View Full Version : Twin Paradox
ElectroPhysics
Dec7-04, 10:45 PM
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?
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.
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
Dec8-04, 10:11 AM
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.
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
Dec9-04, 12:11 PM
..... 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
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
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 (http://physicsforums.com/showthread.php?t=51197&highlight=cosmological+twin+paradox ).
Garth
jdstokes
Dec11-04, 08:54 AM
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
Dec11-04, 10:12 AM
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.
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
Dec12-04, 07:32 AM
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).
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.
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?
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
Dec13-04, 04:32 PM
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") untill you understand the numbers you get this way, And you should be starting to understand simultaneity whitch is jd's point.
Randall B
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 knowlege 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
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
Dec14-04, 06:13 AM
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.
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)
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.
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 travelling 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.
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.
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
Dec16-04, 01:50 PM
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?
And what the heck is “LR” - nothing clear about what that is to me.
I'm pretty sure that he is refering to Lorentzian Relativity.
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
Dec16-04, 02:24 PM
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 recieve data and information. But we know distances, speed of c, times we actually recieve thier 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 alot in explaining the results seen.
Getting clocks in sync when they pass by each other – no big deal.
RB
RandallB
Dec16-04, 04:11 PM
I'm pretty sure that he is refering 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
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
Dec17-04, 10:04 AM
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
Dec17-04, 10:44 AM
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.
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
Dec20-04, 05:51 PM
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.
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.
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 travelling 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
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
Dec21-04, 07:27 PM
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.
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
Dec22-04, 09:44 AM
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 - 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
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
Dec22-04, 01:06 PM
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.
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 instantanous 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.
(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
Dec23-04, 06:18 PM
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
Have a relatively Merry Christmas
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?
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 earths 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 earths 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.
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.
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.
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.
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.
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.
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.
"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????????????
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 thier 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.
Janus - lets 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?
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.
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 - lets 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?
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 travelling (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?
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.
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.
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???
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.
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?
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.
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 - 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.
If the alpha clock is synchronized with the earth clock,
Don't forget -- you mean to determine this using Earth's rest frame.
Hurkyl,
"Don't forget -- you mean to determine this using Earth's rest frame."
Correct.
yogi,
"Would you then permit me to claim that if T immediately turned around at alpha and returned to earth at the same speed, the total time difference would be double that measured for the one way excursion?"
Yes. On T's return to earth, the earth clock will read 2L/v and T's clock will read (2L/v)/gamma.
djavel - Wonderful - we agree upon that - so can we now say that neither acceleration nor turn around is significant in explaining the clock paradox. In other words, while the traveler's return to the starting point is part of the journey, the earth is really a convenience point for measuring the age difference ---the turn around and the consequent changing of frames occassioned thereby does not play a role per se in the age difference upon arrival back on earth.
Hurkyl - when I refer to sync for one instant - I am saying that if T and S clocks both read 12:00 at the time of passby, then since alpha reads the same as S, all three clocks will read the same initially - and for one instant only.
alpha reads the same as S, all three clocks will read the same initially
And I am saying that, until you state how you are comparing spatially separated clocks, these two statements are pure nonsense.
One such way is to select a coordinate chart, such as an inertial reference frame from SR, and then compare readings that occur at the same coordinate time.
so can we now say that neither acceleration nor turn around is significant in explaining the clock paradox ... the turn around and the consequent changing of frames occassioned thereby does not play a role per se in the age difference upon arrival back on earth.
As I've mentioned before, the "clock paradox" arises when you also do the analysis in the rest frame of the spaceship -- the turn around is crucial to explaining why that analysis doesn't predict that earth clock doesn't read less than the space clock.
Hurkyl - I thought you agreed that the two clocks read differently at the halfway point (when T reached alpha).
Clocks can be compared in a common frame and they can be compared in relatively moving frames when they are adjacent - this does not violate any tenant of SR - It is not necessary to specifically set out a particular means of reading a clock or of setting it so long as they both read the same in the same frame - we simply say two clocks in the same frame are in sync - you can use Einstein's method if you like - but this is just another example of your introducing a SR bias into the thought experiments - the very purpose of which is to examine whether the theory comports with the real world in every case - as I have repeatedly stated, Einstien's derivation started with observing events in a moving frame - all measurements were "as viewed from the other frame" as Einstein said 3 times in the first paragraphs of the derivation in his 1905 paper - then w/o reason or explanation, he applies these transforms to predict that clocks will experience actual time differences (loss of sync) when moved apart and returned. It is the propriety of this shift from observation to reality that is at root - so what I was attempting to do was to confine all measurements to those which are proper and those which are adjacent. I know you can always pull yourself up by the bootstraps and use the same shifting methodology to show SR is correct. But if I define as true 1 + 2 = 4 , I can also prove 2 + 2 = 5
Hurkyl - I thought you agreed that the two clocks read differently at the halfway point (when T reached alpha).
Only on the condition that I had correctly guessed how alpha's clock is set.
you can use Einstein's method if you like - but this is just another example of your introducing a SR bias into the thought experiments
I've asked you plenty of times to specify what method you intended to use. Einstein's method, incidentally, conforms to that of any (flat-space) preferred frame theory I know, when done done relative to that preferred frame.
yogi,
"when I refer to sync for one instant - I am saying that if T and S clocks both read 12:00 at the time of passby, then since alpha reads the same as S, all three clocks will read the same initially - and for one instant only."
Not true. If T and S are synched and S and alpha are synched, then T and alpha won't be synched.
Again, you have to be careful about what you mean by "synced". For instance, if S and T coincide when they both read zero, and if S and alpha read 0 simultaneously in Earth's rest frame, then T and alpha will read 0 simultaneously in Earth's rest frame. Of course, in the ship's rest frame, alpha will have some positive reading when S and T are both zero.
ElectroPhysics
Jan2-05, 10:56 PM
Thanks and just continue your discussion. You guys are really Physicists :)
ElectroPhysics
Jan2-05, 10:56 PM
and Happy New Year...
ElectroPhysics - If there is anything to be learned by all this...it is that there is more than one interpretation of both the theory and the experiments. Ultimately I would assume that all but one view will be relegated to the waistbasket.
yogi,
"ElectroPhysics - If there is anything to be learned by all this...it is that there is more than one interpretation of....the theory...."
But only one is correct.
"Ultimately I would assume that all but one view will be relegated to the waistbasket."
They already have by everyone who understands the theory.
The paradox and its resolution depends on the concept of what we think of as 'now', not here where that is obvious, but 'over there'. At distance those events that we think of as happening 'now' are selected according to our frame of reference. Two close observers moving relative to each other would select a different set of contemporary events; simultaneity is relative, or 'frame dependent'.
This is particularly important for the non-inertial twin. As she reversed her course her own timing of events back home would suddenly change. Those distant events back home that she thought of as in her future would suddenly become in her past, so when she arrived back home she would realise that her twin was actually older than herself.
I hope this helps.
Garth
djavel "They already have by everyone who understands the theory"
- your statement is totally incorrect - acknowledged and respected relativity authors take entirely different approaches to explaining the twin and triplet paradox - Read Professor Robert Resnick's book and compare his treatment of the twin paradox to the treatment of Max Born - the relativist views are almost as diverse as the antagonist's views (but not quite).
Garth - what is at issue is not whether SR offers an explanation of some sort or the other - SR has a built-in self consistency which prevents it from being falsified by thought experiments. Relativity always gives an answer - but does it give the right answer for the right reasons? In the posts above - I attempted to reduce the experiment to proper measurements made within the confines of the proper frame of each participant. - while there may be minor errors induced at the time of initial readings (e.g., if all clocks are initially set to read the same in the earth frame - and then the traveler takes off (introducing a small error) we then ask a question - do the eart-alpha clocks run at the same rate as the travelers clock so that all three read the same at the turn around point? If the answer is yes - then all of the age discrepancy that we assume will be measured after the parties are reunited, must be do to something physical that occurs at turn around - while the traveler may observe the earth clock to be changing at turn around - he can also observe the nearby alpha clock (which is in sync with the earth clock) as not changing. Therefore what is observed by the traveler at the time of turn around (for the rapid change in the earth clock reading) must be an illusion. An illusion cannot affect the time on the earth clock - only something physical can cause identical clocks to run at different rates - SR does not provide any inkling as to what causes the age difference - what you have cited is one explanation adopted by some relativity authors - In the triplet problem from which this long thread derived, there is no acceleration at turn around ...simply a reading of the outbound siblings clock by the inbound sibling. Does that make the earth clock rush forward in time?
Clocks tick at the same rate in both frames, relative to their own. Both sisters age differently than the other. But, neither sister will agree upon how old the other is relative to herself. In a sense, they are in different universes. The implications of relativity and quantum physics are both profound. They are not mutually compatible. The effects on both levels of reality are too small to be measurable. The more important point is to measure where they meet. This may not be an important discovery, but may be important to the discovery process,
yogi Clocks always tick "at the same rate" - one second per second - in their own frame, it is how they tick as observed by another frame that is the issue. The twin sisters have no way of comparing their clocks, except by light signal, until they meet again.
The travelling sister, i.e. the one who has changed her own frame of reference by accelerations, will find her clock has ticked less than the inertial sister.
Garth
but does it give the right answer for the right reasons?
An interesting philosophical question -- there's a good argument that getting the right answers (in advance) is all that matters. The "right reasons" are only an explanation made up after the fact to help understand, and be able to make even more predictions.
if all clocks are initially set to read the same in the earth frame - and then the traveler takes off (introducing a small error) we then ask a question - do the eart-alpha clocks run at the same rate as the travelers clock so that all three read the same at the turn around point?
During the outbound trip:
In the earth frame, the traveller's clock run slow, and the earth and alpha clocks do not.
In the outbound frame, the clocks on earth and alpha run slow, and the spaceship clock does not.
If alpha and earth's clocks always agree in earth's frame, then the clock on alpha will read more than that of the spaceship when it arrives.
If alpha and earth's clocks always agree in the outbound frame, then the clock on alpha will less than that of the spaceship when it arrives.
Other comments:
"which is in sync with the earth clock" -- only according to earth's frame.
"SR does not provide any inkling as to what causes the age difference" -- would you also say that Euclidean geometry doesn't provide any inkling as to what causes one side of a triangle to be less than the sum of the other two sides? It is fairly directly analagous.
In a sense, they are in different universes.
Or, more accurately, each twin is merely using a different coordinate chart. Geometrically speaking, it's no more mystifying than, why the apparent width of a piece of paper is different when you look at its edge or its front.
The implications of relativity and quantum physics are both profound. They are not mutually compatible.
Partially incorrect -- special relativity and quantum physics are quite compatable. You're thinking of general relativity.
yogi,
djavel: They already have by everyone who understands the theory
jogi: ....your statement is totally incorrect - acknowledged and respected relativity authors take entirely different approaches....
No they don't. They DID, but not anymore; the issue was settled over thirty years ago.
Anyone who thinks that relative simultaneity or (equivalently) constant light speed, or (again, equivalently) the Lorentz transforms can't account for what everyone sees on everyone's clock, in any reference frame, doesn't understand this theory.
"Why" questions generally do not have any unique answer in science - if they are even addressed at all. Somewhere around 4 years old, most everyone learns that they can always ask "why", and in a short amount of time arive at a point where there is not any answer to their questions. Science is ultimately concerned with "what" rather than "why". This is why scientific questions generally have nswers, even if they are hard to find - as opposed to philosophical questions, which tend to spawn endless debates, with no ultimate resolution.
On a slightly more advanced note, classical Newtonian mechanics has many alternate formulations - the typical "f=ma" introductory formulation, and the more advanced Lagrangian and Hamiltonian formulations. I see very few people criticising Newtonian mechanics because of the fact that alternative mathematical formulations of the theory exist. Most people seem to be quite content with the fact that all valid formulations of Newtoian mechanics give the same results. I would urge people to apply the same standards to relativity theory and quantum theory. Of the two, quantum theory has by far the biggest issue with "interpretations". Ultimately, though, it is the agreement of final results which is important.
pervect - Newton didn't say F = ma ... he said F = rate of change of momentum. That is valid as far as we know in any framework notwithstanding the later developments of Lagrange and Hamilton.
Questions of "why" have to do with pushing the goal post back a few more feet in our attempt to understand nature - there will always be one more question to answer - the question of "why" relates to finding an interpretation that betters our understanding of the next level - if we adopted your position we would still believe that Zeus was the cause of lightning. There is a great story told by Feynman in his chapter on lightning - and the Persian king who sought advice before invading Greece.
Hurkyl - "If alpha and earth's clocks always agree in earth's frame, then the clock on alpha will read more than that of the spaceship when it arrives."
I would agree with that - as for your next statement:
"If alpha and earth's clocks always agree in the outbound frame, then the clock on alpha will less than that of the spaceship when it arrives."
Yes - that is so according to the LT (we don't ever really make this measurement, but assuming arguendo it is true, it is not part of the analysis I have set out in the above posts... I have repeatedly stated that it is of no moment what the moving observer measures in the earth frame - only earth and alpha based observers can measure the proper time in the earth-alpha frame. The traveler measures an illusory rate when he looks at either the alpha or earth clock from afar - but he can read the clock on the church tower on alpha when he arrives - and he can compare it to his own clock at that time because there is no vx/c^2 time slip when the two clocks are adjacent .
djavel - Take a look at Zhangs book - quoted with authority in FAQ in Physics. "There are no experiments that verify the one way speed of light is isotopic" If it is not, then any number of different transforms can be used to explain all of the known experiments. All of the alternative theories are based upon some difference between an isotropic frame and a frame that moves relative thereto. They all predict the same time dilation as Lorentz's transformations - and consequently all of the other predictions that flow therefrom - SR has been a successful theory - but the other theories make the same predictions w/o relying upon one way isotropy - a postulate that was unnecessary to explain MMx
Garth - I agree that the traveling sibling ages less - you say because of acceleration - but there are many authors that argue otherwise (usually they simply invoke a path integral approach using signaling techniques) Since acceleration does not affect local clock rate - nor can it influence the rate of the stay at home clock, how can it add time to the earth system? The temporal influences that are posited to occur due to acceleration or changing frames can only be observational illusions - recall that this whole thread originated with triplets where there is no acceleration at any time - not at the start - nor at turn around (because there is no turn around).
pervect - Newton didn't say F = ma ... he said F = rate of change of momentum. That is valid as far as we know in any framework notwithstanding the later developments of Lagrange and Hamilton.
AFAIK what Newton orginally said (as nearly as exactly as a websearch can find, this may not be perfect) is:
1: A body remains in a state of rest or a state of motion unless a force acting upon it compels it to change.
2: Change occurs in proportion to the force applied and in the same direction.
3: For every action there is an equal and opposite reaction
Formulations of this as "F=ma" and F=dp/dt are all "different" than Newton's original formulation.
As I mentioned, there are additional formulations, such as the principle of least action which are entirely equivalent to Newton's laws.
In spite of the fact that the wording was different in Newton's time, I do not see people claiming that
1) We don't really understand Newton's laws
2) Physics is changing, explanations of Newton's laws are inconsistent
3) Respectable physicists all have "different" interpretations of Newton's laws
all things you've said about SR. In fact, most people (including you, I presume) seem to realize that "different" formulations of Newton's laws are not "different" if they lead one to the same identical results. Including, as I mentioned, the Hamiltonian or Lagrangian formulations (the former, in terms of the principle of least action, is quite elegant).
BTW, if you wish to distinguish Newtonian physics from relativity, you need to specify that momentum=mv, which implies that f=ma. If you don't make this assumption, you have implicitly allowed "Newtonian physics" to include relativistic physics, where p = mv/sqrt(1-(v/c)^2).
On isotropy:
Suppose an airplane leaves Los Angeles, Calif, at noon, and arives at Chicago, Ill at 5:40 pm, nonstop. Suppose the same plane leaves Chicago, Ill, at noon on the next day, and arrives at LA at 2:12 pm nonstop. And suppose Chicago and LA are 1749 miles apart. Is it physically meaningful to say that the plane flew at a speed of 308 mi/hr on the first trip, and 795 mi/hr on the trip back? Why or why not?
pervect:
1) We don't really understand Newton's laws
2) Physics is changing, explanations of Newton's laws are inconsistent
3) Respectable physicists all have "different" interpretations of Newton's laws
I have made no such statements about SR - if SR is incomplete or wrong it was just as wrong in 1905 as it is today. There were competing theories at the time - but there was no way to verify time dilation until we begin observing the lifetimes of muons and pions.
The reason no one is criticizing Newton's Laws is because they don't lead to paradoxical interpretations. And I don't need to write p = mv to know what is meant by rate of change of momentum - d/dt(mv). This impliedly takes into account the fact that mass may not be constant.
Well, your'e at least partially consistent then, Yogi, I suppose. Since we don't really understand Newton's laws after all these years, perhaps we should just give up science and become monks? I mean, what's the point, after all?
:-) for the humor impaired
Lets substitute a photon for the traveling twin - we will put a mirror on alpha and assume that alpha is 3 x 10^8 meters from earth. Clocks at earth and alpha are in sync and the time read when the photon passes the earth clock is zero. A clock in the photon frame logs "0" when the photon strikes the alpha mirror - the earth and alpha clocks both read one second - upon return the photon clock still reads "0" but the earth clock reads 2 seconds. Time passage in the two frames is not equal - half the time is accumulated in the earth-alpha frame on the outbound journey and half is logged on the inbound leg. How does acceleration (reflection) explain the difference between the time lost in the one way trip (between 1 second vs 0)? If the time lost is truly one second on the one way trip, does it not follow that acceleration and turn around have nothing to do with resolving the twin paradox?
Now lets look at things from the photon frame - no time is logged in the photon frame going out or returning - on the outbound leg the photon must see time in the earth alpha frame passing more slowly if the situation is reciprocal - but this would mean the earth time is accumulating at a lesser rate that zero [the proper time measured by the photon clock] Again, if that is what is observed, it cannot be a real.
Pervect - I was merely copying your statement from post 95 - forgot to put in quote marks - as I said - the interesting issue(s) with SR is whether two frames in relative motion can be treated as truly reciprocal as Einstein hypothesized - didn't mean to infer anything about Newtonian Physics.
only earth and alpha based observers can measure the proper time in the earth-alpha frame.
Your phrasing sounds awfully like you're assuming a preferred frame.
(1) Anybody can make measurements in any coordinate chart they want. There's nothing stopping the spacebound sibling from using an unusual methodology that produces the exact same picture that the Earthbound sibling would get.
(2) Proper time has nothing to do with coordinate charts -- it is an (invariant) quantity describing a time-like path through space-time. (aka the reading of a clock attached to the path) All observers everywhere will agree on the proper time interval of a time-like path.
The traveler measures an illusory rate when he looks at either the alpha or earth clock from afar
No more illusory than when Earth looks at alpha's clock from afar. Each traveller determines that rate by comparing the readings of the distant clock to the time coordinate in their coordinate chart.
nor can (acceleration) influence the rate of the stay at home clock
Sure it can. That rate is, by definition, simply the comparison of readings on the stay at home clock with the time coordinate of your coordinate chart, and accelerated frames have different coordinate charts than nonaccelerated frames.
does it not follow that acceleration and turn around have nothing to do with resolving the twin paradox?
I'll say it again, the twin paradox involves doing the analysis in some rest frame of the spacebound traveller. You have never addressed the twin paradox, because all of your analyses have been done with the coordinate chart of Earth's rest frame.
It's as if a student came to you with his homework and said "I did this problem two different ways, and got different answers. What did I do wrong?" And then you only look at his first approach and say "I don't see any problem!", never looking at his second approach.
yogi,
Referring to clock rates in the earth frame and the "photon frame" you arrived at a conclusion and then said, "....if that is what is observed, it cannot be a real."
It's not observed. Nothing is observed from a "photon frame" because there is no such thing as a phton frame.
Huykyl - the only supposition is that the earth-alpha frame is an isotroptic light frame - it may turn out that it is preferred for physical reasons but that is not a part of our discussion. We cannot make the same claim about the travelers frame based upon any experimental evidence - that is, if light is isotroptic in earth-alpha, it is only isotropic in the travelers frame by fiat (Einsteins postulates).
Perhaps the traveler can make measurments in the earth-alpha frame that yield the same time as the proper time measured by earth clocks - but it will involve some complex relationships that are not part of the present discussion - such diversions simply cloud the issues.
When the earth and alpha clocks are in sych there is no illusion as between them - knowing their distance L apart either would be able to see that he simply has to subtract L/c from what he sees of the other clock in his own frame - there is no illusion - simply a correction which is immaterial to the discussion
I do not have to do any analysis of what the traveling twin sees to expose the fact that the traveler's clock and the alpha clock have logged different times when the traveler arrives at alpha. You are again trying to derail the implications of the different times measured by the proper clocks in each frame - we are not looking at what moving observers may think of our time as they take notice of our clocks on the fly - it is inconsequential unless they are adjacent to the clocks, and that only occurs at the beginning and end (earth and alpha).
As far as not being able to see another point of view as per your student analogy - I would bounce the ball back into your court. You use the reciprocal frame postulates of SR to justify its validity - but it is these very postulates that the critics of the threory have come to suspect.
Einstein derived his transformations based upon "what is observed in the other frame" ...He then proceeded (without giving a reason) to utilize the transforms to predict actual time discrepancies for moving clocks. But he believed for his own reasons (symmetry of nature maybe) that all inertial frames are equivalent,- so the frames had to be reciprocal - and so what is observed is sometimes taken as real when need be to save the theory (e.g. actual age differences measured for pions and other decay particles) or they are taken as observed, when it is necessary to save reciprocity. I suspect near the end of his life he began to realize his own folly - and much to his credit he so stated ...that probably non of his theories would long last.
it is only isotropic in the travelers frame by fiat
Wrong. Once you state the precise procedure by which the traveller makes measurements, the physics of his frame can be mathematically derived from that of the Earth-alpha frame.
but it will involve some complex relationships that are not part of the present discussion - such diversions simply cloud the issues.
I disagree. The very notion of frames and measurement is a central issue to this discussion, and you've been avidly avoiding it. My statement was a response to yet another apparent misconception of yours.
When the earth and alpha clocks are in sych there is no illusion as between them - knowing their distance L apart either would be able to see that he simply has to subtract L/c from what he sees of the other clock in his own frame - there is no illusion - simply a correction which is immaterial to the discussion
What does it to mean to be in sync? And why would being in sync be a meaningful criterion for not being an illusion? I ask not because I wish to assert that the twin's measurements aren't an illusion, but because I have no idea what you attempt to mean, and that your argument doesn't seem to have any physical meaning -- rather, it appears to be an emotional appeal to discredit the notion of measurement in the twin's frame so you can rationalize ignoring this issue.
I do not have to do any analysis of what the traveling twin sees to expose the fact that the traveler's clock and the alpha clock have logged different times when the traveler arrives at alpha.
Correct. (Depending on how alpha's clock get's set, of course)
If this were a homework problem saying "A twin leaves earth, arrives at alpha, then goes back to earth. Blah blah...", then this is how you should approach the problem.
However, you claim to be addressing the twin paradox, and the very statement of the twin paradox involves analyzing what the travelling twin sees. If you are not doing that analysis, you are not addressing the twin paradox.
You are again trying to derail the implications of the different times measured by the proper clocks in each frame
You cannot even begin speak about the implications of clock measurements in frames until you start to address the notion of frames and measurements. (This is the avoidance I mentioned above)
we are not looking at what moving observers may think of our time as they take notice of our clocks on the fly
What if Earth and alpha were moving observers? This seems to invoke some notion of absolute rest, and there is no justification that such a concept makes sense in the universe -- it's a throwback to geocentricism, that the universe rotates around the Earth.
it is inconsequential unless they are adjacent to the clocks, and that only occurs at the beginning and end (earth and alpha).
And, by the same token, Earth's clock is inconsequential to alpha, because they are not adjacent.
As far as not being able to see another point of view as per your student analogy - I would bounce the ball back into your court. You use the reciprocal frame postulates of SR to justify its validity - but it is these very postulates that the critics of the threory have come to suspect.
I don't think the course of this thread has gotten nearly that far.
I find your rebound irrelevant -- I've not professed to be making any sort of defense of SR, but you've repeatedly stated you are attempting to consider the twin paradox.
Secondly, you have assumed the existance of one frame with an isotropic speed of light. I hinted at this earlier -- that's the only assumption I need to derive the Minowski space-time of Special relativity.
You can't talk about frames until you decide how to define frames. One way any inertial observer can perform a measurement is this: fire a beam of light at an object, and wait for its reflection to return. Then, decide that the beam of light struck the object halfway between when you emitted and received the light, and it struck at a distance ct/2 where t was the round trip time.
Using only your assumption of a single reference frame with an isotropic speed of light, I can mathematically deduce all the geometrical facts about Special relativity, such as time dilation, length contraction, and constancy of the speed of light, are valid for the frames I defined in the previous paragraph.
I don't really know what you mean by "reciprical frame postulates". Do you mean the principle of relativity? (Which, incidentally, was part of physics long before Einstein. He was just the first one bold enough to stop assuming that Maxwell's equations contradicted it)
Using only your assumption of a single reference frame with an isotropic speed of light, I can mathematically deduce all the geometrical facts about Special relativity, such as time dilation, length contraction, and constancy of the speed of light, are valid for the frames I defined in the previous paragraph.
Addendum -- I also assumed translation invariance (something true of any theory I know except GR), and I cannot determine the scale of the other frames.
yogi,
This thread is becoming a waste of time.
You told me to "take a look at Zhangs book". I thought we were discussing different interpretations of Einstein's theory which he based on the postulate of constant light speed. Zhang doesn't accept that postulate so anything he says is an ALTERNATE theory, not a different interpretation of Einstein's theory.
On another point, you don't seem to be able to get anyone to understand what you mean by simultaneity. There's a way to describe the trip from earth to alpha without worrying about simultaneity. Give each observer (T, E and A) a telescope so each of them can compare what their own clock reads with what they see (through their telescope) on the other clocks, any time they want. Try working out what everyone will see at the start of T's trip, along the way, and when he gets there. It's all very continuous, very agreeable, and not at all open to interpretation!
RandallB
Jan6-05, 06:38 PM
Now lets look at things from the photon frame - no time is logged in the photon frame going out or returning - on the outbound leg the photon must see time in the earth alpha frame passing more slowly if the situation is reciprocal - but this would mean the earth time is accumulating at a lesser rate that zero [the proper time measured by the photon clock] Again, if that is what is observed, it cannot be a real.
No fair Yogi – that just a magicians trick of miss-direction!
I enjoy looking in every once in awhile, and yogi you’ve been changing your view to suit yourself unfairly. You can use a “Photon” as a traveler but not so casually as you have.
1)“from the photon frame”
you want us to accept this as being just one frame IT’S NOT the returning frame is much different that the out bound frame! If you can get people to believe this is one frame of course you can trick them disagreeing with SR.
2) “photon must see time in the earth alpha frame passing more slowly”
No you’ve already agreed in posts long ago when you look across to stations or ships with synced clocks they appear to run FAST. This confirms that the Earth and Alpha are running SLOW as the traveling photon sees Alpha clock stuck on “1 sec”
3) It works
But if the photon uses refection to join a “fellow photon” that started from Beta (at Earth-Alpha-Beta time stamp “0”) on its way to earth intersecting with Alpha at “1 sec”. Then same rules must apply our fellow photon and it is seeing earth ‘stuck’ already at “2 sec” as it comes in at v = c over a distance of “0”. Now the traveling photon is going the see the excactly same thing when it reflects, because it's now in the “fellow photon’s” frame going c in the opposite direction. Earth will arrive stuck on a time of “2 sec”. NOT because its clock or distance LURCHED about, like to many folks enjoy saying, but because in the new frame of the fellow proton Earth already was and is that way! The traveling photon has just changed frames that all.
4) “if that is what is observed, it cannot be a real“
It is observed and is real in every test I’ve ever heard of.
In fact I’m finding hard to believe you don’t see it, and are just being contrary for the fun of it.
In SR there is no Paradox:
If you want to convince me that LR is worth looking into at all.
Show me all the times, locations by distances, using two ships passing Earth and Alpha in one direction. The 2nd ship follows the first to pass Earth by a distance in their frame equal to the separation between Earth and Alpha in the Earth frame. Add a third ship going the other way at Alpha when the first ship is at Earth in Earth time. I know anyone here can detail the passing time that with ease for SR. (And of course someone can yell that we’re all wrong) But I’ve never seen detailed what LR says the passing times in the three different frames should be using LR. Can LR even do it? It would at least demonstrate the difference from SR if there is one. If you could do that, I would be impressed. Use you favorite speeds and distances.
Alkatran
Jan6-05, 11:29 PM
I always think a picture helps with the twin paradox: here's a really bad one.
http://www.vbforums.com/attachment.php?attachmentid=33201&stc=1
The black line is the ship (or ships, whatever)
The green bar is the earth
The blue bar is alpha
The grey bar are 'now' lines for the spaceship: Consider them snapshots of everything happening in the rest frame of the ship
Similarly the blue and green lines are snapshots for earth and alpha
The red lines are also snapshots for earth and alpha.
Ignore the picture on the right, it's... umm not consistent at all! (notice how alpha is on the wrong side...)
The main thing to notice is the left picture, how the 'now' lines jump when the ship(s) speed changes.
This isn't a faster than light effect because the ship can't know about this until light reach it from that frame... It's like saying "oh, if I rotate a spotlight, the circle of light can exceed c" but that's because the 'circle of light' isn't a particle... it's an abstract thing.
If you don't follow the methodology of reducing the problem to separate frames where all measurements are proper, I cannot think of any other way to get the point across.
There are literally hundreds of articles on the net dealing with these issues - I would guess that everyone who writes on the subject has started out with the same introduction to SR in some book or some course ...and being told that SR is unassailable - but literally thousands have found they cannot accept the smoke and mirrors - back and forth rationale, that attempts to anchor real time dilation to distorted illusions that derive from subjective interpretations of space and time in a relatively moving frame. To many, this isn't physics - its metaphysics.
I can find serious fault with many of the statements that have been made in posts 104 - 107 but to answer them would only proliferate this already too long thread in many different directions.
RandallB - you have asked a question that deserves an answer - While I am not totally sold on LR, I think it may better approximate nature than either SR or MLET. You would get exactly the same answer in the problem you posed as you would get in SR or MLET. So why question SR. Because even though the answers are the same, they come about for different reasons. Theories that depend from a preferred frame say that time flows slow in the frame that is in motion wrt the preferred frame - but unlike SR (which asserts that all inertial frames are equivalent) LR claims that if you were in a frame in motion with respect to the earth's gravitional field, time on earth would run faster not slower. In other words, there is no reciprocity between the earth centered reference frame and the frame of the high speed pion for example. In MLET, the preferred frame is an ether. In one of my earlier posts, I took as the first frame one where light is isotropic (not because of Einstein's postulate) but because it will always be possible to find a frame where that is the case. It might be a frame centered on the G field of the earth as LR postulates or it might be a frame where the CBR is isotropic.
Hope that helps
ElectroPhysics
Jan7-05, 12:39 AM
Stop it Please...
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 have a series of clocks which always show the correct time in some other reference frame, and you fly by them, you will see each clock running at the same rate, slower than your onboard clock. But you will also see that the clocks appear to be out-of-sync relative to your own reference frame, although they are in-sync in the frame whose time they are measuring. So, for example, if I travel at relativistic speeds from one end of the galaxy to another, and pass by a long row of clocks which measure time in the galaxy's rest frame, then each clock will run slower than my onboard clock, but in my frame the clock on the far end of the galaxy may start out hundreds of thousands of years ahead of the clock on the end I start the journey, so that when I arrive on the far end it will be hundreds of thousands of years in the future according to "galaxy time", even if the journey only took a few years for me and every clock I passed by appeared to be running slower than my onboard clock.
To restate what JesseM said, the high speed train observes:
If I measure Earth time by looking out the window and observing the time on the nearby clock, then Earth time is running faster than my clock.
If I measure Earth time by focusing on one single Earth clock, and adjust the readings to account for the delay due to light travel, then Earth time is running slower than my clock.
But anyways, the point I want to make clear is this:
LR claims that if you were in a frame in motion with respect to the earth's gravitional field, time on earth would run faster not slower.
This statement is absolutely meaningless until you specify how you plan on measuring the time on earth.
SR does say specifically what it's measuring: the second case I gave above.
And, if LR does happen to agree with SR when all measurements are done in Earth's inertial frame, then LR absolutely, positively must agree with SR on the results of that experiment.
You don't even need to assume that the agreement is in Earth's inertial frame -- just that they agree in any one frame.
Why is this true? Because SR precisely defines a method of measurement, and the results of that measurement can be determined in any frame. Probably the simplest method is this, which I've stated before:
An observer measures the position and time of an event as follows:
(1) It shines a beam of light at time S.
(2) The beam of light is reflected back.
(3) It receives its beam of light at time T.
Then, the observer decides that the beam of light struck the object at time (S + T)/2, and that the object was at a distance of (T - S) c / 2.
This is a well-defined experimental procedure for determining positions and times of events, and the decision made by the observer can be computed in any reference frame.
In particular, if, say, LR and SR agree in your favorite reference frame. Let's call it F. Then, for any observer travelling with a constant speed in F, one can compute, entirely in F, the results that the observer will get for any measurement. Since LR and SR agree in F, they must agree on what this observer measures too.
In other words:
If any theory agrees with Special Relativity for one particular frame of reference, then that theory absolutely, positively, must agree with the predictions of Special Relativity for all reference frames, provided that all observers perform measurements in the way I specified above (or in some equivalent way).
RandallB
Jan7-05, 03:57 PM
FTL > faster than light
EPR > Einstein, Podelesky and Rosen
GPS > Global Position Satellite
LR > Lorenz Relativity
SR > Special Relativity
GR > General Relativity
MLET> ???
light is isotropic> ???
I agree with the originator of this thread, ElectroPhysics, May be time to stop this one and close it for the archives.
Just - What is “MLET”
Also: Is there such a thing as a “Frame” where Light is isotropic
I don’t understand what that could mean. Is there any realistic way of making measurements from it (Including looking at light going the other way) ?
Yogi
Yes it has been helpful, but I’ve come up with different answers than you.
Your GPS stuff confirm SR when looked realistically
I believe high speed pion example does show ‘reciprocity’ with earth.
And my review of EPR does not show a FTL event.
But still need to work on extracting GR from SR. But I’ll put that in another post.
In time you may learn the same. good luck .
Also: Is there such a thing as a ?Frame? where Light is isotropic
I assume yogi meant a coordinate chart in which light would be measured as travelling with constant speed, no matter where it is, when it is, or which direction it travels.
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 have a series of clocks which always show the correct time in some other reference frame, and you fly by them, you will see each clock running at the same rate, slower than your onboard clock. But you will also see that the clocks appear to be out-of-sync relative to your own reference frame, although they are in-sync in the frame whose time they are measuring. So, for example, if I travel at relativistic speeds from one end of the galaxy to another, and pass by a long row of clocks which measure time in the galaxy's rest frame, then each clock will run slower than my onboard clock, but in my frame the clock on the far end of the galaxy may start out hundreds of thousands of years ahead of the clock on the end I start the journey, so that when I arrive on the far end it will be hundreds of thousands of years in the future according to "galaxy time", even if the journey only took a few years for me and every clock I passed by appeared to be running slower than my onboard clock. By the way yogi, I just posted this thread (http://physicsforums.com/showthread.php?t=59023) with some illustrations of a scenario like this, with two rulers moving in parallel next to each other, and clocks placed at regular intervals along each ruler, sychronized within the ruler's reference frame. You may find it helpful to look at the diagrams and see exactly how things work out consistently in this scenario.
It would be pretty easy to extend this sort of thing to the "triplet paradox" you were describing earlier on this thread. Imagine each triplet is riding along a ruler, and all the rulers are moving at constant velocity relative to one another. We can say triplet A corresponds to the earthbound triplet in your scenario, triplet B corresponds to the one travelling away from earth, and triplet C corresponds to the one travelling towards the earth. At the initial moment when A and B are right next to each other, their clocks read the same time; then we can also specify that at the moment B and C pass next to each other, their clocks must also read the same time. In this case, when C passes A, C's clock will be behind A's clock. In A's frame, the clocks of both B and C are ticking slower than his own, by the same amount; but both B and C see A's clocks ticking slower then their own clocks, also by the same amount. However, B sees all the clocks along A's ruler to be out-of-sync, just like in my illustrations--he sees clocks closer to where A is sitting being behind clocks farther from where A is sitting. On the other hand, C also sees the clocks along A's ruler being out-of-sync, except he sees clocks closer to where A is sitting being ahead of clocks farther from where A is sitting. This is the explanation for why there is no inconsistency in the fact that C's clock will be behind A's clock when they finally pass, despite the fact that both B and C saw A's clocks running slower throughout the journey. If you're still having trouble seeing this, even after looking at the illustrations in my other post, I can make up a more detailed scenario and calculate some numbers explicitly to show how this will work.
note: this discussion is continued on this thread (http://physicsforums.com/showthread.php?t=59052).
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