[Dimensional (OP)]

I can't seem to wrap my head around why this twin paradox thought experiment fails. 

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.

[alancalverd]

The space twin has undergone acceleration, the earth twin has not.

Einstein did not overturn Newtonian physics, but built on it.

[Origin]

The diagram on the right shows the earth accelerating away from the twin in the space ship, since that clearly does not happen that diagram is not correct.  It is that simple.

[Janus]

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. 

[Dimensional (OP)]

Thank you for your replies.  They seem to be unanimous that acceleration is the reason.  I tend to agree.

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.

[Origin]

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.

[alancalverd]

Or maybe they don't!

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!

[Origin]

Or maybe they don't!

No, it's Dimensional's problem.  Everyone agrees that one twin must accelerate to a different reference frame.

[alancalverd]

But he said that

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.

[Dimensional (OP)]

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.

Then you must not have seen what they said.

[Dimensional (OP)]

But he said that

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.

Not necessarily, I am pretty sure they can synchronize clocks as one twin passes by the other.

[alancalverd]

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.

[Halc]

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 rate

That 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.

[alancalverd]

Quote from: Dimensional on Yesterday at 23:54:32
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.

Setting 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.

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".

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. 

[Janus]

It is important not to conflate "time dilation" with " The difference in accrued time"
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.

[MikeFontenot]

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.

[Halc]

Correcting Janus is a bit like critique of Sabine. I think there's some typos.

It is important not to conflate "time dilation" with " The difference in accrued time"
The first is the comparison of clock rates as made from one frame of reference at any particular point.

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.

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

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.

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.

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.

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.

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.

[Dimensional (OP)]

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)

Thanks, this is all very clear.  However, I am still not completely convinced for the following reason.

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")?

[Halc]

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.

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.

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.

[Dimensional (OP)]

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.

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?

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.

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?

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.