The Twin Paradox & Frame of Reference

[dr_mabeuse]

I'm sure there's an easy answer to this, but it's bothered me for a while. It's about the Twin Paradox.

 

So Allen stays on earth while twin brother Bob roars off in a space ship to some distant star at a significant fraction of the speed of light. Bob reached his destination and completes his business, then roars back to earth again at again, some near-light speed.

 

When the brothers finally meet back up on earth again, Bob is significantly younger than Allen. Bob's near-c velocity has slowed time for him compared to what Allen experienced.

 

That's how I understand the Twin Paradox.

 

But-- All things being relative, couldn't we just as easily look at this as Bob's space ship sitting stationary while the earth, Allen, and the whole universe rushes past Bob at near-light speeds? In that case, isn't it Allen who's traveling at near-c speeds, and Allen who would come back younger than Bob?

 

Obviously, Bob can't be both older and younger than Allen. Where did I go wrong?

Edited July 3, 2016 by dr_mabeuse

[Janus]

The difference between the two is that Bob and his space ship have to undergo a acceleration at his destination in order for Allen and Bob to meet again and Allen does not. So while on the outbound and return legs of the trip Bob can say that Allen ages slower than he does, During while he is accelerating, he can't. During this time (while he is slowing down to stop at his destination and then accelerate back towards Earth, Allen, according to Bob, ages much faster than he does. How much faster depends on the magnitude of the acceleration and the distance to Earth.

So according to Bob, Allen ages slower than he does for the first part of the trip, ages much faster during the "turnaround" part of the trip, and then ages slower again during the return trip, with the total amount that Allen ages being more than what he himself ages.

[mathematic]

Acceleration ca be ignored as such. The key point is that Bob has to change from Alan's frame to the space ship, then stop (switch frame) get on spaceship for return (switch frame), and then stop (switch frame). During the two spaceship legs, time is moving much slower than the stopped legs.

[pzkpfw]

But-- All things being relative, couldn't we just as easily look at this as Bob's space ship sitting stationary while the earth, Allen, and the whole universe rushes past Bob at near-light speeds? In that case, isn't it Allen who's traveling at near-c speeds, and Allen who would come back younger than Bob?

The above answers are good, I'll just point that that's why the word "paradox" appears in "twins paradox". At first glance symmetry would seem to mean there shouldn't be an age difference - but in fact the situation isn't symmetric.

[granpa]

I'm sure there's an easy answer to this, but it's bothered me for a while. It's about the Twin Paradox.

 

So Allen stays on earth while twin brother Bob roars off in a space ship to some distant star at a significant fraction of the speed of light. Bob reached his destination and completes his business, then roars back to earth again at again, some near-light speed.

 

When the brothers finally meet back up on earth again, Bob is significantly younger than Allen. Bob's near-c velocity has slowed time for him compared to what Allen experienced.

 

That's how I understand the Twin Paradox.

 

But-- All things being relative, couldn't we just as easily look at this as Bob's space ship sitting stationary while the earth, Allen, and the whole universe rushes past Bob at near-light speeds? In that case, isn't it Allen who's traveling at near-c speeds, and Allen who would come back younger than Bob?

 

Obviously, Bob can't be both older and younger than Allen. Where did I go wrong?

[TakenItSeriously]

The traveler's distance covered when traveling to a distant planet and back again was shorter due to length contraction. than the observer witnessed back on earth. He could only observe the traveler covering the entire distance which would take longer, thus explaining the asymetrical results of time experienced by the twins due to an asymetrical experiences of distance traveled by one twin and witnessed differently by the other twin.

 

If you wish, I have a proof written up to show the numbers balance but it's pretty long.

 

BTW I believe you could provide the same arguement to show why distance appears to be expanding across the universe. In that case we would be the ones moving at relativistic speed Away from observers at the far end of the universe, so we would be experiencing length expansion, but It doesnt actually serve as a proof, I think, so much as an out to avoid the need out to avoid the need for dark energy since the observers never actually meet.

Edited July 4, 2016 by TakenItSeriously

[michel123456]

I'm sure there's an easy answer to this, but it's bothered me for a while. It's about the Twin Paradox.

 

So Allen stays on earth while twin brother Bob roars off in a space ship to some distant star at a significant fraction of the speed of light. Bob reached his destination and completes his business, then roars back to earth again at again, some near-light speed.

 

When the brothers finally meet back up on earth again, Bob is significantly younger than Allen. Bob's near-c velocity has slowed time for him compared to what Allen experienced.

 

That's how I understand the Twin Paradox.

 

But-- All things being relative, couldn't we just as easily look at this as Bob's space ship sitting stationary while the earth, Allen, and the whole universe rushes past Bob at near-light speeds? In that case, isn't it Allen who's traveling at near-c speeds, and Allen who would come back younger than Bob?

 

Obviously, Bob can't be both older and younger than Allen. Where did I go wrong?

That is the reason why it is called a paradox.

A paradox appears when contrary results occur from a same situation.

The paradox is solved when one explains that B is younger than A. It becomes simply an unexpected result of Relativity.

[swansont]

 

 

Clocks ran backward?

That is the reason why it is called a paradox.

A paradox appears when contrary results occur from a same situation.

The paradox is solved when one explains that B is younger than A. It becomes simply an unexpected result of Relativity.

 

It's a result of not initially noticing that one of the assumptions of relativity was not in place — observers are assumed to be in inertial frames.

[granpa]

You didnt know that?

[swansont]

You didnt know that?

 

 

Didn't know that clocks ran backwards? No, that's news to me. Can you back this claim up? I'd like to know how someone else accelerating can make my clock run backwards. Or even run backwards as seen by the accelerating clock.

[granpa]

Some of the clocks run backwards from the point of view of the accelerating rocket

Consider what happens to a clock very very far away from the accelerating rocket

The further away the clock is the more out of sync it becomes

Edited July 4, 2016 by granpa

[Delta1212]

Some of the clocks run backwards from the point of view of the accelerating rocket

Consider what happens to a clock very very far away from the accelerating rocket

The further away the clock is the more out of sync it becomes

It slows down, yes. Under what circumstances does it run backwards?

[granpa]

Consider what happens to a clock very very far away from the accelerating rocket

The further away the clock is the more out of sync it becomes

[Strange]

But under what circumstances does it run backwards?

[granpa]

Consider what happens to a clock very very far away from the accelerating rocket

The further away the clock is the more out of sync it becomes

 

consider what happens during the acceleration from the Rockets point of view. What time does the clock start with. What time does the clock end with

Edited July 4, 2016 by granpa

[Strange]

consider what happens during the acceleration from the Rockets point of view. What time does the clock start with. What time does the clock end with

 

Without more information, it is not possible to answer this. But I'm assuming the latter time is later than the first. But please show a worked example if I am wrong.

[granpa]

Okay so it's later. Now reverse the process. Put the brakes on the rocket and what happens then?

[Strange]

Okay so it's later. Now reverse the process. Put the brakes on the rocket and what happens then?

 

You tell me. I assume the clock will continue to run forward. But please show a worked example if I am wrong.

[granpa]

https://www.quora.com/What-is-the-Andromeda-paradox

https://en.m.wikibooks.org/wiki/Special_Relativity/Simultaneity,_time_dilation_and_length_contraction#The_Andromeda_Paradox

https://en.wikipedia.org/wiki/RietdijkPutnam_argument

Edited July 4, 2016 by granpa

[Strange]

https://www.quora.com/What-is-the-Andromeda-paradox

https://en.m.wikibooks.org/wiki/Special_Relativity/Simultaneity,_time_dilation_and_length_contraction#The_Andromeda_Paradox

 

How is that relevant?

[granpa]

 

Notice that neither observer can actually "see" what is happening on Andromeda now. The argument is not about what can be "seen", it is purely about what different observers consider to be contained in their instantaneous present moment. The two observers observe the same, two million year old events in their telescopes but the moving observer must assume that events at the present moment on Andromeda are a day or two in advance of those in the present moment of the stationary observer.

 

So when I start moving (in the right direction) my calculation of the time on Andromeda moves forward a few days and when I stop moving it moves backward a few days

Edited July 4, 2016 by granpa

[MigL]

A clock will move faster or slower WITH RESPECT to another clock, giving the APPEARANCE of having moved backwards.

No clock will ever move backwards.

As a matter of fact, any SINGLE clock ( without comparison to another frame ) will only ever measure 'regular' time.

Edited July 4, 2016 by MigL

[Delta1212]

But you will not actually see any clocks run backwards. What you are doing is calculating what time you will eventually see on the clock after some x period of time has passed, and you will get different values depending on what speed you are traveling at. You can switch back and forth between frames and so get an "earlier time" than the one you would have gotten before switching frames, but that earlier time will still be a time after the time you are currently seeing on the distant clock. The Andromeda paradox is an artifact of trying to calculate a universal "now" that is shared with a distant location, which you cannot do because of relativity of simultaneity.

 

You will never actually observe a clock running backwards.

[granpa]

Hence "from the rockets point of view"

[Strange]

.

Edited July 4, 2016 by Strange