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Old 18th August 2020, 09:41 AM   #281
Ziggurat
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Originally Posted by SDG View Post
This is very hard to understand.
I consider this as the stay home frame view but it does not make sense to me, what are the blue lines?
The time and space axes for the traveling twin after he has come to rest at the turnaround point P. His own position is x'=0, right? So we draw his time axis where he is, which is now shifted right from the starting point. He's not at t'=0, though, so we don't draw his space axis through his current position. Instead, we draw it backwards in time from where he is, using his current proper time. But since less proper time has elapsed for him than for the earthbound twin, his blue space axis is shifted up relative to the earthbound twin.

Quote:
How about to have the red timeline vertical, not under the angle.
Then we would need to tilt the black lines and the blue lines. And that's more complicated.

Quote:
Isn't it just one frame between A and P?
Yes: that's the red lines. But then you're back to a third frame for the traveling twin when he stops at P. He doesn't go back to the black frame. His frame is stationary compared to the black frame, but it isn't actually the same frame if you want him to STAY in his own frame. You can redefine his frame to the black frame if you want, but then you need to account for having done so, and all you're doing by that is sweeping the time difference under the rug.
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Last edited by Ziggurat; 18th August 2020 at 09:45 AM.
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Old 18th August 2020, 10:18 AM   #282
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Originally Posted by Ziggurat View Post
The time and space axes for the traveling twin after he has come to rest at the turnaround point P. His own position is x'=0, right? So we draw his time axis where he is, which is now shifted right from the starting point. He's not at t'=0, though, so we don't draw his space axis through his current position. Instead, we draw it backwards in time from where he is, using his current proper time. But since less proper time has elapsed for him than for the earthbound twin, his blue space axis is shifted up relative to the earthbound twin.
What are the coordinates of the blue x, t intersect in relation to red and black axis?
Black and red are inertial, correct?
I would assume black and blue x, t intersects are in the same position when the motion starts.
If this is a black frame view then the blue x, t intersect does not make sense.
No way there is a blue worldline looking like this in the black frame.
Accelerated worldline is not straight line, it is curved, if seen from the black stay home frame.

Quote:

Then we would need to tilt the black lines and the blue lines. And that's more complicated.
... and???
That's what I am getting at, show me, please, as I tried to show it to everybody.
Your diagram above is a no go from the start though.

Quote:

Yes: that's the red lines. But then you're back to a third frame for the traveling twin when he stops at P. He doesn't go back to the black frame. His frame is stationary compared to the black frame, but it isn't actually the same frame if you want him to STAY in his own frame. You can redefine his frame to the black frame if you want, but then you need to account for having done so, and all you're doing by that is sweeping the time difference under the rug.
How do we sweep it in the diagrams?

Last edited by SDG; 18th August 2020 at 10:19 AM.
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Old 18th August 2020, 10:33 AM   #283
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Originally Posted by SDG View Post
What are the coordinates of the blue x, t intersect in relation to red and black axis?
Black and red are inertial, correct?
Black, red and blue are all inertial..

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No way there is a blue worldline looking like this in the black frame.
These are axes, not worldlines. A worldline might follow one of the time axes for a segment, but the time axis is not the same as the worldline.

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Accelerated worldline is not straight line, it is curved, if seen from the black stay home frame.
We've been over why this doesn't matter.

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That's what I am getting at, show me, please, as I tried to show it to everybody.
I already showed the equivalent with my three panel diagram. Either you understand how you get from one to the other, or you don't.

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Your diagram above is a no go from the start though.
Meaning you can't understand it.

There's a limit to what I can do about that, though.

Quote:
How do we sweep it in the diagrams?
You don't. The diagram doesn't capture that change. You're just offsetting x' and t' when you do that. Which means that your proper time no longer matches your coordinate time. And that's OK, as long as you keep track of the difference.
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Old 18th August 2020, 10:37 AM   #284
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SDG, have you tried to just work out the problem using the equations instead of these diagrams? Perhaps it's the diagrams that are confusing you.
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Old 18th August 2020, 12:12 PM   #285
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Originally Posted by Ziggurat View Post
Black, red and blue are all inertial..



These are axes, not worldlines. A worldline might follow one of the time axes for a segment, but the time axis is not the same as the worldline.



We've been over why this doesn't matter.
The problem are the blue angled lines, those are not SR worldlines any more.



I already showed the equivalent with my three panel diagram. Either you understand how you get from one to the other, or you don't.



Meaning you can't understand it.

There's a limit to what I can do about that, though.



You don't. The diagram doesn't capture that change. You're just offsetting x' and t' when you do that. Which means that your proper time no longer matches your coordinate time. And that's OK, as long as you keep track of the difference.

So how is this:




That much different from the left part here?
Remember I show front and back world lines. The event B is the P event in the other diagram.
It is an average approximation of the acceleration/deceleration curved world line.





What about your take on the right side diagram?

Last edited by SDG; 18th August 2020 at 12:14 PM.
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Old 18th August 2020, 12:43 PM   #286
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Originally Posted by SDG View Post
So how is this:

http://www.internationalskeptics.com...bfdcebde8c.png


That much different from the left part here?
You're trying to make the traveling twin's world line into a coordinate axis. That makes those coordinates non-inertial, and you haven't accounted for that non-inertiality at all. I'm showing three different inertial frames. The traveling twin can switch which inertial frame he's using, but he never has to use a non-inertial frame. His world line is not a coordinate axis, but it follows different coordinate axes at different times.

Plus you've got extra lines that don't need to be in here, and you made your x and x' axes the same but they aren't.

Don't use non-inertial reference frames. You aren't even close to being able to comprehend them.

Quote:
What about your take on the right side diagram?
It's nonsense. It's completely wrong.
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Old 18th August 2020, 12:53 PM   #287
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Originally Posted by Ziggurat View Post
...

It's nonsense. It's completely wrong.
How would you create yours?
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Old 18th August 2020, 01:00 PM   #288
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Originally Posted by SDG View Post
This is the 'weirdness' of the relativity.
The traveling twin goes 1010 light years away.
Then he stops and the stayed home frame origin traveled 1010 light years in 90 years from travelers point of view.

Yes. And?

Queen seems to have been able to understand this (see the song "39"), and they were a rock band.
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Old 18th August 2020, 01:07 PM   #289
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Originally Posted by Ziggurat View Post
You're trying to make the traveling twin's world line into a coordinate axis. That makes those coordinates non-inertial, and you haven't accounted for that non-inertiality at all. I'm showing three different inertial frames. The traveling twin can switch which inertial frame he's using, but he never has to use a non-inertial frame. His world line is not a coordinate axis, but it follows different coordinate axes at different times.

Plus you've got extra lines that don't need to be in here, and you made your x and x' axes the same but they aren't.
...
What extra lines?
The x and x' axis have different origin. There is 0' right beneath the ct's axis to show the ct's axis position as you have it in yours.
Your diagram does not capture the original starting position of the x' axis as well.

Look, you have axes and I show the worldline 'jumping' along the axes.
Your diagram does not show when the motion starts, where is the acceleration, ...
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Old 18th August 2020, 01:24 PM   #290
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Originally Posted by Myriad View Post
Yes. And?

Queen seems to have been able to understand this (see the song "39"), and they were a rock band.
A rock band whose lead guitarist has a PhD in astrophysics, to be fair.
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Old 18th August 2020, 01:55 PM   #291
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Originally Posted by Pixel42 View Post
A rock band whose lead guitarist has a PhD in astrophysics, to be fair.
And kind of an Einstein hair vibe as well.
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Old 18th August 2020, 01:56 PM   #292
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Originally Posted by SDG View Post
Your diagram does not capture the original starting position of the x' axis as well.
You keep trying to use non-inertial reference frames. Stop doing that. x' is for the moving frame. It doesn't start anywhere other than where it's already drawn.
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Old 18th August 2020, 03:29 PM   #293
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Originally Posted by SDG View Post
Robin,
good honest statement.
Followed by the dishonesty of images from a textbook that you have obviously read, SDG, and are ignoring. Ditto for your next post.
The textbook makes the same point I made. The accelerations of the twins can be included in SR calculations as instantaneous accelerations of the traveling twin (O').
The dishonesty is that you have the textbook in front of you. You have basically the same scenario. Just put the twins on a platform and on a train. The diagrams and calculations are the ones you have just cited (missing out the return) !
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Old 18th August 2020, 03:36 PM   #294
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Originally Posted by SDG View Post
The only thing what I am trying to say that at the mid point P the twins are in the same frame.
They are.
So what does it mean?
The trouble with the simplified traveling twin point of view diagram.
That needs a well duh, SDG ! It means that they are moving with the same speed as in the definition of an inertial frame of reference. No problem there. With a "simplified" fantasy when both twins are being treated with textbook physics. Unless this is your irrelevant "simplified" diagrams?
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Old 18th August 2020, 03:47 PM   #295
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Originally Posted by SDG View Post
What is important is that before and after a/d they have the same size ruler.
You are wrong, SDG. The textbook SR you are ignoring says the twins always have the same size ruler. The physical length of an individual observer's ruler does not change.

What special relativity says is that their measurement of other lengths depends on their relative speed. This is called length contraction. The twins will measure that the other twin's ruler is the same length as their ruler at D and this is trivial.
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Old 18th August 2020, 03:53 PM   #296
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Originally Posted by SDG View Post
This is the 'weirdness' of the relativity.
That is the way the real universe works so it is not weird. Time dilation is fundamental and experimentally tested SR.
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Old 18th August 2020, 04:10 PM   #297
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Originally Posted by SDG View Post
What was this discussion about?
You treated the accelerated frames as inertial.
The image shows that this is an ignorant assertion. Ziggurat explicitly stated there was no acceleration during the leg. It was you, SDG, who wrote ignorance about the diagrams.
The twin paradox is an SR paradox and only has inertial frames of reference.
The twin paradox has a twin traveling at a constant speed outward from Earth and then returning at a constant speed. There is an instantaneous acceleration at the turnaround as in the textbook you are citing. There is no acceleration in any of the legs. Ditto for the twin leaving and arriving back at Earth.

Then we have the silliness of "miraculous instantaneous change of the frames" when this is textbook physics as above.

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Old 18th August 2020, 07:31 PM   #298
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To get this 8 seconds business into context note the x' coordinate for C

A=(0,0,0,0) A'=(0,0,0,0)

B=(4,3.464,0,0) B'=(2,0,0,0)

C=(4,0,0,0) C'=(8,-6.928,0,0)

In other words 8 seconds would be the time on the clock of a traveller that was going at 0.866c at t'=0 from a position 2 million kilometres away from.the twin's initial position.

What has that to do with either of the twins?
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Old 18th August 2020, 07:59 PM   #299
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I am so far from understanding this thread, but I'm loving it anyway.
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Old 18th August 2020, 09:20 PM   #300
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This still appears to be the best representation of the situation:

A is when the two twins are together with synchronised clocks and twin 2 accelerates off.
B is when twin 2 has decelerated until his velocity is the same as the original twin who hasn't moved
C is when the original twin looks at his clock and sees 4 seconds



If we were to try to show the situation where twin 2 experiences being stationary then the path for twin 1 would be greater than 45 degrees, not because he is travelling faster than light with respect to his twin, but because in that section the underlying geometry would no longer be Euclidean.

And there is no problem here, other than the difficulty of drawing non-Euclidean paths onto a Euclidean grid.
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Old 19th August 2020, 11:46 AM   #301
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Originally Posted by Ziggurat View Post
You keep trying to use non-inertial reference frames. Stop doing that. x' is for the moving frame. It doesn't start anywhere other than where it's already drawn.
Ziggurat,
here is the reciprocity of the Special Relativity in full glory:






It takes 4s' for the train car to cross 3.4641cs's of the train frame in regards to platform origin.
That's only 2s of the platform frame and the length contraction is inverted now.
That is based on the Lorentz transformation.

Why the crossing would take only 2s' when the acceleration is involved?




The right diagram is wrong.
This table is wrong.






How do we know that?
Because this table breaks the Equivalence Principle.
This makes the time dilation a function of the acceleration and HOW LONG is the acceleration applied.
The longer application of the 1g acceleration and the Lorentz factor is bigger.
We apply the 1g acceleration on a circle trajectory and the velocity is not increasing in magnitude, the Lorentz factor is not changing.
The above table contradicts the Lorentz factor that is a function of speed.

Last edited by SDG; 19th August 2020 at 11:50 AM.
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Old 19th August 2020, 12:02 PM   #302
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Originally Posted by SDG View Post
This table is wrong.


https://i.imgur.com/tzVytej.png



How do we know that?
Because this table breaks the Equivalence Principle.
This makes the time dilation a function of the acceleration and HOW LONG is the acceleration applied. The longer application of the 1g acceleration and the Lorentz factor is bigger.
Time dilation is a function of velocity. But velocity is a function of acceleration. So of course acceleration comes into play in that scenario.

Quote:
We apply the 1g acceleration on a circle trajectory and the velocity is not increasing in magnitude, the Lorentz factor is not changing.
Sure, but that's not the scenario that your source was considering. So that doesn't matter. For the scenario they were considering, the acceleration does change the magnitude of the velocity.

Quote:
The above table contradicts the Lorentz factor that is a function of speed.
No, actually, it doesn't, because again, speed in that scenario is a function of acceleration.
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Old 19th August 2020, 12:14 PM   #303
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Originally Posted by SDG View Post
This makes the time dilation a function of the acceleration and HOW LONG is the acceleration applied.

Uniform acceleration * how long the acceleration is applied = velocity.

Time dilation is a function of velocity.

Quote:
We apply the 1g acceleration on a circle trajectory and the velocity is not increasing in magnitude, the Lorentz factor is not changing.

The table you copied from a textbook applies to uniform acceleration, not centripetal acceleration.
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Old 19th August 2020, 03:27 PM   #304
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Originally Posted by SDG View Post
This table is wrong.


https://i.imgur.com/tzVytej.png



How do we know that?
Because this table breaks the Equivalence Principle.
This makes the time dilation a function of the acceleration and HOW LONG is the acceleration applied.
The longer application of the 1g acceleration and the Lorentz factor is bigger.
We apply the 1g acceleration on a circle trajectory and the velocity is not increasing in magnitude, the Lorentz factor is not changing.
The above table contradicts the Lorentz factor that is a function of speed.
I imagine the table is talking about acceleration on a single axis.

For a circular path you need two dimensions and a constantly changing acceleration, ie if you have a constant acceleration of 1g, in order to get a circular path you need to be constantly changing the unit direction vector.
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Old 19th August 2020, 03:28 PM   #305
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Originally Posted by SDG View Post
This table is wrong.
....
How do we know that?
Because this table breaks the Equivalence Principle.
We know that the table is correct because we can understand this physics in a physics textbook. Another display of ignorance does not make any textbook physics wrong, SDG.
  • The equivalence principle is general relativity, not the special relativity of the twin paradox.
    It is possible that the textbook applies GR to a constantly accelerating twin (as iin the table captions) but you neglected to include that part of the textbook.
  • The equivalence principle is not an arbitrary equivalence that someone comes up. It is an equivalence between gravitational and inertial mass.

Then the ignorance of "We apply the 1g acceleration on a circle trajectory and the velocity is not increasing in magnitude, the Lorentz factor is not changing". High school science students know that an acceleration changes velocity. The constantly accelerating twin constantly increases their velocity and thus the Lorenz factor constantly increases. Getting ever closer to the speed of light is why the time dilation is enormous.

ETA: As above, you snipped the preceding pages including the referenced equation 2:46. The table is on page 53. The previous pages from the textbook stopped at page 44. The table seems to just add a constant acceleration. So we do not have a "circle trajectory" we have a to and fro trip as in the normal twin paradox.
  1. The travelling twin accelerates away from Earth at 1 g.
  2. The travelling twin gets to a distance d and reverses their velocity. If they were going 0.9c away from Earth they are now going 0.9c toward Earth.
  3. The travelling twin accelerates toward Earth at 1 g.
  4. The travelling twin reaches Earth and comes to a stop with respect to the stay at home twin.
The twins now compare their ages. For d = 0.065 light years the stay at home twin has aged 1.01 years, the travelling twin 1 year. For d = 1.58 x 1011 light years. the stay at home twin has aged 3.15 x 1011 years, the travelling twin 100 years. This is what anyone who has read and understood a physics textbook expects. It is basic that if a constant velocity gives time dilation from the Lorentz equation then increasing that velocity will give a greater time dilation.

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Old 20th August 2020, 12:18 AM   #306
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Originally Posted by Ziggurat View Post
Time dilation is a function of velocity. But velocity is a function of acceleration. So of course acceleration comes into play in that scenario.
Well, my understanding stops a bit short of GR, as you well know, but I was under the impression that acceleration itself causes such effects too. After all, that's why you get red shift on the Hawking radiation, right?
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Old 20th August 2020, 12:26 AM   #307
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Originally Posted by HansMustermann View Post
Well, my understanding stops a bit short of GR, as you well know, but I was under the impression that acceleration itself causes such effects too.
Accelerating reference frames do all sorts of weird stuff. But if you're just talking about an accelerating object that you're observing from an inertial frame, then no, the acceleration doesn't enter directly into time dilation, but only through how it affects velocity. If you do the twin problem with the traveling twin going around in a circle and constant speed, you only need the speed, not the acceleration, to calculate the time dilation. So the traveler could go in one big loop with a small acceleration, or they could go in a bunch of small loops with a large acceleration, and only the speed will matter in the end.
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Old 20th August 2020, 12:47 AM   #308
HansMustermann
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Originally Posted by Ziggurat View Post
Accelerating reference frames do all sorts of weird stuff. But if you're just talking about an accelerating object that you're observing from an inertial frame, then no, the acceleration doesn't enter directly into time dilation, but only through how it affects velocity. If you do the twin problem with the traveling twin going around in a circle and constant speed, you only need the speed, not the acceleration, to calculate the time dilation. So the traveler could go in one big loop with a small acceleration, or they could go in a bunch of small loops with a large acceleration, and only the speed will matter in the end.
Well, yes, if the frame isn't accelerating, it's not GR. Even I can grok it that far. I was talking about the frame that is accelerating. The "paradox" isn't just about calculating it all from one frame, but about the difference in what the people in two different frames observe. If one of them is accelerating, so does their frame. (Well, chart.)
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Old 20th August 2020, 01:06 AM   #309
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This is the difference acceleration makes, as I see it.

If the twins begin at t=t'=0 and x=x'=0 and one twin is travelling away from the other at constant velocity, as though he was already moving when they were together then twin 1 can do the calculations and say "twin 2 is younger than me" and twin 2 can do the calculations and say "twin 1 is younger than me".

Once twin 2 accelerates then the situation is no longer symmetrical, both twins can no longer do the same calculations on each other. So now twin 1 does the calculations and says 'twin 2 is younger than me and twin 2 does the calculations and says 'twin 1 is older than me'
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Old 20th August 2020, 02:04 AM   #310
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Pretty much, yes. I was just getting at the fact that when one of them is actually accelerating, then one of the frames is no longer SR, and, in as much as I understand GR at all, some of the difference will be not just due to the speed at a particular moment, but also because of the acceleration at that particular moment.
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Old 20th August 2020, 04:06 AM   #311
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SDG - do you really think you have spotted something that literally generations of physicists and mathematicians have got wrong?
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Old 21st August 2020, 10:43 AM   #312
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Originally Posted by Ziggurat View Post
Time dilation is a function of velocity. But velocity is a function of acceleration. So of course acceleration comes into play in that scenario.



Sure, but that's not the scenario that your source was considering. So that doesn't matter. For the scenario they were considering, the acceleration does change the magnitude of the velocity.



No, actually, it doesn't, because again, speed in that scenario is a function of acceleration.



How do we settle the time of the traveling twin that stops?
Is it 4s' or 2s'?
I showed exactly why it is 4s'.
The times are identical considering we trust the idea of averaging the acceleration comoving frames.
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Old 21st August 2020, 10:52 AM   #313
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Originally Posted by SDG View Post
https://i.imgur.com/xpNOk1P.png



How do we settle the time of the traveling twin that stops?

Is it 4s' or 2s'?

I showed exactly why it is 4s'.

The times are identical considering we trust the idea of averaging the acceleration comoving frames.
By the way



Originally Posted by Darat View Post
SDG - do you really think you have spotted something that literally generations of physicists and mathematicians have got wrong?
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Old 21st August 2020, 11:05 AM   #314
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Originally Posted by Darat View Post
SDG - do you really think you have spotted something that literally generations of physicists and mathematicians have got wrong?
This is what I too struggle to understand about threads like this: how anyone can manage to convince themselves that one of science's most well established theories, which has been proved correct to the last decimal place the instruments are good for, is wrong in a way which they have managed to spot, but which humanity's best minds have somehow missed for over a century. Surely it's much more likely that the error is theirs? Yet time and again they come here, proudly displaying their ignorance and refusing to be taught.
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Old 21st August 2020, 11:11 AM   #315
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Originally Posted by SDG View Post
https://i.imgur.com/xpNOk1P.png

How do we settle the time of the traveling twin that stops?
Is it 4s' or 2s'?
It's 2, not 4.

Quote:
I showed exactly why it is 4s'.
No you didn't. You made a drawing which makes no sense.

Quote:
The times are identical considering we trust the idea of averaging the acceleration comoving frames.
What the hell does that mean, averaging the acceleration? Only one twin accelerated. Why would we average? That makes no sense.
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Old 21st August 2020, 11:18 AM   #316
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Originally Posted by Robin View Post
I imagine the table is talking about acceleration on a single axis.

For a circular path you need two dimensions and a constantly changing acceleration, ie if you have a constant acceleration of 1g, in order to get a circular path you need to be constantly changing the unit direction vector.
It is easy to show how to distinguish between linear and rotational acceleration.
An experiment can be done to detect that.
No signal from the outside is required to do so.
The gravitational acceleration is very much like the acceleration on a circle trajectory.
The distinction between the elevator standing on the Earth and the elevator linear acceleration can be done.
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Old 21st August 2020, 11:41 AM   #317
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Originally Posted by Ziggurat View Post
It's 2, not 4.



No you didn't. You made a drawing which makes no sense.



What the hell does that mean, averaging the acceleration? Only one twin accelerated. Why would we average? That makes no sense.





This is the view of comoving inertial observer with the traveling twin.



The blue time axis belongs to this comoving observer.
It takes 4s' for this comoving observer to cross 3.4641cs' between the A, P events.
Why would this be 2s' for the accelerated one?
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Old 21st August 2020, 12:11 PM   #318
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Originally Posted by Darat View Post
By the way
I posted questions.
Do you have some answers?
It is not important what I think in regards to your question.
Your question is off topic.
I am not going to discuss that.
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Old 21st August 2020, 12:33 PM   #319
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Originally Posted by SDG View Post
I posted questions.
Do you have some answers?
You have been given answers in this thread, and in previous ones. Your errors have been explained to you as simply as they can be explained. That you still do not understand how relativity works is your problem, and yours alone. Nobody here is under any obligation to educate you.
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Old 21st August 2020, 12:39 PM   #320
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Originally Posted by SDG View Post
The blue time axis belongs to this comoving observer.
It takes 4s' for this comoving observer to cross 3.4641cs' between the A, P events.
No it doesn't. What made you think it does?
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