Twin Paradox Resolution -- Inertial frames

[Charles Carter]

Thinking and reading about the twin paradox recently, I encounter a lot of explanations and resolutions that don't make sense to me.
At its most basic, the issue is- when two bodies are in different frames of reference, why shouldn't relativistic effects affect both equally, negating time dilation, length contraction, etc for one inertial frame compared to the other? (Note that as usually formulated, the twin paradox includes the round trip. But if a round trip is required, that implies no relativistic effects on the outgoing trip, which is not the case.)
That said, the resolution of the 'paradox' is solely that the origin and destination are in the same inertial frame. If desired, I will elaborate.
Has this never been posited? It seems the only solution.
I think asking a related but different question sheds a little light on this-
Imagine each twin boards a ship and travels in opposite directions at identical speeds to equidistant destinations. (Imagine a return trip if you want.) The relativistic effects on each will be equal and the twins remain the same age, though they age less than someone remaining at their origin.

 

[Orodruin]

At its most basic, the issue is- when two bodies are in different frames of reference

Objects do not "belong" to any particular frame of reference. All objects can be described using any reference frame.

But if a round trip is required, that implies no relativistic effects on the outgoing trip, which is not the case.)

No, you got this wrong. If there is no reunion, then there is no way to uniquely compare the clocks because of the relativity of simultaneity. Both observers will then think that the other's clock is running slower and there is no contradiction here, just the fact that the observers do not agree on what "simultaneous" means.

 

[Dale]

At its most basic, the issue is- when two bodies are in different frames of reference

Hi Charles Carter, welcome to PF!

Although it is unfortunately common, I believe that you may have fallen prey to bad terminology. Two bodies cannot be "in different frames of reference", they can only be "at rest in different frames of reference". Every body is in every frame of reference. They may be at rest in or moving in any given frame, but either way they are in it.

 

[Charles Carter]

Objects do not "belong" to any particular frame of reference. All objects can be described using any reference frame.No, you got this wrong. If there is no reunion, then there is no way to uniquely compare the clocks because of the relativity of simultaneity. Both observers will then think that the other's clock is running slower and there is no contradiction here, just the fact that the observers do not agree on what "simultaneous" means.

Very easy to work around. The traveling twin carries a stopwatch. At any point it can be carried back to the origin of the trip. Meanwhile an EM signal sent to the origin can be used to indicate the time of arrival, calculated by c and the known distance.
Were a third observer present, in motion relative to both our traveler and her destination, simultaneity would be an issue.
Or do you believe time dilation can only be observed and measured with a round trip?

 

[Charles Carter]

Hi Charles Carter, welcome to PF!

Although it is unfortunately common, I believe that you may have fallen prey to bad terminology. Two bodies cannot be "in different frames of reference", they can only be "at rest in different frames of reference". Every body is in every frame of reference. They may be at rest in or moving in any given frame, but either way they are in it.

Dale and Orodruin are of course correct.
So - ... when two bodies are at rest in different inertial frames of reference...
Perhaps I should re-phrase in terms of bodies at rest relatively as opposed to not.
Your concern with my phrasing, which should be more precise, doesn't pose a substantive problem for the concept in my post.

 

[Dale]

Your concern with my phrasing, which should be more precise, doesn't pose a substantive problem for the concept in my post.

Hmm, I don't see it. Given the phrasing problem it is hard to see what is meant by this:

the resolution of the 'paradox' is solely that the origin and destination are in the same inertial frame

There just isn't anything substantive left if you remove that. And instead of removing it, if you change it to "the origin and the destination are at rest in the same inertial frame" then it becomes false.

 

[Charles Carter]

I feel you are simply dismissive of this notion out of hand. What becomes false?The origin and the destination are at rest with respect to each other. Neither is at rest with respect to the traveler.
Of other arguments for asymmetry, I am unconvinced.
For reasons in my original post, I am not convinced that a round trip is required. Even so, if a round trip, how does one assign velocity and direction to the traveler as opposed to the origin or destination? They are still moving relative to each other. Acceleration is simply not required- a simple but equivalent reconstruction with clocks, two spaceships and radio at km distances should demonstrate the same effect. And I find it hard to believe general relativity is required as I believe Einstein used this example to demonstrate SR (a weak reason, yes). Discussions of Doppler effects, monthly EM emissions from the origin &/or traveler seem to me descriptive enough but do not really explain why the effect occurs- some come very close to suggesting that all the time dilation occurs on the return only.
I'll take some time to see if I can develop the idea a little further. I was actually hoping to find help with that here, but you don't seem interested. (Sorry, but concern with semantics and your dismissal as false the latter assertion, perhaps poorly worded, suggest to me you are mostly interested in easy discouragement and facile refutation.) I perceive some potential problems myself but was hoping for feedback based on actual examination of the idea.

 

[Mister T]

For reasons in my original post, I am not convinced that a round trip is required.

Required for what? It's not clear what it is you're trying to demonstrate.

You have two clocks located in the same place at the same time and you set them both to read zero, then you separate them for awhile, then you reunite them and compare their readings. They will either match or they won't. Under what conditions will they match and under what conditions will they not match?

If they have symmetrical experiences then their readings will match, but if they have asymmetrical experiences then their readings will not match.

Scenario A: As in the example you gave, they move away from each other for awhile, then they both turn around and come back to reunite in a symmetrical way. Upon reuniting they find that the clock readings match.

Scenario B: As in the example you read about, only one of them turns around before reuniting. Then the clock readings don't match.

There are lots of ways to demonstrate that Scenarios A and B are physically different. In Scenario A neither clock is inertial for the entire duration. In Scenario B only one of the clocks is inertial for the entire duration. (Inertial means at rest, or equivalently, moves in a straight line at a steady speed.)

You do not need general relativity to analyze the noninertial motion. Thinking that you do is an all too common misconception, found unfortunately in many textbooks and other publications.

 

[PAllen]

The fact is, all of the standard explanations of the twin scenario (it is not a paradox) are valid. You come here claiming none are valid despite 100s of years study by great physicists. The least you can do is state your case clearly and precisely if you expect to be taken seriously. So far, you have simply not done so.

 

[Orodruin]

Regarding the no-return scenario: Yes, both will observe the other as time dilated. No, there is no contradiction in this. If you think there is you are stuck in a thinking of absolute time and should read my insight post on the geometric view of the twin paradox.

 

[Dale]

I feel you are simply dismissive of this notion out of hand.

I am sorry you felt that way, it was certainly not my intention to make you feel dismissed. Unfortunately I am traveling so my answers are shorter than normal.

What becomes false?The origin and the destination are at rest with respect to each other. Neither is at rest with respect to the traveler.

What becomes false is that this is a resolution to the paradox. You can posit scenarios where the origin and destination are moving wrt each other, and where they are moving wrt one or both twins. You could even posit scenarios where the departure and reunion events take place in vacuum so there is no origin or destination velocity.

It is simply not a true resolution, because it focuses on details that are not at the core of the scenario and may be omitted or changed.

but concern with semantics and your dismissal as false the latter assertion, perhaps poorly worded, suggest to me you are mostly interested in easy discouragement and facile refutation

My interest in this particular piece of semantics is that I believe that the bad semantics permits incorrect thinking in students which leads to unnecessary confusion. Using the correct semantics is actually very helpful for students to properly organize their thoughts.

 

[Jun Pan]

I understand that no matter if there is return trip or not, time dilation exists in the whole period.
In any scenario, observer 1 in the inertial frame 1 observes observer 2 in the inertial frame 2 moves at v, while observer 2 in the inertial frame 2 observes observer 1 in the inertial frame 1 moves at -v. So in any scenario, the relativistic effect is symmetric for each observer in each inertial frame. Observer 1 thinks observer 2 has time dilation, and observer 2 thinks observer 1 has the same value of time dilation.
Time dilation is not because of simultaneity problem between observers (Simultaneity can only cause event delay but can not cause time dilation.). Time dilation is because of time units change to each other.

 

[Ibix]

It's not quite that simple. You can't have symmetric time dilation without the relativity of simultaneity - if there's a universal "now" then there's a universal time coordinate and someone is running slow in an absolute sense. But because of the relativity of simultaneity there isno way to do the one-way twin paradox that the OP is talking about without simply asserting that one choice of definition of "now" is Right and all others are Wrong. That's an arbitrary choice, and the results are arbitrary.

 

[Jun Pan]

Time dilation means time units dilation but does not specifically mean time points shift. The time units dilation between observer 1 in inertial frame 1 and observer 2 in inertial frame 2 are symmetrical for each other. There is not much relation between time units dilation and the relativity of simultaneity. Time units dilation only has direct relation with the relative speed between the two observers. From any chosen inertial frame, any other inertial frame has specific time units and relativity of simultaneity. However here only inertial frame 1 where observer 1 is in and inertial frame 2 where observer 2 is in are considered. The third inertial frame is not considered.

 

[Orodruin]

There is not much relation between time units dilation and the relativity of simultaneity.

This is just plain wrong. The essence of time dilation is in the determination of how many ticks a clock in motion does in comparison to a global time, which defines what simultaneous implies.

 

[Jun Pan]

The essence of time dilation is in the determination of how many ticks a clock in motion does in comparison to a global time, which defines what simultaneous implies.

My understanding is time dilation is in the determination of how many ticks a clock in motion within time period of inertial frame 1 observed from another inertial frame 2 or how much time elapsed within one tick of the clock of inertial frame 1 observed from another inertial frame 2. In special relativity, there is not global time. Every inertial frame is equally effective. Simultaneity only affects time point shift or delay but can not affect time units change or dilation.

 

[Orodruin]

My understanding is time dilation is in the determination of how many ticks a clock in motion within time period of inertial frame 1 observed from another inertial frame 2 or how much time elapsed within one tick of the clock of inertial frame 1 observed from another inertial frame 2.

Yes, for this to be well defined you need a definition of what events are simultaneous. Otherwise there is no way of comparing clocks at different positions and concluding that they are ticking at different rates. Since (at least) one clock needs to be moving, the clocks will not be co-located at all times and the definition of simultaneity therefore plays a central role.

In special relativity, there is not global time.

There is global time, there is no absolute time. A global time is defined by any inertial frame and "global" only refers to "applicable in all of Minkowski space". The global time is going to be different depending on which inertial system you base your time coordinate on and the global time of different inertial systems are going to disagree on what events are simultaneous. This is the main conceptual reason why you get time dilation. This is in sharp contrast to general relativity, where it is not even certain that you can define a global time (and even less an absolute one).

Every inertial frame is equally effective. Simultaneity only affects time point shift or delay but can not affect time units change or dilation.

This is not very clear to me in terms of what you want to say. Please read my insight: A Geometrical View of Time Dilation and the Twin Paradox

 

[PAllen]

My understanding is time dilation is in the determination of how many ticks a clock in motion within time period of inertial frame 1 observed from another inertial frame 2 or how much time elapsed within one tick of the clock of inertial frame 1 observed from another inertial frame 2. In special relativity, there is not global time. Every inertial frame is equally effective. Simultaneity only affects time point shift or delay but can not affect time units change or dilation.

Look, you can mathematically derive reciprocal time dilation from relativity of simultaneity, and vice versa. Obviously they are intrinsically connected.

 

[Jun Pan]

Yes, for this to be well defined you need a definition of what events are simultaneous. Otherwise there is no way of comparing clocks at different positions and concluding that they are ticking at different rates. Since (at least) one clock needs to be moving, the clocks will not be co-located at all times and the definition of simultaneity therefore plays a central role.

I have read your insight "A Geometrical View of Time Dilation and the Twin Paradox". I understand your meaning. Thank you. Indeed simultaneity not only links to time delay but also links to time units change. In this regard, simultaneity indeed plays a central role in time dilation. If I interpret your geometrical view, then the observer 1 on the Earth observes the turnaround time at t1 on the earth, while the observer 2 in the spacecraft observes the turnaround time on the Earth is t1', and t1 does not equal to t1'. I understand this is indeed the key to solve twin paradox. In fact, I think my understanding is the same as your view expressed in geometry and linked formulas. The expression of geometry and linked formulas is better
For global time, my meaning is there is no preferred inertial frame. In special relativity, all inertial frames are equivalent and any inertial frame can be a global inertial frame and so the inertial frame 1 or the Earth where the observer 1 rests can be chosen as a global inertial frame.

 

[Jun Pan]

Look, you can mathematically derive reciprocal time dilation from relativity of simultaneity, and vice versa. Obviously they are intrinsically connected.

The reciprocal time dilation and relativity of simultaneity can be derived from each other. I understand now. Thank you. If to consider the light travels in spaceship from A to B in the perpendicular direction to the spaceship move direction, this light beam observed from the Earth has the speed component of perpendicular direction and the speed component of horizontal direction and so travels in the hypotenuse from A to C. If to think this light beam observed in the spaceship arrives B and this light beam observed from the Earth arrives C simultaneously, The relation of time dilation can be derived.
Also in Lorentz transformation, if to put the above mentioned A as origin and BC=x=vt, (v is the speed of spaceship, t is the time observed from the earth.), then, the time observed from the spaceship t'=(t-vx/c^2)*gama factor=t*gama factor, or the time dilation relation.

 

[Charles Carter]

I appreciate the replies and see I've stirred up discussion of some related issues.
I actually have serious doubts about the notion in my original post, but haven't found time to examine it more closely.
Where I started was looking for a resolution to the twin paradox. Many explanations have been put forth, which suggests there is not a firm consensus. And, while I do not know GR well enough to form an opinion, all other explanations I find insubstantial. The unresolved issue remains lack of symmetry- exchanging the 'resting' and traveling' twin (or clock) appears to result in a contradiction.

 

[Mister T]

The unresolved issue remains lack of symmetry- exchanging the 'resting' and traveling' twin (or clock) appears to result in a contradiction.

It's all rather trivial, as can be seen from examining a spacetime diagram of the situation.

 

[Dale]

Many explanations have been put forth, which suggests there is not a firm consensus.

Interesting. This meta-objection is specifically mentioned in the most common twins-paradox FAQ.

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

 

[Charles Carter]

Interesting. This meta-objection is specifically mentioned in the most common twins-paradox FAQ.

http://math.ucr.edu/home/baez/physics/Relativity/SR/TwinParadox/twin_paradox.html

Thanks!

 

[PeterDonis]

The unresolved issue remains lack of symmetry

That's not an "unresolved issue"; it's a physical fact about this particular scenario. The stay at home twin and the traveling twin are not symmetric; they have different physical experiences. The FAQ article that Dale linked to discusses this.

In the alternate scenario you suggested in a previous post, where there are two traveling twins who go off in opposite directions and then return, the two traveling twins are symmetric--and indeed, when they meet again, they have both aged by the same amount. But neither of them is symmetric with the stay-at-home twin (who is really a triplet in this scenario), who has aged more when they all meet up again.

 

[Jun Pan]

If there is good definition of simultaneity, the Earth coordinate system and the spaceship coordinate system are symmetrical and the so the time dilation effects are symmetrical for these two systems.

 

[PeterDonis]

If there is good definition of simultaneity, the Earth coordinate system and the spaceship coordinate system are symmetrical

I'm not sure what you mean here. The definition of simultaneity is coordinate-dependent; it's not an absolute. And in the standard twin paradox, there is no single inertial frame in which the spaceship is always at rest, so the "earth coordinate system" and the "spaceship coordinate system" are certainly not symmetrical.

the time dilation effects are symmetrical for these two systems.

The relative aging of the two twins when they meet up again, in the standard twin paradox, is not symmetrical; the traveling twin ages less. And this fact is independent of any choice of coordinates. So again I'm not sure what you mean here.

 

[Jun Pan]

The definition of simultaneity is coordinate-dependent; it's not an absolute. And in the standard twin paradox, there is no single inertial frame in which the spaceship is always at rest, so the "earth coordinate system" and the "spaceship coordinate system" are certainly not symmetrical.

Yes, the definition of simultaneity is coordinate-dependent. There are two coordinate systems considered here or the Earth coordinate system (x,y,z,t) and the spaceship coordinate system (x',y',z',t'). Define when t=t'=0, x=x'=0. Spaceship is always at rest in the spaceship coordinate system. The two coordinate systems are symmetrical. So, (x',y',z',t') moves at v relative to (x,y,z,t), while (x,y,z,t) moves at -v relative to (x',y',z',t'), and the time dilation effects are symmetrical for the two systems.

The relative aging of the two twins when they meet up again, in the standard twin paradox, is not symmetrical; the traveling twin ages less. And this fact is independent of any choice of coordinates. So again I'm not sure what you mean here.

It is supposed to me when the two twins meet, the twin backs from the travel will not be older than the twin on the earth.
I am sorry there is a mistake of my last sentence. My meaning is that it is supposed to me the twin going away will not be younger than the twin on the Earth upon return.

 

[Orodruin]

It is supposed to me when the two twins meet, the twin backs from the travel will not be older than the twin on the earth.

The twin going away will be younger! (Upon return.)

 

[Jun Pan]

The twin going away will be younger! (Upon return.)

I am sorry there is a mistake of my last post. It is supposed to me the twin going away will not be younger than the twin on the earth.

 

[Orodruin]

I am sorry there is a mistake of my last post. It is supposed to me the twin going away will not be younger than the twin on the earth.

Then you are simply wrong. Please read my insight A Geometrical View of Time Dilation and the Twin Paradox.

 

[Jun Pan]

Then you are simply wrong. Please read my insight A Geometrical View of Time Dilation and the Twin Paradox.

I have read your insight. If to chose the spaceship as the rest inertial frame, from the view of the twin in the spaceship, the twin on the Earth is younger. When the two twins meet, neither one is younger.

 

[Orodruin]

I have read your insight. If to chose the spaceship as the rest inertial frame, from the view of the twin in the spaceship, the twin on the Earth is younger. When the two twins meet, neither one is younger.

No, you are wrong. You have not understood the geometrical perspective at all. Reread the part where I explain (in the standard geometry case) why the "relativity of the x-coordinate" solves the problem by showing that the point on the straight line with the same x' coordinate as the turning point is not the half-way point. The twin paradox works exactly the same way.

 

[Jun Pan]

No, you are wrong. You have not understood the geometrical perspective at all. Reread the part where I explain (in the standard geometry case) why the "relativity of the x-coordinate" solves the problem by showing that the point on the straight line with the same x' coordinate as the turning point is not the half-way point. The twin paradox works exactly the same way.

True, the turning point is the half way point observed from the Earth (x,y,z,t). But it seems to me that the turning point observed from the spaceship (x',y',z',t') can not be regarded as not the half way point. If according to the (x,y,z,t), the turning point observed from (x',y',z',t') is not the half way point defined in (x,y,z,t), but should be the half way point defined in (x',y',z',t').
If to chose the spaceship (x',y',z',t') as the rest frame, the Earth (x,y,z,t) should be observed to move at the same speed in the opposite direction. So at the turning point, the observer in the spaceship should observe the Earth moves at the halfway point defined in the (x',y',z',t').

 

[Orodruin]

So at the turning point, the observer in the spaceship should observe the Earth moves at the halfway point defined in the (x',y',z',t').

No, this is wrong precisely because of the simultaneity of relativity. The spaceship does not have the same rest frame and applying the time dilation formula without taking relativity of simultaneity into account, you will be missing a large part of the time for the Earth observer. The spaceship changes system and that changes which event on the Earth is simultaneous with the turnaround.