The Twin Paradox: Understanding Time Dilation in Space Travel

[Garth]

there are no experiments that show that Earth clocks run slow when viewed from the standpoint of the traveler.

The difference in clock rates between two traveling observers is observed by each receiving signals from the other as a red shift effect. A spacecraft leaving Earth at high velocity will receive radio signals red shifted both by SR time dilation and GR gravitational effects. Has this not been allowed for in narrow band-width transmissions?

Garth

 

[yogi]

Garth - these are Doppler shifts that are observed when two frames are moving apart -they are blue shifted when the two frames are approaching - a lot of texts attempt to validate the reciprocity of SR using thought experiment signalling - but it is not a validation of SR - only a verification of Doppler.

 

[RandallB]

reciprocity! -I think I spoted your problem

Thanks for EPR

- there are no signals going back and forth between the Earth and the traveler - - the analogy to GPS I gave - we can endow the traveler with a second clock .

Nor do I use any "signals going back and forth" only monitoring a signal beacon continuously being sent out to the entire universe with some time and date stamps imbedded in it. If you like just use the TV and Radio broadcasts in place of a Beacon tower plenty of time stamps given in those.

While GPS is all about having signals going back and forth for the propose of keeping an artificial time piece on the satellites in-sync with Earth time. Easy to get confused in the GPS area.

BUT I think I spotted your problem if your willing to do the math to prove it to yourself.
In a word ‘reciprocity’:
Of course there is ‘reciprocity’ between the two observers. Otherwise well meaning but inaccurately descriptive statements like Earth clocks and distance lurching and jumping around would have to actually be true. The best way to see this ‘reciprocity’ is to make direct and immediate observations of the time in the other reference frame! Not that hard to construct even for the twins. You need a string of stations with clocks on display from Earth Station to the Turn-around Station. And following behind the ship a string of ships or attached probes displaying their clocks to the stations.

Ship clocks in sync with ship clocks – Station clocks in sync with stations. Now when the twin on Earth that waves goodbye to the traveling twin hangs around the station to watch the clocks chasing after him will clearly see that the traveling clocks are running FASTER than the station clock. Just as the traveling twin looking at the stations go by can clearly see that the station clocks are also running FASTER. Perfect ‘reciprocity’. Each twin can directly see the other is already getting “older” faster and if you were to jump across to the other reference frame speeding by and walk up to find the twin the age difference is already set and won’t change. To make the reunion quicker with any effort to 'walk' at near Light Speed will only make the difference larger.
Observing clocks in the other frame running FASTER from their view out the Station or Ship is a direct result of the individual clocks in the other frame running SLOWER!

GPS
Now the same ‘reciprocity’ applies to GPS. But be sure your using real time on a series of GPS “ships” chasing a leader all synchronized within there own reference frame. As the Earth observer looks up as they go by, the “Clock in Display” overhead will show as running fast. Just as the observer looking down sees the same. But the real clock on the lead ship (and all of them) would actually be running slow.
What your doing is assuming that the lead clock that comes back around on the next orbit is still in sync with itself as if it were one following behind the leader. It is not. If you don’t sort out the time synchronization and distances of the GPS ships within their own long line reference frame, you cannot just slam in SR or LR calculations. If you do -- the ‘reciprocity’ your looking for will fall into hands with ease.

Remember the clock that the Earth clock is running slow against the clock in the lead orbit. That is not the same as the same physical clock that has come around and views or is viewed in any furture orbits. To make that direct comparison you need take the test Earth clock up into a chasing faster orbit until catching up to the same lead lap as the starting clock. And then ‘reciprocity’ THAT traveling Earth clock will indeed be younger than the clock it chased down after it has lapped it enough times. Thus ‘reciprocity’ still holds.
Only accounting for SR of course not GR.

 

[yogi]

RB - In the series of clock(s) systems thought experiments - what results is that each observer, when viewing a single clock in the other frame, will see it going slower - but when viewing a succession of passing clocks the opposite is true - but that doesn't address the problem because we can never have two clocks each running slower than the other - and we can never have a first clock running slower than a second clock w/o some physical reason.

If you read Einstein's first relativity paper, he develops the transforms by making observations as to how things would appear in a moving frame -- during this development he states parenthetically three times (the other clock appears to run slow when viewed from the other reference frame). Then he makes a profound change - and goes on to discuss how two clocks in the same frame would be out of sync if originally in sync and one is moved with respect to the other and returned - he gives no physical reason for this - there is no justification for utilizing transforms derived from observational distortion viewed from another frame to predict actual time dilation in your own frame. When the GPS system was under development, a number of physicists and engineers believed that no SR correction would be required for the on board clocks - since according SR, neither clock should be running faster than the other because of the equivalence of the two inertial frames. Now, while it is undoubtedly true that, were you to make measurements of the rate of a single Earth clock using a proper distance in the satellite frame and two synced clocks on board, you would measure the Earth clock to be running slower (again we are not considering the height). But as I keep saying - that is observational - it does not mean the Earth clock is really running slower. In reality, the Earth clock is running faster and that is why the GPS satellite clocks are preset to run faster prior to launch so that they will run at the same speed as Earth clocks when in orbit.

The problem is not with the transforms -but with their application - they can be applied one way - and then the predictions correspond with the experiments.

 

[RandallB]

RB - In the series of clock(s) systems thought experiments - what results is that each observer, when viewing a single clock in the other frame, will see it going slower - but when viewing a succession of passing clocks the opposite is true - but that doesn't address the problem because we can never have two clocks each running slower than the other - and we can never have a first clock running slower than a second clock w/o some physical reason.

What in the world are you talking about?

"we can never have two clocks each running slower than the other"
Are you talking about the twins oor are you confusing it by jumping over to GPS all ready.

The clocks on the ship don't run slower than each other - the run at the same rate! And when measured from Any Earth Frame Station they are slow. BUT when viewing the succession of passing clocks they appear to run FAST.! How and WHY is that??

If you cann't answer that! Your not ready to to even consider GPS.
But I think you can - you only need to apply the same, correctly, to the GPS area and you will be fine.

Qouting something from history won't help here just the simple and correct and complete problem layout math will. You don't need a second clock on board the GPS_Sat to see "Earth Time" - Just look out the window.
Problem is as your go around the eath and find the same physical clock below you, your thinking it is the same clock you saw several orbits ago --- IT IS NOT --- that clock is running slower, in a different time and space miles and miles (and orbits) behind you. From the GPS-Sat you have already traveled into Earth's future by traveling out - turning around - and coming back - just like the Twin.

It's just that simple.

RB

 

[Garth]

Garth - these are Doppler shifts that are observed when two frames are moving apart -they are blue shifted when the two frames are approaching - a lot of texts attempt to validate the reciprocity of SR using thought experiment signalling - but it is not a validation of SR - only a verification of Doppler.

The Relativistic Doppler formula is the classical doppler shift multiplied by a factor to account for time dilation. Alternatively this relativistic correction can be interpreted as an allowance for 'relativistic mass'. They are the same effect. If relativistic doppler is verified by measurement, and not just standard non-relativistic doppler, then indeed the mutuality of SR time dilation has been confirmed.

Garth

 

[Hurkyl]

Time dilation has nothing to do with one clock running faster or slower than another clock -- the idea doesn't even make sense, except possibly for a brief instant when both clocks are at the same place.


Time dilation is about a clock running faster or slower than the time coordinate of a coordinate chart.

 

[RandallB]

Time dilation has nothing to do with one clock running faster or slower than another clock -- the idea doesn't even make sense, except possibly for a brief instant when both clocks are at the same place.


Time dilation is about a clock running faster or slower than the time coordinate of a coordinate chart.

What can that possibly mean?
The idea that a clock can somehow refer to a time coordinate on a chart to determine its dilation doesn’t make sense to me.

We can and have seen clocks in different reference frames display different rates of time and those differences have been shown to be real. Time dilation as defined in SR & GR has everything to do with explaining those differences.

 

[yogi]

RB - there is a time slippage term vx/c^2 that accounts for the fact that when a series of clocks are viewed by a moving traveler in the other frame - time appears to go faster. But if you make measurments in a frame using the method endorsed by the standard relativity texts, you use two clocks in your own frame and a measured proper distance between them in your own frame and you read the passing clock as it passes the first clock in your frame and again when it passes the second in your frame and that will tell you the relative clock rate difference - you do not do it by making an instantaneous look at the hands of a single clock in the other frame, or by viewing different clocks in the other frame.

The history I gave you is not a subtrifuge - it is the reason for the difference between LR and SR - Einstein made an unjustified transitition from observed clock slowing to real time dilation - in consequence the velocity transforms are correct but they cannot be reciprocally applied - when there are two clocks in different systems, each cannot be running slower than the other - the reciprocity ends when it is shown that one clock actually runs slower than another. This is the lesson of GPS and hi speed particle lifetimes.

 

[Hurkyl]

(Coordiante) time, in a reference frame, is not merely measuring the time of an event with your local clock -- your clock can only measure the times of things near it. You need some additional method to "extend" your clock to work at distant points. In any flat space-time theory, one way to do this is to hypothesize you have a network of co-stationary clocks¹, and have applied some algorithm for synchronizing them. Now, you have a way to measure time anywhere in the universe, called coordinate time.


One way of synchronizing a pair of co-stationary clocks is this:

Clock A sends a signal to clock B.
When clock B gets the signal, it sends a signal back to clock A.
When clock A gets the signal, it sends its time on a signal back to clock B.
When clock B gets the signal, it can then compute the "current time" to be the time it received from clock A, plus half the time it took for a round trip from B->A->B.

(A simple modification can be made if you don't want to make the initial assumption that A and B run at the same rate)


Once you have this explicit definition of how time is computed in a reference frame, it's fairly easy to show, in both frames, that the clocks stationary in that frame run faster WRT coordinate time than those that are moving.


1: you need the assumption of a flat space-time to have a notion of co-stationary

 

[RandallB]

Thanks

Thanks guys – It has been interesting seeing at least part of the argument for LR. And yogi I really do understand how your viewing GPS and your helping to convince me that the arguments for LR (at least that I’ve seen so far) are a canard since they don’t maintain a flat space-time. When I see other arguments for LR, I’ll know to look for the basics to spot the flaw.

Thanks Hurkly for the support; you’ve given the best outline for showing the flat space-time in the orbiting GPS. I have to admit it was a little hard to see at first.

Using the synchronizing method as recommended on just one GPS satellite. Use it’s Master clock as clock A. Set aside an onboard area to represent the clock B of the satellite following one orbit behind (Sat. Ref Frame). Sending the light synchronizing signal around and back divide the interval by 2 add to the time on the Master clock and you have the time for that perfectly time synchronized B clock in the “following satellite”. Although it isn’t the same time as the master clock just an inch away, it is exactly the same time. Plus once you have this “winding” difference you can easily interpret the cock time on forward orbits and following orbits (Or windings).

For me SR shows itself, not LR.

Once again yogi the circle / the orbit going away and coming back, is most like the Twin that has gone out and returned not the one that has kept going.
RB

 

[yogi]

Have a relatively Merry Christmas

 

[jdavel]

yogi,

I just made it through this thread. Actually, I had an absolutely merry christmas, but thanks anyway!

One question. If the outbound triplet travels at a speed v to a star that is a distance L from the Earth (as measured by the stay-at-home triplet) what will the traveler's clock read when he arrives at the star?

 

[yogi]

jdavel - I thought the thread had died - but still some interest - your question is at the center of the controversy - If I try to answer from the SR standpoint, I will probably be attacked by those who have a definite conviction as to how SR explains these things - but I will try in any event. 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. If one champions LR, then they would answer that the clock carried by traveler would accumulate less time because it is in motion wrt the Earth reference system which appears to be an isotropic frame for light. We don't ever really do the twin and triplet experiments of course - what we do is offset GPS clocks so that the one which moves relative to the Earth frame runs faster to account for time rate difference. To eliminate the gravitational potential difference we can use a hi speed train on the Earth's surface. The LR advocate will say the clock in the train actually runs slower, so we have to preset before departure so that it will correspond to the Earth clocks everywhere it travels - the SR advocate will claim that the train clock runs the same as the Earth clock in the train frame, but it appears to run slow when viewed in the Earth system - so likewise he will use the same transform to preset the clock to run faster so that it sends signals that correspond to Earth's clocks. At this point, both have used the same transforms and both will argue that the preset is needed to make GPS work, but both the premise and reasoning are different. Which is right? You cannot tell in this case because you don't have enough data - but if the train carred a second clock that had not been modified by preseting its rate - you would have a way to distinguish how nature really behaves - because if you bring the train to a stop and the second clock reads the same as the Earth clock when they are compared, you would have to conclude that SR is correct and the train time clock rate difference is/was apparent because of the trains motion. On the other hand, if, when you brought the train to a stop the second train clock has accumulated less time during the trip than the Earth clock(s), you would be disposed to believe that motion with respect to the earth, for whatever reason, causes clocks to actually run slow. And if the second train clock is in fact found to have lost time during the experiment, so also would the clock carried by the traveling sibling.

 

[Hurkyl]

One question. If the outbound triplet travels at a speed v to a star that is a distance L from the Earth (as measured by the stay-at-home triplet) what will the traveler's clock read when he arrives at the star?

Making the assumptions I think you intended (ignore gravity and rotation, and the star is stationary WRT Earth), SR certainly says it will read

$$\frac{L}{v} \sqrt{1 - \left(\frac{v}{c}\right)^2}$$

I'm pretty sure LR would as well.


It doesn't make sense to ask what the Earthbound triplet's clock reads until you have selected a procedure for assigning times to distant events. (Einstein's procedure, for the thing SR calls his rest frame, would yield L/v)

...

Your train experiment isn't crystal clear, but I do think it's clear you're mistaken about what SR says -- assuming the Earth's frame is inertial, if you put a normal clock that reads the correct time (your "second clock") on a train, let the train run, then stop, then SR says that clock has indeed measured less elapsed time than stationary Earth clocks.

 

[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.