The Twin Paradox: Understanding Time Dilation in Space Travel

[jdavel]

yogi,

"One can argue in the case where the motion is one way, that according to SR, both the stay at home sibling and the one way traveler will read the same time on the clocks they own at the time the traveler reaches some distant point "alpha" that is at rest in the Earth "alpha" frame."

How? The distance to the star is Lorentz contracted for the traveler but not for the stay-at-home guy. They agree on the speed of travel, so the time spent has to be shorter for the traveler. And you can't argue symmetry, because there is none. The destination star is in the same direction as the traveler's velocity. So once the destination, and its fixed distance from Earth are agreed upon, there's no symmetry.

 

[yogi]

hurkyl - This is where SR jumps back and forth between the notion that 1) no frame is preferred so there is no bases for inferring that the travelers clock runs slow - and 2) the diametrically opposite view that the train clock actually runs at a different rate during the one way journey so when the clocks are compared at the end of the one way excursion there will be a time difference. If you look at many of the relativity texts in print you will see the authors do not admit that the travelers clock runs at a different rate in the one way trip - the authors wait for the turn around - then introduce an asymmetry based upon the traveling twin feeling an acceleration force or they go to the bull pen for a change in frame argument, which may take the form of shifting hyperplanes, counting transmissions back and forth, etc ...hoping to satisfy their not too inquisitive readers that all was well with their explanation.

djavel - I do not disagree with your observation that once you define the proper distance in the Earth frame between Earth and alpha, and you measure the proper time in the Earth frame by the Earth clock (or alternatively by the clock on alpha which also reads proper Earth time since Earth and alpha are in the same frame) that has elapsed in traveling from Earth to alpha, and both observers agree that the frames are moving with relative velocity v, you have created a non-symmetrical situation because - while the interval will be invariant during transformation, the individual elements ds' and ct' in the train frame will be different from ds and dt in the Earth frame i.e., the components of the interval will be different in the two frames

But with regard to using length contraction I would argue that there is never a real length contraction (See my several posts quoting Eddington, Robert Resnick and other respected relativity authors in previous disdussions with janus and other relativity experts). The only theory that continues to assert real length contraction is Lorentz Ether theory where it is claimed that a physical foreshortening results from motion wrt to the ether. I am not advocating that we go back to Lorentz's view of the contraction (actually I am not advocating anything - just trying to sort out for me what is paradoxical). Anyway - if some SR advocates (e.g. hurkyl) and LR types are in agreement that the travelers clock runs slow and we agree that both frames perceive the travel velocity as equal then the traveler will calculate that the distance between Earth and alpha is less because it took less time, not vice versa (he would be using a non-proper distance - although it turns out to be the same but for wrong reasons). This non-proper distance is not a real contraction - it is real only in the sense that the measurements are real - but the travelers time as measured by his own clock is a proper time in his frame - so he can use the velocity and his proper time to calculate the apparent distance.

 

[Hurkyl]

This is where SR jumps back and forth

SR doesn't jump back and forth -- that's the person doing the analysis. SR works perfectly well if an entire analysis is done in a single reference frame.

the diametrically opposite view that the train clock actually runs at a different rate during the one way journey

SR does not hold that view. In fact, that is precisely the kind of view that is forbidden by the notion of relativity -- such measurements are dependent on the frame of reference.

when the clocks are compared at the end of the one way excursion there will be a time difference.

Clocks need to be together to be compared -- thus, you cannot compare them both at the beginning and the end of a one-way excursion.

If you look at many of the relativity texts...

Do you know the statement of the twin paradox? It goes like this:

"...

In the Earthbound frame, the Earth clock is stationary, and the space clock is moving, and thus is running slower than the Earth clock. Therefore the Earth clock measures more elapsed time.

In the Spacebound frame, the space clock is stationary, and the Earth clock is moving, and thus running slower than the Space clock. Therefore, the space clock measures more elapsed time.

This is a contradiction!"

The flaw, of course, is that the person has applied the basic time dilation formula, which is only valid in inertial frames, to the spacebound frame, which is not inertial. That is why, when addressing the twin paradox, that authors mention the acceleration.

Anyway - if some SR advocates (e.g. hurkyl) and LR types are in agreement that the travelers clock runs slow

The notion of relativity forbids such a statement, because you have not specified the reference frame.

 

[yogi]

Hyrkyl - I will address a couple of your points which are crucial to your position - you claim that the clocks cannot be compared at the end of the one way trip - yes they can - I have stated that there is a clock on alpha that is in sync with the Earth clock (they are in the same frame and both clocks read proper Earth time and the separation distance is a proper Earth length) - when the traveler arrives the traveling clock will be together with the alpha clock and can be compared. If you state that SR dictates that these two clocks (the one fixed to alpha and the one carried by the traveler) read different times when the traveler arrives then there is no twin paradox because you are defacto advancing LR explanation - in LR there is no paradox because the clock that moves relative to the Earth centered reference frame runs slow - no acceleration is needed to distinguish the traveling sibling from the Earth sibling - no observation in other frames is significant and your own statement from a previous post attempting to explain the triplet paradox by saying that the reading of the outbound sibling's clock by the third inbound sibling will result in an informational change to a different reference frame causing a temporal shift... are exemplary of relatitivsts shifting positions when faced with the reality that clocks in relative motion run at different local rates.

 

[yogi]

Hurkyl - on the other hand, if you claim that the clock carried by the traveler will read the same as the clock fixed to alpha at the end of the one way trip - then there is a conflict between Einstein's statement that: if two clocks are originally in sync and one is moved relative to the other, they will no longer be in sync - nor will they be in sync if one is carried on a path that returns it to the original position. Winding up on alpha where you encounter an Earth synced clock is no different - the Earth clock will be out of sync according to Einstein and the alpha clock will be proximate to the moving clock at the end of the one way journey so that two clocks can be viewed simultaneously to see how much time has been lost.

 

[jdavel]

"djavel - I do not disagree with your observation..." (in #52)

There are no paradoxes in SR. The so called twin paradox is the result of describing the situation with sloppy language, nothing more.

Whenever there's an apparent paradox in SR, it's easily resolved in three steps:

1) Describe everything with events.
2) Define or caculate the coordinates of each event in one frame.
3) Use the LTs to find the coordinates of each event in any other frame.

That's it!

In this case,

1) Event 1: The traveller leaves the Earth at a speed v.
2) In the Earth frame, define this event's coordinates as x=0 and t=0.
3) In the moving frame the LTs give x'=0 and t'=0.

1) Event 2: The traveller arrives at the star.
2) In the Earth frame, let x=L, then t = L/v
3) In the moving frame the LTs give x'=0 and t'=(L/v)/gamma

That's it!

So when the traveller compares his clock with a clock on the star (synchronized with the one on the earth) the traveller's clock will be the one that's behind.

Where is the paradox??

 

[Janus]

Hyrkyl - I will address a couple of your points which are crucial to your position - you claim that the clocks cannot be compared at the end of the one way trip - yes they can - I have stated that there is a clock on alpha that is in sync with the Earth clock (they are in the same frame and both clocks read proper Earth time and the separation distance is a proper Earth length) - when the traveler arrives the traveling clock will be together with the alpha clock and can be compared. If you state that SR dictates that these two clocks (the one fixed to alpha and the one carried by the traveler) read different times when the traveler arrives then there is no twin paradox because you are defacto advancing LR explanation

No, because in SR there is the Relativity of Simultaneity. Let's by-pass any acceleration for now and just assume that our traveler is making a high speed fly-by of both the Earth and Alpha. We'll assume that the Ship clock can pass so close to the Earth and Alpha clock, so that at that instant the two clocks can be regarded as being at the same point, and that both Any observer can take a instant "snap-shot" of the clocks at this moment of passing to compare their readings.

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.

According to the Traveler the Earth and Alpha fly by in order and it takes a certain amount of time from the instant the Earth passes to the instant Alpha passes. Since the distance between Alpha and Earth undergoes length Contraction, the Time that the Traveler's clock records between the Passing of the Earth and Alpha then the Earth clock records in its Frame for the Traver to pass from Earth to Alpha. In fact the length contraction makes it work out that both the Traveler and the Earth agree as to what time is on the Traveler clock when it passes Alpha (but for different reasons).

The Traveler will also measure time dilation as effecting the Alpha and Earth clocks and will determine that less time will have accumulated on them between their respective passing.

But, According to the Traveler, the Earth and Alpha Clock are not in sync. They run at the same rate but the Alpha clock will read a more advanced time then the Earth clock. Thus when the Earth passes by and reads a certain time, at that instant the Alpha clock reads a much later time. Adding this Alpha clock reading to the time dilated accumulated time of the Alpha clock will give a certain time on the Alpha Clock it passes the Traveler. And this time will be the same as the time the An Earth observer would read on the Alpha clock as the traveler and Alpha Passed each other.

Again both observers agree as to what time is on both clocks, read when they pass each other,but for different reasons According to Earth the times read the way they do because the Traver clock ran slow, and according to the Traveler the times read the way they do becuase, While the Alpha clock ran slow, the time it started at( at the instant the Earth and traveler passed) was later than that that the Earth observer determined it was at that instant.

- in LR there is no paradox because the clock that moves relative to the Earth centered reference frame runs slow - no acceleration is needed to distinguish the traveling sibling from the Earth sibling - no observation in other frames is significant and your own statement from a previous post attempting to explain the triplet paradox by saying that the reading of the outbound sibling's clock by the third inbound sibling will result in an informational change to a different reference frame causing a temporal shift... are exemplary of relatitivsts shifting positions when faced with the reality that clocks in relative motion run at different local rates.

There is no paradox in SR because, when applied fully and correctly all observers will agree as to what time are read on clocks that are local to each other at any given time no matter which observer is considered the stationary one.

 

[yogi]

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?

 

[Hurkyl]

you claim that the clocks cannot be compared at the end of the one way trip - yes they can - I have stated that there is a clock on alpha that is in sync with the Earth clock

No, at the end of the one-way trip, you're comparing the space clock to the alpha clock. Whatever relationship the alpha clock has to the Earth clock is irrelevant to this statement.

there is no twin paradox

Of couse there is no twin paradox when you're only doing the entire problem in a single reference frame. I've stated at least twice, now, just what the twin paradox is, and I'll state it a third, hoping you'll read it this time:

(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.

If you're not talking about this argument, then you're not talking about the twin paradox.

If you state that SR dictates that these two clocks (the one fixed to alpha and the one carried by the traveler) read different times when the traveler arrives

If, in Earth's reference frame, the alpha clock and the Earth clock are syncronized (in a SR compatable way), and the spaceship's clock matches Earth's clock when the ship is on Earth, then the yes, SR states that when the ship arrives at alpha, the ship's clock does not match alpha's clock.

the triplet paradox

State the situation, and I'll tell you what SR says about it.

 

[yogi]

djavel -didn't mean to ignor your post - and yes - I fully agree there is no paradox if you claim that the clocks in the Earth alpha frame accumulate more time than the traveler's clock in the one way journey. Depending upon what janus says, I will follow-up on your interpretation of SR

 

[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.

 

[yogi]

pervect - Newton didn't say F = ma ... he said F = rate of change of momentum. That is valid as far as we know in any framework notwithstanding the later developments of Lagrange and Hamilton.

Questions of "why" have to do with pushing the goal post back a few more feet in our attempt to understand nature - there will always be one more question to answer - the question of "why" relates to finding an interpretation that betters our understanding of the next level - if we adopted your position we would still believe that Zeus was the cause of lightning. There is a great story told by Feynman in his chapter on lightning - and the Persian king who sought advice before invading Greece.

 

[yogi]

Hurkyl - "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."

I would agree with that - as for your next statement:

"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."

Yes - that is so according to the LT (we don't ever really make this measurement, but assuming arguendo it is true, it is not part of the analysis I have set out in the above posts... I have repeatedly stated that it is of no moment what the moving observer measures in the Earth frame - only Earth and alpha based observers can measure the proper time in the earth-alpha frame. The traveler measures an illusory rate when he looks at either the alpha or Earth clock from afar - but he can read the clock on the church tower on alpha when he arrives - and he can compare it to his own clock at that time because there is no vx/c^2 time slip when the two clocks are adjacent .

 

[yogi]

djavel - Take a look at Zhangs book - quoted with authority in FAQ in Physics. "There are no experiments that verify the one way speed of light is isotopic" If it is not, then any number of different transforms can be used to explain all of the known experiments. All of the alternative theories are based upon some difference between an isotropic frame and a frame that moves relative thereto. They all predict the same time dilation as Lorentz's transformations - and consequently all of the other predictions that flow therefrom - SR has been a successful theory - but the other theories make the same predictions w/o relying upon one way isotropy - a postulate that was unnecessary to explain MMx

 

[yogi]

Garth - I agree that the traveling sibling ages less - you say because of acceleration - but there are many authors that argue otherwise (usually they simply invoke a path integral approach using signaling techniques) Since acceleration does not affect local clock rate - nor can it influence the rate of the stay at home clock, how can it add time to the Earth system? The temporal influences that are posited to occur due to acceleration or changing frames can only be observational illusions - recall that this whole thread originated with triplets where there is no acceleration at any time - not at the start - nor at turn around (because there is no turn around).

 

[pervect]

pervect - Newton didn't say F = ma ... he said F = rate of change of momentum. That is valid as far as we know in any framework notwithstanding the later developments of Lagrange and Hamilton.

AFAIK what Newton orginally said (as nearly as exactly as a websearch can find, this may not be perfect) is:

1: A body remains in a state of rest or a state of motion unless a force acting upon it compels it to change.

2: Change occurs in proportion to the force applied and in the same direction.

3: For every action there is an equal and opposite reaction

Formulations of this as "F=ma" and F=dp/dt are all "different" than Newton's original formulation.

As I mentioned, there are additional formulations, such as the principle of least action which are entirely equivalent to Newton's laws.

In spite of the fact that the wording was different in Newton's time, I do not see people claiming that

1) We don't really understand Newton's laws
2) Physics is changing, explanations of Newton's laws are inconsistent
3) Respectable physicists all have "different" interpretations of Newton's laws

all things you've said about SR. In fact, most people (including you, I presume) seem to realize that "different" formulations of Newton's laws are not "different" if they lead one to the same identical results. Including, as I mentioned, the Hamiltonian or Lagrangian formulations (the former, in terms of the principle of least action, is quite elegant).

BTW, if you wish to distinguish Newtonian physics from relativity, you need to specify that momentum=mv, which implies that f=ma. If you don't make this assumption, you have implicitly allowed "Newtonian physics" to include relativistic physics, where p = mv/sqrt(1-(v/c)^2).

 

[pervect]

On isotropy:

Suppose an airplane leaves Los Angeles, Calif, at noon, and arives at Chicago, Ill at 5:40 pm, nonstop. Suppose the same plane leaves Chicago, Ill, at noon on the next day, and arrives at LA at 2:12 pm nonstop. And suppose Chicago and LA are 1749 miles apart. Is it physically meaningful to say that the plane flew at a speed of 308 mi/hr on the first trip, and 795 mi/hr on the trip back? Why or why not?

 

[yogi]

pervect:

1) We don't really understand Newton's laws
2) Physics is changing, explanations of Newton's laws are inconsistent
3) Respectable physicists all have "different" interpretations of Newton's laws

I have made no such statements about SR - if SR is incomplete or wrong it was just as wrong in 1905 as it is today. There were competing theories at the time - but there was no way to verify time dilation until we begin observing the lifetimes of muons and pions.

The reason no one is criticizing Newton's Laws is because they don't lead to paradoxical interpretations. And I don't need to write p = mv to know what is meant by rate of change of momentum - d/dt(mv). This impliedly takes into account the fact that mass may not be constant.

 

[pervect]

Well, your'e at least partially consistent then, Yogi, I suppose. Since we don't really understand Newton's laws after all these years, perhaps we should just give up science and become monks? I mean, what's the point, after all?

:-) for the humor impaired

 

[yogi]

Lets substitute a photon for the traveling twin - we will put a mirror on alpha and assume that alpha is 3 x 10^8 meters from earth. Clocks at Earth and alpha are in sync and the time read when the photon passes the Earth clock is zero. A clock in the photon frame logs "0" when the photon strikes the alpha mirror - the Earth and alpha clocks both read one second - upon return the photon clock still reads "0" but the Earth clock reads 2 seconds. Time passage in the two frames is not equal - half the time is accumulated in the earth-alpha frame on the outbound journey and half is logged on the inbound leg. How does acceleration (reflection) explain the difference between the time lost in the one way trip (between 1 second vs 0)? If the time lost is truly one second on the one way trip, does it not follow that acceleration and turn around have nothing to do with resolving the twin paradox?

Now let's look at things from the photon frame - no time is logged in the photon frame going out or returning - on the outbound leg the photon must see time in the Earth alpha frame passing more slowly if the situation is reciprocal - but this would mean the Earth time is accumulating at a lesser rate that zero [the proper time measured by the photon clock] Again, if that is what is observed, it cannot be a real.

 

[yogi]

Pervect - I was merely copying your statement from post 95 - forgot to put in quote marks - as I said - the interesting issue(s) with SR is whether two frames in relative motion can be treated as truly reciprocal as Einstein hypothesized - didn't mean to infer anything about Newtonian Physics.