Twin Paradox Problem: Do Twins Age Differently?

[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.