Twin paradox

[Dr Jekyll]

We are all familiar with the thought experiment of an astronaut going off somewhere at a high proportion of the speed of light, sufficient to cause noticeable time dilation, with the result that they are younger than their twin who stayed behind. Of course we also have the clocks that come back from orbit running a bit behind, proving the principle. But what's always puzzled me is from whose point of view the astronaut has travelled faster than the twin who stayed on earth. Surely from the astronaut's point of view the earth has gone off and returned at high speed so the ground based twin should be younger. It seems a totally symmetrical situation. I did wonder if it's something to do with the fact that the astronaut has turned round/reaccelerated.

I think I've asked this question on here a couple of times but not managed to put it very clearly, but now I've found what seems a plausible explanation.


https://www.scienceforums.net/topic/113821-the-log...

The point, if I understand it correctly, is that an astronaut will not only experience less time on the journey than a earth bound observer would measure, but they might in principle experience less time than light would take to make the journey. Since they couldn't possibly seem (to themselves) to be travelling faster than light, the time dilation is actually caused by relativity making the journey appear shorter than the earth bound observer thought it was. It isn't symmetrical because only one of them has experienced the contraction of distance.

[Mr Pointy]

Try these two videos:
https://www.youtube.com/watch?v=Bg9MVRQYmBQ
https://www.youtube.com/watch?v=0iJZ_QGMLD0

It's part of this series which is worth a watch - especially the bit around Loretz Transformations:
https://www.youtube.com/watch?v=1rLWVZVWfdY

[Kent Border Kenny]

There are several ways to look at the calculation, geometrically, or just via the maths, but the key point in each is that their two experiences differ. One had to experience acceleration to turn around and come back, and with whichever way you look at it, whichever frame you pick, or representation you use, he ends up being the one who aged less.

Geometrically you can draw their paths in spacetime (x axis is space, y is time) as lines. The stay at home one is a straight line, his position never changes. The other one draws two sides of a triangle, starting and ending at the start and end of the other line. The way the maths works out is that the longer path equates to the shorter elapsed time, and changing frame just rotates the picture that you have drawn. No matter which way you rotate it you don’t change which one had the longer path.

It shouldn’t really be described as a paradox, as it isn’t one.

[Clive Milk]

" Of course we also have the clocks that come back from orbit running a bit behind, proving the principle."

Even this is a simplistic view because a clock orbiting the earth might run faster depending on how it is orbiting.


An orbiting body around a sphere has two Einstein rules pertaining to it considering inertial frames of reference for the two bodies

1. Special relativity

2. General relativity.

Assuming the earth and an astronaut orbiting. If the astronaut was in a geostationary orbit above the position of the observer on earth than relative velocities would not apply and so special relativity would have no effect.

General relativity would still have an effect and as the observer on the earth would be in a greater gravitational field strength his "clock" would run slower than the orbiting astronaut. The person on the ground would age faster.

General and special relativity were both indicated by the Hafele–Keating experiment.

Of course these effects are rather minor, around a black hole with an accretion disk both special and general relativity take on a lot more importance.

[Clive Milk]

"The point, if I understand it correctly, is that an astronaut will not only experience less time on the journey than a earth bound observer would measure, but they might in principle experience less time than light would take to make the journey. Since they couldn't possibly seem (to themselves) to be travelling faster than light, the time dilation is actually caused by relativity making the journey appear shorter than the earth bound observer thought it was. It isn't symmetrical because only one of them has experienced the contraction of distance."

You can't use "appear" and "experience" as if it is some sort of mind thing.

If you planted a see in the spaceship, maybe a broad bean, it would still have grown bigger at the end of a relativistic journey, compared to one on earth.

[Dr Jekyll]

Clive Milk said:

"The point, if I understand it correctly, is that an astronaut will not only experience less time on the journey than a earth bound observer would measure, but they might in principle experience less time than light would take to make the journey. Since they couldn't possibly seem (to themselves) to be travelling faster than light, the time dilation is actually caused by relativity making the journey appear shorter than the earth bound observer thought it was. It isn't symmetrical because only one of them has experienced the contraction of distance."

You can't use "appear" and "experience" as if it is some sort of mind thing.

If you planted a see in the spaceship, maybe a broad bean, it would still have grown bigger at the end of a relativistic journey, compared to one on earth.

I'm not using the expressions as a 'mind thing'', it' just an easy way of referring to a different frame of reference.

[Kent Border Kenny]

Clive Milk said:

An orbiting body around a sphere has two Einstein rules pertaining to it considering inertial frames of reference for the two bodies

1. Special relativity

2. General relativity.

Assuming the earth and an astronaut orbiting. If the astronaut was in a geostationary orbit above the position of the observer on earth than relative velocities would not apply and so special relativity would have no effect.

This isn’t correct, there is no inertial frame in which both are stationary

[Jim1064]

Kent Border Kenny said:

There are several ways to look at the calculation, geometrically, or just via the maths, but the key point in each is that their two experiences differ. One had to experience acceleration to turn around and come back, and with whichever way you look at it, whichever frame you pick, or representation you use, he ends up being the one who aged less.

Geometrically you can draw their paths in spacetime (x axis is space, y is time) as lines. The stay at home one is a straight line, his position never changes. The other one draws two sides of a triangle, starting and ending at the start and end of the other line. The way the maths works out is that the longer path equates to the shorter elapsed time, and changing frame just rotates the picture that you have drawn. No matter which way you rotate it you don’t change which one had the longer path.

It shouldn’t really be described as a paradox, as it isn’t one.

^^^^ Yes. nicely explained!

[Clive Milk]

Kent Border Kenny said:

Clive Milk said:

An orbiting body around a sphere has two Einstein rules pertaining to it considering inertial frames of reference for the two bodies

1. Special relativity

2. General relativity.

Assuming the earth and an astronaut orbiting. If the astronaut was in a geostationary orbit above the position of the observer on earth than relative velocities would not apply and so special relativity would have no effect.

This isn’t correct, there is no inertial frame in which both are stationary

It is the relative velocity that is important here not that both have to be stationary. In fact, neither observer on earth or the orbiting observer are stationary in space time.

[Clive Milk]

Kent Border Kenny said:

One had to experience acceleration to turn around and come back, and with whichever way you look at it, whichever frame you pick, or representation you use, he ends up being the one who aged less.

The difference in aging here is not due to acceleration or "coming back ". Special relativity is only concerned with relative velocities.

Both could be travelling in the same direction parallel
to each other and the effect would still happen as long as the relative velocities are different.

General relativity describes acceleration effects.

Edited by Clive Milk on Saturday 2nd January 07:04

[Clive Milk]

Now lying in bed I am starting to doubt my own answer to the geostationary satellite because these are circular velocities, I will have to get out of bed later and check. Hopefully time will slow down before then though....

[LeoSayer]

The travelling twin ages less because he exists in two frames of reference (travelling away from earth and then returning) compared to one frame of reference for the non-travelling twin.

As described in the video below, this effect doesn't require acceleration to have occured.

https://www.youtube.com/watch?v=svwWKi9sSAA

[Kent Border Kenny]

Clive Milk said:

It is the relative velocity that is important here not that both have to be stationary. In fact, neither observer on earth or the orbiting observer are stationary in space time.

Relative velocity in an inertial frame. You can’t just throw in a rotating frame and then not correct for it. In either person’s rest frame the other one is accelerating, and as in the twins paradox, that acceleration matters.

[Kent Border Kenny]

Clive Milk said:

The difference in aging here is not due to acceleration or "coming back ". Special relativity is only concerned with relative velocities.

Both could be travelling in the same direction parallel
to each other and the effect would still happen as long as the relative velocities are different.

General relativity describes acceleration effects.

Edited by Clive Milk on Saturday 2nd January 07:04

If the only thing that mattered was relative velocity then the twin paradox would not work, and special relativity can handle accelerations, you just need to integrate the effects with respect to time.

I think that you are describing this in the simplified form that you’ll get in popular science books, so are oversimplifying. Your claim that one person orbiting another will not experience time dilation is not correct.

Edited to add a link to a page on special relativity in accelerating frames.

https://en.m.wikipedia.org/wiki/Acceleration_(spec...

Edited by Kent Border Kenny on Saturday 2nd January 11:19

[Kent Border Kenny]

LeoSayer said:

The travelling twin ages less because he exists in two frames of reference (travelling away from earth and then returning) compared to one frame of reference for the non-travelling twin.

As described in the video below, this effect doesn't require acceleration to have occured.

https://www.youtube.com/watch?v=svwWKi9sSAA

Saying that there is a change of rest frame and saying that there is acceleration are equivalent statements, one implies the other.

I’m not pulling this stuff out of my bottom, I’ve a doctorate in the subject.

[Gary C]

As said its all about the relative velocity and for me this helps

Person A travels at 2/3 speed of light towards Person B who is also travelling towards person A at 2/3 speed of light, this is observed by Person C who is at at the point they will meet.

What speed does Person A see Person B travelling towards them ?

From a simple calculation performed by Person C, they have a closing speed above the speed of light, but from Person A's perspective the relative speed between A and B is less than the speed of light as they experience a slower passage of time (relatively, of course)

I think I have that right

[Kent Border Kenny]

Gary C said:

As said its all about the relative velocity and for me this helpsght

Yes, that’s what you said, and I’m pointing out that that’s not correct. Both twins see the other as always moving at speed v relative to them, so if this was all that mattered then they would not have aged differently, each would see the other as being younger when they were back together, which is impossible, that’s why it’s referred to as a paradox.

The paradox is resolved by noting that one changed direction, meaning that they underwent an acceleration. If you believe that you can ignore this feature then what, in your scheme, accounts for the asymmetry?

You are also adding velocities incorrectly, and mixing this up with time dilation.

I’m not sure which text you used when you first covered this, but Halliday and Resnick’s Fundamentals of Physics covers it properly.

Edited by Kent Border Kenny on Saturday 2nd January 11:56

[Gary C]

Kent Border Kenny said:

Gary C said:

As said its all about the relative velocity and for me this helpsght

Yes, that’s what you said, and I’m pointing out that that’s not correct. Both twins see the other as always moving at speed v relative to them, so if this was all that mattered then they would not have aged differently, each would see the other as being younger when they were back together, which is impossible, that’s why it’s referred to as a paradox.

The paradox is resolved by noting that one changed direction, meaning that they underwent an acceleration. If you believe that you can ignore this feature then what, in your scheme, accounts for the asymmetry?

You are also adding velocities incorrectly, and mixing this up with time dilation.

I’m not sure which text you used when you first covered this, but Halliday and Resnick’s Fundamentals of Physics covers it properly.

Edited by Kent Border Kenny on Saturday 2nd January 11:56

Fair enough smartypants, I didn't say anything before so don't have a go at me.

[Esceptico]

Gary C said:

Fair enough smartypants, I didn't say anything before so don't have a go at me.

Fairly typical PH. Someone who really is an expert tells us how it is. People who are not experts “correct” them and then get shirty when their misunderstandings are pointed out!

[Kent Border Kenny]

Gary C said:

Fair enough smartypants, I didn't say anything before so don't have a go at me.

I don’t know why I bother. You posted something incorrect, someone with an actual doctorate in the subject politely pointed out why it was wrong, and you respond with an insult.

Do you not actually have any interest in the subject?