Twin Paradox Problem: Do Twins Age Differently?

[Dale]

"according to the special theory of relativity the coordinate systems K and K' are by no means equivalent systems. Indeed this theory asserts only the equivalence of all Galilean (unaccelerated) coordinate systems, that is, coordinate systems relative to which sufficiently isolated, material points move in straight lines and uniformly. K is such a coordinate system, but not the system K', that is accelerated from time to time."
- https://en.wikisource.org/wiki/Dialog_about_Objections_against_the_Theory_of_Relativity

(note to Dalespam: another definition of "Galilean coordinate systems").

Yes, this is the definition I am familiar with. In the absence of gravity the phrase "sufficiently isolated, material points" means that the material point does not feel any acceleration.

Btw, don't try to tell me that you don't want to discuss something here and then continue to discuss it here. If you really think it is off topic then that is fine, but as it is it just seems to be a tactic to avoid answering a difficult question.

 

[stevendaryl]

PAllen wrote:

There is only one way, sort of, to do this (ignoring GR/gravity). Pick any arbitrary inertial clock, and its rest frame and call it universal (say, pick the clock tower at Emerald City). Declare, by fiat...

I don't have to do any of that, I can just use common sense. If I make a trip to Centauri that lasts 1 year:
- When I get there, i'll look at your clock in Emerad City and see t0+1y. My clock shows t0+1y. I am not stupid, so I know that the picture of your clock took 4y to arrive, so I conclude that if you didn't move from your couch in 4 years, it must be that your clock that's running faster.
- When you see me arrive at Centauri, your clock will show t0+9y and you'll see that the picture of my clock shows t0+1y. You are not stupid either, so you conclude the same way that my clock is running slower.
- In fact we can do this for any leg of the trip, without needing Mikowski, or Einstain, or his wife -- which was also Serbian by the way - like myself and Tesla :) -- to conclude whose clock is running slower.

Why is such a simple thing made so complicated? I don't understand.

It's not complicated. It's just that, as PAllen says, you can pick ANY reference frame to serve as your basis for your absolute time. The "common sense" works out exactly the same.

You say that "I know that the picture of your clock took 4y to arrive". HOW do you know that? That's true in some frames of reference, but not in other frames of reference. So your reasoning is circular--you picked a frame of reference to use for your measurements, and then concluded that that frame of reference was the one whose clocks are running the fastest. If you had picked a different frame of reference, you would have gotten different measurements, and you would have gotten a different answer to the question of which clock is running fastest.

 

[PAllen]

Of course you can have accelerated observers in SR; and in SR, acceleration is not rest.

Here's how Einstein clarified, in the context of the twin paradox, the use of SR (which is a label that he invented):

"according to the special theory of relativity the coordinate systems K and K' are by no means equivalent systems. Indeed this theory asserts only the equivalence of all Galilean (unaccelerated) coordinate systems, that is, coordinate systems relative to which sufficiently isolated, material points move in straight lines and uniformly. K is such a coordinate system, but not the system K', that is accelerated from time to time."
- https://en.wikisource.org/wiki/Dialog_about_Objections_against_the_Theory_of_Relativity

(note to Dalespam: another definition of "Galilean coordinate systems").

My point was that just as in classical mechanics, in SR an accelerated observer is not "in rest" - that is wrong terminology for both. The traveler can certainly say to be in rest in his capsule, but he can not "prefer to think to have traveled zero distance", for that equals "being in rest all the time", and thus being "unaccelerated all the time".

As this subtle point is at the heart of the "twin paradox", it is not something to overlook.

Saying that an accelerated observer is objectively different from an inertial observer does not mean that an accelerated observer is somehow not allowed to do distance measurements relative to themself. They cannot use Lorenz transforms, or Minkowski metric, but they can choose to set up a coordinate system at which they are the origin.

Remember, this was all in relation to whether 'distance traveled' has anything to do with the twin paradox. I have shown multiple ways that this is not true (distance traveled does not correlate with aging differential in general, and is therefore not a valid way to understand it). [see esp. #245, #252]

We've also been over in what way acceleration is responsible for differential aging. The most you can say is:

- in flat spacetime with normal topology, at least one path having acceleration is a necessary but not sufficient condition for differential aging. You cannot localize the differential aging to the acceleration, and it is up for debate whether you consider the acceleration per se causative.

(I say normal topology, because in a closed universe with locally flat geometry everywhere, you can have differential aging with no path experiencing any acceleration. Obviously, we don't normally assume this applies to our universe, but we don't know for sure. We only know our universe is very big.)

 

[harrylin]

Saying that an accelerated observer is objectively different from an inertial observer does not mean that an accelerated observer is somehow not allowed to do distance measurements relative to themself. They cannot use Lorenz transforms, or Minkowski metric, but they can choose to set up a coordinate system at which they are the origin.

As long as they say to be accelerated, they still can use Lorenz transformations - be it one, two, or an infinite set of them. That is still SR. However, if they say to be not accelerated but "in rest", then they are talking GR - exactly as Einstein explains in his paper.

Remember, this was all in relation to whether 'distance traveled' has anything to do with the twin paradox. I have shown multiple ways that this is not true (distance traveled does not correlate with aging differential in general, and is therefore not a valid way to understand it). [..] We've also been over in what way acceleration is responsible for differential aging. [..]

Sure - I merely spotted a significant phrasing issue. In sofar as I followed it, I have no issues overall with what you say (except philosophical ones perhaps; but that is out of place here).

 

[PAllen]

As long as they say to be accelerated, they still can use Lorenz transformations - be it one, two, or an infinite set of them. That is still SR. However, if they say to be not accelerated but "in rest", then they are talking GR - exactly as Einstein explains in his paper.

This is our core terminological difference. Because it is terminology, there is ultimately no right answer. As I understand it;

rest - your definition: inertial; my definition: stationary in some coordinate system, equally for SR as GR. I don't see any contradiction between this and the statement that SR says only that all inertial frames are equivalent. To distinguish simple form for laws versus complex, I distinguish inertial from non-inertial. This is based on a local measurement with an accelerometer. Distance is a non-local measurement, based on conventions. A passenger in a rocket can measure distances from themself, and call themself at rest in their coordinate system.

SR vs. GR You say if you use generalized coordinates and metric, it is GR even if no curvature. I say it is GR only if the EFE is used, and there is curvature.

 

[phyti]

I never said any of that stuff you are supposedly agreeing with me about. I don't even know what you're talking about.

What's so hard about saying that the time that a clock displays and measures is legitimate and not compromised just because it doesn't agree with what another clock with a different history displays? Einstein says they're all correct. You never have to make an excuse for one of them saying it lost some time and the other one is correct. They're all correct. Furthermore, all the objects and observers that are local to a clock, experience objective time (and subjective, if we can identify that) the same as the clock. This doesn't have anything to do with the number of events in the universe, which is infinite, by the way.

I won't refer to anything you post again after this.

Robinpike is only asking for an explanation of why the two reunited clocks show different times.

Einstein referred to the observers time as subjective. Who am I to argue with him.

 

[phyti]

I am interested in avoiding so called explanations that are tied to a specific formulation of differential aging. A good understanding will apply equally to any formulation.

What is 'longer path'? The only invariant along timelike paths through spacetime is proper time. If you mean 'distance traveled' each twin may prefer to think they have traveled zero distance and the other has done the traveling. Travel distance has really nothing to do with differential aging, and is strictly frame or coordinate dependent quantity.

Maybe you mean longer as drawn on a conventional spacetime diagram? If so, I missed where you stated this. It is true that for different (timelike) paths between two given events drawn on conventional SR spacetime diagram, the longer one has less proper time.

There should be someone here who can give robinpike a SIMPLE explanation for why the reunited clocks read differently. If the clocks read the same before parting, and read differently when rejoined, it doesn't require a government study to conclude one ticked less than the other. Labelling the time is not an answer. It comes down to the physics of objects in motion. Who will answer?

 

[ghwellsjr]

Einstein referred to the observers time as subjective. Who am I to argue with him.

For the record, here is what you said:

I agree with you, the same amount of time (number of events in the universe) does not change for any observers.
If we say a clock measures the rate of activity for each observer, it would correspond more to reality, i.e. subjective time.

I don't believe Einstein ever equated reality with an observer's subjective time. I'm sure he pointed out that a person's perception of time is quite fickle and rarely corresponds to any objective measure of time on a clock.

When we are discussing the passage of time in the context of Relativity, and we use a phrase like the "observer's time", we always mean the time on a clock colocated with him (even if there isn't really one there), never his subjective perception of time. Subjective time is irrelevant in discussions of relativity, except to point out that we are not talking about an observer's perception of time.

 

[ghwellsjr]

There should be someone here who can give robinpike a SIMPLE explanation for why the reunited clocks read differently. If the clocks read the same before parting, and read differently when rejoined, it doesn't require a government study to conclude one ticked less than the other. Labelling the time is not an answer. It comes down to the physics of objects in motion. Who will answer?

He's been given many answers and he rejects every one because he wants an answer that fits his preconceived notion that the traveling twin's clock must lose time at a particular point in the trip:

I have suggested that the reason for the loss in time is because his rate of time slowed down at some point in his journey. If that is the reason, then how does Relativity explain this (and please note I am not asking for the calculation).

If the deduction that his rate of time slowed down at some point in his joureny is incorrect, then all I ask is that the correct explantion for the loss in time is stated for me to see.

The problem is that nature does not reveal to us the answer in a way that makes him feel comfortable. He wants an absolute answer. "It happened right here or it happened in this particular way." He's not going to get that answer. The best we can do is explain how the Theory of Special Relativity deals with it which is that time is relative. Every clock keeps track of time legitimately. It's just what happens.

It's really no different than the concept of relative speed. After the traveling twin departs, he can consider himself to be at rest and the Earth twin to be moving at some relative speed or the Earth twin can consider the traveling twin to be the one to be moving at that same speed but in the opposite direction. What would you tell someone that rejects that kind of ambiguity in assigning speed and insists that there must be only one correct answer?

If robinpike can ever feel comfortable with the notion that speed is relative to an arbitrary frame of reference and that the two twins will have different speeds in a different frame of reference, then he should have no trouble understanding that the rate of ticking on each twin's clock is related to his speed in the arbitrarily chosen frame of reference, the faster the speed, the slower the clock ticks. Keep track of the ticks of each clock throughout the scenario and you have the answer. Transform the scenario into any other frame of reference where the twins have different speeds and therefore their clocks tick at different rates, keep track of the ticks of each clock throughout the scenario and you end up with the same answer, even though the tick rates of the clocks are totally different in the different frames.

And it's not just the final answer at the end that comes out the same in different frames of reference, it's also the observations of each twin looking at the other ones clock compared to their own throughout the entire scenario from start to finish that comes out the same no matter which frame of reference is used.

That is the simplest way I know to answer robinpike's question but it doesn't nail down where along the trip the slow down occurred because that comes out different in each frame of reference and nature won't disclose to us anything more than the explanation we already have with Special Relativity.

 

[kamenjar]

If it takes 1 year by your clock, then your speed was 97%c.

No, you won't see that one year has passed, you will only see about a month and a half has passed. At 97%c, the Relativistic Doppler Factor is about 8.1 so you divide your 1 year by 8.1 to see how much time has advanced on the Earth clock.

You may not be stupid but you are ignorant of how to do these calculations.

Ok I admit, I missed that part and I added 1+1=2. I don't do relativity every day.

We can just re-do the scenario where numbers are made so that return trip takes 10 years. In that case only my understanding of what I would read on my watch is incorrect. My watch would show more than 2 years when I return to Earth and 1/2 that when I arrive at Centauri. The clocks on centauri and Earth are still synched (and have same timestamps stated in the thought experiment), my watch is still slow and that's what matters.

Wrong again, the Earth clock will be at just over 8 years. Remember, you are traveling at almost the speed of light so it takes you just over 4 years to get there and 4 years for the image of you to get back to earth.

I think we all agree that you don't understand.

I absolutely do not disagree here. First of all, you have a wrong conception of simultaneity in the common sense. Drop your 100% relativity thinking relativity for 1 second and use it to apply common sense. Maybe too much relativity gets someone thinking too much in one direction that it clouds their judgement. The part where you say and 4 years for the image of you to get back to earth is where your basis of thinking confuses you. You consider two synchronized timestamps to be equal when one receives the timestamp of another. In static frames, if any of the receivers receive clock timestamp of another receiver that is equal or later than their own, their clocks are not synchronized. Clock rates maybe, but not timestamps.

And here is an example: If we synchronize our watches that our times are in synch to UTC time, if we would be looking at Greenwitch's clock and my watch at the same time, it would be off by a fraction of a second. It doesn't mean that my clock is off, it means that it appears to me that Grenwitch clock is off by an amount that makes it correct. That fraction of a second corresponds to the time the light takes form Greenwitch to us. Same thing would be true if we were on Centauri, when looking at Greenwitch (UTC -

You are saying at what time "on earth" is the time when Earth receives my image and that is why your doppler based explanation is asymmetric (though correct) where my analysis is 100% symmetric. You didn't read how I synchronized clocks and what is and what is seen. You can consider that the real time on Earth and centauri you forgot that Earth sees 2008 on centauri's clock at t=0. Saying that time on Earth is Centauri + 8 is not correct when applying common sense thinking.

The only way to make clock timestamps symmetric is to is to make each clock off by 4 years when compared to the observed clock. Remember - if you are looking (both at rest) at someone's clock and it it shows the same exact time as yours, your clock is wrong!

Edit: To clarify -- Two rest clock timestamps are truly synched if only and only if an observer placed exactly in the middle between clocks is reading the same time on both clocks.

 

[TrickyDicky]

It's not complicated. It's just that, as PAllen says, you can pick ANY reference frame to serve as your basis for your absolute time. The "common sense" works out exactly the same.

You say that "I know that the picture of your clock took 4y to arrive". HOW do you know that? That's true in some frames of reference, but not in other frames of reference. So your reasoning is circular--you picked a frame of reference to use for your measurements, and then concluded that that frame of reference was the one whose clocks are running the fastest. If you had picked a different frame of reference, you would have gotten different measurements, and you would have gotten a different answer to the question of which clock is running fastest.

I guess the flaw in kamenjar's view is that one cannot mix GR with SR like that and pretend that it still works.
The CMB frame cannot be introduced in the twin paradox SR set up as an absolute frame.
The inertial frames are always preferred in SR, and any of them can be used as reference.

 

[pervect]

There should be someone here who can give robinpike a SIMPLE explanation for why the reunited clocks read differently. If the clocks read the same before parting, and read differently when rejoined, it doesn't require a government study to conclude one ticked less than the other. Labelling the time is not an answer. It comes down to the physics of objects in motion. Who will answer?

People have already tried to give the simple explanations, they mostly seem to get ignored as not being explanations.

The problem with robinpike's request is that there are an infinite number of ways one could compare the clocks - basically one for every inertial observer. This is what we mean by "the relativity of simutaneity". This result isn't going to even give one explanation - it can't.

As a consequence, one will have multiple, DIFFERENT "explanations" of why the time is less on one clock than the other. You won't have an explanation, you'll have many. The two major ones have (inertial observers comoving with each of the twins) have already been discussed, I'm sure. Discussing all the infinite numbers of different possible viewpoints isn't going to make anyone any happier, I'm sure, because you can't make a "simple" explnaation out of an infinite number of different ones.

The simple explanation is really simple - just deal with it! The clocks read differently - and there really wasn't ever really any good reason to ever think that they SHOULD be the same when they reunite. Thinking that they should be the same is ultimately a consequence of some latent belief in absolute time.

To go back to the simple explanations again (the ones that seem to be ignored as not-explanations), if you drive two cars over different courses and they later reunite, you're not surprised when their odometers do not read the same. In fact, you don't particularly expect them to be the same. But you are surprised when the clocks don't read the same. The reason for this is that you are thinking of the clocks as being different from the odometers. But if you take the block universe approach, for example you can see that measuring time is measuring the "length" of a wordline on a space-time diagram, just like an odometer measures distances on a space diagram. And it's not paradoxical at all for odometers to read differently when cars re-unite. So why the hangup when clocks re-unite? It's not because of logic, it's because of habit. You're used to absolute time, where the clocks read the same after they take different paths. If you use pure logic, untainted by habit, you can realize that there isn't any particular reason to demand that the clocks read the same when they reunite.

 

[ghwellsjr]

I don't do relativity every day.

You don't do relativity any day.

I absolutely do not disagree here.

I'm glad you do not disagree. I like it when people agree with me. (Maybe you should preview your posts and proof-read them before you hit the Submit button.)

IFirst of all, you have a wrong conception of simultaneity in the common sense. Drop your 100% relativity thinking relativity for 1 second and use it to apply common sense. Maybe too much relativity gets someone thinking too much in one direction that it clouds their judgement.

I'm sure someone's judgment is clouded. I wonder if we can figure out whose.

The part where you say and 4 years for the image of you to get back to earth is where your basis of thinking confuses you. You consider two synchronized timestamps to be equal when one receives the timestamp of another. In static frames, if any of the receivers receive clock timestamp of another receiver that is equal or later than their own, their clocks are not synchronized. Clock rates maybe, but not timestamps.

And here is an example: If we synchronize our watches that our times are at any point in time are showing atomic UTC time, if we would be looking at Greenwitch's clock and my watch at the same time, it would be off by a fraction of a second. It doesn't mean that my clock is off, it means that it appears to me that Grenwitch clock is off by an amount that makes it correct. That fraction of a second corresponds to the time the light takes form Greenwitch to us. Same thing would be true if we were on Centauri, when looking at Greenwitch (UTC -

You are saying at what time "on earth" is the time when Earth receives my image and that is why your doppler based explanation is asymmetric (though correct) where my analysis is 100% symmetric. You didn't read how I synchronized clocks and what is and what is seen. You can consider that the real time on Earth and centauri you forgot that Earth sees 2008 on centauri's clock at t=0. Saying that time on Earth is Centauri + 8 is not correct when applying common sense thinking.

The only way to make clock timestamps symmetric is to is to make each clock off by 4 years. Remember - if you are looking (both at rest) at someone's clock and it it shows the same exact time as yours, your clock is wrong!

I was just following your method:

Mehod of Synchronization:
Define "real" time to be such that when remote clock is viewed from each system to be showing "real"-4years.

Your mistake has been in thinking that if 1 year progressed on your clock as you traveled from Earth to Centauri, then that would take 1 extra year beyond what it takes for light to make the trip, from the Earth's frame and it doesn't. It only takes an extra month and a half. So the total time it takes for you to get from Earth to Centauri is four years plus 1.5 months. But it takes another four years (your definition) of how long it takes for the image of your arrival at Centauri to propagate back to earth. That's a total of 8 years plus 1.5 months. You said it would be 9 years which is incorrect.

This issue, by the way, has absolutely nothing to do with any synchronized clocks because we're not talking about what the Earth observer sees or measures or calculates of the clock that was originally on Centauri, we're talking about the clock that was transported a distance of 4 light-years in such a way that 1 year transpired on the clock during the trip and what time is on the Earth clock when it sees the traveling clock arrive at Centauri.

Kamenjar, it's time for you to back off and learn Special Relativity instead of accusing those of us who are trying to help you of not knowing what we're talking about.

 

[ghwellsjr]

Edit: To clarify -- Two rest clock timestamps are truly synched if only and only if an observer placed exactly in the middle between clocks is reading the same time on both clocks.

That's one way but it's not the only way. And it's not a way that works in your scenario because there is no one half way between Earth and Centauri.

It's also not the original way that Einstein proposed in his 1905 paper. There he said that two clocks are synchronized if a light pulse is sent from one and reflected off the other and arrives back at the first, and the average time between the start and finish on the first one equals the time when the reflection occurs on the second.

And another way is the one you proposed which is to say if both clocks see the same difference between their local time and the remote time, then they are synchronized.

 

[kamenjar]

Your mistake has been in thinking that if 1 year progressed on your clock as you traveled from Earth to Centauri, then that would take 1 extra year beyond what it takes for light to make the trip

You are correct. I remodeled the trip so that total trip takes 10 years, so please use new numbers.

I tried to tell you that the only thing that was wrong is that I made a wrong call that traveler would age 1 year during legs of the trips. I used to be making those kinds of mistakes before, but forgot and it's a very dumb mistake. I apologize about the error, but I believe that nothing is invalidated when I make the correction. I will rephrase to correct it, and maybe there truly is a fatal flaw here:

Given: Return trip time = 10 years. Distance to Centauri=4ly. Velocity = 0.8c. Lorentz factor reciprocial=0.6. Traveler ageing at arrival on earth=6y

At take off: Earth 2012, Viewed Centauri Clock 2008, "real" time in both systems = 2012. Traveler watch = 2012

At Centauri landing: Viewed Earth Clock 2013, Centauri 2017, "real" time in both systems = 2017. Traveler watch = 2012+3=2015. Traveler concludes that his watch runs slow compared to ("real" time).

At Earth landing: Earth Clock 2022, Viewed Centauri Clock 2018, "real" time in both systems = 2022. Traveler watch = 2012 + 6=2018, where 2018 is less than "real" time (2022). Traveler concludes that his watch runs slow compared to ("real" time).

... accusing those of us who are trying to help you of not knowing what we're talking about.

I never said that what you said was not correct, nor that you don't know what you are talking about. I was suggesting that you (or someone) tries to introduce previously synchronized clocks and event times (wrt timestamps received) by method that I described into their solution, it should at least help explain the solution.

 

[ghwellsjr]

Given: Return trip time = 10 years. Distance to Centauri=4ly. Velocity = 0.8c. Lorentz factor reciprocial=0.6. Traveler ageing at arrival on earth=6y

At take off: Earth 2012, Viewed Centauri Clock 2008, "real" time in both systems = 2012. Traveler watch = 2012

At Centauri landing: Viewed Earth Clock 2013, Centauri 2017, "real" time in both systems = 2017. Traveler watch = 2012+3=2015. Traveler concludes that his watch runs slow compared to ("real" time).

At Earth landing: Earth Clock 2022, Viewed Centauri Clock 2018, "real" time in both systems = 2022. Traveler watch = 2012 + 6=2018, where 2018 is less than "real" time (2022). Traveler concludes that his watch runs slow compared to ("real" time).

Perfect. And thanks for the excellent job of proof-reading. It really helps.

Let me just add in the Doppler Analysis. At 0.8c, the Doppler Factor is 3. So since it takes 3 years for the traveler to get to Centauri, he will see the Earth clock progress through 3/3 or 1 year as you pointed it. The Earth clock goes from 2012 to 2013 as viewed by the traveler.

For the return trip, which also takes 3 years, the traveling sees the Earth clock going 3*3 of his rate so it progresses through 9 years bringing it to 2022 when they reunite.

Excellent post. Thanks for getting it right.

 

[kamenjar]

Starting with Paul Langevin in 1911, there have been numerous explanations of this paradox, many based upon there being no contradiction because there is no symmetry—only one twin has undergone acceleration and deceleration, thus differentiating the two cases. Max von Laue argued in 1913 that since the traveling twin must be in two separate inertial frames, one on the way out and another on the way back, this frame switch is the reason for the aging difference, not the acceleration per se.[1] Explanations put forth by Albert Einstein and Max Born invoked gravitational time dilation to explain the aging as a direct effect of acceleration.[2]

Explanation put forth by (lol infamous noob) kamenjar invoked clock rate difference and virtual simultaneity to explain aging as a direct effect of the clock rate being reduced by travel under relativistic speeds in any direction wrt rest frame.

Seriously, I am still not sure if there's a consensus on cause of difference in aging, or is this opening a new can of worms again?

 

[jtbell]

Ever hear of the expression, "there's more than one way to skin a cat?"

 

[PAllen]

Explanation put forth by (lol infamous noob) kamenjar invoked clock rate difference and virtual simultaneity to explain aging as a direct effect of the clock rate being reduced by travel under relativistic speeds in any direction wrt rest frame.

Seriously, I am still not sure if there's a consensus on cause of difference in aging, or is this opening a new can of worms again?

If you state this as: for any arbitrarily chosen reference rest frame, this is fine. If you insist there is one unique choice for 'the rest frame', you have to specify it, and this attempt will fail. Let's say there are only two solar systems in the universe, with high relative velocity. How do you pick 'the unique rest frame'?

Further, even if you come up with your rule for picking, SR guarantees I can pick a different one, or none, and have identical results. Thus your explanation will satisfy no one but you.

 

[D H]

And that is a good place to lock this thread.