Relativity & Twins: What Happens When Two Move Away & Return?

[Tim Edilation]

I am new to relativity, believe I have a grasp on some key points. I get that the twin that accelerated away, came back had a slower running clock...but...

I was thinking about two other people (twins not required) who from point A both accelerate evenly away, one to the 'left' , the other to the 'right' for some period, then return back to point A symmetrically.

We are told that both would 'observe' the other's clock to tick 'slower' both while moving apart and while coming back together as the other is moving relatively.

I can't get my head around the surprising looks that each have when they find out that the other's clock reads the same as theirs ? or does it ? What am I missing ? (something simple I assume) but I'm stumped...

 

[JesseM]

We are told that both would 'observe' the other's clock to tick 'slower' both while moving apart and while coming back together as the other is moving relatively.

That's not correct--only inertial observers are supposed to "observer" that clocks in motion relative to themselves run slow (as measured in their own rest frame), the same does not apply to accelerating observers.

 

[Tim Edilation]

That's not correct--only inertial observers are supposed to "observer" that clocks in motion relative to themselves run slow (as measured in their own rest frame), the same does not apply to accelerating observers.

Sorry, I shoud have said they accelerated 'briefly' then were not under acceleration just moved for say a year in opposite directions, then acclerated briefly and came back. During the whole 2 year period apart from brief acceleration did they not 'observe' the other's clock as running slower ?

 

[JesseM]

Sorry, I shoud have said they accelerated 'briefly' then were not under acceleration just moved for say a year in opposite directions, then acclerated briefly and came back. During the whole 2 year period apart from brief acceleration did they not 'observe' the other's clock as running slower ?

During the period where they were moving apart inertially, each observed the other to be aging more slowly in their own inertial rest frame during that period. And during the period where they were coming back towards each other inertially, they each observed the other to be aging more slowly in their own (different) inertial rest frame during that period. But because of the relativity of simultaneity, no matter how brief the acceleration, there will be a major difference between (age of other twin in my current inertial rest frame immediately before accelerating) and (age of other twin in my current inertial rest frame immediately after finishing accelerating). For example, if you and I move apart with a relative velocity of 0.8c for 10 years according to our own clocks, and then instantaneously accelerate so we're moving towards each other with a relative velocity of 0.8c for another 10 years according to our own clocks, then in my rest frame during the outbound phase, immediately before the acceleration I have aged 10 years but you only have only aged 6 years, but then in my rest frame during the inbound phase, immediately after the acceleration I am still 10 years older than when we departed but you are now 14 years older than when we departed, and in the next 10 years you will age another 6 years in this second inertial frame, so you'll be 20 when we reunite and I'll be 20 too. Ages never "jump" like this in any single inertial frame, but here you are trying to switch from one inertial frame to a different one midway through the trip, and the different frames define "simultaneity" differently so they disagree about what event on your worldline was simultaneous with the event of my instantaneous acceleration.

The twin paradox page has a similar analysis based on simultaneity (though of course they are analyzing a situation where only one of the twins accelerates), in the time gap objection section, and in the too many analyses they have a helpful diagram:

If you aren't already familiar with the "relativity of simultaneity", it's important to learn, as almost all the "paradoxes" people come up with in special relativity are based on a failure to understand this notion. The wiki page I linked to above has a basic intro, as does this page. You might also take a look at the various introductions I listed on this thread.

 

[John232]

I have wondered if the relativity of simultaneity has anything to do with quantum uncertainty. The more you try to measure the speed the less you know about the position at a certain time. If different observers measured the exact speed they may find it to be in different positions because of the light postulate that every observer measures it to travel at the same speed.

The observer moveing with the emmitter could find the photon to be at a different position than the observer that is not at a particular moment in time. Then the exact location could turn out to be a little fuzzy...

If you where to track the position of a photon relative to two observers at the same time just useing ct and they expereinced different amounts of time the the distance traveled would be different for each observer, right?

If the beam was seen to be shot at an angle then each observer could measure the photon to be at the same position since one observer would see it travel a greater distance if it was sent perpendicular to the direction of motion. The added foward velocity (not speed) would allow it to cover a greater distance in one frame of reference.

There could be differences in the observed photon due to direction of motion relative to the moving object. I find it hard to see how spacetime dilation alone can account for a forward and backward moveing photon traveling with an observer. Lenght contraction would shorten the traveling distance for the photon traveling along with a ship and in the reverse direction. The shorter distance alone couldn't account for each showing the same measurement due to their direction of motion. Unless, the added or shortened distance created due to its velocity was proportial to the length contraction so that the added or shorted distance due to its velocity couterbalanced the extra or shorter distance traveled from the ships forward velocity.

 

[Mike_Fontenot]

[...]
I was thinking about two other people (twins not required) who from point A both accelerate evenly away, one to the 'left' , the other to the 'right' for some period, then return back to point A symmetrically.

We are told that both would 'observe' the other's clock to tick 'slower' both while moving apart and while coming back together as the other is moving relatively.

I can't get my head around the surprising looks that each have when they find out that the other's clock reads the same as theirs ? or does it ? What am I missing ? (something simple I assume) but I'm stumped...

You are asking good questions.

Whenever a traveler (who might be unaccelerated almost all of the time) suddenly changes his velocity, he will conclude that the age of a distant person (who is located along his direction of motion) suddenly changes (by a large amount, if the distance is large). If the acceleration is TOWARD the distant person, that person will suddenly get older (according to the traveler). If the acceleration is AWAY FROM the distant person, that person will suddenly get younger (according to the traveler). (The distant person's perception of the progression of her own age is of course unaffected by the accelerations of anyone else).

The total of the age changes of the distant person during the traveler's accelerations, added to the total age change of the distant person during the traveler's unaccelerated segments (given by the well-known time-dilation result), will always agree with what the traveler sees with his own eyes, when and if he is ever co-located with that distant person in the future.

The links below describe how those sudden age changes can be easily calculated, in the case where the distant person is perpetually inertial:

https://www.physicsforums.com/showpost.php?p=2923277&postcount=1

https://www.physicsforums.com/showpost.php?p=2957404&postcount=5 .

Mike Fontenot

 

[JesseM]

Whenever a traveler (who might be unaccelerated almost all of the time) suddenly changes his velocity, he will conclude that the age of a distant person (who is located along his direction of motion) suddenly changes (by a large amount, if the distance is large).

As always, Mike's comments are a bit misleading. This is not any sort of basic physical truth, but only a fact about what the traveler concludes if he is committed to using a particular type of non-inertial coordinate system, namely one whose judgment about simultaneity at each instant always matches the definition of simultaneity in the travelers' instantaneous inertial rest frame at that instant. Other types of non-inertial frames which don't have this property are also possible, and there is no compelling physical reason to see anyone non-inertial frame's conclusions as more "real" than any other, it's just a question of convenience.

 

[Tim Edilation]

[QUOTE

If you aren't already familiar with the "relativity of simultaneity", it's important to learn, as almost all the "paradoxes" people come up with in special relativity are based on a failure to understand this notion. The wiki page I linked to above has a basic intro, as does this page. You might also take a look at the various introductions I listed on this thread.[/QUOTE]


Thank you very much..Sorry I couldn't respond quicker, was out... Thank you for responding.

 

[Tim Edilation]

If you aren't already familiar with the "relativity of simultaneity", it's important to learn, as almost all the "paradoxes" people come up with in special relativity are based on a failure to understand this notion. The wiki page I linked to above has a basic intro, as does this page. You might also take a look at the various introductions I listed on this thread.

Thank you very much..Sorry I couldn't respond quicker, was out... Thank you for responding.