The Twin Paradox: Understanding Time Dilation in Space Travel

[Janus]

Janus - let's just concentrate on your statement:

"According to the Earth and Alpha clocks, the Traveler speeds by and crosses the distance in some given time, but due to time dilation, the traveler clock runs slow and thus when it passes Alpha less time will have accumlated on the traveler clock then on either Earth or Alpha."

So you will agree that the traveler's clock does not read the same as clocks in the earth-alpha system at the end of the one-way journey, for whatever reason. We can nail that down I presume - observers on Earth and alpha are reading only Earth synced clocks and the traveler is reading only the clock which has escorted him and when the Earth time on the alpha clock is compared to the travelers clock at the end of the one way journey, the travelers clock has accumulated less time - Am I making the correct conclusion as to this aspect of the experiment?

Only as measured by Earth's and Alpha's Observer. As measured by the Traveler, Earth's and Alpha's clocks have accumulated less time. Assuming that both the Earth clock and Traveler clock read "zero" when they passed each other, then, according the Traveler, the Earth clock will read less than the Traveler's clock when the The Traveler and Alpha pass each other. The Alpha clock will read greater amount of time on it than the Traveler's clock when they pass, not because more time accumulated on Alpha's clock, but because ALpha's clock did not read "Zero" when the Earth and Traveler passed each other, it read some greater time.

If the Earth and Alpha observers are only reading their own clocks, and the Traveler is only reading his own, Then how either can say which accumlated more time according to any of them?

 

[jdavel]

Hurkyl said:

"(1) In the Earthbound frame, the time dilation formula says that the spacebound clock accumulates less time than the Earth clock.
(2) In the Spacebound frame, the time dilation formula says that the Earth clock accumulates less time than the space clock.
(3) When can compare both clocks at the beginning and end of the round trip, both (1) and (2) must be true, which is a contradiction."

Not if the stay-at-home (S) and traveling (T) twins disagree on what the alpha clock says when the traveller leaves earth. And they do.

S thinks it says t=0. T thinks it says Lv/c2 (L is the proper distance between Earth and alpha).

T thinks he travels a distance L/gamma, so he thinks it takes him (L/v)/gamma. But since he sees the clock on alpha coming toward him, he thinks it will only accumulate ((L/v)/gamma)/gamma. So he expects that when he arrives at alpha, the alpha clock will say:

Lv/c2 + ((L/v)/gamma)/gamma

which is exactly what S thinks it should say, and exactly what it does say, namely L/v.

Where's the paradox?

 

[yogi]

djavel - I am attempting to disect the experiment so that there are no measurements or observations as between the two frames except when all clocks are initally set to correspond to Earth time when T passes S on Earth - thereafter each frame has no communication with the other until T passes Alpha. The reading on the proper clock carried by T is then compared with the clock at alpha (which has remained in sync with the proper Earth clock). They either read the same or different - which? The problem as posed has nothing to do with what the T observer would measure about the alpha clock at the time the T clock is initially set to correspond with Earth time.

 

[jdavel]

yogi,

"I am attempting to disect the experiment so that there are no measurements or observations as between the two frames except when all clocks are initally set to correspond to Earth time when T passes S on earth"

You can't do that. You can synchronize the Earth clock with the alpha clock, and you can synchronize the traveller's clock with one of them, but not both.

 

[yogi]

jdavel - I am not trying to sync the T clock with the alpha clock - I can sync the T with the Earth clock - after that the T clock will simply continue to run according to its own physics - accumulating proper time in the T frame ...when it arrives at alpha there will be a clock awaiting - it will read something - does it read more or less than the T clock?

 

[Hurkyl]

jdavel - I am not trying to sync the T clock with the alpha clock - I can sync the T with the Earth clock - after that the T clock will simply continue to run according to its own physics - accumulating proper time in the T frame ...when it arrives at alpha there will be a clock awaiting - it will read something - does it read more or less than the T clock?

I would presume more... but you've yet to say how to set the clock at alpha. I assume you would set it in some manner equivalent to the method I described earlier for synchronizing co-stationary clocks in their (SR) rest frame.

 

[yogi]

Hurkyl - it does not even have to exist at the start point - if the train takes off at 10,000 mph and travels for one year to alpha, I have plenty of time thereafter to send a radio message to alpha telling them how to build a clock and at what time it should be set to correspond with my Earth clock.

The problem with all this is that in dealing with those that advocate SR as unquestionable, the tenants of SR are proclaimed as needed to be either reality or apparent ... - but it is these shifting applications and interpretations of the transforms that are under consideration - so if you cannot admit to the proposition that the Earth clock can be synced to T w/o taking into account the apparent reading on another clock at alpha - then there is no point to this - After 5 posts, we cannot even get two clocks in sync. And if I ever get the clock at S in sync with T, you will proclaim it cannot be in sync with alpha for one instant - is that not correct?

 

[jdavel]

yogi,

"does it (the alpha clock) read more or less than the T clock?"

If the alpha clock is synchronized with the Earth clock, then when the traveller arrives at alpha, the alpha clock will read L/v and the T clock will read (L/v)/gamma. Since gamma is always > 1, the alpha clock will read more (i.e., later) than the T clock.

 

[yogi]

jdavel - good - I would agree that this must be the case if, as under all theories, the spacetime interval transforms w/o variance. Would you then permit me to claim that if T immediately turned around at alpha and returned to Earth at the same speed, the total time difference would be double that measured for the one way excursion?

 

[Hurkyl]

Hurkyl - it does not even have to exist at the start point - if the train takes off at 10,000 mph and travels for one year to alpha, I have plenty of time thereafter to send a radio message to alpha telling them how to build a clock and at what time it should be set to correspond with my Earth clock.

Yes -- and until you specify the procedure by which alpha's clock is set, your thought experiment is incomplete.

The problem with all this is that in dealing with those that advocate SR as unquestionable

Good thing none of them are here.

And if I ever get the clock at S in sync with T

I've said it before -- when two things are at the same place and the same time, there's no problem, be it comparing them, setting them equal, etc. The problem arises when they're spatially separated...

you will proclaim it cannot be in sync with alpha for one instant - is that not correct?

No, I will not -- the phrase "it cannot be in sync with alpha for one instant" is entirely meaningless without specification of the meaning of "sync".

Why? Because there are lots of ways to synchronize spatially separated clocks, and they generally give inequivalent results.

Einstein gave a procedure for synchronizing clocks, after which one might describe the clocks as being "synchronized in this (inertial) reference frame". Different reference frames yield inequivalent results. In particular:

If one synchronized the clocks on Earth and alpha in Earth's rest frame, then the ship's clock will read less than alpha's clock when it arrives.

If one synchronized the clocks on Earth and alpha in the ship's rest frame, then the ship's clock will read more than alpha's clock when it arrives.

 

[Hurkyl]

If the alpha clock is synchronized with the Earth clock,

Don't forget -- you mean to determine this using Earth's rest frame.

 

[jdavel]

Hurkyl,

"Don't forget -- you mean to determine this using Earth's rest frame."

Correct.

 

[jdavel]

yogi,

"Would you then permit me to claim that if T immediately turned around at alpha and returned to Earth at the same speed, the total time difference would be double that measured for the one way excursion?"

Yes. On T's return to earth, the Earth clock will read 2L/v and T's clock will read (2L/v)/gamma.

 

[yogi]

djavel - Wonderful - we agree upon that - so can we now say that neither acceleration nor turn around is significant in explaining the clock paradox. In other words, while the traveler's return to the starting point is part of the journey, the Earth is really a convenience point for measuring the age difference ---the turn around and the consequent changing of frames occassioned thereby does not play a role per se in the age difference upon arrival back on earth.

Hurkyl - when I refer to sync for one instant - I am saying that if T and S clocks both read 12:00 at the time of passby, then since alpha reads the same as S, all three clocks will read the same initially - and for one instant only.

 

[Hurkyl]

alpha reads the same as S, all three clocks will read the same initially

And I am saying that, until you state how you are comparing spatially separated clocks, these two statements are pure nonsense.

One such way is to select a coordinate chart, such as an inertial reference frame from SR, and then compare readings that occur at the same coordinate time.

so can we now say that neither acceleration nor turn around is significant in explaining the clock paradox ... the turn around and the consequent changing of frames occassioned thereby does not play a role per se in the age difference upon arrival back on earth.

As I've mentioned before, the "clock paradox" arises when you also do the analysis in the rest frame of the spaceship -- the turn around is crucial to explaining why that analysis doesn't predict that Earth clock doesn't read less than the space clock.

 

[yogi]

Hurkyl - I thought you agreed that the two clocks read differently at the halfway point (when T reached alpha).

Clocks can be compared in a common frame and they can be compared in relatively moving frames when they are adjacent - this does not violate any tenant of SR - It is not necessary to specifically set out a particular means of reading a clock or of setting it so long as they both read the same in the same frame - we simply say two clocks in the same frame are in sync - you can use Einstein's method if you like - but this is just another example of your introducing a SR bias into the thought experiments - the very purpose of which is to examine whether the theory comports with the real world in every case - as I have repeatedly stated, Einstien's derivation started with observing events in a moving frame - all measurements were "as viewed from the other frame" as Einstein said 3 times in the first paragraphs of the derivation in his 1905 paper - then w/o reason or explanation, he applies these transforms to predict that clocks will experience actual time differences (loss of sync) when moved apart and returned. It is the propriety of this shift from observation to reality that is at root - so what I was attempting to do was to confine all measurements to those which are proper and those which are adjacent. I know you can always pull yourself up by the bootstraps and use the same shifting methodology to show SR is correct. But if I define as true 1 + 2 = 4 , I can also prove 2 + 2 = 5

 

[Hurkyl]

Hurkyl - I thought you agreed that the two clocks read differently at the halfway point (when T reached alpha).

Only on the condition that I had correctly guessed how alpha's clock is set.

you can use Einstein's method if you like - but this is just another example of your introducing a SR bias into the thought experiments

I've asked you plenty of times to specify what method you intended to use. Einstein's method, incidentally, conforms to that of any (flat-space) preferred frame theory I know, when done done relative to that preferred frame.

 

[jdavel]

yogi,

"when I refer to sync for one instant - I am saying that if T and S clocks both read 12:00 at the time of passby, then since alpha reads the same as S, all three clocks will read the same initially - and for one instant only."

Not true. If T and S are synched and S and alpha are synched, then T and alpha won't be synched.

 

[Hurkyl]

Again, you have to be careful about what you mean by "synced". For instance, if S and T coincide when they both read zero, and if S and alpha read 0 simultaneously in Earth's rest frame, then T and alpha will read 0 simultaneously in Earth's rest frame. Of course, in the ship's rest frame, alpha will have some positive reading when S and T are both zero.

 

[ElectroPhysics]

Thanks and just continue your discussion. You guys are really Physicists :)

 

[ElectroPhysics]

and Happy New Year...

 

[yogi]

ElectroPhysics - If there is anything to be learned by all this...it is that there is more than one interpretation of both the theory and the experiments. Ultimately I would assume that all but one view will be relegated to the waistbasket.

 

[jdavel]

yogi,

"ElectroPhysics - If there is anything to be learned by all this...it is that there is more than one interpretation of...the theory..."

But only one is correct.

"Ultimately I would assume that all but one view will be relegated to the waistbasket."

They already have by everyone who understands the theory.

 

[Garth]

The paradox and its resolution depends on the concept of what we think of as 'now', not here where that is obvious, but 'over there'. At distance those events that we think of as happening 'now' are selected according to our frame of reference. Two close observers moving relative to each other would select a different set of contemporary events; simultaneity is relative, or 'frame dependent'.

This is particularly important for the non-inertial twin. As she reversed her course her own timing of events back home would suddenly change. Those distant events back home that she thought of as in her future would suddenly become in her past, so when she arrived back home she would realize that her twin was actually older than herself.

I hope this helps.

Garth

 

[yogi]

djavel "They already have by everyone who understands the theory"

- your statement is totally incorrect - acknowledged and respected relativity authors take entirely different approaches to explaining the twin and triplet paradox - Read Professor Robert Resnick's book and compare his treatment of the twin paradox to the treatment of Max Born - the relativist views are almost as diverse as the antagonist's views (but not quite).

Garth - what is at issue is not whether SR offers an explanation of some sort or the other - SR has a built-in self consistency which prevents it from being falsified by thought experiments. Relativity always gives an answer - but does it give the right answer for the right reasons? In the posts above - I attempted to reduce the experiment to proper measurements made within the confines of the proper frame of each participant. - while there may be minor errors induced at the time of initial readings (e.g., if all clocks are initially set to read the same in the Earth frame - and then the traveler takes off (introducing a small error) we then ask a question - do the eart-alpha clocks run at the same rate as the travelers clock so that all three read the same at the turn around point? If the answer is yes - then all of the age discrepancy that we assume will be measured after the parties are reunited, must be do to something physical that occurs at turn around - while the traveler may observe the Earth clock to be changing at turn around - he can also observe the nearby alpha clock (which is in sync with the Earth clock) as not changing. Therefore what is observed by the traveler at the time of turn around (for the rapid change in the Earth clock reading) must be an illusion. An illusion cannot affect the time on the Earth clock - only something physical can cause identical clocks to run at different rates - SR does not provide any inkling as to what causes the age difference - what you have cited is one explanation adopted by some relativity authors - In the triplet problem from which this long thread derived, there is no acceleration at turn around ...simply a reading of the outbound siblings clock by the inbound sibling. Does that make the Earth clock rush forward in time?

 

[Chronos]

Clocks tick at the same rate in both frames, relative to their own. Both sisters age differently than the other. But, neither sister will agree upon how old the other is relative to herself. In a sense, they are in different universes. The implications of relativity and quantum physics are both profound. They are not mutually compatible. The effects on both levels of reality are too small to be measurable. The more important point is to measure where they meet. This may not be an important discovery, but may be important to the discovery process,

 

[Garth]

yogi Clocks always tick "at the same rate" - one second per second - in their own frame, it is how they tick as observed by another frame that is the issue. The twin sisters have no way of comparing their clocks, except by light signal, until they meet again.
The traveling sister, i.e. the one who has changed her own frame of reference by accelerations, will find her clock has ticked less than the inertial sister.

Garth

 

[Hurkyl]

but does it give the right answer for the right reasons?

An interesting philosophical question -- there's a good argument that getting the right answers (in advance) is all that matters. The "right reasons" are only an explanation made up after the fact to help understand, and be able to make even more predictions.

if all clocks are initially set to read the same in the Earth frame - and then the traveler takes off (introducing a small error) we then ask a question - do the eart-alpha clocks run at the same rate as the travelers clock so that all three read the same at the turn around point?

During the outbound trip:

In the Earth frame, the traveller's clock run slow, and the Earth and alpha clocks do not.
In the outbound frame, the clocks on Earth and alpha run slow, and the spaceship clock does not.


If alpha and Earth's clocks always agree in Earth's frame, then the clock on alpha will read more than that of the spaceship when it arrives.

If alpha and Earth's clocks always agree in the outbound frame, then the clock on alpha will less than that of the spaceship when it arrives.


Other comments:

"which is in sync with the Earth clock" -- only according to Earth's frame.

"SR does not provide any inkling as to what causes the age difference" -- would you also say that Euclidean geometry doesn't provide any inkling as to what causes one side of a triangle to be less than the sum of the other two sides? It is fairly directly analagous.

In a sense, they are in different universes.

Or, more accurately, each twin is merely using a different coordinate chart. Geometrically speaking, it's no more mystifying than, why the apparent width of a piece of paper is different when you look at its edge or its front.

The implications of relativity and quantum physics are both profound. They are not mutually compatible.

Partially incorrect -- special relativity and quantum physics are quite compatable. You're thinking of general relativity.

 

[jdavel]

yogi,

djavel: They already have by everyone who understands the theory

jogi: ...your statement is totally incorrect - acknowledged and respected relativity authors take entirely different approaches...

No they don't. They DID, but not anymore; the issue was settled over thirty years ago.

Anyone who thinks that relative simultaneity or (equivalently) constant light speed, or (again, equivalently) the Lorentz transforms can't account for what everyone sees on everyone's clock, in any reference frame, doesn't understand this theory.

 

[pervect]

"Why" questions generally do not have any unique answer in science - if they are even addressed at all. Somewhere around 4 years old, most everyone learns that they can always ask "why", and in a short amount of time arive at a point where there is not any answer to their questions. Science is ultimately concerned with "what" rather than "why". This is why scientific questions generally have nswers, even if they are hard to find - as opposed to philosophical questions, which tend to spawn endless debates, with no ultimate resolution.

On a slightly more advanced note, classical Newtonian mechanics has many alternate formulations - the typical "f=ma" introductory formulation, and the more advanced Lagrangian and Hamiltonian formulations. I see very few people criticising Newtonian mechanics because of the fact that alternative mathematical formulations of the theory exist. Most people seem to be quite content with the fact that all valid formulations of Newtoian mechanics give the same results. I would urge people to apply the same standards to relativity theory and quantum theory. Of the two, quantum theory has by far the biggest issue with "interpretations". Ultimately, though, it is the agreement of final results which is important.