1

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 26/01/2023 17:59:06 »

I am not sure I am following.  An event is just a point.
Let me try to "prove" it to you geometrically.

Prove what?

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.

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.

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.

Ok, I understand.

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?

2

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« 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?

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.

3

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 24/01/2023 15:13:08 »

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?

I didn't mention a formula, but it was given before by ES:
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.

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.

I totally agree.

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,

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.

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.

4

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« 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.

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?

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.

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.

5

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 23/01/2023 23:52:07 »

Can you please tell me why I am doing this?

So that you'll understand the twin paradox.

What part don't I understand?

6

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 23/01/2023 22:49:26 »

Dimensional, start by determining the two twins' ages at the reunion, using ONLY the home twin's (her) conclusions.  Do the case where the speed used by him on both his outbound and inbound legs is 0.866 ly/y, so that gamma is the nice value 2.0.  And take the case where she says he gets to the turnaround when she is 40 years old.

Hint #1: Using the above information, determine how far away (in lightyears) the turnaround point is from her, according to her.

Hint #2:  Use this information that I provided in my last post:

"Any two inertial (i.e., non-accelerating) people, who are moving at a constant relative velocity, will each conclude that the other's age is changing more SLOWLY than their own age, by the factor 1/gamma.  For example, gamma is 2.0 when their relative velocity is 0.866 lightyears per year (ly/y).  This is true whether they are moving AWAY from each other, or TOWARD each other."

Can you please tell me why I am doing this?

7

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« 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.

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.

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?

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.

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"?

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.

Yes, I agree.  But I am not sure if this response agrees or not with what I said.

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.

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?

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.

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.
 

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.

Okay, that's what I was thinking too.

So I am saying that acceleration is the only reason for time dilation.

Then you're not getting it.

Oh 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.   

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.

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. 
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.

8

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« 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? 

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.

Ok, that is my understanding too. 

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).

Oh how frustrating, I meant to put, "So I am not saying ...".  Sorry.

I don't know if that counts as time dilation.

It exactly counts as dilation.

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.

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.

9

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 23/01/2023 01:44:13 »

I think the light is beginning to dawn!

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.

Yeah, good point!

10

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 22/01/2023 23:52:43 »

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".

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. 

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.

11

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« 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.

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.

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.

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.

There is acceleration in this case. It is the standard twins scenario, same story, different way of looking at it.[/quote]

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.

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.

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?

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.

I meant for my example with the two clocks.

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.

12

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« 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.

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.

13

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 22/01/2023 16:41:40 »

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")?

14

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 20/01/2023 23:54:32 »

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.

15

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 20/01/2023 23:50:53 »

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.

16

Physics, Astronomy & Cosmology / Re: Why does this twin paradox thought experiment fail for me?

« on: 19/01/2023 20:08:00 »

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.

17

Physics, Astronomy & Cosmology / Why does this twin paradox thought experiment fail for me?

« on: 19/01/2023 03:53:23 »

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.

18

Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« on: 13/01/2023 03:55:11 »

Hi.

     I'm concerned you might be adding a bit more confusion @Alanacalverd but there's every chance I'm also doing the same.
    When  @alancalverd    says something like "there is no relative velocity",   he means the velocity of one thing relative to the other thing was numerically 0.     Don't assume there was no relative velocity in any other sense,  there was one, there always is a velocity of one thing relative to another thing, it just is numerically 0 sometimes.

- - - - - - - - -

Do you know any math formulas to see how acceleration and time dilation are related?

      Yes.   It's in most textbooks.   Did you want to see it here?

Δt =   time elapsed for the twin remaining on earth  =   

[Eqn 1]

   
where  x_A = x co-ordinate position of Andromeda   and we have chosen the axis so that x=0 is where Earth is located;    v(t) = velocity of the traveller at time t  and we can assume  the position x(t) of the traveller is an invertible function of time so that we can express the time t as a function of the position,   t = t(x) because then v(t) = v(t(x)) can also be expressed as a function of x and then we can perform the integral appropriately.   (If the traveller wasn't always travelling away from earth but spent some time moving to/from it  like taking 2 steps forward with 1 step backward then we can't  invert the function x(t)  to find t(x)  but we can still perform the calculation - we would just break the integral into a sum of smaller sections where the traveller was always travelling in one direction on each section.   This is needlessly complicated, so in most simple treatments of the problem the traveller only ever moves in 1 direction along each leg of the journey and we only ever need to split it into two pieces, the outward journey and the return journey back to earth).

Meanwhile, the elapsed time for the travelling twin (who goes to Andromeda) is given by:

Δτ =   

[Eqn 2]

   That formula is based on using the proper time interval, dτ,  which will be the identical to the time elapsed on a clock that was moving with the traveller.

   Now, when we assume the speed v(t) was constant,  then the gamma factor γ(t) is also constant and can be taken outside the integral as a constant.    Ultimately we then have     Δτ  =   Δt / γ    as usual.

    If you want to know the difference between the elapsed times, then just subtract them.   Also, we have deliberately only looked at the outward journey.   The calculation for the return journey is much the same and indeed there is an obvious symmetry.   We would just add the times for the two sections together.  I'm sure you know that adding two things that are the same is equivalent to multiplying by 2.   So you should multiply  both  Δt    and   Δτ   by 2  if you want to consider the total elapsed time for the combined outward + return journey.

   Now the point that Don Lincoln was trying to communicate is that only  v(t) = velocity of the traveller   and  x_A = distance to Andromeda      appeared in the integrals and therefore influence the elapsed times, the acceleration does not directly appear.   However, it's a superficial comment.    v(t) is related to the acceleration, a(t) by the following:
  v(t) = v₀ +      

[Eqn 3]

    So the acceleration is there, it's just hidden in the assumptions about what v(t) is like.  (In the simplest situation the velocity is always kept constant).

   So we would just substitute  v(t) with that expression [Eqn 3] in the two formulae earlier [Eqn 1] and [Eqn 2].   It's obviously a bit messy but still useable.   

   For the purpose of getting the basic principles of  physics across, it's easier to assume a(t) is constant and especially easy if a(t) = 0 everywhere   (i.e.  to assume the traveller maintains constant speed except for a negligible and completely ignorable amount of time at Andromeda where they turn around and possibly at planet Earth if you want them to start and stop there.   So that is what is generally done.  However, if you must have a varying acceleration, a = a(t), then you can.

     Look, I don't know how to phrase this carefully:   Don Lincoln was just saying that acceleration doesn't appear in the usual formula for the twin paradox, which is true.  However, this is only because a simple pattern of movement is usually assumed, in particular the speed is constant everywhere except where the travelling twin is rapidly turned around at Andromeda, which is such a rapid turn around that it can be completely ignored.   He was also boosting or reinforcing the claim that general relativity was never required, which is also true.   
    You ( @Dimensional ) are just taking some bits of the video too literally and out of context.   Don Lincoln is not without fault here - he has promoted or up-sold his video with some short and snappy sounding phrases and it was too easy for a viewer to walk away with the wrong ideas.
    Take the phrasing at 4:25 which you point to in the broader context it was intended:   The time dilation isn't JUST happening at the time or place where the traveller experienced some acceleration (made the turn around Andromeda), it was happening somewhere or all the way through the journey.  This is why the things that are important and will affect the total time elapsed are  (i) the total distance travelled  and  (ii) the speed of travel during the whole journey.     The dilation happens everywhere along the journey.  Take a moment to let that sink in before you read the next paragraph.....
   Now, the time dilation was happening everywhere along the journey, however, there is still some discrepancy, some reason to explain why it wasn't happening exactly the same way to the twin who remained on Earth.   Recall that this is the fundamental issue in the twin paradox,  why can't we consider the situation as being perfectly symmetric (the travelling twin stayed still while the earth twin appeared to move away and come back).  Indeed, if you really do take the time and effort to study the paradox situation, then you will see that the travelling twin really does think that the clocks on planet Earth are ticking more slowly.  If nothing else happened then the travelling twin should have found that LESS time had elapsed for his Earth twin and not the MORE time which we know is the correct result.   There is a "discrepancy" of some sort.  It is the discrepancy in the elapsed times for the two twins which is explained by the acceleration that only one of them experienced around Andromeda.  When the travelling twin was abruptly shifted into a new rest frame, they "jumped tracks" or "skipped over some events for the earth twin".   Some moments of time that the twin on Earth would have experienced were skipped over.   Some events (which is a formal mathematical term, the nearest ordinary English language idea is to say those "moments of time at that place on earth") were in the travelling twins future (in the old rest frame) but they abruptly changed to being events that were in their past (in the new rest frame), they were never in their present or "now" , they were skipped over entirely.    Where you don't assume an instantaneous acceleration but just a very rapid one, then those events aren't completely skipped they are just very tightly compressed, they all occur over a very small time interval for the travelling twin.   
    I know that the idea of skipping over or missing out some events is difficult to get your head around.    LATE EDITING:  I can show you the maths but I reckon this post is long enough already.

    So I would say that Don Lincoln is mis-representing what many physicists think.  Those who have spent some time studying the problem know that "the discrepancy" in elapsed time happens because of the acceleration at Andromeda but they are well aware that it's not as if the time dilation effect was only happening during the acceleration.   It is impossible to say exactly "where" it was happening - some time dilation effect was happening everywhere along the journey but it wasn't a discrepancy in the right way (it would make the earth twin experience more time than the traveller), the major discrepancy (which does make the change in the right way) occurs at Andromeda where the traveller jumps rest frames with the result that some events the earth twin experiences are abruptly shifted from the travellers future into their past (skipped over).   That "discrepancy" is obviously due to the abrupt shift in rest frames, which is a consequence of an abrupt acceleration (no matter how hard Don Lincoln protests about it).   So, what I'm trying to say as politely as possible is that Don Lincoln has over-emphasised or over-sold something.  Many of the statements you have highlighted are just wrong IF you insist on taking them on their own, out of the general context, or as being more than just an impression or summary using English that is accessible to the general public.

Best Wishes.

Thank you very much, I think it makes sense now. 

19

Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« on: 13/01/2023 03:54:24 »

Time dilation requires (a) that two clocks were synchronised at some point and (b) that they are now moving relative to one another. Therefore one must have accelerated. Hence no paradox - you do something to a clock, and something changes. If you do nothing, they have no relative velocity and nothing changes.  If they were "always" moving relative to one another, you had no means of synchronising them.

I had the odd experience of hearing Hermann Bondi explaining this to Shirley Williams on a broken-down train one morning when both were famous and trains usually worked.

Thanks, I think I get it now.

20

Physics, Astronomy & Cosmology / Re: What is the exact cause of the time dilation of the twin?

« on: 12/01/2023 19:10:41 »

Thrown - acceleration. Change of velocity vector from one ship to another - acceleration. Acceleration is nothing more or less than a change of velocity: speed, direction or both.

If both clocks have the same velocity, there is no discrepancy between them (observed fact!).

Then this would mean that acceleration played a role in the time dilation.  Do you know any math formulas to see how acceleration and time dilation are related?  A possible problem might be that acceleration is infinite using,   
a = (vf - vi)/t