faster. Relative to some select frames, both tick at the same rate. It's all an abstract consequence of frame choice.
Differential aging is not a function of frame choice since the same answer is found regardless of choice of coordinate system with which to describe the situation.
Ok, that is my understanding too.
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Oh how frustrating, I meant to put, "So I am not saying ...". Sorry.QuoteSo I am saying that acceleration is the only reason for time dilation.Then you're not getting it. I gave several examples of the dilated clock being the non-accelerated one, or the less accelerated one. Without gravity, clocks can have dilation without acceleration (such as in your example of passing clocks) but since they never meet more than once, there is no pair of paths between the same two events that can be compared. Without resorting to gravity there is no way to make the clocks meet twice without one or both of them accelerating (or by staying in each other's presence the entire way).
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I pretty much agree. I am still a little foggy how the dilation no longer becomes dilation as the two clocks approach each other from the example above, but I will wait for your response.QuoteI don't know if that counts as time dilation.It exactly counts as dilation.
Getting back to the twins, I will try to use what I have learnt from this discussion (I have double checked much of what you said, and everything seems to be correct, just for my own peace of mind).
I have learnt that when there is velocity/speed involved, the result is that both twins seem to undergo time dilation relative to the other (just like in the clock example). But this is telling me that the speed/velocity is not the reason for the change in aging.
And regarding the path lengths, if I look at a simple spacetime diagram of the "instant-acceleration-version" of the twin paradox, I see that the stationary twin's worldline/path is straight up, and the travelling twin's makes a shape like this > only stretched out much more. And the only logical thing that I can think of is that the difference is that the twin had to change directions. So I am saying that the path length is what it is because the twin changes directions. Now the question is, does "change directions" absolutely imply acceleration? If so, then I see no alternative than to say that the change in age is caused by acceleration.
Post by: alancalverd on 23/01/2023 16:52:50
Here is an example of how my brain gets scrambled when thinking about this scenario.Oddly, I was sitting in a doctor's waiting room thinking about this at the time you were writing it!.
Imagine that someone was watching the clocks come together. It is a perfectly symmetrical situation. The observer is between the clocks at their meeting point. The clocks are on a collision course as they have the same velocity relative to the observer in the middle. The clocks are synchronized.
If I am correct, each clock will see the other ticking more slowly. How does this get resolved as they come together?
From the central observer's point of view the two clocks may indeed be synchronised with each other as each is approaching with velocity v, but each sees the other as advancing at 2v, therefore speeded up (or blue shifted) relative to his own.
Post by: alancalverd on 23/01/2023 16:56:06
Now the question is, does "change directions" absolutely imply acceleration?Acceleration is a change of velocity, whether speed, direction, or both.Hence the occasionally quoted "instantaneous relative velocity" is meaningless.
Post by: Halc on 23/01/2023 19:30:13
Imagine that someone was watching the clocks come together. It is a perfectly symmetrical situation. The observer is between the clocks at their meeting point. The clocks are on a collision course as they have the same velocity relative to the observer in the middle. The clocks are synchronized.They would tick at the same rate in the inertial frame in which that middle observer is stationary. They'd be synchronized only if they happen to read the same value simultaneously in that frame.
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If I am correct, each clock will see the other ticking more slowly. How does this get resolved as they come together?It doesn't need resolution. Observers with both clocks will always compute (not see) the other ticking slower relative to their own frame. This doesn't change when they come together and part company again.
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I am still a little foggy how the dilation no longer becomes dilation as the two clocks approach each other from the example above, but I will wait for your response.It never stops being dilation. The other clock is always moving at some speed relative to you, so it is dilated relative to you, before, during, and after it passes by.
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I have learnt that when there is velocity/speed involved, the result is that both twins seem to undergo time dilation relative to the other (just like in the clock example). But this is telling me that the speed/velocity is not the reason for the change in aging.Differential again and time dilation are different things. The former is due to physically different path lengths. The latter due to abstract coordinate choices and speed relative to those choices.
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And regarding the path lengths, if I look at a simple spacetime diagram of the "instant-acceleration-version" of the twin paradox, I see that the stationary twin's worldline/path is straight up, and the travelling twin's makes a shape like this > only stretched out much more.That's right. It's because paper is Euclidean and cannot correctly represent spacetime which is not. The mathematics says the > path is shorter (because of the -x² instead of the +x² you get with Euclidean geometery), and the mathematics is what counts.
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So I am saying that the path length is what it is because the twin changes directions.In this case, but not necessarily so. I can have a twin with more direction changes and still have him come out older than another with less.
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Now the question is, does "change directions" absolutely imply acceleration?To change your direction of nonzero motion, yes, that's acceleration. To just face/point a different way is to change direction without implying any acceleration, but I don't think you're talking about that.
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So I am saying that acceleration is the only reason for time dilation.
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Then you're not getting it.
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Oh how frustrating, I meant to put, "So I am not saying ...". Sorry.But here you are asserting the same thing again:
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If so, then I see no alternative than to say that the change in age is caused by acceleration.As I said before, I don't think I can help you further. I gave several examples contradicting this suggestion, and it seems pointless to post in a topic with so many obfuscating and often outright wrong replies being given.
Post by: Dimensional on 23/01/2023 20:39:59
Imagine that someone was watching the clocks come together. It is a perfectly symmetrical situation. The observer is between the clocks at their meeting point. The clocks are on a collision course as they have the same velocity relative to the observer in the middle. The clocks are synchronized.They would tick at the same rate in the inertial frame in which that middle observer is stationary. They'd be synchronized only if they happen to read the same value simultaneously in that frame.
I agree. Let's say that is what happened.
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But when they meet, don't they have to have the same time if they synchronized correctly? In other words, the middle observer should always "see" their clocks as the same until they meet, right?QuoteIf I am correct, each clock will see the other ticking more slowly. How does this get resolved as they come together?It doesn't need resolution. Observers with both clocks will always compute (not see) the other ticking slower relative to their own frame. This doesn't change when they come together and part company again.
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What do you mean by "you" in the scenario? In the scenario there are the 2 clocks closing in on each other and an observer in the middle, which is the "you"?QuoteI am still a little foggy how the dilation no longer becomes dilation as the two clocks approach each other from the example above, but I will wait for your response.It never stops being dilation. The other clock is always moving at some speed relative to you, so it is dilated relative to you, before, during, and after it passes by.
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Yes, I agree. But I am not sure if this response agrees or not with what I said.QuoteI have learnt that when there is velocity/speed involved, the result is that both twins seem to undergo time dilation relative to the other (just like in the clock example). But this is telling me that the speed/velocity is not the reason for the change in aging.Differential again and time dilation are different things. The former is due to physically different path lengths. The latter due to abstract coordinate choices and speed relative to those choices.
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QuoteAnd regarding the path lengths, if I look at a simple spacetime diagram of the "instant-acceleration-version" of the twin paradox, I see that the stationary twin's worldline/path is straight up, and the travelling twin's makes a shape like this > only stretched out much more.That's right. It's because paper is Euclidean and cannot correctly represent spacetime which is not. The mathematics says the > path is shorter (because of the -x² instead of the +x² you get with Euclidean geometery), and the mathematics is what counts.
Yes, that I understand. Whatever other-worldly shape it actually is, it is not the straight vertical line that the other twin has, which seems to be due to the turn around. Do you agree?
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QuoteSo I am saying that the path length is what it is because the twin changes directions.In this case, but not necessarily so. I can have a twin with more direction changes and still have him come out older than another with less.
Okay, you agree, so for the sake of my side of the argument, let us just stick with this case in this part of the post and really try to nail down the exact "cause" of the differential aging.
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QuoteNow the question is, does "change directions" absolutely imply acceleration?To change your direction of nonzero motion, yes, that's acceleration. To just face/point a different way is to change direction without implying any acceleration, but I don't think you're talking about that.
Okay, that's what I was thinking too.
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QuoteSo I am saying that acceleration is the only reason for time dilation.Quote from: HalcThen you're not getting it.QuoteOh how frustrating, I meant to put, "So I am not saying ...". Sorry.But here you are asserting the same thing again:
No, it is not the same thing. The adjusted statement with the word "not" is very much different than the statement that I made by mistake.
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Well I am sorry you feel that way. I was trying to create a chain of logic that throughout my post that results in what I said.QuoteIf so, then I see no alternative than to say that the change in age is caused by acceleration.As I said before, I don't think I can help you further. I gave several examples contradicting this suggestion, and it seems pointless to post in a topic with so many obfuscating and often outright wrong replies being given.
Please tell me what I said that was wrong, and I will address it directly. And please tell me the contradictions that I did not address. I really want to understand this topic once and for all.
Post by: MikeFontenot on 23/01/2023 23:29:50
Can you please tell me why I am doing this?
So that you'll understand the twin paradox.
Post by: Halc on 24/01/2023 01:51:11
I agree. Let's say that is what happened.OK. We'll have clock coming from the left, one in the middle, and one coming from the right. We'll name the frames and the observers L, M, and R. Clocks L and R have been,
The L and M clocks, both equally dilated in the M frame, are synced relative to that M frame, so they'll always say the same thing at all times. They will still run slow since they're moving, just equally slow.
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But when they meet, don't they have to have the same time if they synchronized correctly?Yes to all.
In other words, the middle observer should always "see" their clocks as the same until they meet, right?
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What do you mean by "you" in the scenario?[/quote]You at say the L clock. Relative to frame L, the R clock is moving always, so it will always run slower than the clock by you. It passing you doesn't change that. It was an answer to the statement: "If I am correct, each clock will see the other ticking more slowly.".QuoteI am still a little foggy how the dilation no longer becomes dilation as the two clocks approach each other from the example above, but I will wait for your response.It never stops being dilation. The other clock is always moving at some speed relative to you, so it is dilated relative to you, before, during, and after it passes by.
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Yes, I agree. But I am not sure if this response agrees or not with what I said.[/quote]For the twins scenario, you can always compute it purely in terms of speeds. Pick any inertial frame, but stick with it for all calculations. No matter the frame chosen, the result (the differential ages) will always be the same. That's computing the differential aging via speed computations. It's quite simple and doesn't involve complicated Lorentz transforms.QuoteI have learnt that when there is velocity/speed involved, the result is that both twins seem to undergo time dilation relative to the other (just like in the clock example). But this is telling me that the speed/velocity is not the reason for the change in aging.Differential again and time dilation are different things. The former is due to physically different path lengths. The latter due to abstract coordinate choices and speed relative to those choices.
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Whatever other-worldly shape it actually is, it is not the straight vertical line that the other twin has, which seems to be due to the turn around. Do you agree?The bend to the line causes it to not be a straight line, yes. In this case, it's the only way they're going to meet again. You can construct scenarios where both lines bend, or with lots of bends, or with smooth curves instead of these brutal instant speed changes.
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Okay, you agree, so for the sake of my side of the argument, let us just stick with this case in this part of the post and really try to nail down the exact "cause" of the differential aging.You can say that the bends (the accelerations) cause the path length to change, and the shorter path length results in less duration than the straight path. You seem to really need accelerations to be a cause even though there's no function for acceleration to duration. It's not like you need to pass a college test. Sabine was wrong because people will generalize what she says and imply that clocks on Mercury run faster than on Earth because the proper acceleration is less on Mercury, but clocks there actually run slower. That's why I'm resisting coupling acceleration with 'causes the age difference.
Post by: Dimensional on 24/01/2023 04:38:09
For the twins scenario, you can always compute it purely in terms of speeds. Pick any inertial frame, but stick with it for all calculations. No matter the frame chosen, the result (the differential ages) will always be the same. That's computing the differential aging via speed computations. It's quite simple and doesn't involve complicated Lorentz transforms.
What formula are you referring to?
Sometimes math does not tell the whole story even though it is correct. For example, it may take 10 minutes for me to walk to a park and back. If I walked at constant speed, the math says that it takes 5 minutes to get there and 5 to get back, which gives the just of the story. But it did not mention anything about an acceleration at the turn-around. It's not really the part of the description that people want to know about.
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You can say that the bends (the accelerations) cause the path length to change, and the shorter path length results in less duration than the straight path.
So if acceleration can cause shorter temporal path lengths, and shorter path lengths can cause differential aging, then doesn't this mean that acceleration can cause differential aging?
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You seem to really need accelerations to be a cause even though there's no function for acceleration to duration. It's not like you need to pass a college test.
I don't need the cause to be acceleration; I just want to know what the cause is. I am only leaning towards acceleration because at the moment it makes the most sense to me.
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Sabine was wrong because people will generalize what she says and imply that clocks on Mercury run faster than on Earth because the proper acceleration is less on Mercury, but clocks there actually run slower. That's why I'm resisting coupling acceleration with 'causes the age difference.Yeah, I agree that she was definitely wrong about that.
Post by: Halc on 24/01/2023 12:21:14
I didn't mention a formula, but it was given before by ES:For the twins scenario, you can always compute it purely in terms of speeds. Pick any inertial frame, but stick with it for all calculations. No matter the frame chosen, the result (the differential ages) will always be the same. That's computing the differential aging via speed computations. It's quite simple and doesn't involve complicated Lorentz transforms.
What formula are you referring to?
Δτ =
For the very simple case of choosing Earth frame and having the traveler always traveling at some constant speed, this works out to Δτ =
You only have to do the tedious integration if the speed varies along the way, such as with any actual rocket.
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So if acceleration can cause shorter temporal path lengths, and shorter path lengths can cause differential aging, then doesn't this mean that acceleration can cause differential aging?Yes, you can say that, so long as you don't generalize 'can cause' to 'causes' since the following statements about differential aging are false:
1) The twin that has accelerated (or accelerated more) will be found younger.
2) If a differential age shows one twin to be younger, that twin must have accelerated.
Meanwhile, both those statements would be true if we substituted the bit about path lengths instead of the accelerations. It does happen to be true that in the typical twin scenario, the twin that has accelerated will be found younger.
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I don't need the cause to be acceleration; I just want to know what the cause is.You've been told that repeatedly, and you keep pushing back to accelerations. You don't accept the answers, which is admittedly hard to do when you have all these people giving different stories and all insisting on being the right one. The physicsforums members are more consistently knowledgeable and will downvote users that give wrong answers.
It's not much of a claim, but I know my relativity better than anyone on this forum with the possible exception of Janus. The guys on physicsforums are a different league of expert and can get into the exact language required, and tensor calculus, and all that.
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Yeah, I agree that she was definitely wrong about that.Which is horrible since she's very respected and shouldn't make such obvious mistakes like that. Does she invite peer review of her vids before publishing them?
Post by: Dimensional on 24/01/2023 15:13:08
I didn't mention a formula, but it was given before by ES:For the twins scenario, you can always compute it purely in terms of speeds. Pick any inertial frame, but stick with it for all calculations. No matter the frame chosen, the result (the differential ages) will always be the same. That's computing the differential aging via speed computations. It's quite simple and doesn't involve complicated Lorentz transforms.
What formula are you referring to?
Δτ =
For the very simple case of choosing Earth frame and having the traveler always traveling at some constant speed, this works out to Δτ =
You only have to do the tedious integration if the speed varies along the way, such as with any actual rocket.
Isn't this just for time dilation? What about the differential aging because that is what this is really about.
Math works, but it also needs proper context.
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QuoteSo if acceleration can cause shorter temporal path lengths, and shorter path lengths can cause differential aging, then doesn't this mean that acceleration can cause differential aging?Yes, you can say that, so long as you don't generalize 'can cause' to 'causes' since the following statements about differential aging are false:
1) The twin that has accelerated (or accelerated more) will be found younger.
2) If a differential age shows one twin to be younger, that twin must have accelerated.
Meanwhile, both those statements would be true if we substituted the bit about path lengths instead of the accelerations. It does happen to be true that in the typical twin scenario, the twin that has accelerated will be found younger.
I totally agree.
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QuoteI don't need the cause to be acceleration; I just want to know what the cause is.You've been told that repeatedly, and you keep pushing back to accelerations. You don't accept the answers,
That is because I have not been given a convincing argument. At this point in the discussion, please give your argument/s for how acceleration is not necessary in the case where the twin instantly accelerates in the turnaround.
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It's not much of a claim, but I know my relativity better than anyone on this forum with the possible exception of Janus. The guys on physicsforums are a different league of expert and can get into the exact language required, and tensor calculus, and all that.
Yes, but I think this topic is a little more controversial. Even though Sabine was incorrect about generalizing acceleration as a cause of time dilation the way she did, I find it impossible to pick apart her reasoning in the case of the turnaround in the twin paradox.
Post by: Halc on 24/01/2023 16:32:39
Isn't this just for time dilation? What about the differential aging because that is what this is really about.Yes, it is a dilation computation. If there are two paths delimited by the same two events, then it is also using those dilation equations to compute a differential age. If the delimiting events are not the same, then the calculation is still valid but it isn't a differential aging situation.
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At this point in the discussion, please give your argument/s for how acceleration is not necessary in the case where the twin instantly accelerates in the turnaround.Don't understand. You seem to be asking how acceleration is not necessary in a scenario with acceleration. If there wasn't acceleration, it would be a different scenario.
So tell me, using a simple geometric example. You have a paper with 2 dots on it. You draw several lines with meandering paths between the dots. What would you consider to be a convincing argument about what 'causes' one line to be longer than another? Maybe it's the amount of ink that causes the longer lines. It isn't the number of turns taken or how sharp or gradual those turns are. The turns are equivalent to accelerations. I personally don't see it as a causal situation at all. Some lines are just longer than others. A cause might be that you had an argument with your wife this morning and took out the frustration by scribbling one of the lines furiously. So as for the 'cause' of the twin scenario, it was the one twin's decision to make this trip that makes him younger than his sibling. See what I mean about 'cause' being sort of open to interpretation?
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Yes, but I think this topic is a little more controversial.No, it's actually kindergarten phase, a most simple situation that has been beaten to death over the decades and is only controversial to a novice because it grinds with the sort of Newtonian physics that seem more intuitive.
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Even though Sabine was incorrect about generalizing acceleration as a cause of time dilation the way she did, I find it impossible to pick apart her reasoning in the case of the turnaround in the twin paradox.Agree. Her mistake was generalizing it, asserting that all dilation and differential aging is due to acceleration, which contradicts the mathematics.
Post by: alancalverd on 24/01/2023 18:30:03
I don't need the cause to be acceleration; I just want to know what the cause is.The cause is relative velocity.
But you can't have a relative velocity between initially synchronised twins unless one of them accelerates: twins are conceived with zero relative velocity and generally reach maturity with v << c. If one becomes a pilot or an astronaut, the result of the Haefle-Keating experiment tells you exactly how much their ages will differ after each tour of duty.
Post by: Dimensional on 24/01/2023 20:26:53
Isn't this just for time dilation? What about the differential aging because that is what this is really about.Yes, it is a dilation computation. If there are two paths delimited by the same two events, then it is also using those dilation equations to compute a differential age. If the delimiting events are not the same, then the calculation is still valid but it isn't a differential aging situation.
I am not sure I am following. An event is just a point.
Let me try to "prove" it to you geometrically.
Imagine a 2d spacetime diagram (as you know time is the y axis, and x is the spatial axis). How can any 2 points horizontal with each other (in other words have the same time) have differential aging without a curve or bend?
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Don't understand. You seem to be asking how acceleration is not necessary in a scenario with acceleration. If there wasn't acceleration, it would be a different scenario.
So tell me, using a simple geometric example. You have a paper with 2 dots on it. You draw several lines with meandering paths between the dots. What would you consider to be a convincing argument about what 'causes' one line to be longer than another? Maybe it's the amount of ink that causes the longer lines. It isn't the number of turns taken or how sharp or gradual those turns are. The turns are equivalent to accelerations. I personally don't see it as a causal situation at all. Some lines are just longer than others. A cause might be that you had an argument with your wife this morning and took out the frustration by scribbling one of the lines furiously. So as for the 'cause' of the twin scenario, it was the one twin's decision to make this trip that makes him younger than his sibling. See what I mean about 'cause' being sort of open to interpretation?
Yes I understand. But we can say that cause should be the same for all observers as time passes (of course except in extreme cases in GR).
As for the "causes" like in the scenario you described, we should stay consistent with only fundamental physics/math terms if we can.
Post by: Halc on 24/01/2023 22:38:56
I am not sure I am following. An event is just a point.Prove what?
Let me try to "prove" it to you geometrically.
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Imagine a 2d spacetime diagram (as you know time is the y axis, and x is the spatial axis)x and t (ct techmically) axis since y is traditionally another spatial axis.
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How can any 2 points horizontal with each other (in other words have the same time) have differential aging without a curve or bend?Points in spacetime (events) don't age. If they did, they be a different point since they'd have a different t coordinate. Furthermore, two events at the same time are space-like separated. It is impossible to travel from one to the other since it would require you to do it in no time. All events at the beginning and end of scenarios like the twins scenario are time-like separated, meaning their coordinates differ more by ct than they do by x. So if the two events (ct, x) are at (0, 0) and (2, 1), something can travel between those if it moves at 0.5c. If the second event is at (2, 0) then the thing can stay stationary and get there, path length t = 2. The path length to the (2, 1) event is √(2² - 1²) = √3, shorter than the path to the (0,0) event.
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Yes I understand. But we can say that cause should be the same for all observers as time passes (of course except in extreme cases in GR).Sorry, but still have no idea what you mean by 'cause'. Differential aging is about geometry, not causation. Causation is not the same for everybody. I like vanilla for the flavor, the other guy picks it because he thinks the drips will not be as easily seen on his shirt. Same effect, different causes. This has nothing to do with Minkowskian geometry, where the mathematics accurately describes (doesn't cause) the ages the the twins at the reunion.
Post by: Janus on 25/01/2023 17:02:53
They would only be "at the same time" for one given inertial frame.
Imagine a 2d spacetime diagram (as you know time is the y axis, and x is the spatial axis). How can any 2 points horizontal with each other (in other words have the same time) have differential aging without a curve or bend?
Draw your two dots on sheet of paper, so that from your view, they are horizontal to each other. In this view vertical is the time axis and horizontal is the space axis.
Now rotate the paper. The time and space axis do not turn with the paper, but stay with your view of vertical and horizontal. This is the equivalent of viewing the events from a different inertial frame. The two dots are not horizontal to each other,and the events then represent do not happen at the same time for this inertial frame.
Post by: alancalverd on 26/01/2023 08:13:55
instantaneous velocity changeI must take issue with anyone who uses this phrase!
For any body with nonzero mass, an instantaneous velocity change requires the input of a finite quantity of energy (½m(Δv)²) in zero time, i.e infinite power. This implies that the laws of physics have been suspended, including those of relativity and time dilation. The subsequent analysis is therefore invalid.
Post by: Janus on 26/01/2023 15:57:12
The issue with considering "instantaneous velocity change" is that the magnitude of the acceleration becomes undefined.instantaneous velocity changeI must take issue with anyone who uses this phrase!
For any body with nonzero mass, an instantaneous velocity change requires the input of a finite quantity of energy (½m(Δv)²) in zero time, i.e infinite power. This implies that the laws of physics have been suspended, including those of relativity and time dilation. The subsequent analysis is therefore invalid.
v =at, so to find acceleration needed for a known change of v over a known period of t, you use a= v/t. but if t is zero, this is division by zero which is undefined. (not infinite).
Post by: alancalverd on 26/01/2023 17:31:55
v =at, so to find acceleration needed for a known change of v over a known period of t, you use a= v/t. but if t is zero, this is division by zero which is undefined. (not infinite).No. v = aΔt assuming constant a applied for a duration Δt or ∫adt if a is variable.
a = dv/dt at any time, including t = 0.
Post by: Dimensional on 26/01/2023 17:59:06
Ok, I understand.I am not sure I am following. An event is just a point.Prove what?
Let me try to "prove" it to you geometrically.QuoteImagine a 2d spacetime diagram (as you know time is the y axis, and x is the spatial axis)x and t (ct techmically) axis since y is traditionally another spatial axis.QuoteHow can any 2 points horizontal with each other (in other words have the same time) have differential aging without a curve or bend?Points in spacetime (events) don't age. If they did, they be a different point since they'd have a different t coordinate. Furthermore, two events at the same time are space-like separated. It is impossible to travel from one to the other since it would require you to do it in no time. All events at the beginning and end of scenarios like the twins scenario are time-like separated, meaning their coordinates differ more by ct than they do by x. So if the two events (ct, x) are at (0, 0) and (2, 1), something can travel between those if it moves at 0.5c. If the second event is at (2, 0) then the thing can stay stationary and get there, path length t = 2. The path length to the (2, 1) event is √(2² - 1²) = √3, shorter than the path to the (0,0) event.QuoteYes I understand. But we can say that cause should be the same for all observers as time passes (of course except in extreme cases in GR).Sorry, but still have no idea what you mean by 'cause'. Differential aging is about geometry, not causation. Causation is not the same for everybody. I like vanilla for the flavor, the other guy picks it because he thinks the drips will not be as easily seen on his shirt. Same effect, different causes. This has nothing to do with Minkowskian geometry, where the mathematics accurately describes (doesn't cause) the ages the the twins at the reunion.
After thinking about all of this for the past few days, I think I know why this topic is so unclear (at least for me).
In physics, we observe a quality of something, for example; mass, redness, or gravity. Then we try to quantify, relate, reduce them down to their simplest forms, predict, formulize, etc. Well with this situation, a velocity and a "turnaround" seems to be the necessary, and I think the minimum, that makes differential aging happen. The turnaround by itself (without acceleration if that even makes any sense) is not really quantifiable, so I don't think it can be a function of anything.
I am really trying to figure this out, but it seems like this is a different kind of physics problem than we are used to.
What do you think is minimally necessary for a twin to have differential aging, without gravity?
Post by: pzkpfw on 26/01/2023 19:19:14
Alice sits on her deck chair.
Bob zooms past Alice, away from Earth.
Bob later meets Carol, zooming towards Earth.
Carol eventually passes Alice too.
Nobody changes speed or direction at any time. No acceleration by anyone.
They all have perfect second-per-second timers (stopwatches).
When Bob passes Alice, they both start their timers.
When Bob passes Carol, he stops his timer, she starts hers.
When Carol passes Alice, they both stop their timers.
Some time later (experiment over) they get together and compare timers. Without relativity you'd expect Bob timer + Carol timer = Alice timer.
But they find Bob timer + Carol timer < Alice timer
(Essentially this is the instantaneous acceleration version of the twins paradox, but without the spherical cow.)
((In terms of your diagram in post #1, Alice's timer shows 10, Bob's and Carol's both show 4, adding to 8.))
Very very informally: when two observers are in relative motion, for both of them the others' time is slower. The "turnaround" has a sort of effect of picking up one of those "slower times" and bringing it to the other.
Post by: Zer0 on 26/01/2023 21:13:06
Perhaps it would be Best to just put a lifetime Space Travel Ban on any twins/triplets/quadruplets etc..
That would surely solve this problem once n for all & put an end to all this fuss!
Post by: Peter11 on 27/01/2023 15:14:12
Post by: alancalverd on 27/01/2023 17:32:11
For a fixed finite velocity change delta_v in a finite time delta_t, the energy required to make that happen is independent of delta_t ... i.e., it takes no more energy to change his velocity quickly (including instantaneously) than to change it slowly!Which is why I discussed power, not energy.
Post by: MikeFontenot on 27/01/2023 18:05:04
For a fixed finite velocity change delta_v in a finite time delta_t, the energy required to make that happen is independent of delta_t ... i.e., it takes no more energy to change his velocity quickly (including instantaneously) than to change it slowly!Which is why I discussed power, not energy.
The power DOES go to infinity as delta_t goes to zero. But that is not important. It just means that, if you were doing this experiment in a spaceship, doing a sequence of experiments with different amounts of thrust from your engine, but always making the velocity change be the same each time, you would find that no matter how quickly you make the velocity change, the amount of fuel you have to burn is the same in each experiment. As the time to make the velocity change decreases, you need to squirt more fuel into the engine per unit time (to get more thrust), but the total amount of fuel burned stays the same in each experiment.
You can never actually DO the experiment with the duration of thrust being infinitesimal, and the thrust being infinite. That limit is just a mathematical process that describes where your results are converging to as you keep repeating the experiments. You can't ever actually have an infinite acceleration with zero duration, but that limiting value is nevertheless a useful concept, and your experimental results can get arbitrarily close to the computed limit.
If you understand what Dirac did when he invented his "Dirac delta function", that's really all that's happening here. In the limit, our rocket power is described by a Dirac delta function, which gives a finite and constant result (the energy supplied) when integrated with respect to time.
Post by: alancalverd on 28/01/2023 11:21:10
The power DOES go to infinity as delta_t goes to zero. But that is not important.I rather think that it might be just a tad significant. We don't like singularities in physics, particularly those that prevent us from conducting an experiment.