The Twin Paradox: Understanding Time Dilation in Space Travel

[ElectroPhysics]

As I'm involved in electronics industry due to my job requirements, I can't manage myself for Physics study. That is why I'm putting my questions here and hope you guys will try to answer them. Similarly, I will also try to answer some of your questions.

Suppose A and B are two persons at rest on the Earth surface. Then suddenly B starts its journey in a spaceship towards space in a straight line. When they both meet again we see that B is younger than A. How is it possible?

 

[pervect]

Look through this board for the words "twin paradox". You can also do a websearch for the same phrase, but there's a lot of misinformation on relativity on the web. You can rely on the sci.physics.faq entries, though, and there is definitely a discussion of the twin paradox there. I'm feeling a bit lazy tonight, so I'm not going to type the URL in, because this topic has been discusses a bazillion times already, and it should be easy to find.

 

[yogi]

You will find literally hundreds of articles on the subject of time dilation - and you will find that the explanations fall into several different catagories. Those that strictly adhere to the formalism of SR usually explain the age difference as being due to one of two causes 1) The dynamic theory states that one of the two observers experiences acceleration in turning around and returning, and therefore he changes inertial frames whereas the stay at home observer remains in the same frame so either SR doesn't stricly apply, or what amounts to the same thing - the problem is resolved via resort to GR 2) The kinetic theory dismisses the acceleration explanation and presupposes that the totality of the path integral going away and returning will always involve less time as accumulated on a clock carried by the traveler. This line of inquiry is adopted by some well known and respected Relativity authors such as Robert Resnic. If you venture further into alternative theories like Lorentz Ether, the age difference is explained as a physical consequence of motion wrt space. The point of all this is that there is no universally accepted answer.

 

[selfAdjoint]

Yogi, your point one is a confused double of point two. The curved worldline which accumulates less proper time is necessarily the world line of an accelerated body; the slope of a world line relative to the time axis gives its speed, and if the slope varies (curvature) so does the speed (acceleration). Then the lesser proper time comes directly out of the Minkowski version of Pythagoras' theorem (with a minus where P. has a plus). This is all entirely within SR, you don't need GR at all. The idea that you need GR to handle acceleration is a myth.

And your third explanation is an ether one that is not accepted by 99 and 44 one hundredths of physicists, so really shouldn't be included.

 

[yogi]

SA - I would agree that you don't need GR to deal with Time dilation in the turn around - but you will find it in many analysis of the subject which was the subject of my post (not my belief). Nor do I endorse the kinematic explanation proferred by Resnic.

99 and 44 one hundredths of the physics must be pure - like ivory, they float... but they cannot explain the triplet version of the twin paradox. Until the moral majority can provide answers that are verifiable, it is important to keep an open mind.

 

[RandallB]

... but they cannot explain the triplet version of the twin paradox.

. Yogi
What is the "triplet" version of the twins 'paradox'.?
Once someone understands and can explain the twins COMPLETLY. I don't see how a triplet could be a problem.

RB

 

[yogi]

RandallB - the triplets version has the two siblings clocks in sync as they depart (we avoid the issue of initial acceleration by having the outbound traveler (2) already up to speed as he flys by the stay at home sibling (1) at which point they sync their clocks. The traveling sibling (2) proceeds at a high uniform velocity to some destination where he would normally turn around and head home and incur the turn around acceleration forces that are normally invoked to explain why there will be an age difference. Instead of decelerating, travler (2) simply transfers his clock reading to an inbound traveler (3) (doesn't have to be a sibling - rather any inbound traveler will do) who had left some time previously and is now returning home to reunite with (1). Traveler (3) is inbound at the same velocity as traveler (2) outbound velocity - from the standpoint of the path integral approach, the total time accumulated by the clock (2) and clock (3) will be less that the time accumulated by clock (1).

When inbound 3 reaches (1) back on Earth ---If the total time logged by clocks (2) and (3) taken together is less than the time logged by (1) there is an intrinsic difference in the frames of the moving clocks. But this is contrary to postulate that neither (1) nor (2) nor (3) can measure velocity wrt absolute space, and therefore there is no reason to presume that clocks (2) and (3) run slower than clock (1). Since the transference of the reading from outbound (2) to the inbound traveler (3) does not involve acceleration - the paradox continues

 

[Garth]

ElectroPhysics - The fact that the two observers age at different rates is not a paradox. What is a paradox is that as each observer is in an inertial frame of reference each twin thinks the other is 'younger'. When they meet again one must be actually be younger than the other, but which one? It is the one who has had to accelerate to turn round, and therefore not continue in an inertial frame of reference. The SR twin paradox is resolved by considering the two observers different surfaces of simultaneity.

However in the cosmological twin paradox in a closed universe two observers could meet and one circumnavigate the universe and they meet again much later. Now each one has been in an inertial frame of reference, each one thinks the other has circumnavigated the universe and is therefore the 'younger'. So when they meet again which one will actually be the younger?

This has been discussed here.

Garth

 

[jdstokes]

RandallB - the triplets version has the two siblings clocks in sync as they depart (we avoid the issue of initial acceleration by having the outbound traveler (2) already up to speed as he flys by the stay at home sibling (1) at which point they sync their clocks. The traveling sibling (2) proceeds at a high uniform velocity to some destination where he would normally turn around and head home and incur the turn around acceleration forces that are normally invoked to explain why there will be an age difference. Instead of decelerating, travler (2) simply transfers his clock reading to an inbound traveler (3) (doesn't have to be a sibling - rather any inbound traveler will do) who had left some time previously and is now returning home to reunite with (1). Traveler (3) is inbound at the same velocity as traveler (2) outbound velocity - from the standpoint of the path integral approach, the total time accumulated by the clock (2) and clock (3) will be less that the time accumulated by clock (1).

When inbound 3 reaches (1) back on Earth ---If the total time logged by clocks (2) and (3) taken together is less than the time logged by (1) there is an intrinsic difference in the frames of the moving clocks. But this is contrary to postulate that neither (1) nor (2) nor (3) can measure velocity wrt absolute space, and therefore there is no reason to presume that clocks (2) and (3) run slower than clock (1). Since the transference of the reading from outbound (2) to the inbound traveler (3) does not involve acceleration - the paradox continues

The resolution is trivial. Proper time is defined as the time as measured by a single clock. It is obtained by integrating the proper time differential along an observer's worldline. The clocks in (2) and (3) belong to different inertial frames of reference. It makes no sense to add the proper times of two different clocks in the same integral.

 

[selfAdjoint]

Exactly, it is the proper time of the clock, not the observer's, and when you separate the two, and accelerate the clock, by passing it between two frames with a speed difference between them, you invoke the Minkowskian rule, and the clock shows less. The triplets all in their own frames remain symmetric.

 

[yogi]

If The total time logged by clock (2) going out is the same as the total time logged by clock (3) in returning to Earth and the total time (2) + (3) is less than (1) then clocks (2) and (3) will be running at a different rate than clock (1). There is no acceleration at any point in the experiment -reading a passing clock cannot have a physical affect.

 

[jdstokes]

If The total time logged by clock (2) going out is the same as the total time logged by clock (3) in returning to Earth and the total time (2) + (3) is less than (1) then clocks (2) and (3) will be running at a different rate than clock (1). There is no acceleration at any point in the experiment -reading a passing clock cannot have a physical affect.

The time difference is not caused by acceleration. The transfer of the clock reading from (2) to (3) changes the inertial frame of reference, instantaneously swinging the hyperplane of simultaneity through time so that the Earth time jumps many years into the future, accounting for the time difference when (3) passes by (1).

 

[yogi]

This is the absurdity of trying to rationalize age difference using the "apparent times" observed by clocks in motion relative to the observer as "physically real times." Reading a local clock (2) cannot influence the reading on the clock, nor can it influence the proper time of the Earth clock. The total proper time logged on clock (2) at the time it is read when added to the proper time logged by clock (3) after being set to the clock (2) reading at the meeting point of (2) and (3) will determine the age difference when compared to the proper time accumulated by (1) when (3) returns.

Changing the inertial frame by reading clock (2) and setting clock (3) in reference thereto is no different that the pass-by sync of clock (2) with (1) at the outset - where is the physics that requires the hands on clock (1) to instantly spin forward at the time of the transfer. Apparent times cannot be magically invoked to bring about physical changes.

 

[gonzo]

I'm curious about something in general here. I've seen a lot of references to thought experiments involving the reading or syncing of two clocks in different reference frames as they "pass by" each other in an attempt to avoid dealing with acceleration.

I really must be missing something here, because it seems to me that this is invoking some magic faster than light method of conveying information. If a ship passes an oberserver at high eough speed that we are dealing with noticeable relativistic effects, aren't there problems with defining how you read each other's clock when they pass, and what that even means?

How do you even theoretically attempt to sync two clocks rapidly moving with respect to each other?

 

[Garth]

The observers are passing close by each other, they can measure their relative velocity, predict the point of closest approach, pass a light signal and make any necessary adjustments as they read their respective clocks. In due time they can send each other the time recorded on their own clock for comparison.

Garth

 

[RandallB]

ElectroPhysics
When they both meet again we see that B is younger than A. How is it possible? Well first you will need to define when and where B is going to turn around. Because that's the only way they will meet again and unless they meet nobody gets older than anybody - at least not that they can tell.

The time difference is not caused by acceleration.

jd is letting you know that the Triplets thing and using Sync data Xfer infromation to create 'new clocks' in other referance frames all to avoid "Acceleration" is not needed at all.
Acceleration has nothing to do with what your looking at - if needed just assume you make your speed changes in a very short time like one minute - or even less.
To account for acceleration when when make speed changes you may just assume time clock going with B simply stops for the duration of the acceleration. That missing one minute ( or nano second) makes no differace to the rest of your problem.

The important part is that during the transfer of the Twin from frame (2) to the returning refrance frame (3) -- or as jd puts it:

The transfer of the clock reading from (2) to (3) changes the inertial frame of reference, instantaneously swinging the hyperplane of simultaneity through time so that the Earth time jumps many years into the future, accounting for the time difference when (3) passes by (1).

... that you know when and where you are.

Now as jd put it - it's a little hard to figure -- here is the EASY way to understand it.
Figure the returning speed change in two steps. from Ref frame (2) to Ref Frame (1). Stay for just a minute (Or just a nano second if you like).. Then go from Frame (1) to Frame (3) for the return trip to Earth.

Now the key thing is to take the time to figure out just exactly WHERE and WHEN you are while in sync with Earth in frame (1) as your making this turn in direction. Remember only the clocks in Frame one are the same as back on Earth the clock with the twin, having been 'slow' will be behind.
Now that you know for sure what time it already is back on Earth, and how far away it is in Earth's frame, then start your trip back.

You won't understanding the "swinging the hyperplane of simultaneity" (not that you need to, & I'm not sure there is such a thing a "Hypeplane") until you understand the numbers you get this way, And you should be starting to understand simultaneity whitch is jd's point.

Randall B

 

[yogi]

The point of introducing a third traveler is to provide a graphic example that does away with acceleration as the "easyout" explanation that purports to resolve the twin paradox in about 60% of the relativity texts. Experiments have shown that acceleration in and of itself has no effect on time dilation (e.g., hi centrifugal accelerations yield the same clock rate changes as those which correspond to the velocity difference between the two frames).

Experiments also show that when objects move relative to the non-rotating Earth centered reference frame they will experience clock rate slowing. There are no experiments to my knowledge that show the reciprocity demanded by SR. If we substitute a high speed pion for the outbound traveler, the clock carried by the pion will read less at the turn around point. There can also be an Earth referenced clock (4) at the turnaround point and this can always be maintained in sync with (1) since these two clocks are not in motion wrt one another and the distance between them is a proper distance as measured in the Earth frame. Since the pion's clock shows less time than (4) at the time they are proximate, the explanation for the outward age difference is due to a difference in the velocity of the pion with respect to the earth. If the pion is reflected off a mirror (e.g., like a photon) the acceleration would be infinite, but there is no time added to the pions clock, and there is certainly no time added to the Earth synced clocks (1) and (4). Upon returning to (1) the total age difference is = (1) - [(2) + (3)]. This may look like SR but its not - its a clear example of LR

 

[Garth]

Draw two diagrams from the point of view of each observer and accurately draw in the surfaces of simultaneity of each. The observer that reverses direction "swinging the hyperplane of simultaneity" is the one with the shortest proper time.

Garth

 

[jdstokes]

Gonzo's point is an excellent one. It is impossible to synchronize two clocks in a given point as it requires infinite bandwidth---violating shannon's theorem. In order to transfer any information, an acceleration is required to generate the signal, two such signals are required to determine a velocity, separated by a distance of at least a wavelength. By introducing triplets you have merely recast one unphysical aspect (a discontinuity in the worldline corresponding to infinite energy) into something equally unphysical. The only way to circumvent the bad coordinate is to use a worldline for which the tangent vector is defined everywhere along the path.

 

[Hurkyl]

The point of introducing a third traveler is to provide a graphic example that does away with acceleration as the "easyout" explanation that purports to resolve the twin paradox in about 60% of the relativity texts.

It does explain the misconception maintained by most people befuddled by the twin paradox, which is as follows:

If I'm the outbound observer, how can:
(1) I observe the Earthbound clock running slower than mine as I head out.
(2) I observe the Earthbound clock running slower than mine as I head back.
(3) I find that the Earthbound clock reads more than mine when I arrive.

The problem with this perspective, of course, is that it neglects the change of reference, caused by the acceleration, that causes the Earthbound clock to lurch forward in your coordinate reference frame.

If we substitute a high speed pion for the outbound traveler...

As an aside, in the pion's frame of reference, the two earthbound clocks were never synchronized -- the one to which it is headed will always read more than the other one. (Yes, that means that will change after reflection)

 

[yogi]

Hurkyl: "The problem with this perspective, of course, is that it neglects the change of reference, caused by the acceleration, that causes the Earthbound clock to lurch forward in your coordinate reference frame."

There is admittedly a change in reference - but the lurching forward of the Earth time is strictly an observational consequence of viewing clocks in other reference frames which cannot alter the reading of clocks in your own frame - and it can't change the Earth clock. It is a distortion, an apparent effect. It is an artifact to which relativists must resort to avoid the anathema of a preferred frame of some sort.

When we increase the rate of GPS transmitter clocks to account for their relative velocity wrt the Earth centered reference system, things work fine. If we viewed the satellite frames as equal (totally equivalent) to the Earth centered frame, we could in principle instead adjusted the Earth clocks to run faster - but the system would not work.

What I said above ignors the GR correction which actually requires an opposite offset. But in GR the difference in clock rates is absolute, not reciprocal - both can agree upon which clock runs slower - and we use this fact to offset for the altitude in GPS - and whether relativists like it or not, we treat the SR correction as absolute rather than reciprocal when we preset the rate for both corrections prior to launch.

 

[Hurkyl]

but the lurching forward of the Earth time is strictly an observational consequence of viewing clocks in other reference frames which cannot alter the reading of clocks in your own frame

I'm not sure precisely what you're saying here, but it might be related to an imprecision of speech. The measurements of an accelerated reference frame, in SR, are generally given by a "co-moving inertial reference frame". That is, the reference frame of an accelerating observer should always agree with a hypothetical inertially traveling observer that happened to be at the same point, moving with the same velocity, and oriented in the same way.

When you accelerate, the hypothetical inertial observer must switch -- thus we say that when you accelerate, you switch reference frames, meaning that you have switched which inertial reference frame agrees with your observations.

It is a distortion, an apparent effect. It is an artifact to which relativists must resort ...

It is the measure of the rate change of the proper time of the observed object against the coordinate time of your reference frame -- nothing more, nothing less. (And nothing that isn't part of Lorentzian relativity either)

to avoid the anathema of a preferred frame of some sort.

The "avoiding" of the preferred reference frame is precisely because the designation of which reference frame is preferred is irrelevant. You've been tacitly assuming that the Earth's reference frame is the preferred one, but how do you know? Even if you're wrong, you still get the right results! (Thus, the lack of a preferred frame!)

and whether relativists like it or not, we treat the SR correction as absolute rather than reciprocal when we preset the rate for both corrections prior to launch.

No, you don't. You're synchronizing the clocks to agree with a very precisely defined coordinate reference frame, not to some notion of an absolute time.

 

[yogi]

Hurkyl - when I said absolute I was referring to the non-reciprocity of the clocks at different altitudes - not absolute in the sense of a universal time - there is, as you say, a precise clock rate associated with the Earth reference frame - GPS works because the non rotating Earth centered frame is taken as preferred for the purpose of clock synchronization.

 

[Hurkyl]

And the reason for that "preference" is because it's a simple means to an end, not because there's some cosmological reason that makes it an innately "better" frame.

 

[RandallB]

If the pion is reflected off a mirror (e.g., like a photon) the acceleration would be infinite, but there is no time added to the pions clock, and there is certainly no time added to the Earth synced clocks (1) and (4). Upon returning to (1) the total age difference is = (1) - [(2) + (3)]. This may look like SR but its not - its a clear example of LR

May look like SR? If you mean Special Relativity it IS only an effect of SR, it certinly doesn’t have anything to do wiith GR (General Relativity)! And what the heck is “LR” - nothing clear about what that is to me. Did I miss somebody named Larry coming up with an additional relativity theory?

 

[Janus]

And what the heck is “LR” - nothing clear about what that is to me.

I'm pretty sure that he is referring to Lorentzian Relativity.

 

[Janus]

There can also be an Earth referenced clock (4) at the turnaround point and this can always be maintained in sync with (1) since these two clocks are not in motion wrt one another and the distance between them is a proper distance as measured in the Earth frame.

You do realize that clocks 1 & 4 are only in sync (show the same time) in the frame of clocks 1 & 4, and will not be so in the frame of the pion, don't you?

 

[RandallB]

Gonzo's point is an excellent one. It is impossible to synchronize two clocks in a given point as it requires infinite bandwidth---.

Of couse you can synchronize any two clocks and at given time and place for each. We do it all the time you just need one good Sync Pluse to coordnate with. Don't matter if it's a Clock on Mars, or a GPS Orbiting earth, or the Space Ship going at 0.8c we can easily plan and sync the clocks. We have all the time we need before the event to exchange data and information. And we may need a bit of time after the event to receive data and information. But we know distances, speed of c, times we actually receive their synce pulse. We can share or observations back to the other "observer"
as they share theirs back to us. The fact the time dilation becomes involved in the adjustment required is a result of accurately interpreting the data and information received.

And for the propose of the TWINS we can be sending out timed light pluses at regular intervals from all points of interest - helps a lot in explaining the results seen.

Getting clocks in sync when they pass by each other – no big deal.

RB

 

[RandallB]

I'm pretty sure that he is referring to Lorentzian Relativity.

Thanks - made for an intesting search.
– suppose I should have guessed from the L
BUT,
The aether is real, Speed of light is not always “c”, and particle influences can exceed the speed of light.

And this from LR being right and SR is wrong ?

mmmm - I think I’ll stick with SR.
RB

 

[yogi]

JANUS - yes I am fully aware that (1) and (4) will not appear to be in Sync in any other frame - as you will recall during our previous discussion dealing with this paradox, I have attempted to synthesize the geometry by insisting that each participant read only clocks which are at rest in his frame -these times are not distorted by relative motion. There is only one point where the traveler (2) looks at (4) and that is when he is adjacent (2 and 4 are proximate).

If you use two clocks in the outbound travelers spaceship and set (say clock 5) to run faster (to account for the velocity difference) so that at all points it corresponds with the Earth time at (1) and (4) as we do in GPS, and the other on board clock (2) reads the proper time according to the frame of the moving twin - the two clocks (5) and (2) will not keep the same time.

Either the outbound traveler sees his local clock (2) as different from his on board GPS clock (5), or he doesn't. But if GPS is to work - (2) cannot read the same as (5) in the frame of the outbound traveler at any point in the journey. If the two clocks read the same, why would we bother to preset the trasmitter clocks prior to launch?

RB - if you don't like the reality of the ether, you won't like Einstein's 1920 address at the university of Leyten. And if you don't like influences faster than c, you won't like the experiments that were conducted by Alain Aspect that disproved EPR, and before you cast your vote for SR you might want to reflect upon what it's founder had to say near the end of his life:

“There is no idea of which I would be sure that it would stand the
test of time, and I have doubts whether I am on the right way
In general ...feelings of dissatisfaction come from the inside.”

 

[pervect]

The EPR experiments are spooky, but they don't involve sending actual signals faster than light.

Believing in the ether isn't a guarantee of bad physics, as long as one realizes that it's not detectable by any known experiment. Most ether propoponents, though, have a false notion that the ether is detectable experimentally, including much of the LR crowd which I gather you are a member of.

There's not much to say on this topic that hasn't been said a zillion times before, though.

 

[russ_watters]

RB - if you don't like the reality of the ether, you won't like Einstein's 1920 address at the university of Leyten.

You're referring to the oft discussed quote where he says something to the effect of 'I can't imagine a universe without an ether'? We've discussed it here and if you take it in context you will see that he is not talking about the same ether that you are.

 

[yogi]

Russ - what Einstein was talking about is anybody's guess - it isn't just one little statement - it is several strong paragraphs - bolstered by later statements. As I read them they are meant to correct the impression that Einstein did not believe in a physical ether (albeit he renamed it space). AS you previously commented he concludes with a comment that the idea of motion cannot be applied to it (a SR saving statement). All the rest is aimed at describing a "sui generus" medium

Pervect - I didn't say Bells Theorem could be used for sending informational signals - but what did come out of the experiments was a defeat for EPR. Whether entangled quantum states can be used to transmit information is not known as yet. Moreover, LR as I interpret it, does not say that information can be transmitted FTL, it is simply silent on the issue as opposed to SR where c is an absolute limit.


I don't want to take the time to dwell on this - but one could argue that the instantaneous change in the reading of the Earth clock as observed by the turn-around traveler is an FTL effect.

Regarding LR - I do believe strongly in the ether 1) because of its detectable and measurable electrical properties, 2) because it determines the velocity of light and radio waves,
3) because the distortion of space as per GR is the best explanation of gravity that has been put forth and 4) because we detect an inertial force instantaneously whenever we accelerate masses.

If a preferred frame better explains nature, then I would not apologize for being in that camp. Physics should be based upon something other than majority opinion. While it is saver to be on the SR bandwagon if you want to publish in peer reviewed journals, there are vexing questions that are not answered to the satisfaction of many. AS I have often quoted, Einstein's doubts grew as he aged - we know the velocity transforms work to yield the many successes of the theory - but in truth Einstein was shifting back-and-forth between the reality of time dilation and the apparency of time dilation as observed in a frame in motion relative to the frame of the observer.

 

[RandallB]

What is EPR?

I’m not up on as much of the History of Einstein or even some of the short hand ‘code’ used in the forum. I hope I’ve interpreted FTL to mean ‘Fast Than Light’ correctly - what does “EPR experiments” refer to?

the instantaneous change in the reading of the Earth clock as observed by the turn-around traveler is an FTL effect.

SR ----- there are vexing questions that are not answered to the satisfaction of many.

Yogi – I assume your one of those many.

But I cannot find one of those “VEXING” questions not answered here.
Can you give an example of one that details what the expected or obvious result is in enough detail that I can see where SR fails to describe it. Or at what level of “Satisfaction” it comes up short. I’m just not finding a conflict, error or even confusing point here.

As to the FTL effect:

I don’t think they mean too; but Hurkyl Garth and others all seem to agree with you that a real FTL event is taking place when the traveler turns around with comments like:
"swinging the hyperplane of simultaneity"
that causes the Earthbound clock to lurch
Earth time jumps many years into the future
These seem to show that big changes in Distance and Clock times are taking place!

But, at the time of reversal at an “Earth Based Reference Frame” Space Station. If the traveler transfers to the Station for a few minutes before boarding another Ship heading back to Earth. And all the while monitoring light signals constantly being sent from earth. The traveler is going to see exactly the same light timing pulses and imbedded data in all three places. Remaining on the outbound Ship would have meant that they’d still be red shifted and coming in slower. At he station they may look more ‘normal’. And Once on the return ship they are coming in faster and be blue shifted. Still the signals coming from Earth viewable in the greater local area of the “Transfer point” are unchanged. No Swinging Lurching or Jumping of anything related to Earth at all. Things look (and are different) for the traveler because they are not in Kansas any more! (Kansas - Name of the first ship).

FTL events are not hard to find – I can create them in my back yard. I’m not sure what an EPR is but my guess is that for FTL it is no more significant than tossing a rock in the pond.

 

[yogi]

RandellB - FTL is faster than light as you surmised - EPR - Einstein, Podelesky and Rosen - (I don't have the spelling correct) had conceived a thought experiment that at first dumbfounded Bohr. It is based upon the idea that if two photons are emitted in opposite directions, the momentum of one could be measured without disturbing the other and therefore falsify the uncertainty principle - but according to Bells theorem and the experiments of Alain ASpect, the measurement of one affects the other though they are separated by great distances. Your can read many articles on the net.


You have introduced a number of factors into what I had said - there are no signals going back and forth between the Earth and the traveler - nothing is relied upon other than the clock(s) carried fby the traveler - in the analogy to GPS I gave above - we can endow the traveler with a second clock that is preset to run at the same rate as Earth clocks when the traveler is in motion wrt the earth. The traveler will thus know at all locations during his journey what the Earth "time" is w/o having to look outside his spaceship. He will also know how fast he is aging by looking at his regular clock that is running at a rate determined by his velocity wrt earth. If we were to adopt the tenants of SR that require absolute reciprocity, then one could argue that the traveler could set the Earth clocks to run faster to account for the relative velocity - rather than the way it is done in GPS - but of course - that cannot work because the Earth clock is being offset in the wrong direction (it needs to run slower to correspond with the time loss in the traveling system - not faster). While the relativistic velocity transforms are applied, they are being applied "one way" Every experiment shows that clocks which move at a high velocity wrt to Earth centered reference system run slow - there are no experiments that show that Earth clocks run slow when viewed from the standpoint of the traveler.

 

[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

<br /> \frac{L}{v} \sqrt{1 - \left(\frac{v}{c}\right)^2}<br />

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.