View Full Version : The Reality of Relativity
Einstein asserts in his 1905 paper that if two separated clocks at rest in the same frame are synchronized, and one is put in motion at a constant velocity v, it will be out of sync upon arrival at the second clock. No turn around is involved - so since the amount of time difference depends upon the velocity and the length of travel - we can presume that during the travel time the clock that is put in motion runs slower.
Now we take two clocks A and B at the origin of the xy axis and a third clock C located at some distance L along the positive x axis. A, B and C are all initially sychronized while at rest in the same frame - then A and B are accelerated to a uniform velocity v in the direction of C (along the x axis). When A and B reach their cruise velocity (no longer accelerating), it is presumed that their reference frame is equally as good as that of C which has not moved.
As A and B pass C, B is accelerated in the -X direction until B reaches a velocity v relative to A. Therefore, from C's inertial perspective, clock A will be running slower as measured by clock C. From A's perspective, B will be running slower as measured by the rate of clock A. So we have A running slower than C and B running slow than A. But since B is no longer in motion with respect to C, B and C should be running at the same rate.
Einstein asserts in his 1905 paper that if two separated clocks at rest in the same frame are synchronized, and one is put in motion at a constant velocity v, it will be out of sync upon arrival at the second clock. No turn around is involved - so since the amount of time difference depends upon the velocity and the length of travel - we can presume that during the travel time the clock that is put in motion runs slower. It's running slower in the frame where they were synchronized to begin with. But Einstein would say you are free to analyze the whole situation from the perspective of any frame, including one where they were not synchronized at the moment the clock was accelerated, and in which it ran faster as it approached the other clock. Do you disagree that any frame's analysis of this situation would be equally valid, according to Einstein or any other physicist? Now we take two clocks A and B at the origin of the xy axis and a third clock C located at some distance L along the positive x axis. A, B and C are all initially sychronized while at rest in the same frame - then A and B are accelerated to a uniform velocity v in the direction of C (along the x axis). When A and B reach their cruise velocity (no longer accelerating), it is presumed that their reference frame is equally as good as that of C which has not moved.
As A and B pass C, B is accelerated in the -X direction until B reaches a velocity v relative to A. So you're saying B would now be at rest in C's frame, right? Therefore, from C's inertial perspective, clock A will be running slower as measured by clock C. From A's perspective, B will be running slower as measured by the rate of clock A. So we have A running slower than C and B running slow than A. But since B is no longer in motion with respect to C, B and C should be running at the same rate. Well, this is only confusing if you don't say which frame you're talking about when you say one clock is running slower than another. In the inertial frame where C is at rest at the end, A is running slower than B and C; in the inertial frame where A is at rest at the end, B and C are running slower.
Hi Jesse - I do not agree with the last statement of yours - something we have discussed previously - When the A clock is compared to the C clock, it will read less - that is the fundamental significance of time in SR as opposed to Lorentz's development wherein Lorentz regarded the time factor in the transforms as more or less illusory ... in SR time dilation is not just an observational (apparent) phenomena - clocks that are put in motion really do lose time - they run slower - that is why we must compensate every orbiting GPS clock that is put in motion relative to the earth centered reference frame - I cannot find a single reference from Einstein that says that the C clock will be running slower than A ...or that it would be observed to run slower. Clock A will read less than C at the end of the experiment. Einstein's theory recogonized time dilation as real - and that means it is not a reciprocal situation - even though you will find many references by others that each clock appears to be running slow when viewed from the other frame - there is no experimental verification that time dilation is reciprocal - if it is reciprocal it can't be actual (two clocks cannot each be running slower than the other) - and Einstein's concluding statement in Part 4 of his paper that "a clock at the equator will be found to run slower than a clock at the pole" is meaningless if it is only observational (apparent). (Actually because of the earths oblateness they run at the same speed, but that is incidental).
Hi Jesse - I do not agree with the last statement of yours - something we have discussed previously - When the A clock is compared to the C clock, it will read less
Then, simply put, you are not discussing Special Relativity. You are discussing something else that has a universal notion of time.
Lorentz's formulation assumed that there was a universal notion of time, and had to explain why clocks don't measure it.
Einstein's formulation says that time is what clocks measure, nothing more, nothing less.
Hi Jesse - I do not agree with the last statement of yours Fair enough, but if you don't think Einstein would have agreed with it, then it's obvious you're misinterpreting him, and you have no basis for doing so in anything he wrote.
Hurkyl - not so - We are looking at two clocks, A and C during the first part of the experiment - when A reaches C, both clocks will have logged a certain number of minutes - the owner of the C clock looks at the A clock as it passes by his C clock and observes the number of minutes on the A clock and compares them to the reading on his C clock - Einstein and every experiment that that has been conducted to measure particle lifetimes, satellite clocks or airplane clock dilation confirms that the A clock will read less - why do you think this involves universal time? What is measured is the relative rate of time passage in the two frames.
Jesse - Is it fair to conclude you believe time dilation to be reciprocal in the one way travel scenereo Einstein described in Part 4 of his Electrodynamics paper of 1905? If after A and C are set to the same reading in the same frame, then A travels to C in the manner above described, and is stopped at C, and both clocks are read when there is no motion between them - will there be a difference in their readings?
Jesse - Is it fair to conclude you believe time dilation to be reciprocal in the one way travel scenereo Einstein described in Part 4 of his Electrodynamics paper of 1905? If after A and C are set to the same reading in the same frame, then A travels to C in the manner above described, and is stopped at C, and both clocks are read when there is no motion between them - will there be a difference in their readings? Of course there'll be a difference, but each frame's analysis will make the same prediction what the two clocks will read at the moment they meet, yet each frame will disagree on the ratio between the rates the two clocks were ticking. There are certainly frames where A is ticking faster than C--but in these frames, A and C were not synchronized to begin with (you always have to remember that different frames define simultaneity differently), instead A was well behind C when it first accelerated in C's direction, so even with a faster rate of ticking it was still behind C when they met. Einstein, with all mainstream physicists, would say that any inertial frame's analysis of the problem is equally valid.
why do you think this involves universal time? What is measured is the relative rate of time passage in the two frames.
That's certainly not what you're saying in your original post.
"Therefore, from C's inertial perspective, clock A will be running slower as measured by clock C."
You're making a comparison between clock A and clock C, and specifying relative to what that comparison is made. Or maybe you're making a comparison between clock A and the coordinate time in C's reference frame. Either way, that's fine. In particular, you are not making any sort of comparison between two reference frames. (I don't think such a notion can even make sense!)
Then, you turn around and say:
"So we have A running slower than C and B running slow than A."
You've suddenly dropped any reference to inertial frames, and are saying absolutely that A is running slower than C and B is running slower than A.
As you've said, "A running slower than C" is true from C's inertial perspective. "B is running slower than A" is true from A's perspective.
These two statements are about different "inertial perspetives" -- you simply cannot combine them to conclude that B is running slower than C.
RandallB
Jan9-06, 04:34 PM
I cannot find a single reference from Einstein that says that the C clock will be running slower than A ...or that it would be observed to run slower. Clock A will read less than C at the end of the experiment. Einstein's theory recogonized time dilation as real - and that means it is not a reciprocal situation Of course Einstein recognized both clocks would observe the other clock as running slower and that time dilation was real! That what the relative observation means, and why he used the name relativity. What references made you think otherwise??
Have you not read of his main points that none of the clocks never actually run slow. They all see light cover a one foot distance in the same one nano-sec of time within their own reference frame. But that they both “observe” the time on any individual clock in the other frame a running slow. The key thing to see is that this means the “apparent” local time in that other reference frame will seem to be running FAST! Now be clear here, the time doesn’t run fast, just the times observed on the “slow” clocks passing by in the moving reference frame are only observed once each locally going by, as running fast. To determine the rate and time on the individual clocks you need to collect data from the other station locations in your own reference about an individual traveling clock. To see this you need to focus on his points about simultaneity to understand it.
Do yourself a favor and work though a simultaneity problem.
Using 0.8c or 0.866c for the speed of a train, pick a pair of stations, clocks synced of course, have them work out a synchronized bright light flash from both stations that all can see. One and only one station will receive these signals together at the same time, half way between the sending stations right. Beginning of the train “car #0” has passed two of these stations and just reached the last station at the time of the signal. That time zero for that car and station. Likewise this car has arranged to send its own flash of light for all to see and one of other cars following it is picked to also send a signal at the same time BASED ON THE TRAINS SYNCED CLOCKS i.e. train time zero.
Now obviously this has to be prearranged, planning that for the stationmasters and car conductors is simple based only on their own clocks and observations of what the time should be.
Also obvious is the only train car that receives both train light signals at the same time will be half way between the two cars sending them.
Now the information to calculate, all station and train numbers a based on distance from car and station “0”, Time passes one unit for light moving one station or one train car length.
1) Based on train time what station AND WHAT TIME IS IT AT THAT STATION are all three cars at a) train time zero, b) at the time the middle car receives both signals from the other cars, and c) when the sending cars receive the signal from the other car.
2) Based on station time which train car is passing AND THE TIME SEEN IN THAT CAR AS IT PASSES for all three stations at station times a) zero when the station flashes are sent, b) the middle station receives both signals from the other stations, and c) when each sending station receives the signal from the other station.
3) Now working calculations in station time and using the stations identified in step #1) as being local to the sending of the train signals which station should receive both train signals simultaneously and when, what train car is passing and it’s time when it does.
4) Also working calculations in train time for the cars identified as local to the signals send by sending stations in step #2). Which train car should receive both station signals simultaneously, which station is it passing and the time in that station it when it does.
Every car and station will always have a station or car passing by it from which to pick up a number and time in that other reference.
It’s a lot to work out, BUT when you do:
Do step #3 results agree with step #1?
Do step #4 results agree with step #2?
IF not, before your claim relativity is broken you need to carefully check your math.
Rigorously going though this classical analysis should convince you that at least SR is real.
When done correctly I don’t see how a flaw can be found in it to argue against it, but if you want to build a convincing example to argue against SR you will have to do so in this kind of detail.
It’s all straight forward classical linear time and distance dilation calculations, just a lot of number crunching.
Maybe one draw back; it may convince you that four dimensional Minkowski “space-time curves” are not needed in SR which would leave you at odds with many that believe space-time is a legit part of SR.
That’s OK; I’d enjoy the company, as I’ve never seen a requirement for space-time in SR when a rigorous classical calculation as above will always give the same result. {If anyone can contrive a SR problem and solution using space-time, I’ll be happy to match the solution with a classical one}
Space-time is certainly a requirement in GR, as its 4D provides a means of warping to explain gravity without connecting forces or particles. But SR works fine in 3D classical physics without space-time.
Take your time in working up your own example and be careful to double check your numbers. You will have a lot data that makes it hard to help review in a forum like this.
Randall - I don't follow a lot of your post and obviously you and some of the others have missed the point of mine.
Einstein began his development of the mechanical aspects of SR by assuming symmetry between two assertedly equal inertial frames - so length contraction is a reciprocal observational effect since each observer is as good as the other, and therefore the phenomena must be apparent only. Likewise, time dilation based upon measurements made between two relativly moving clocks (while they are in relative motion) is also reciprocal (the observers in relatively moving inertial frames are in symmetrical disagreement about which clock is running slow). What Einstein did in Part 4 of his paper is make a transition from apparent phenomena (length contraction) and dynamical time dilation, to assert that if two clocks are in sync initially in one frame, and one clock is accelerated to a velocity v where it travels some distance L, and is later returned to the original frame of the stationary clock, it will have logged less time than the stationary clock. Here there is a record left by the two clocks when they are compared later in the same frame - they have recorded different times
RandallB
Jan11-06, 10:08 AM
Randall - I don't follow a lot of your post and obviously you and some of the others have missed the point of mine. NO, I think it’s you that have missed out on making your own point to yourself completely.
Of course a clock that speeds away from earth 10 units distance and returns those same 10 units back to earth at the same speed will read the same time as on a second clock that continued to 20 units distance. The only diff is the earth bound observer gets to record the traveler time and earth time when it happens locally and must wait for the radioed data from 20 units away to see that the other clock and earth time there were exactly the same there.
What your failing to account for in detail is dealing with all three or four reference frames. The returning clock is in a ‘fourth’ frame that since it changes direction we have no way of making easy valid distance measurements before and after the turn, but we can track the clock time easy enough. BUT, I see no effort on your part to detail accurately the locations and times in the other two frames namely a) the outbound frame and b) the inbound frame. ALL simple SR math, just more of it than you're doing so far.
Specifically: When the clock(s) depart earth in reference frame “a” exactly where are they (the clocks and earth together) as measured in reference frame “b”? It can only be one unique time and location there.
At the turn around, easy to define in the earth frame, but you don’t say where and when is the earth in reference frame “a” at that earth time of the turn around.
Also for both the earth and that location in “a”; where and when are they in reference frame “b”?
And finally in detail where and when does the clock that turns around step into reference frame “b” as measured in “b”.
Now during the return the clock doesn’t change location in frame “b” but we can see the clock will still allow time to pass.
But when it does return to earth the and a local clock comparison can be made. The traveling clock is only reading time at the same rate as frame “b” what is the “b” time.
Also where and where is the clock and earth as measured in frame “a”.
Finally for the turn around point a fixed distance from earth, where and when is that point in frame “a” and frame “b” at the start of the trip and also at the end of the trip.
Unless your willing to do a complete job of this you have no basis for claiming relativity is broke (at least nor SR), just that your evaluation is incomplete.
– If not mine that you don’t follow, at least your own, worked out completely.
And as I said, once you do the work, you can see where simultaneity is a big issue, totally dependent on reference frame.
Peterdevis
Jan11-06, 02:38 PM
we can presume that during the travel time the clock that is put in motion runs slower.
No, because you can't decide wich clock is in motion. Motion is always relative to someting. So for clock A clock B moves with a velocity B and for clock B clock A moves with velocity v
then A and B are accelerated to a uniform velocity v in the direction of C
When you deal with accelleration, your clocks are not longer connected with an inertial frame and so you left SR and comes in the world of GR.
In GR you will learn that propertime (that is the time reading by the clock) depends of the path of that clock and that you can only compare two clocks if there in the same place
Randall - your in the wrong post - there is another post entitled relativity is broken - why do you keep insisting that I said that - I am not concerned with doing a complete numbers crunch using the traditional approach which presupposes that in some way what we observe in another frame is actually going to impact the clock - in almost every analysis I have seen, there is a transition from apparent phenomena to explain actual time dilation - and I know you can get to the desired result (a number that conforms to measured time dilation in GPS and particle disintegration). But its pseudo science - I have over 30 books on relativity and none of them is able to explain actual time dilation - Einstein did not have an answer and neither do you - the best attempts I have seen has been by the critics of SR - Curt Renshaw for example makes a plausible argument based upon energy considerations - but what i am looking for is something conceptual - Einstein made a bold prediction in his 1905 paper when he asserted that when one oif two clocks is put in motion relative to the other - the one in motion would arrive out of sync.
He dosn't not convey how or why this can result - becuse prior to that bold assertion he was dealing only with observational effects - whcih do not explain how a clock that is moving will run at a different rate than the one which did not - but it does - that is why we have to offset every GPS clock put into orbit in order for it to read the same as the clock in the earth centered reference frame
russ_watters
Jan11-06, 03:38 PM
...Einstein made a bold prediction in his 1905 paper when he asserted that when one oif two clocks is put in motion relative to the other - the one in motion would arrive out of sync.
He dosn't not convey how or why this can result... That's your whole problem? You want to toss out a theory that works because you don't think the explanation for how/why it works is satisfactory?
He dosn't not convey how or why this can result - becuse prior to that bold assertion he was dealing only with observational effects - whcih do not explain how a clock that is moving will run at a different rate than the one which did not - but it does - that is why we have to offset every GPS clock put into orbit in order for it to read the same as the clock in the earth centered reference frame As long as the fundamental equations of physics have the mathematical property of Lorentz-symmetry, it is guaranteed that they will work the same way in the different coordinate systems allowed by the Lorentz transformation, and thus that time dilation and other effects will be observed. If you were designing the laws of nature in a simulated universe on a computer, and the equations you programmed in as the fundamental laws governing the simulation happened to have this property of Lorentz-symmetry, then you would automatically see these relativistic effects in your simulation, even if you had not planned or expected this.
Why do the fundamental laws of physics all have the property of Lorentz-symmetry? I don't know, but I also don't know why they have spatial translation symmetry, or rotation symmetry, or any other symmetry. Do you need an "explanation" for these other symmetries?
Russ - did I say i wanted to toss out SR - that is a strange comment. I pose an interrogatory in the hope it will lead to some interesting comments and what I get back is a sermon.
Jesse - That is the whole point - things are symmetrical as long as it is assumed there are no preferred reference frames and every inertial system is equal to all others - There is reciprocal behavior of each clock in such a world but things are not symmetrical when one clock is accelerated wrt to the other. We know things are asymmetric during the acceleration - but once the accelerated clock levels off to a constant velocity v wrt the stay behind clock, things can no longer be symmetrical if at the end they are both returned to the same original frame and the clocks compared - The question posed is whether there is complete symmetry between the two clocks during the uniform velocity phase - and if so, why do they read differently when brought together in the same frame at a later time (where the amount of difference depends upon the uniform velocity and the length of travel at said velocity). Or do you think they will both read the same when later compared in the same frame?
Peterdavis - I did not mean to ignor your post - but briefly - we do know which was put into motion and which remained stationary - read part 4 of Einstein's original paper where the experiment is described.
Jesse - That is the whole point - things are symmetrical as long as it is assumed there are no preferred reference frames and every inertial system is equal to all others No, you miss my point, I'm talking only about a mathematical property of the equations of the fundamental laws of physics. That a particular equation has the property of "Lorentz-symmetry" can be checked just by looking at the equation, without any notion of "reference frames" whatsoever. But as long as all the fundamental equations have this mathematical property, it is guaranteed that the laws of physics will be the same in the different coordinate systems provided by the Lorentz transformation. Again, if you were creating a simulated universe with its own laws of physics, then even if you gave no thought to how the laws would look in different reference frames, if the equations you wrote down were Lorentz-symmetric, this alone would be enough to be absolutely certain that relativistic phenomena like time dilation would appear in your simulation. For example, Maxwell's laws are Lorentz-symmetric, so if you programmed a simulation to be governed entirely by Maxwell's laws then this simulation would automatically obey the rules of relativity, despite the fact that physicists came up with Maxwell's laws well before they had even conceived of relativity. There is reciprocal behavior of each clock in such a world but things are not symmetrical when one clock is accelerated wrt to the other. We know things are asymmetric during the acceleration - but once the accelerated clock levels off to a constant velocity v wrt the stay behind clock, things can no longer be symmetrical if at the end they are both returned to the same original frame and the clocks compared - The question posed is whether there is complete symmetry between the two clocks during the uniform velocity phase - and if so, why do they read differently when brought together in the same frame at a later time (where the amount of difference depends upon the uniform velocity and the length of travel at said velocity). Or do you think they will both read the same when later compared in the same frame? I don't know what it means to ask whether the clocks themselves are symmetrical, it only seems meaningful to ask whether the way the clocks appear in different reference frames is symmetrical or not. And if you're talking about a reference frame where the non-accelerated clock is at rest vs. a reference frame where the clock that accelerates comes to rest after it finishes accelerating, then clearly their respective views of this specific situation are not symmetrical--one frame will see the two clocks reading the same time up until the first clock accelerates, the other frame will see the two clocks being out-of-sync up until the first clock accelerates. The only symmetry is in how the laws of physics work in each frame--in either frame, a clock which is moving at velocity v will be slowed down by a factor of \sqrt{1 - v^2/c^2}.
The question posed is whether there is complete symmetry between the two clocks during the uniform velocity phase - and if so, why do they read differently when brought together in the same frame at a later time (where the amount of difference depends upon the uniform velocity and the length of travel at said velocity). Or do you think they will both read the same when later compared in the same frame?
I'm looking for clarification of your question. Does "together in the same frame" mean "same constant velocity but different spatial position", meaning parallel but not coincident worldlines?
I am not concerned with doing a complete numbers crunch using the traditional approach which presupposes that in some way what we observe in another frame is actually going to impact the clock
--snip--
- but what i am looking for is something conceptual - Einstein made a bold prediction in his 1905 paper when he asserted that when one oif two clocks is put in motion relative to the other - the one in motion would arrive out of sync.
He dosn't not convey how or why this can result - becuse prior to that bold assertion he was dealing only with observational effects - whcih do not explain how a clock that is moving will run at a different rate than the one which did not - but it does -
So, is the key question: "explain how a clock that is moving will run at a different rate than the one which did not"? Can you succinctly clarify what you mean by the "traditional approach which presupposes that in some way what we observe in another frame is actually going to impact the clock"?
RandallB
Jan11-06, 07:11 PM
Randall - your in the wrong post - there is another post entitled relativity is broken - why do you keep insisting that I said that - Sorry I probable did see that other post and interpreted your “Reality” of Relativity and inconsistencies your finding with it as relativity having a problem – i.e. it's broke. Didn’t mean to put words in your mouth, but that is the upshot of what you’ve been saying.
I am not concerned with doing a complete numbers crunch Why not get your fingers dirty with a little real work no need to be like an old Greek philosopher where work like that is above your station. Plus in this thread you’ve already given examples of using the formulas you don’t seem to believe in but refuse to take them to a complete logic limit of a full explanation. Why not finish what you started.
But its pseudo science - I have over 30 books on relativity and none of them is able to explain actual time dilation Not true – how can you consider it pseudo science if you won’t subject it to your own complete thought experiment and analyses. Don’t count on one of 30 books, I’d be surprised if you didn’t see considerable contradictions between them, mostly because they never give a complete picture – just go far enough to where they are satisfied, I agree with you I’ve never seen one done in a complete manner – including Einstein. The idea of working it through yourself, is to be complete for no one but yourself. How else are you going to believe you really “get it” just count on some author that sounds good? No author was good enough for me – including Einstein.
but what I am looking for is something conceptual Great idea, how about working out the problem in a full and complete manner to confirm or falsify the results as matching what everyone says they will or not. The conceptual part you need to deal with is working the analysis completely enough to accept the possibility the results may falsify your own preconceptions. But, if you just stop if it gets close to doing so, then that’s just denial not science.
whcih do not explain how a clock that is moving will run at a different rate than the one which did not - but it does - that is why we have to offset every GPS clock put into orbit in order for it to read the same as the clock in the earth centered reference frame But SR formulas do explain it, formulas built from the simple experimentally confirmed in the 1800’s fact, of the speed of light is the same fixed speed, regardless of relative motions of source or receiver.
The point your still missing is that no clock ever runs slow. AND all the observations are “reciprocal”. Including the ‘fact’ that the clock traveling away from you can be understood as actually “running faster” (unlike slower as everyone keeps saying). It’s all in how you compare them, instead allowing it to return to earth, send a earth clock chasing after it at double the speed (Use Rel. Speed Addition i.e. .5 +.5 = .8) to run it down and compare the times directly without the traveling clock changing its frame. No need to bend a hyper-space-time curve just plain old SR number crunching.
But if your unwilling to do the work and considerer the falsification of your own concepts, Then your just dealing with argumentative philosophy, not science, and not ready to apply anything useful to the GPS example.
Again - I am talking only about measurements made at the end - where the two clocks are reunited in the same frame (though not necessarily at the same spatial location). Based upon the difference between the clock readings - we know that things could not have been symmetrical when the two clocks were in motion. The apparent symmetry that is postulated during uniform relative motion (note we never do this experiment) is what is at issue
Peterdevis
Jan12-06, 01:57 AM
read part 4 of Einstein's original paper where the experiment is described.
May be you don't know but Einsteins Paper from 1905 was only the beginning of the formulation of a whole new theorie. Einstein realised that there where fundamental problems with SR. One of the fundament of SR are the inertial frame and the Lorentztransformation between this sort of frames.
There are two problems with the inertial frame:
1) Nobody can define what a inertial frame is whithout circular reasoning.
2) In SR inertial frames are preferred frames. This is against one of the basic concept of nature: Nature don't know frame's, Laws of nature are the same for al observers.
For this reasons Einstein didn't stop thinking and came with general relativity.
So your problem, what is basically the twin paradox, can only properly resolved in GR.
(For the good order, I agree you can calculate the time dillitations of accellerating particles also just with SR, but you can not explain correctly why).
Conclusion: If you really want to know the finesse of part4 you have to study GR, just like Einstein did!
Karthikeyan
Jan12-06, 03:01 AM
Then, simply put, you are not discussing Special Relativity. You are discussing something else that has a universal notion of time.
Lorentz's formulation assumed that there was a universal notion of time, and had to explain why clocks don't measure it.
Einstein's formulation says that time is what clocks measure, nothing more, nothing less.
Hi,
I ve a basic question. Einstein's formulation says that the clock running in a moving object will run slower than the one which is stationary. Now, let me assume that we ve two frames of reference. One stationary A and another B which is moving with a uniform velocity of V. U synchronise two clocks exactly and place one in the moving refence frame and the other in the stationary reference frame. Let the time of one click ( or 1 sec) depend on the speed of light ( which is assumed to be constant throughtout). After a time 't', when the moving reference frame stops, we look at the two clocks. Will it show different time ???:confused:
yogi - one last try with the good old euclidean analogy:
Two cars starting at same speed in slightly different directions - corresponding to two frames with different velocities.
Which one will win the race? - which clock will show more time?
You can´t tell because the situation is completely symmetrical.
One car turns to drive in the same direction as the other - one clock accelerates to match velocity with the other.
The symmetry is broken.
The car which turned will be behind the other and lose the race - the accelerated clock will show less time.
There´s no point in trying to assign one of the cars less speed than the other or to claim that one clock ticks slower in an absolute sense. But still you have the difference when the cars drive in the same direction/ the clocks have matched speed.
Based upon the difference between the clock readings - we know that things could not have been symmetrical when the two clocks were in motion. The apparent symmetry that is postulated during uniform relative motion (note we never do this experiment) is what is at issue Your concept of "symmetry" is too vague. The symmetry is in the laws of physics as seen in different frames, but the specific situation you describe involving the two clocks is not symmetrical, because different frames disagree about whether the two clocks were synchronized at the moment before one accelerated (or the moment immediately after one accelerated, if you assume the acceleration was instantaneous). A symmetrical physical situation would be one where you could look at the situation in one frame, then exchange the names of the two clocks, and possible flip the labels on your spatial directions (exchanging left for right, for example), and then you'd have an exact replica of how the original situation looked in a different frame. For example, if clock A is at rest in one frame and B is approaching it at constant velocity from the right, and both clocks read the same time at the moment they meet, then if you switch the names of A and B and flip the left-right spatial direction, you have a replica of how the original scenario would have looked in the frame where B is at rest and A is approaching it at constant velocity from the left. But in any situation where the clocks read different times when they meet, there's no way you can exchange the names and get a replica of how the original situation looked in a different frame. Relativity does not demand that specific physical situations be "symmetrical" in this way, only that the fundamental laws of physics be symmetrical (ie work the same way) in different frames.
Hi Ich - I agree with your first sentence - to make it perfectly analogous to Einstein's description we can use two clocks in sych and at rest wrt to each other - and accelerate each one by exatly the same amount - we have perfect symmetry - I think everyone would agree that each observer could make measurements on the other using the two clock techique described in almost every text on the subject and each would observe the other clock to be running slow - we have reciprocal apparent time dilation - now stop them both with equal accelerations and they are returned to the original frame and we see there has been no difference in the amount of time logged by each clock. Ergo, we can conclude that although there was apparent time dilation, there was no actual time lost or gain - we have perfect symmetry.
I don't follow what you are getting at in the remainder of your post. But I would again try to keep everything as close as possible to the examples given in part 4 - so lets take your two cars each with clocks and accelerated them unequally so that the relative velocity reaches v at which point they continue moving with constant relative velocity v - it shouldn't make any difference whether they are moving in the same direction, opposite or at a relative angle - and at some point they are both quickly decelerated until the relative velocity is zero -- now we measure the times logged on the two clocks - and as I understand your post you would say that one of the clocks would have accumlated more time than the other, but it does not follow that the clocks ran at different rates during the experiment. Well yes, that is true in the sense that each clock runs at its own proper rate in its own frame - so a cross frame reference is meaningless.
I realize there are several posts to which I have not responded - but will try to take them up later as a few provocative issues have been raised.
RandallB
Jan12-06, 11:54 AM
Again - I am talking only about measurements made at the end - where the two clocks are reunited in the same frame (though not necessarily at the same spatial location). Based upon the difference between the clock readings - we know that things could not have been symmetrical when the two clocks were in motion. The apparent symmetry that is postulated during uniform relative motion (note we never do this experiment) is what is at issueTo see what you call "apparent", as being real and why; you just need look at exactly what the local times and locations are for each point (start turn end etc) in the other reference frames not just the frame(s) you want to look at. They all need to be understood, that’s all it will take.
Till you do you’re not opening your eyes to the simple view of a thought experiment you can easily make complete on your own.
BUT, it’s your choice if you prefer to keep your eyes closed.
I’ll leave it to you how you wish to learn and quit bugging you on it.
Good Luck.
Just to correct the record Randall - i spend a great deal of my spare time (whenever I am lucky enough to have some) working through different ideas which i find in conflict. I go to those that are suppose to be able to give some insight on these matters and find that there is not at all agreement on the subject - if it were as simple as you would have it to be, there would not be thouands or articles and hundreds of books all attempting to explain the same paradox - whenever I pose a question that reflects upon the different explanations, i always get the same resonse "you just don't understand SR" You know something - no one does - you have a version, but it is only one of many attempts to make sense out of the experiments - take a look at those that claim you need GR to explain the twin paradox (Scima, Born and Lederman for example) Two of these were Nobel winners - they ought to know what they are talking about - but they each give a different explanation - Born goes all the way through the book telling you he is going to give you the great final explanation - only to wind up using the acceleration formula that applies if there were a continuous acceleration on the outbound leg - or you can look at any of the numerous explanations that claim GR is not needed - shifting hyperplanes and missing time at turn around and so on - or the old favorite that its somehow connected with acceleration at a distant place which makes your local clock run fast ...don't you think I have been through all of these.
The only persons that have their eyes closed are those that think they have all the answers - I know I don't and in actuality, I do not think we will have a final verdict on SR until some experiments are made in free space - away from the effects of earth gravity - until then I think its worthwhile to pose questions - even though interrogtories that suggest that SR may need to be modified are anathema on these boards.
RandallB
Jan12-06, 07:22 PM
- if it were as simple as you would have it to be, there would not be thouands or articles and hundreds of books all attempting to explain the same paradox - You’d be surprised at how many smart people don’t get simple things like SR. look at those that claim you need GR to explain the twin paradox (Scima, Born and Lederman for example) Two of these were Nobel winners - they ought to know what they are talking about I understand it's amazing to me how guys like these don't get it. continuous acceleration, GR, shifting hyperplanes, acceleration at a distant place ...don't you think I have been through all of these. Of course you have, what else could get you so bollixed up on the issue that should be so simple. Trust me – no one, including me, is going to be able to convince you or show you an answer.
A tip - attributed to NEWTON:
Truth is the offspring of silence and unbroken meditation.
I.E. Work out the all the angles, all of them, using just classical SR, on your own without listening to anyone else like me, for as many variables you can think of and can stand to do.
You might just be surprised at how amazing simple SR really is.
PS: By complete I mean something like what JessseM did in post #4 of;
http://www.physicsforums.com/showthread.php?t=106600
take a look at those that claim you need GR to explain the twin paradox (Scima, Born and Lederman for example) Two of these were Nobel winners - they ought to know what they are talking about - but they each give a different explanation...
In my opinion, it is a mistake to think that a Nobel prize winner is somehow an authority on issues in special and general relativity, particularly when the prize is awarded for a non-GR achievement. Don't get me wrong... they're great at what they do... but that doesn't make them a modern authority on SR and GR. Interpretations have tightened up somewhat after the rise of global methods/geometrical viewpoints. Unfortunately, it'll probably take a generation or two before those interpretations are better appreciated.
Although there are all sorts of interpretations and calculations concerning the twin paradox and its variants, the modern bottom line and the always-applicable explanation uses the fact that the proper time is a spactime arc-length along a worldline.
take a look at those that claim you need GR to explain the twin paradox (Scima, Born and Lederman for example) What did they say, specifically? You may need GR to explain the twin paradox from the point of view of the non-inertial twin, but I don't think anyone would say you can't calculate the proper time along both twin's worldlines from the point of view of an inertial frame. Two of these were Nobel winners - they ought to know what they are talking about - but they each give a different explanation - Born goes all the way through the book telling you he is going to give you the great final explanation - only to wind up using the acceleration formula that applies if there were a continuous acceleration on the outbound leg - or you can look at any of the numerous explanations that claim GR is not needed - shifting hyperplanes and missing time at turn around and so on - or the old favorite that its somehow connected with acceleration at a distant place which makes your local clock run fast ...don't you think I have been through all of these. All the explanations you're discussing are ways of describing how the twin paradox works from the point of view of the non-inertial twin. But why are you so concerned with that issue? Again, there is no question that the time elapsed on each twin's clock from the time they depart to the time they reunite can be calculated exclusively from the point of view of an inertial reference frame.
Randall - I do agree that SR - in particular the cause of actual time dilation, is fundamentally simple - I guess that is the problem: "God hath chosen the most simple things to confound the mind of man" And as I have said, there are many ways of ariving at the same result - although some of them are mutually inconsistent. So when you say you have a simple answer, I believe that you believe it is true and correct. But when i go through the reasoning - a always find a transition - a shift from observation to reality - often its very subtile, but its always there. If you have an electrical engineering background you will relate to a phenomena known as jump resonance - it occurs in non-linear system - and i am always reminded of it when I see the carefully laid out mathmatical transforms that relate measurements made between observers in moving frames - somewhere there is jump from apparent clock rates to actual time slippage
Perhaps in the last analysis, I won't ever be convinced - even a perfectly conducted MMx experiment in free space with null results should bring about surrender - but instead i will probably just go skiing
robphy - I agree that a Nobel award does not qualify a writer as an authority - i guess i wanted to get across the idea that there is disagreement among respected authors - persons who are presumably a cut above the cranks.
I once made a list of statements made by recogonized authors re relativity - in particular those that dealt with the reality of spatial contraction and time dilation ...like the bible, there was support for every theology.
sorry, I´m quite out of sync, but maybe it´s worth to work out my point.
yogi - i didn´t make myself very clear in post #26. The analogy is as follows:
Two cars with the same speed - two observers with the same four-velocity (c or 1, whatever you prefer).
Two cars heading in different directions - two observers in relative motion.
The core of the analogy is: each car will symmetrically see the other fall behind. That´s what you would call "apparent". But if they match directions, one of those cars will really be behind the other. That´s what you would call an "actual difference".
Translate this to Einstein´s chapter 4: car A initially drives parallel to car B. Then it steers towards car B until it is on the same track. Of course it will be behind car B in this track. And of course you wouldn´t bother about "real" and "apparent" car positions. You wouldn´t even claim that car A is slower than B in an absolute sense while it steers towards B.
RandallB
Jan13-06, 09:37 AM
the cause of actual time dilation
Again; in classical SR there is no “actual time dilation”, no clock ever “actually” runs fast or slow, thus there can be no time slippage for a individual clock.
So when you say you have a simple answer. But when I go through the reasoning - always find a transition - a shift from observation to reality - non-linear system - somewhere there is jump from apparent clock rates to actual time slippage. Not my solution or answer – just a complete workup of the Classical math applied to the SR factors.
Look at the rates and ratios SR uses, once your committed to selected fixed speeds there are no “non-linear” functions. It’s all algebra, you cannot have a conflict in measurement between reference frames or transition from one observation to another’s, algebra doesn’t work that way. Only errors in the math, so double check the work, not by just doing it again but by completely solving for the same numbers from within each of the 3 reference frames.
Even if some “clocks” need to run fast!
Example, as the observer sits in the station waiting for the twin to return as the train goes by clocks in each car can be seen flashing creating an animated clock like one of those cartoons drawn in a stack of cards you flip through. Isn’t that also in the traveling twins reference frame where all those clocks are synchronized with each other. It should be just as valid for defining the age of the traveling twin. What formula would you use to define this clock time based on the station clock time. If it doesn’t match with your expectation of the clock traveling with the twin, when is the “imaginary” clock the correct way to gage the age of the traveling twin??
Don’t conceptualize on it, don’t look to me or anyone for an opinion, just do all the Classical SR algebra for all the variations yourself. Then see if you cannot absorb your own work till you “get it”.
- but instead I will probably just go skiing Don’t give up on yourself, you can do this algebra in an evening and absorb it in a weekend.
RandallB - its not that I wont do the algebra - I have done it many times from different perspectives - one telephone call to my wife and you would be convinced that I fill up pad after pad of paper with equations and notes almost every night - I go through the derivations until I can not think anymore - then hit the sack - generally about 3 or 4 or the morning - she gets up and finds a mess of scribbling. Maybe thats the problem - too late - too many beers
ich - i want to consider your post 37 more before responding
Thanks
yogi
Ich - I must be missing something - when Car A and B are moving parallel at the same speed the relative velocity is zero - no time dilation. When car B turns and drives toward A there is a relative velocity v and each would judge the time in the other car to be running slow - there is apparent time dilation in this case
RandallB
Jan14-06, 10:31 AM
RandallB - its not that I wont do the algebra - I have done it many times from different perspectives - one telephone call to my wife and you would be convinced that I fill up pad after pad of paper with equations and notes almost every night - I go through the derivations until I can not think anymore - then hit the sack - generally about 3 or 4 or the morning - she gets up and finds a mess of scribbling. Maybe thats the problem - too late - too many beers beerS - Maybe so,
Think of it like a check book register. You can keep the total balance several different ways. A running total balance as each record is entered; A running balance of deposits separate from checks, only combining the two when you need to now a current total.; Or only summing deposit and check balances by page & only summing the page totals when you need to work a total balance. Three different way to get exactly the same result, that can all be done at the same time serving as a triple check of the balance because if any one disagrees there must be a math error somewhere.
Working SR is the same way. I assume you start with three reference frames, two going the same speed but in opposite directions of a third (usually assigned to earth).
And define a time = 0 and location = 0 to be local to all three frames at that one instant in time.
Now for any location at any time you pick in any frame it will have only one location in each of the other two frames local to it. And each of those will have their own
time that can be “seen” (calculated) from the frame you’re working from.
Now the point is when you redo all those measurements from any other frame you must come up with the same combinations of times and locations local to each other for any giving point and time in a frame.
Such as location #0 (Station, train car, space ship, whatever based on + or – distance) at a different time say +20 or -20 time units, there is one and only one location, with its own unique time, in each of the other two frames that is local to that point and time.
But you can double and even triple check those numbers by also calculating them completely from within those other frames.
If while doing those cross checks you find any of those sets of six numbers for an individual location and time, not be identical with the other calculations. Then there can only be one of two problems:
1) There is an error in the math or its application; it’s just a matter of finding it, just like balancing a check book.
OR
2) Unlike a check book there is something about the lambda and dilation factors being used that are not linear; this leading to a condition called background independence that will make it impossible to “balance” these kinds of cross checks; BUT you should be able to define where that non-linear part of the formulas is causing the problem.
But where in SR is there anything non-linear? Sure GR starts into curving and warping things and is accepted by many, even most, as being background independent. That’s a problem for GR not SR. I think IMO the problems you find in most books and these posts on SR are too short, vague, or incomplete (including Einstein’s) to make the point clear.
You’ll just have to decide for yourself; is it #1 and fix it;
or #2 and find the non-liner piece.
Try A Barleywine instead of beers; maybe that will help.
I find Bigfoot aged two years in bottle to be excellent, but fresh is very good too.
Ich - I must be missing something - when Car A and B are moving parallel at the same speed the relative velocity is zero - no time dilation. When car B turns and drives toward A there is a relative velocity v and each would judge the time in the other car to be running slow - there is apparent time dilation in this case
I think you are missing the point of the analogy.
Each car respresents a clock.
The path each car travels represents progression through time as determined by that clock.
The angle of the two cars' paths to each other represent the relative velocity between the cars.
Each clock(car) measures the other clock(car)'s progression through time as compared to its own present heading.(draw a line that run through the clock(car) along the line that the clock(car)1 is pointed. Now draw a line perpendicular to this line that intersecrts the other clock(car)2. Where this line crosses the first line, is how much time clock(car)1 will determine has passed for clock(car)2.
Clock(car)2 will determine clock(car)1's progression through time by the same procedure.
A change in velocity is represented by a change in heading.
If clock(car)2 changes its velocity to match clock(car)1, this shown by its changing its course until it parallels that of clock(car)1. After which clock(car)1 and clock(car)2 both measure each other as progressing through time at the same rate, and clock(car)1 will be ahead of clock(car)2 (has accumlated more time) according to both cars.
RandallB
Jan14-06, 01:46 PM
Ich & Janus
I really don’t see how making the problem more complex by introducing vectors of undefined angles makes anything any easier.
There is nothing that can do that isn’t more simply represented by different speeds defined for reference frames moving along one straight line.
The only thing needed are different fixed speeds and instant transfers between frames without accelerations of GR to account for. (Transfer time 0 as seen by all frames)
Why make it more complex than that?
RandallB,
I did not intend to make things more complex; instead I tried to translate yogi´s problem of real and apparent effects to an example of every day life.
To me, the SR question "which clock really ticks slower" is absolutely equivalent to the non-SR question "which car is ahead" when they drive in different directions. It simply does not make sense.
Yogi´s conceptual problem of "real" vs "apparent" arises in a nearly perfect analogy in our every day experience. But it´s resolution is much easier when you consider the example of the two cars.
Of course, first of all it´s most important to get the point of the analogy. Janus kindly explained it some more where I obviously failed.
RandallB
Jan14-06, 03:23 PM
Ich
OK, but it still retains some of the implication that maybe some clock does "really tick slower" which is not true.
That’s why is important to build an example that reveals the full nature of simultaneity to show that no clock ever runs fast or slow.
Since it's not a technical term with a clear definition, I spent some time earlier today trying to figure out what you might mean by words like "illusory".
The first two situations that popped in my mind were these:
If I'm in a car driving towards the source of a sound, I will hear it at a higher pitch. I could imagine someone calling this illusory.
If I'm in a car, I see person sitting next to me in a fixed place. I could imagine someone saying that I see that person as stationary was illusory.
Both observations are certainly real. Although the musician was trying to play a 440 Hz note, it really did triger that 460 Hz region of my ear. And when I hold out my ruler to measure your position, the passenger is always right there at the end.
These two examples have a common element: that there is a commonly agreed "right" way to make these measurements. E.G. it is the common convention that we measure speeds relative to the ground, as opposed to ourselves.
So, in these examples, the usage of "illusory" would simply mean that the measurements were performed in reference frames different from the commonly agreed one.
This usage of "illusory" is fundamentally different from other situations, such as that of a magician who hides things behind curtains, or a demon who sends you misleading light signals, all to deceive your vision.
If I recall correctly, your usage of "illsuory", yogi, is akin to the first two examples I stated.
Usage of this term in such a circumstance is highly misleading (and I think you have even misled yourself), since the word carries the negative connotation of the magician or demon who is actually tricking you.
A lot to answer - but as far as illusory - it has to me the same meaning as a measurement of distances in a relatively moving frame - if there is a real measurment of a 10 foot pole that appears to be 8 feet - I would call that illusory - Hurkyl - some time back we had a private discussion and I responded to your explanation that the one twin is halfway there because of the "time jump" before he starts - and I drew an analogy to the explanation offered by Rindler which gets the same result - namely that the traveling twin travels a shorter distance to Vega (or whatever star you pick) and therefore less time is involved because the distance is half to start with - I know you get the desired answer - but the method subverts the issue - it makes the rationale more important than the reality principle ...arriving at the right numerical value for the wrong reason does not help if the object is to understand the underlying physics.
In summary - the fact that the traveler sees the distance from earth to Vega is not a bases for time dilation - its the other way around - time dilation is the cause - the consequence is that the traveler measure the distance to the object to be shorter because it is the reality of temporal changes that is fundamental - not vice versa.
let me try to get back after the sideline discourse on what I meant by illusory. Here is a situation from the real world - we have two clocks A and B both at rest at a 100 mile high tower at the North Pole - then we put A in orbit in a GPS satellite at the same altitude - but prior to launch we set it to run faster to compensate for the orbital velocity.
Each time A pases over the North Pole, the orbiting clock A will be in sych with the earth clock B- but lets say we forget to make the velocity correction before launch - the orbiting clock A will continue to lose time on each pass - this is not a case where each clock sees the other to be running slow - the tower clock B sees the A clock running slow, and the A clock sees the tower clock B to be running fast. This is real time dilation - it is an intrinsic result of the fact that they were initially synchronized at the top of the tower and A is accelerated into orbit. It has nothing to do with the fact that the orbiting clock A is moving in a circle - A is in an inertial free fall environment. Isn't this a straight forward verification of Part 4 of Einstein's paper?
Now - while A is in clockwise orbit we arrange to build another clock J on board and sync it with A; each pass by the tower, A and J are seen to fall progressively behind B. Now J is accelerated in a counterclockwise direction until it comes to rest on the tower. Because A and J were initially synchronized while they were traveling together, the reverse acceleration of J away from A presents an interesting situation when analysed from A's frame, but not from the tower frame. From the Tower frame, it makes no difference whether A or J returns to B since both will have been running slow wrt to B by the same amount, either will run at the B rate upon arrival at the tower.
if there is a real measurment of a 10 foot pole that appears to be 8 feet - I would call that illusory - Hurkyl
Illusory or not, you can still fit it through a 9 foot barn door the long way. (As measured from Earth's inertial frame)
Allow me to explain this one in more detail:
I will always carry the 10-foot pole so that it is pointing in the East-West direction. (As measured in the Earth frame)
There is a 9-foot wide door on the South side of the barn.
By running sufficiently fast in a Northeasterly (or Northwesterly) direciton, I am able to take the pole inside the barn.
arriving at the right numerical value for the wrong reason does not help if the object is to understand the underlying physics.
Why do you think it's the wrong reason? It almost seems that you're of the opinion that there can only be one way to solve any problem!
and the A clock sees the tower clock B to be running fast.
Wrong. Clock A will observe clock B to be running slow, when they're near each other.
Hurkyl - if the tower clock B reads one hour on the first pass, 2 hours on the second, 3 hours on the third etc, in other words a precise 60 minutes per orbit, and the orbiting clock A reads 59 minues, 118 minutes, 177 minutes etc on each successive fly-by, the orbiting observer with clock A will note that B is gaining one minute each orbit, ergo, B will conclude A is running fast wrt to his own measurement of time. This is an example of real time dilation - failure to correct for the relativistic velocity of A prior to launch will cause the two clocks to accumulate different times during each successive orbit.
Each time A pases over the North Pole, the orbiting clock A will be in sych with the earth clock B- but lets say we forget to make the velocity correction before launch - the orbiting clock A will continue to lose time on each pass - this is not a case where each clock sees the other to be running slow - the tower clock B sees the A clock running slow, and the A clock sees the tower clock B to be running fast. This is real time dilation - it is an intrinsic result of the fact that they were initially synchronized at the top of the tower and A is accelerated into orbit. It has nothing to do with the fact that A rather than B was the one that was accelerated after they were initially comoving, if that's what you mean. If instead A and B were two synchronized clocks orbiting together, and then B was accelerated so it came to rest on top of the tower while A continued on its freefall path, the time dilation effects on subsequent orbits would be exactly the same. It has nothing to do with the fact that the orbiting clock A is moving in a circle - A is in an inertial free fall environment. Isn't this a straight forward verification of Part 4 of Einstein's paper? Well, if you tried to analyze this problem using only SR you'd have to ignore the curvature of spacetime caused by the earth's gravity, in which case A would not be moving inertially. Even in the context of GR, I'm not sure if it would be correct to say that A is moving "inertially" even though it is in free fall, I dunno if the concept of inertial vs. non-inertial motion makes sense except in a purely local sense (in an arbitrarily small region of spacetime which is arbitrarily close to flat) in GR. In any case, it definitely makes no sense to say that a situation which involves curved spacetime in an essential way is a "straight forward verification of part 4 of Einstein's paper" when that section dealt purely with velocity-based time dilation in the flat spacetime of SR.
Hurkyl - if the tower clock B reads one hour on the first pass, 2 hours on the second, 3 hours on the third etc, in other words a precise 60 minutes per orbit, and the orbiting clock A reads 59 minues, 118 minutes, 177 minutes etc on each successive fly-by, the orbiting observer with clock A will note that B is gaining one minute each orbit, ergo, B will conclude A is running fast wrt to his own measurement of time. This is an example of real time dilation - failure to correct for the relativistic velocity of A prior to launch will cause the two clocks to accumulate different times during each successive orbit.
You're only looking at the "average".
Everybody will agree that, over the long term, the tower clock runs faster than the orbiting clock, for the reasons you describe.
I think that it would be inaccurate to call this "dilation", though, since you're considering a discrete series of events.
However, as the tower and orbiting clock pass each other, the orbiting clock will observe the tower clock running slowly. (and vice versa)
I dunno if the concept of inertial vs. non-inertial motion makes sense except in a purely local sense (in an arbitrarily small region of spacetime which is arbitrarily close to flat) in GR.
I thought that "inertial" was interpreted to mean "travelling along a geodesic"?
I thought that "inertial" was interpreted to mean "travelling along a geodesic"? Is an object in freefall said to be moving "inertially"? Have you seen specific examples (in textbooks, say) of physicists using "inertial" in this way in the context of GR?
I don't remember. :frown:
I thought that "inertial" was interpreted to mean "travelling along a geodesic"?
Is an object in freefall said to be moving "inertially"? Have you seen specific examples (in textbooks, say) of physicists using "inertial" in this way in the context of GR?
In GR, an object in freefall is said to be moving "inertially", "geodesically".
OK, I'll take you guys' word for it. Still, it seems to me that yogi's statement "It has nothing to do with the fact that the orbiting clock A is moving in a circle - A is in an inertial free fall environment" is confusing the SR meaning of "inertial" and the GR meaning of "inertial".
By the way, if we calculated the time difference between the two clocks by treating A as if it was just moving in a circle in flat spacetime, does anyone have a sense of how far off this would be from the correct GR calculation in which A is moving on a geodesic in curved spacetime? Would it be close since earth's gravity is not too strong, or would it be far off?
pervect
Jan16-06, 04:22 PM
OK, I'll take you guys' word for it. Still, it seems to me that yogi's statement "It has nothing to do with the fact that the orbiting clock A is moving in a circle - A is in an inertial free fall environment" is confusing the SR meaning of "inertial" and the GR meaning of "inertial".
I agree - the clock in a free-fall orbit certainly has a local inertial frame, but it's limited in extent.
By the way, if we calculated the time difference between the two clocks by treating A as if it was just moving in a circle in flat spacetime, does anyone have a sense of how far off this would be from the correct GR calculation in which A is moving on a geodesic in curved spacetime? Would it be close since earth's gravity is not too strong, or would it be far off?
It will be very close, because g_{tt} is close to 1, and \sqrt{g_{\phi\phi}} is exactly equal to r in the Schwarzschild metric.
I.e. SR says that
d\tau = \int \sqrt{1- r^2 \, (\frac{d\phi}{dt})^2} \, dt
becaause d\tau^2 = dt^2 - r^2 d\phi^2 , \phi being the angle of the object in its circular orbit.
GR says that
d\tau = \int \sqrt{g_{tt} - r^2 \, (\frac{d\phi}{dt})^2} \, dt
because d\tau^2 = g_{tt} dt^2 - g_{\phi\phi} d\phi^2
here g_{tt} is given by the formula for the Schwarzschild metric e.g.
d\tau^2 = (1-\frac{2M}{r})dt^2 - \frac{1}{1-\frac{2M}{r}} dr^2 - r^2 d\theta^2 - r^2 sin^2(\theta)d\phi^2
so g_{tt} = 1-\frac{2M}{r}
and \theta is zero for an equatorial orbit, so g_{\phi\phi} = r^2
(Note: I've used geometric units like I always do, so that c=G=1, adjust for standard units if desired).
hurkyl - wrt your post 53 - I agree that if each observer sets up the classical two clock measuring experiment to determine time in the other frame, each could measure the apparent rate of the other clock to be running slow - at least during portions of the orbit - but what I am attempting to say, is that, with reference to the tower clock B, A actually always runs slow during the entire orbit - for example let me construct a plurality of towers equally spaced along on the earth along the path of the orbiting clock with clocks B through Z all in sync in the earth centered reference frame. These clocks check the rate of A whenever A passes overhead . Each will read A's clock and see A running slow when it passes near - this is the actual time dilation asserted by Einstein in part 4 - admittedly without a sound foundational bases - but nonetheless verified by experiments that were not conducted until many years later. This is what Einstein is referring to when he concludes "a clock at the equator will run slower than a clock at the North pole"
Jesse - as to the orbit as a valid inertial frame - you might check out Spacetime Physics by Wheeler and Taylor - 2nd edition ...they frequently refer to the free fall inertial fame
Jesse - as to the orbit as a valid inertial frame - you might check out Spacetime Physics by Wheeler and Taylor - 2nd edition ...they frequently refer to the free fall inertial fame I'm still not sure if this means a coordinate system where an object is at rest throughout its entire orbit can be called an "inertial frame", or if this notion of inertial motion only applies "locally", in an arbitrarily small region of spacetime which includes an infinitesimal section of the object's path. This is what I meant when I said: I'm not sure if it would be correct to say that A is moving "inertially" even though it is in free fall, I dunno if the concept of inertial vs. non-inertial motion makes sense except in a purely local sense (in an arbitrarily small region of spacetime which is arbitrarily close to flat) in GR. And pervect's last post seemed to suggest it does only make sense to say the path is locally inertial: I agree - the clock in a free-fall orbit certainly has a local inertial frame, but it's limited in extent. In any case, aside from the issue of how the word "inertial" is defined by physicists in GR, you didn't address my other points, like the fact that the time dilation effects would be the same regardless of whether A or B accelerated initially, or the fact that an example involving curved spacetime cannot be said to confirm statements made by Einstein in his 1905 paper which dealt purely with velocity-based time dilation in flat spacetime.
Jesse - it doesn't make any difference which one accelerates into orbit in the example I have given - If B accelerates into orbit - B's clock runs slower than A's ...but i suspect that is not what you meant ... you are saying things should be symmetrical after one of two synchronized clocks in the same frame is accelerated - and I am saying they are not - and I am also saying that Einstein said they are not. In summary, a literal reading of part 4 is that time dilation in SR is like time dilation in GR - 1) in GR the clock that is at a lower gravitational potential runs slow as measured by the clock at the higher gravitational potential, and the clock at the higher gravitational potential runs fast compared to the clock at the lower gravitational potential and 2) in SR, when one of two synchronized clocks in an inertial system is accelerated to a constant velocity v relative to the other clock, the clock in motion runs slow relative to the clock which was not moved, and the clock which was not moved runs fast wrt to the clock whichn was accelerated.
Only apparent effects are reciprocal (e.g., length contraction). If Einstein says the clock at the equator runs slower than the clock at the pole - he also means the clock at the pole runs faster than the clock at the equator when measured by the reading on the clock at the equator - otherwise they both run at the same speed.
Jesse - it doesn't make any difference which one accelerates into orbit in the example I have given I didn't say which clock "accelerates into orbit", I said which clock is the one that initially accelerates, period. That was why I offered the example where they both start out travelling together in orbit, then one accelerates until it comes to rest on top of the tower. The clock on the tower will always be the one that runs faster, regardless of whether it's the one that initially accelerated to separate them or not. I was responding to this quote of yours: This is real time dilation - it is an intrinsic result of the fact that they were initially synchronized at the top of the tower and A is accelerated into orbit. Weren't you saying here that the time dilation is explained by the fact that the clock in orbit has to accelerate? If so, your point makes no sense, as shown by my alternate scenario where they start out both moving on a geodesic in orbit, then one accelerates (moves on a non-geodesic path) to come to rest on the tower while the other one continues on the geodesic path. ...but i suspect that is not what you meant ... you are saying things should be symmetrical after one of two synchronized clocks in the same frame is accelerated No, I am obviously not saying that, since that doesn't match the predictions of relativity. See above. In summary, a literal reading of part 4 is that time dilation in SR is like time dilation in GR Einstein hadn't even invented GR when he wrote that, so how can you possibly interpret him to be saying anything about GR in part 4? 2) in SR, when one of two synchronized clocks in an inertial system is accelerated to a constant velocity v relative to the other clock, the clock in motion runs slow relative to the clock which was not moved, and the clock which was not moved runs fast wrt to the clock whichn was accelerated. Are you saying that Einstein or any other mainstream physicist would deny that any situation in SR can equally well be analyzed from any inertial reference frame? Would you deny that in any situation where a clock accelerates and changes velocities, you can find an inertial frame where the clock's final velocity after it finishes accelerating is zero, and that in this frame the clock is therefore running faster after it finishes accelerating? If Einstein says the clock at the equator runs slower than the clock at the pole He would only say a clock on the equator runs slower on average over an entire orbit than a clock at the pole. He would certainly never say that a clock at the equator is running slower at every moment, because there are inertial frames where this is not true. But no matter which inertial frame you pick, it will indeed be true that the average ticking rate for a clock moving in a circle will be slower than the average ticking rate for a clock at rest relative to the center of that circle, over the course of an entire orbit.
Every inertial frame is equally valid when analyzing any particular problem in SR. Do you seriously think Einstein would have disagreed with this principle? Note that in any situation where two clocks depart each other and then later reunite, all inertial frames will make the same prediction about which one will be behind when they reunite, so it will do you no good to bring up such situations in an attempt to "disprove" this principle.
pervect
Jan17-06, 01:04 AM
Every inertial frame is equally valid when analyzing any particular problem in SR. Do you seriously think Einstein would have disagreed with this principle?
Nope. But I don't think he would apply the term "inertial frame" to the orbit of a planet or satellite, either.
Basically, if you are interested in only small distances, if you were on a space-station orbiting the Earth you could totally ignore the tidal forces and variations of the metric, and consider yourself to be in a locally inertial frame, for purposes of walking around inside the space-station. Some very sensitive experiments might still require more careful analysis, but you wouldn't be hit in the face with the non-inertiality of the frame.
But when you start to consider the path of the space station as a whole, the concept breaks down. The distances are to large - the effects of gravity are too large to ignore. They insist on making themselves noticed.
If you actually sit down and write the equations to calculate the Lorentz interval (i.e. proper time), it is very much easier to write down the metric and calculate the proper time from the same POV in GR as it is in SR - with the sun (or other massive body) being at the center. In fact I don't recall ever seeing it done any other way.
If you have multiple orbiting bodies, there is a specific coordinate system that's good for approximate work, too. This approximate coordinate system (used in the PPN formalism) is based on the center of mass of the system. It's not based on an orbiting body. The physics really is simpler with (for example) the Sun as the center of the solar system rather than the Earth.
The orbiting coordinate system may be "locally inertial", but as far as calculations go, it is far simpler to put the origin of your coordinate system at the local center of mass than it is to attempt to deal with the universe "wobbling" around some particular orbit.
Each will read A's clock and see A running slow when it passes near - this is the actual time dilation
(from #59)
As A passes through B, C, ..., Z, it will observe each of them as running slowly. It sounds as if you're suggesting that this is not "actual" time dilation -- upon what grounds do you suggest that?
Hurkyl - i don't follow what you are saying - in my post 59 I intended to say that the A clock reads the time by looking at the visible counter attached to each tower B, C, D, ...Z the tower clocks always get progressively further ahead. This is not the same as making a measurement using the standard two clock method to determine apparent time dilation in a relatively moving frame - its a simple reading of the counter on the fly.
Now with regard to what has been introduced as an average time loss of each orbit - what I am saying that the orbiting clock A has exactly the same forces, dynamics and whatever else is involved - at every point in the orbit - A clock always runs at its proper time in its Free Float Inertial Frame - the phrase coined by Wheeler and Taylor - nothing changes - therefore what you want to refer too as an average loss of time during one orbit is not average - rather is a sum - you take the time loss in one orbit and divide that by the time for one orbit as measured by any one of the tower clocks (e.g., B) and you have a real value for the constant rate of time loss as between the two reference frames - The actual rate of passage of time on the A clock does not change during the orbit - this is what I have been refering to as real time dilation -
Jesse - as for your post 63 - i know Einstein didn't invent GR until 10 years later ....I was trying to give you an analogy
Now with regard to what has been introduced as an average time loss of each orbit - what I am saying that the orbiting clock A has exactly the same forces, dynamics and whatever else is involved - at every point in the orbit - A clock always runs at its proper time in its Free Float Inertial Frame - the phrase coined by Wheeler and Taylor - nothing changes - therefore what you want to refer too as an average loss of time during one orbit is not average - rather is a sum - you take the time loss in one orbit and divide that by the time for one orbit as measured by any one of the tower clocks (e.g., B) and you have a real value for the constant rate of time loss as between the two reference frames - The actual rate of passage of time on the A clock does not change during the orbit - this is what I have been refering to as real time dilation - You never answer my simple question, which I've asked you a few times: Every inertial frame is equally valid when analyzing any particular problem in SR. Do you seriously think Einstein would have disagreed with this principle? Do you agree, incidentally, that if an object is moving in a circle at constant speed in the rest frame of the center of the circle, then its speed will be non-constant in other inertial frames? This is just as true in Newtonian mechanics as it is in relativity, although in Newtonian mechanics of course speed has nothing to do with the rate a clock ticks.
Pervect - When we attempt to remove one of two orbiting synchronized clocks to the top of one of the towers - as per jesse's query,do you think it will thereafter run faster or slower than the clock that remained in orbit,
(I know the math is messy - just looking for a conceptual answer if you have one).
Jesse as to your post 67- yes - I think Einstein would have disagreed with that - I think he had doubts as to the validity of SR - he said he did not think it would survive the test of time - the CBR is certainly different in different frames
Moreover, i do not think he would say, as to the two synced clocks which I described, where one is put in motion, that the one in motion would measure the non moving clock to be running slow (at least by the same factor) He Never said this - some authors do - others stop short of making this statement - we have never made this experiment - and until we make a freespace experiment that shows that a pion traveling at 0.99c relative to the earth will measure earth time to be slow, I think the question should remain unresolved - after all, relativity works fine whether or not all frames are perfectly equal. In short - I think the symmetry you demand does not comport with actual time dilation - it is consistent with apparent time dilation, and there is complete symmetry as to contaction - but as I have said - there is not complete symmetry when only one of two clock have been accelerated
Since I won't be able to follow pervects mathematical solution to the removing of a clock in orbit - I will propose the following - initially we have 3 clocks J, K, and L on the earth - at the top of the tower - then we put two (J and K) in the same satellite and launch them into orbit - they should both run at the same speed and slower than the third clock (L) left atop the tower - then we decelerate (K) so that it comes to rest on the tower - it should now run at the same rate as the stay behind clock (L) since it has been returned to the original frame where it was synchronized
On the other hand, from the perspective of the J clock still in orbit - (K) has undergone an acceleration, and it should now run slower than J while J is in orbit. So we have returned to the original puzzle - The orbiting clock J runs slower than either K or L on top of the tower - but K should run slower than the orbiting clock J.
Jesse as to your post 67- yes - I think Einstein would have disagreed with that - I think he had doubts as to the validity of SR - he said he did not think it would survive the test of time When did he say this? Can you give me the quote? Since GR incorporates SR, do you think he had doubts about GR as well? the CBR is certainly different in different frames the CBR is not a law of physics. The moon is different in different frames too, do you think that violates the principle that all inertial reference frames are to be treated equal? Moreover, i do not think he would say, as to the two synced clocks which I described, where one is put in motion, that the one in motion would measure the non moving clock to be running slow (at least by the same factor) He would certainly say that in the inertial reference frame where the accelerated clock came to rest after accelerating, the non-accelerated clock which is not at rest would run slow. To say he would disagree with this is to say he would disagree with one of the most basic principles of relativity as understood by all physicists then and now, yet for some reason he never noticed that all physicists were interpreting relativity differently from him or never voiced this difference of opinion. It's completely ridiculous, in other words. He Never said this - some authors do - others stop short of making this statement - we have never made this experiment - and until we make a freespace experiment that shows that a pion traveling at 0.99c relative to the earth will measure earth time to be slow How would this experiment work, exactly? The statement that a pion would measure earth time to be running slow is simply a statement about the coordinate system we choose to define as the pion's "rest frame" in relativity. If you use the Lorentz transform to go between our rest frame and the pion's, this is automatically true. Of course, the Lorentz transform has to be physically motivated, and the pion's coordinate system can be defined in a physical way in terms of measuring-rods and clocks at rest with respect to the pion (as Einstein defined different coordinate systems in his 1905 paper), but if you grant that moving rods will Lorentz-contract and moving clocks will slow down in the earth's rest frame, and if the pion uses these rulers and clocks to define its own rest frame and uses the Einstein synchronization procedure to synchronize its own clocks, then it's automatically true that the Lorentz transform will give the correct relationship between our coordinate system and the pion's, and therefore it follows logically that in the pion's rest frame the earth clocks must be running slow and the earth rulers are Lorentz-contracted. It's logically impossible that things could work otherwise, provided Lorentz-contraction and time dilation hold in the earth's own rest frame. I think the question should remain unresolved - after all, relativity works fine whether or not all frames are perfectly equal. Uh, how do you figure? Wouldn't that obviously violate the first of the two basic postulates of relativity, which Einstein laid out at the start of section 2 of his 1905 paper? In short - I think the symmetry you demand does not comport with actual time dilation - it is consistent with apparent time dilation, and there is complete symmetry as to contaction - but as I have said - there is not complete symmetry when only one of two clock have been accelerated Let me get this clear--are you arguing that even given the current known fundamental laws, which are definitely Lorentz-symmetric, you don't think there is a symmetry between the way the laws of physics work in each reference frame? If so you're talking obvious nonsense, the latter follows mathematically from the former, it's logically impossible that you could have Lorentz-symmetric fundamental laws and yet the laws of physics would not work exactly the same in all the inertial frames given by the Lorentz transformation.
But part of the problem is that you are maddeningly vague about what you mean by "symmetry", you often use this term in ways that totally depart from the standard meaning. Did you read and understand my post #27? Here it is again: Your concept of "symmetry" is too vague. The symmetry is in the laws of physics as seen in different frames, but the specific situation you describe involving the two clocks is not symmetrical, because different frames disagree about whether the two clocks were synchronized at the moment before one accelerated (or the moment immediately after one accelerated, if you assume the acceleration was instantaneous). A symmetrical physical situation would be one where you could look at the situation in one frame, then exchange the names of the two clocks, and possible flip the labels on your spatial directions (exchanging left for right, for example), and then you'd have an exact replica of how the original situation looked in a different frame. For example, if clock A is at rest in one frame and B is approaching it at constant velocity from the right, and both clocks read the same time at the moment they meet, then if you switch the names of A and B and flip the left-right spatial direction, you have a replica of how the original scenario would have looked in the frame where B is at rest and A is approaching it at constant velocity from the left. But in any situation where the clocks read different times when they meet, there's no way you can exchange the names and get a replica of how the original situation looked in a different frame. Relativity does notdemand that specific physical situations be "symmetrical" in this way, only that the fundamental laws of physics be symmetrical (ie work the same way) in different frames. If you understand this distinction, do you see why your comment about the CBR, for example, is a non sequitur?
Pervect - When we attempt to remove one of two orbiting synchronized clocks to the top of one of the towers - as per jesse's query,do you think it will thereafter run faster or slower than the clock that remained in orbit,
(I know the math is messy - just looking for a conceptual answer if you have one). There's no need for any tricky math here, because regardless of which scenario you look at:
1) two clocks are orbiting next to each other and then as they pass the top of the tower one instantaneously accelerates to come to rest on it while the other continues in its orbit
or
2) the two clocks are next to each other on the top of the tower and one instantaneously accelerates to go into orbit
...the paths of each through spacetime after this instantaneous acceleration will be exactly the same, and it's only the proper time along the two paths between the point in spacetime where they depart each other and the point in spacetime where they reunite that determines which has elapsed less time.
As A passes through B, C, ..., Z, it will observe each of them as running slowly.
Hurkyl - i don't follow what you are saying - in my post 59 I intended to say that the A clock reads the time by looking at the visible counter attached to each tower B, C, D, ...Z the tower clocks always get progressively further ahead. This is not the same as making a measurement using the standard two clock method to determine apparent time dilation in a relatively moving frame - its a simple reading of the counter on the fly.
Yes, it's different -- one of my points was to make this clear. All you have done is to provide a convenient way for the orbiting clock to measure time according to the Earth frame. (As opposed to its own frame)
I was also leading up to a second hypothetical example. You seem to suggest that because the two clocks pass repeatedly, we can decide which time dilation is "real" and which is "apparent". However, consider this:
We just have the orbiting clock A and the tower clock B. However, B is mounted on an ultra-high speed elevator. When A is far away from B, we rapidly move B up and down the tower, and stop when A draws near from the other side.
In this scenario, we will find that B gains time on A after every orbit. So, your criterion would say that the fact B sees A run slow is the "real" time dilation, whereas the fact A sees B run slow is merely "apparent".
(Or we could set up a network of tower clocks that all do this. Then, B will see the time on consecutive towers lagging behind)
However, the time periods where A and B are near each other are exactly identical situations in both your and my scenarios.
In one scenario, A seeing B run slow was the "real" one.
In the other scenario, B seeing A run slow was the "real" one.
Yet, both scenarios are exactly identical during the interval in which the clocks can see each other.
Thus, your concept of "real" is ill-defined -- it is entirely inapplicable to time dilation (which is "local"), but instead a statement about the global behavior of a system.
Furthermore, I cannot figure out how you would be able to make a determination of "real" and "apparent" in a situation where there is no recurrence.
Hurkyl - I am obviously not making the point clear - in the experiment with one clock in orbit and the other fixed on the tower - there is a difference between the clocks when A flies overhead - each reads the other clock - there is an actual time difference - so best we distinquish this from what is traditionally referred to as time dilation - an experiment made between two objects moving at relative unifor velocity v - that requires two clocks in the measuring frame and it presupposes that the two inertial frames are identical - in that case the thought experiment leads to reciprocal measurments of slowing in the other frame.
So lets call my experiment intrinsic time difference - it corresponds to the time difference between the clock rate on earth and the clock rate of high speed particles - this is a one way experiment - it is the same as the difference between the clocks when we speculate on space travel to a distant star - a one way trip - there is no requirement that the traveler return to earth to reap the benefits of slowing time during the one way excursion. Unfortunately we are not able to make such experiments - but we can take note of the slowing of time in GPS satellites
In your up and down elevator experiment - yes - I would say that you could wind up with varying results - a common example in the literature involves two satellites - one in polar orbit - one in an equatorial orbit - during different times each will see the other as standing still - or having a varying relative velocity - it is not possible to synchronize 3 GPS satellite clocks with each other without a common reference frame
Hurkyl - I am obviously not making the point clear - in the experiment with one clock in orbit and the other fixed on the tower - there is a difference between the clocks when A flies overhead - each reads the other clock - there is an actual time difference - so best we distinquish this from what is traditionally referred to as time dilation - an experiment made between two objects moving at relative unifor velocity v - that requires two clocks in the measuring frame and it presupposes that the two inertial frames are identical - in that case the thought experiment leads to reciprocal measurments of slowing in the other frame. But pervect seemed to confirm my suspicion that a global coordinate system where an orbiting clock is at rest throughout the orbit cannot be called an "inertial frame"--in GR an object moving on a geodesic is only moving inertially in a local sense, not a global one. So there is no reason that the prediction of special relativity that two clocks moving inertially will each observe the other to be running slower in their own reference frame should be extended to general relativity in the case of two objects moving on geodesics (although the tower clock in your example actually isn't moving on a geodesic since it's not in freefall, but you could fix this by replacing the tower clock with a clock that is flying vertically away from the earth at the time it passes the orbiting clock, then slows down and falls back towards the earth, passing the orbiting clock again on the way back down). In general relativity, I don't think the notion of each object having its own unique global "reference frame" even makes sense any more, so there wouldn't be a well-defined answer to the question of how fast one clock "observes" another distant clock to be ticking any more. Given a particular choice of global coordinate system you could answer this, but I don't think there's any "standard" choice of which coordinate system you're supposed to use for a given object moving on a geodesic, unlike in SR where there is a standard way to construct the coordinate system that is defined as the "reference frame" of an object moving inertially.
Jesse - Your post 71 - you obviously have a very different take on what Einstein would have said were he alive today, than I do - I am not going to bother answering all the your assertions because it leads too far astray - except to say - yes as to the fact that he (Einstein) had the same opinion on GR as SR - he stated only a few days before his death that he could not think of a single one of his works that would survive the test of time - if you doubt it - you should read more - you have a very narrow view of things -
I gave an answer to your question regarding the possibility that all inertial free float frames may not be idential - now you want to convince me its absurd - find one real experiment that demonstrates two inertial frames in relative motion measure the same dilation in the other frame - I will look at it - until then, I will retain my skepticism. Absolute equivalence between inertial frames is not necessary to any experiment result - at least not any I am aware of.
Jesse - Your post 71 - you obviously have a very different take on what Einstein would have said were he alive today, than I do - I am not going to bother answering all the your assertions because it leads too far astray - except to say - yes as to the fact that he (Einstein) had the same opinion on GR as SR - he stated only a few days before his death that he could not think of a single one of his works that would survive the test of time - if you doubt it - you should read more - you have a very narrow view of things - Then why didn't you answer my request to provide a specific quote? In any case, the question of whether the ultimate laws of physics are Lorentz-invariant is separate from the question of whether laws of physics such as time dilation must work the same way in different inertial frames given Lorentz-invariant laws--see below. I gave an answer to your question regarding the possibility that all inertial free float frames may not be idential - now you want to convince me its absurd - find one real experiment that demonstrates two inertial frames in relative motion measure the same dilation in the other frame - I will look at it - until then, I will retain my skepticism. Absolute equivalence between inertial frames is not necessary to any experiment result - at least not any I am aware of. So do you deny my claim that any laws of physics that have the mathematical property of Lorentz-invariance must automatically behave the same way in all the frames provided by the Lorentz transformation? Please answer this question yes or no. If you're just suggesting that we may find phenomena governed by new, non-Lorentz-invariant laws, fine, that's an experimental possibility. But if you're denying my claim above, this is analogous to denying that 1+1=2 or that the derivative of x^2 is 2x, we don't need experiments to prove beyond a shadow of a doubt that you're talking nonsense.
Also, are you ever going to address my point about your confusion between symmetry in how the laws of physics work in different frames vs. symmetry in how particular configurations of matter and energy look and behave in different frames? Like I said, there is no requirement that particular configurations look the same in different frames (as in your point about the CMBR, or about the situation where two clocks approach each other after one accelerates), only that the laws governing how they behave work the same way in each frame (for example, in the clock situation, the clock moving faster in a given frame will always be the one ticking slower, although the clocks may not have been synchronized in this frame to begin with so the one that ticks slower won't necessarily be the one that's behind when they meet).
I'm trying to respond, but I'm having trouble pinning down exactly what you're saying.
But I did notice this:
what is traditionally referred to as time dilation - an experiment made between two objects moving at relative unifor velocity v - that requires two clocks in the measuring frame and it presupposes that the two inertial frames are identical
This is incorrect. Time dilation can be measured with nothing but light signals.
In fact, to even begin to talk about "two clocks in the same frame", one must be able to state what that means -- this is done via some protocol with light signals.
If we assume Minowski space from the start, we can talk about clocks with parallel worldlines -- but how do you experimentally determine if two clocks are in the same frame? With light signals! (Or, something relying indirectly on electromagnetism phenomena, such as a ruler)
Hurkyl: Here is what Resnic says at page 77 of Introduction to Special Relativity: "There are shorthand expressions in relativity which can easily be misunderstood....Thus the phrase "moving clocks run slow" means that a clock moving at a constant velocity relative to an inertial frame containing synchronized clocks will be found to run slow when timed by those clocks. We compare one moving clock with two stationary clocks. Those who assume that the phrase means anything else often encounter difficulties."
Hurkyl - Follow up to what i was trying to get across. So when we make these sorts of measurments using two synchronized clocks, we are determining apparent time dilation. And assuming arguendo, that the two frames are equivalent, each frame could carry two clocks and each would measure a clock in the other frame to be running slow. This is what I referred to as a traditional method of establishing time dilation.
The two frames would be equivalent if they were both initally at rest and then given equal accelerations until they reached a uniform relative velocity v - thereafter each frame would measure the apparent slowing of time in the other frame - when they are all returned to the same frame by uniform decelerations - the clocks should read the same (Case 1)
(Case 2) Contrast that with what occurs when only one of two synchronized clocks is accelerated to a uniform velocity v relative to the other as per Einsteins description in Part 4. When the two clocks are brought together they will not read the same - there is something different about the rate at which things occur in the frame which has been accelerated - or about the clock which has undergone acceleration - the two experiments give different results - in the second case there is a residual that can be measured - not so in the first case.
Now
Peterdevis
Jan19-06, 09:13 AM
Since I won't be able to follow pervects mathematical solution to the removing of a clock in orbit - I will propose the following - initially we have 3 clocks J, K, and L on the earth - at the top of the tower - then we put two (J and K) in the same satellite and launch them into orbit - they should both run at the same speed and slower than the third clock (L) left atop the tower - then we decelerate (K) so that it comes to rest on the tower - it should now run at the same rate as the stay behind clock (L) since it has been returned to the original frame where it was synchronized
On the other hand, from the perspective of the J clock still in orbit - (K) has undergone an acceleration, and it should now run slower than J while J is in orbit. So we have returned to the original puzzle - The orbiting clock J runs slower than either K or L on top of the tower - but K should run slower than the orbiting clock J.
No, at the end K and L run at the same rate but clock K(pe 11:55) runs after on L (12:00). J will run slower then K and L not (only) because of its velocity but because the clock is constant accelarating (making a orbit).
So there is no paradox!
yogi -- I figured out why I'm having trouble figuring out what you're saying: it's the same problem you chronically exhibit.
"two synchronized clocks" -- you've not specified how they're synchronized. (Is it that they always agree in a certain coordinate chart? Which one? Or are they synchronized by some light signal protocol? Or something else?)
"frames are equivalent" -- what do you mean by 'equivalent'? Given the context, the most appropriate meaning I could imagine is that it's referring to the hypothesis that the laws of physics remain identical in all reference frames... but your later usage disagrees with this interpretation.
"if they were both initally at rest" -- you've not specified how they're determined to be at rest. (Are you determining this according to a certain coordinate chart? Which one? Or something else?)
"given equal accelerations" -- how, specifically? First off, one cannot "accelerate a frame" -- a frame is simply a (nice) map from coordinates to space-time events. We use the word "accelerated frame" to denote a frame for which a particle that is always located at the spatial origin would not be travelling inertially.
Presumably accelerating a frames suggests accelerating some of the clocks too -- how is this going to be done? You've suggested in the past that you give all of the clocks "equal accelerations", but doing such a thing is "bad". (e.g. if I give the front and back of a train equal accelerations, as measured by the inertial frame in which it started at rest, it will rip apart)
When the two clocks are brought together they will not read the same - there is something different about the rate at which things occur in the frame which has been accelerated - or about the clock which has undergone acceleration - the two experiments give different results - in the second case there is a residual that can be measured - not so in the first case.
This is simply a property of their trips. One trip simply has a greater duration than another.
Incidentally, what you describe is only useful when the clocks start together and end together. It has absolutely no bearing on any scenario that does not satisfy this condition.
For example, this reasoning lets you say absolutely nothing about two clocks that are simply passing by each other. Each clock will observe the other dilated, but you have absolutely no justification for calling one "real" and the other "apparent".
Hurkyl - It should be obvious to what I am referring
Two synchronized clocks in the same frame (means at rest wrt each other) - used to measure a clock in a second frame that moves with uniform relative velocity v - The clocks are in sync in the frame at which they are at rest
Equivalent frames - any property you would measure in one frame would be the same as the property you would measure in another - Since I am not sure that all inertial frames are equivalent - then equivalent is a broader term
We can identify a frame with a spaceship - everything contained in the spaceship is a frame - included in the clocks on board -
For your edification ..the nomencalture "accelerating frames" is common in the literature
Take a look for example at Spacetime Physics - first edition at page 12
".....such an accelerated frame is a non inertial frame"
Things are at rest in the same frame when they are not moving wrt to each other
Now to your conclusions:
To say that "the time difference is a property of their trips" is to say nothing - one clock has not moved - only one clock took a trip
Only useful when they start and end together - how do you reach that conclusion - in reality, the only experments that start and end together are those like the GPS ones I described - or flying clocks around the world and bringing them back to the same place - but most of the experiments involve a particle that starts at one place in the earth reference system and ends at a different. These are the experiments that show the most significant differences in time loss or gain
Finally - I have never labeled two clocks just passing each other as you have suggested ...one real and the other apparent - they are both apparent - all measurements made on the fly (while the clocks are in relative uniform motion) are apparent - but they may not measure the same rate on the passing clock - that would only be the case if all interial frames are not equivalent. That is the subject I have addressed above -
Peterdevis - a clock in orbit is in a freefloat frame - it feels no acceleration --- its rate is only determined by its velocity and its height - I proposed that the tower is at the same height as the height of the orbit - so there is no altitude correction required - all that is left is velocity -J and K run slower than L because J and K have been given a velocity relative to the tower, and all GPS clocks in orbit run slow because they have a velocity relative to the earth frame in which they were originally synchronized.
If its permissible to treat the satellite as a valid inertial frame in the same sense that Einstein described in part 4 of his 1905 paper, then when K decelerates, for example after one orbit, to reduce his velocity to zero ground speed to land atop the tower - it will appear from the standpoint of J that K has been put in motion - the question posed is whether, if J is later returned to the tower after many orbits - will there be a difference in the J and K clock readings that reflects the fact that K should be running slower than J during those orbits - whereas from the standpoint of L and K it is J that should show a slower time consistent with its orbital velocity
Peterdevis
Jan20-06, 02:11 AM
f its permissible to treat the satellite as a valid inertial frame in the same sense that Einstein described in part 4 of his 1905 paper,
Just like Einstein in 1905 you don't know anything about GR. But in difference with you Einstein understands that when you only can deal with inertial frames (where there is no good definition for) you' ve got to deal with a lot of paradoxes. He bypassed this problem by inventing GR.
So here is my suggestion: Study GR
a clock in orbit is in a freefloat frame - it feels no acceleration --- its rate is only determined by its velocity and its height
This is the only way you can describe it in SRT, but it is a simplification and it gives a lot of misunderstanding (this discussion is a fine example).
But there is a fundamental difference between a orbiting clock with a speed v (velocity is a vector) and a clock moving in een inertial frame with speed v. The first is moving in a curved spacetime, the second in a flat spacetime.
If its permissible to treat the satellite as a valid inertial frame in the same sense that Einstein described in part 4 of his 1905 paper I'm pretty sure it's not. The satellite's motion is locally inertial, but I don't think there's any single unique global coordinate system that qualifies as an "inertial frame" in the sense that the satellite is at rest throughout its entire orbit in this coordinate system, and where you are permitted to assume that all the same rules that Einstein laid out for inertial frames in his 1905 paper would also apply in this coordinate system (for example, where the time dilation of the clock on the tower would simply be a function of its velocity in this coordinate system).
Can anyone confirm that an object moving on a geodesic in curved spacetime does not have a non-local "inertial rest frame" in this sense? Pervect? Hurkyl?
RandallB
Jan20-06, 10:14 AM
If its permissible to treat the satellite as a valid inertial frame in the same sense that Einstein described in part 4 of his 1905 paper, No it's not an inertial frame in that sense - it's more like the traveling twin that continually departs and returns. Reversing frames at full speed instantly at each turnaround to return back to earth, just not stopping at the return to earth (The tower); but continuing away again for another round trip of switching reference frames for each orbit to get back again. (If you want, wait till one of the big guys say the same thing.)
RB
In Spivak, a frame is nothing more than an ordered basis for a vector space.
If we have a collection of (enough) everywhere linearly independent vector fields, then these define a frame for each individual tangent space. Spivak calls this a moving frame.
So, frames don't resemble coordinate charts at all.
Intuitively speaking, a frame for the tangent space of a point P does define an "infinitessimal" coordinate chart about P, but that's as far as that goes.
More rigorously speaking, this gives us tangent vectors (and we can talk about the corresponding cotangent vectors), so frames let us do calculus, even though they don't talk about coordinates.
We can take a frame and parallel transport it along an observer's worldline to speak about "his" frame. Presumably we'd like to pick the frame so that it's orthonormal, and so that the time axis is always the tangent to the worldline -- the observer would then be "at rest in this frame".
If my intuition in this context is worth anything, this would let us define an "infinitessimal" coordinate chart about the observer. Of course, it only lets us study things infinitessimally close to him.
The intuitive content of the equivalence principle is that infintiessimal regions behave as special relativity dictates, so this infinitessimal chart should behave as SR tells us.
But, just to emphasize it again, it would only apply to things infinitessimally close to the observer.
RandallB
Jan20-06, 03:30 PM
But, just to emphasize it again, it would only apply to things infinitessimally close to the observer.
And since yogi needs to have a clock go by the tower (leave) and measure it going by again (return) frames that small won't work well.
Which is why the orbiting frame is much more like the traveling twin.
Equivalent frames - any property you would measure in one frame would be the same as the property you would measure in another
Then two frames are equivalent if and only if they are exactly the same.
Given two different frames, I can easily find some property on which they would disagree. (Such as the coordiante velocity of a test particle)
To say that "the time difference is a property of their trips" is to say nothing - one clock has not moved - only one clock took a trip
No, both clocks took a trip. A straight-line path through space-time is still a path.
Only useful when they start and end together - how do you reach that conclusion
Because you are talking about clocks that started together and are eventually brought back together.
pervect
Jan20-06, 04:13 PM
Here's an example of the sorts of problems that arise with accelerated observers.
Attached is a crude drawing of a space-time diagram. The thick red line represents an observer who accelerates briefly (time runs up the page), then stops accelerating. ([clarify] - He maintains his velocity that he picked up while he was acclerating). The section where he accelerates is dotted.
The black lines represent the initial coordinate system of the oberver. Horizontal lines represent his notion of "simultaneous events".
The blue lines represent the new coordianate system of the observer after he accelerates, then stops. Note that his defintion of simultaneous events changes after he accelerates (the blue lines representing simultaneous events, are no longer horizontal, but tilted).
We assume that the observer wants to use coordinates that are compatible with both his initial coordiante system (before he accelerates), and his new coordinate system (after he accelerates) to define his coordiante system.
In a well behaved coordiante system, an event is defined by a pair of coordinates which are unique. Thus lines of simultaneity can never cross, i.e. events where t=0 are always different from events where t=1, and the lines in the space-time diagram defined by "t=0" and by "t=1' never cross.
You can see, however, that the black lines do cross the blue lines!
There is no problem in the neighborhood of the observer, but it is not possible to define a well-behaved global coordinate system for our "briefly accelerated observer" when the region coverd becomes large enough.
I would concur that the frame attached to the clock in orbit must be local - at least from the standpoint of academic purity. I would also say that the analogy to the round trip twin is appropriate - in fact Einstein in his description in Part 4 referred both to a time discrepency for a round trip version and a one way vesion. So even if the free float frame has its limitations as an inertial frame - it is of no significance - there is little or no difference between doing the experiment using a circular orbit or replacing the earth with a zero mass anchor point and tethering a rocket ship which travels the same path w/o gravity - i.e, the Eucledean space version previously raised as a question answered by pervect. What is at issue is why identical clocks record different times - we do not have to bring them together to examine them (although that is one way) but we can continually interrogate the moving clock wrt to the ground clock - and we will find that the clock put in motion falls behind - it is not an answer to say - the path length through space-time is different - we already know that - but how does the clock know its been put in motion after it has been synchronized. The fact that each clock runs at its proper rate in its own rest frame also tells nothing - there is an intrinsic difference between the rate of the earth clock and the moving clock - whether it be in orbit or traveling the same path in Eucledean flat space - the error is small - The difference between the two clocks is given by the SR relationships between moving frames. SR is quite adequate to the job of predicting the time loss. So, while I proposed an orbit to dispell the argument that GR is a factor - there will always be those that claim otherwise, but it does not answer the question.
If I have two pieces of string that begin and end at the same point, and I measure their lengths, should I be surprised if I find the strings have different lengths? And does this require an explanation of why the strings have different lengths?
I would answer no, and no.
Conversely, if I have two observers who start and end at the same point in space-time, and I measure the duration of their paths, should I be surprised to find they have different duration? And does this require an explanation of why the paths have different durations?
I would answer no, and no.
You disagree at least with the last question of this group. So let me ask you this: why do you think an explanation is warranted?
Different paths have different duration -- this should not be surprising. The only reason I could imagine that one would think that an explanation would be required is if you had some reason to think they ought to have the same duration.
E.G. if you adhered to some notion of universal tile. (As you tend to do -- you habitually ignore qualifying anything relative, and you often devise experiments so that all observers are making their measurements according to the same coordinate system... such as when you suggested that the oribiting clock should be reading the times on the network of tower clocks)
What is at issue is why identical clocks record different times - we do not have to bring them together to examine them (although that is one way)
How do you plan to go about examining them?
But that's just a tangential issue: what matters (to me) is how you plan on comparing them.
RandallB
Jan21-06, 10:04 AM
What???In a well behaved coordiante system, an event is defined by a pair of coordinates which are unique. Thus lines of simultaneity can never cross, i.e. events where t=0 are always different from events where t=1, and the lines in the space-time diagram defined by "t=0" and by "t=1' never cross. To be a little clearer; I think you mean to ID the original ref frame as drawn in black with time lines t=0 & t=1. And a second ref frame ID as “primed” and blue with time lines t’=0 & t’=1.
Then you say:You can see, however, that the black lines do cross the blue lines!
. . . it is not possible to define a well-behaved global coordinate system . . . when the region coverd becomes large enough.What do you expect, of course a “well-behaved global coordinate system” will cross!
They are straight lines and don’t overlap; therefore they have to meet once!
The important point is THEY ONLY CROSS ONCE!
You only have a problem if you get these straight lines of SR relationships to cross TWICE!
That’s all yogi is doing – somewhere he has an error in his math or calculations that is giving him a point where these straight lines cross twice that’s all.
Till he can find where and how he is doing that, he won’t make any progress in moving from SR onto GR.
Confusing these simple SR issues by fussing over “brief accelerations” just distracts form the SR problem he is been having for so long.
GR issues are easily removed for SR problems by just using “Light Speed” (instant) transfers from one ref frame to the other (That means ZERO time change during a transfer that takes zero time in both frames).
Staying with the linear relationships (as shown by the straight lines in your graph) and CORRECTLY detailing all the times and locations as seen from all locations in BOTH reference frames is all that’s needed to get clear on SR “simultaneity”.
In yogi’s case, as I recommended earlier, one weekend on his own, NO beers! (Maybe one Barleywine) and he can “get it” right quick.
Till he can get that part understood; GR, Accelerations, local vs. non-local, and Rotations are just going to confuse the issue for him. Plus I don’t see how anyone can help him till he does this part of the work correctly in his own opinion, by crosschecking his own work. He certainly isn’t going to change the minds of the many here that have done the work and do “get it”.
My best advice for yogi – stay focused on SR alone till you either “get it”.
OR; On the chance that you really do know better, before you will having any credibility in discussing GR etc., you need to detail what you “know better” about SR, in a Logical and Complete explanation convincing enough to change the mind of at least one mentor. Till then don’t waste your time on GR, you will only get frustrated in long threads like this one.
To be a little clearer; I think you mean to ID the original ref frame as drawn in black with time lines t=0 & t=1. And a second ref frame ID as “primed” and blue with time lines t’=0 & t’=1.
No, he meant to say they are the same frame. He's talking about a (hypothetical) globally defined non-inertial coordinate system... specifically, one that starts and ends looking like an inertial coordinate system.
So what you see in the picture is the black lines for t=0,1,2,3, and the blue lines for t=8,9,10
They are straight lines and don’t overlap; therefore they have to meet once!
The important point is THEY ONLY CROSS ONCE!
They can, in fact, meet zero times, and the fact they do meet once is a big deal! Because, in the diagram, the same event in space-time can be listed at two different coordinate times!
Incidentally, when I talk about time running backwards at distant places in what I call accelerated reference frames, I'm talking about the phenomena prevect is describing here.
pervect
Jan21-06, 01:56 PM
What??? To be a little clearer; I think you mean to ID the original ref frame as drawn in black with time lines t=0 & t=1. And a second ref frame ID as “primed” and blue with time lines t’=0 & t’=1.
No, I meant what I said. Check out for instance MTW's "Gravitation", pg 168, section $6.3 entitled "Constraints on the size of an accelerated frame".
This is essentially a redrawing of their figure 6.2.
The intent is to explore to what extent it is possible to construct a "natural" coordinate system for a briefly accelerated observer, as a specific example which illustrates some unexpected problems in generalizing the notion of a natural coordinate system. We know that when an observer is not accelerated he has a natural coordinate system given by his inertial frame, so we ask if this idea can be extended to arbitrary observers.
If the briefly accelerated observer has a natural coordinate system, we can quite naturally require that it should be the same as the natural inertial coordinate system he has during the interval before he accelerated, and it should again be the same as his new inertial coordinate system he has after he stops accelerating.
At this point we haven't attempted to address the issue of what coordinates to use while he is accelerating, because the two requirements above already overconstrain the problem.
As the diagram illustrates,we cannot define a consistent uni-valued coordinate system that covers all of space-time and is consistent with both of the inertial coordinate systems that we have demanded it be consistent with. The best we can do is to define such a coordinate system that covers a limited, local region of space-time.
RandallB
Jan21-06, 02:21 PM
No, I meant what I said. Check out for instance MTW's "Gravitation", pg 168, section $6.3 entitled "Constraints on the size of an accelerated frame".Who is MTW ?
This looks to me like miss applying GR to an SR graph. But if I can find it I’ll take a look.
Who is MTW ?
Misner, Thorne & Wheeler, their textbook, Gravitation (http://www.amazon.com/gp/product/0716703440/104-7948792-0354300?v=glance&n=283155), is a standard text of post-graduate gravitation and GR studies.
Garth
RandallB
Jan21-06, 02:57 PM
Misner, Thorne & Wheeler, gravitation and GR studies.
Thanks –Wow, Expensive for a book from 1973,
found where I can borrow one tonight.
I would concur that the frame attached to the clock in orbit must be local - at least from the standpoint of academic purity. If you agree it's local, then do you understand this means you can't ask how fast the tower clock is ticking "in the orbiting clock's frame" once they are no longer at the same position? there is little or no difference between doing the experiment using a circular orbit or replacing the earth with a zero mass anchor point and tethering a rocket ship which travels the same path w/o gravity - i.e, the Eucledean space version previously raised as a question answered by pervect. In this case, one clock is moving inertially and the other is not, so you can't ask how fast the tower clock is ticking in the orbiting clock's frame, because the orbiting clock doesn't have a single rest frame. What is at issue is why identical clocks record different times - we do not have to bring them together to examine them (although that is one way) but we can continually interrogate the moving clock wrt to the ground clock How do you "continually interrogate" one clock wrt the other if they are at different locations? Different inertial frames will have different definitions of simultaneity, and so will disagree about the relative rates of the clocks at different times. If you assume that the clocks obey Lorentz-symmetric laws of physics, then different inertial frames should be able to all use the same laws to predict how the clocks will behave (for example, each frame will predict a clock's ticking rate will be a function of its velocity in that frame), and they will all make the same prediction about what each clock reads when the two clocks reunite at a single location. Do you agree with this?
Jesse - we use the non rotating earth centered reference system to interrogate GPS clocks all the time - we can calculate exactly what their daily drift is and correct them - if instead we do not preset a clock in satellite earth orbit to compensate for the post launch orbital velocity - we can send a radio signal any time no matter where it is in its orbit and we will find it has a slower rate by the same amount relative to the tower clock - moveover, we can of course put different clocks at diffeent heights - e.g., we can arrange a launch platform at 100 milles up and a second at 200 miles above the earth surface etc - and if both satellite clocks are synced respectivly to adjacent earth tower clocks and launched into orbit at 100 miles and 200 miles respectivly, and no correction is made for the orbit velocity of either - when they are in orbit we can interrogate each of the two clocks from the tower at any point in their respective circular orbits. What will we find. The rate of each clock no matter where it is in its orbit, will be running uniformly slow with respect to the tower time - and each is slow by an factor that corresponds to its orbital velocity - i.e., each clock is running at its own uniform intrinsic rate at all times.
Now you can say that each clock runs at its own rate because of the invariance of the interval, or the difference in the space time path, or some other factor that is part of SR ...a lot of true statments - but not an explanation - what I would like to know is how do the two clocks in different orbits know at what rate to run relative to the earth frame. Each clock has its own uniform intrinsic rate relative to the tower in accordance with their velocity relative thereto. - if that question doesn't bother you - so be it
Randall - i am astonised you would lecture on GR having never heard of the MTW - I got my first copy about 10 years ago - seemed like it was about $90 then - later a picked up a slightly used copy for $4 in the Escondido Library used book department - Of course having two copies doesn't make it easier to understand
Jesse - we use the non rotating earth centered reference system to interrogate GPS clocks all the time How does that contradict my point? Once you make an arbitrary choice of which inertial reference frame you want to use, you can of course compare different clocks in that frame. But the choice is totally arbitrary, you could equally well have used some other inertial frame, and using the exact same laws you'd get all the same predictions about what clocks read when they meet, but different answers to how fast their respective rates are when they're apart. Do you disagree? we can calculate exactly what their daily drift is and correct them - if instead we do not preset a clock in satellite earth orbit to compensate for the post launch orbital velocity - we can send a radio signal any time no matter where it is in its orbit and we will find it has a slower rate by the same amount relative to the tower clock - moveover, we can of course put different clocks at diffeent heights - e.g., we can arrange a launch platform at 100 milles up and a second at 200 miles above the earth surface etc - and if both satellite clocks are synced respectivly to adjacent earth tower clocks and launched into orbit at 100 miles and 200 miles respectivly, and no correction is made for the orbit velocity of either - when they are in orbit we can interrogate each of the two clocks from the tower at any point in their respective circular orbits. What will we find. The rate of each clock no matter where it is in its orbit, will be running uniformly slow with respect to the tower time - and each is slow by an factor that corresponds to its orbital velocity - i.e., each clock is running at its own uniform intrinsic rate at all times. Yes, and we could make similar corrections if we wanted to have the clocks be synchronized in an inertial frame moving at 0.99c relative to the earth, as opposed to the frame where the earth's center is at rest. Do you disagree? a lot of true statments - but not an explanation - what I would like to know is how do the two clocks in different orbits know at what rate to run relative to the earth frame. Each clock has its own uniform intrinsic rate relative to the tower in accordance with their velocity relative thereto. - if that question doesn't bother you - so be it The question doesn't bother me, but my answer is simple: the laws governing the clocks are known to have the mathematical property of Lorentz-invariance, which insures they must behave the same way in different inertial reference frames related to each other by the Lorentz transform. I've asked you several times whether you agree that given Lorentz-invariant laws, it is logically impossible that clocks would fail to behave as predicted by relativity or that they would not work the same way in different inertial reference frames, but you've never responded. Can you please do so now?
If you want to argue that the fundamental laws of nature might not be Lorentz-invariant, or that there has to be some conceptual reason they are all Lorentz-invariant, that's fine. But so far a lot of your arguments have seemed to take for granted that clocks follow known relativistic laws in some given frame (say, the frame where two clocks are initially at rest before one accelerates in your previous example), but then you question whether these situations could really be analyzed just as well from the point of view of another inertial frame. But this is a truly incoherent line of argument, because again, if you take for granted that clocks obey the known Lorentz-invariant laws in one inertial frame, then it's logically impossible that they would fail to obey the same laws in all other inertial frames.
pervect
Jan22-06, 03:40 PM
Let me add my $.02.
If we have an inertial observer, and someone moving via a powered orbit in a circle around the observer, the two observers are always a constant distance apart.
Because they are a constant distance apart, the travel time for a light signal will always be constant, and everyone will agree that the observer travelling in a powered orbit has a clock that is ticking slower. Constant travel time makes direct comparison of the rates of clocks possible
The obserer in a powered orbit will not have a "frame" that covers all of space-time. However, he will have a local frame that includes the inertial observer.
The observer in the powered orbit will see the inertial observer's clock as ticking faster, due to "gravitational time dilation" in his local coordinate system, as the inertial observer will always be "above" him.
So, there isn't any ambiguity here - the inertial observer thinks the accelerating observer's clock is ticking slowly, and the accelerating observer thinks the inertial obserer's clock is ticking fast.
This is perfectly consistent with the simple idea that the clock following a geodesic in flat space-time is always the clock that experiences the most time.
RandallB
Jan22-06, 03:42 PM
Randall - i am astonised you would lecture on GR having never heard of the MTW - I got my first copy about 10 years ago - I’m not lecturing on GR I’m talking about SR. And is there some list of acronyms that we should all know so we don’t wise cracks from you guys about not knowing what MTW stands for here? Tens years working on getting SR is more astonishing than having to learn acronyms of others.
Do you have an acronym for your version of relativity; LR BR YR (Lorentz, Broken, Yogi) it sure isn’t SR.
And if you think your issues in this thread are GR, you’re wrong it’s SR where you’re still having problems. Until you understand SR, how can you hope to work from an understandable vocabulary with any mentor that’s not on the same page as you with what ever version of SR you’re using?
If you’re trying to learn the correct way to understand it. Stick with SR alone first. They won’t be able to help you in GR if you don’t have SR down first.
But, if your purpose is to convince someone of your view, do it in a SR environment; in GR you’ll never be able to communicate effectively if they don’t understand your version of SR. And be clear about your purpose if this is the case; at least be fair to the mentors that are only trying to help you see SR, if that is not your intent. I really don’t thing any are looking to pick up a new view of relativity, but some may be willing to look at your augments differently if you’re actually trying to bring forward a new view of relativity.
I honestly cannot tell which you are doing.
RandallB
Jan22-06, 03:45 PM
No, I meant what I said. Check out for instance MTW's "Gravitation", pg 168, section $6.3 entitled "Constraints on the size of an accelerated frame".I took a look at the book and yes the plots should cross as they do for SR frames, where one has been accelerated to a fixed higher speed. (The SR frame work, is the best to be working with yogi on, but if you think you can help him in a truly GR environment go ahead you have 100’s of posts to go)
The issue MTW are dealing with is an accelerating frame for the moving point. And yes those lines should not cross except that they should overlap as they do at t=0.
But why Kip has a problem with seeing an overlap at g-1 I don’t understand. By simply recognizing “simultaneity” (A simple SR issue) and applying it to this accelerating frame it is clear that the “time” at this distance is in the past for this “accelerating frame”. Therefore it has a time of t<0 where the speed and this line are the same and parallel with the original stating line for the point g-0 at t=0.
Thus the correct lines will obviously progress with curves to the left that go to some limit parallel to the original horizontal line off set up somewhat.
Likewise the lines to the right represent points at “future distances” and again by “simultaneity” rule those times will be in the future. Here the speeds are higher for the accelerating frame therefore the slope needs to be progressively steeper and curving the line forward. This Projects an expectation fitting with their other graphs. But they do repeat the concern of the g-1 point again. I’m just an independent non-pro but if I ever meet Kip again and have the chance maybe I’ll bring it up to him. I’m sure the book having been so long ago he’d be allowed some revisions to his old judgments.
RB
Jesse - Do i beleive in Lorentz invarience - yes and no - how is that for a fence sitter. If you ask - do I believe in the invariance of the interval between two spacetime events in two different frames in relative uniform motion - the answer is yes until some experiment yet to be performed castrs doubt upon it - but there is no experiment that tests the transforms completely - when we take two space time points in two frames and derive the interval, the xv/c^2 term cancels - this has not been verified by experiment - so yes - I will withhold judgement at this point as to the universal validity of the transforms.
Is it always permissible to shift from the frame in which the clocks were syncronized to make interrogations of the orbiting clocks? I think not.
The satellite clocks will not be seen as running at a uniform rate in another frame in motion wrt to the non-rotating earth centered reference frame.
pervect - your post 104 - I see no ambiguity either - don't know where you could have acquired the idea that i did - in fact it is what I have been trying to get across - earlier I drew an analogy to GR - the clock at the greater G potential runs faster - that clock at a lower potential runs slower - things are not reciprocal in GR nor are they in SR when only one clock has been accelerated into orbit
Randall - you are obviously going to have a difficult time undertanding the Gravity" book you borrowed - you are having a difficult time with my several statements to the effect that the resolution of the question doesn't involve anything but SR - first you accuse me of saying Relativity is Broken - title of another post - they you allege I am making a claim about GR - my reference to GR is strictly an analogy - nothing to do with it other than the fact that SR has in common with GR the fact that in some experiments things are not reciprocal.
Jesse - Do i beleive in Lorentz invarience - yes and no - how is that for a fence sitter. I don't think you understand, yogi. "Lorentz-invariance" is just a mathematical property of certain equations, deciding whether or not a given equation shows Lorentz-invariance is as straightforward as deciding whether it's a polynomial.
Let's first consider the related concept of "Galilei-invariance", which is a bit simpler mathematically. The Galilei transform for transforming between different frames in Newtonian mechanics looks like this:
x' = x - vt
y' = y
z' = z
t' = t
and
x = x' + vt'
y = y'
z = z'
t = t'
To say a certain physical equation is "Galilei-invariant" just means the form of the equation is unchanged if you make these substitutions. For example, suppose at time t you have a mass m_1 at position (x_1 , y_1 , z_1) and another mass m_2 at position (x_2 , y_2 , z_2 ) in your reference frame. Then the Newtonian equation for the gravitational force between them would be:
F = \frac{G m_1 m_2}{(x_1 - x_2 )^2 + (y_1 - y_2 )^2 + (z_1 - z_2 )^2}
Now, suppose we want to transform into a new coordinate system moving at velocity v along the x-axis of the first one. In this coordinate system, at time t' the mass m_1 has coordinates (x'_1 , y'_1 , z'_1) and the mass m_2 has coordinates (x'_2 , y'_2 , z'_2 ). Using the Galilei transformation, we can figure how the force would look in this new coordinate system, by substituting in x_1 = x'_1 + v t', x_2 = x'_2 + v t', y_1 = y'_1, y_2 = y'_2, and so forth. With these substitutions, the above equation becomes:
F = \frac{G m_1 m_2 }{(x'_1 + vt' - (x'_2 + vt'))^2 + (y'_1 - y'_2 )^2 + (z'_1 - z'_2 )^2}
and you can see that this simplifies to:
F = \frac{G m_1 m_2 }{(x'_1 - x'_2 )^2 + (y'_1 - y'_2 )^2 + (z'_1 - z'_2 )^2}
Comparing this with the original equation, you can see the equation has exactly the same form in the primed coordinate system as in the unprimed coordinate system. This is what it means to be "Galilei invariant". More generally, if you have any physical equation which computes some quantity (say, force) as a function of various space and time coordinates, like f(x,y,z,t) [of course it may have more than one of each coordinate, like the x_1 and x_2 above, and it may be a function of additional variables as well, like m_1 and m_2 above] then for this equation to be "Galilei invariant", it must satisfy:
f(x'+vt',y',z',t') = f(x',y',z',t')
So in the same way, if we look at the Lorentz transform:
x' = \gamma (x - vt)
y' = y
z' = z
t' = \gamma (t - vx/c^2)
where \gamma = 1/\sqrt{1 - v^2/c^2}
and
x = \gamma (x' + vt')
y = y'
z = z'
t = \gamma (t' + vx'/c^2)
Then all that is required for an equation to be "Lorentz-invariant" is that it satisfies:
f( \gamma (x' + vt' ), y' , z', \gamma (t' + vx' /c^2 ) ) = f(x' ,y' ,z' , t')
There may be some more sophisticated way of stating the meaning of Lorentz-invariance in terms of group theory or something, but if an equation is Lorentz-invariant, then it should certainly satisfy the condition above. Maxwell's laws of electromagnetism would satisfy it, for example. And it's pretty easy to see that if it satisfies this mathematical condition, then the equation must have the same form when you transform into a different inertial frame using the Lorentz transform. So this is enough to show beyond a shadow of a doubt that given Lorentz-invariant fundamental laws, all the fundamental laws must work the same in any inertial reference frame, and if you know the equation for a given law as expressed in some particular inertial frame (the rest frame of the center of the earth, for example) then it is a straightforward mathematical question as to whether or not this equation is Lorentz-invariant, it's not an experimental issue (the only experimental issue is whether that equation makes correct predictions in the first place). Do you disagree with any of this? Is it always permissible to shift from the frame in which the clocks were syncronized to make interrogations of the orbiting clocks? I think not.
The satellite clocks will not be seen as running at a uniform rate in another frame in motion wrt to the non-rotating earth centered reference frame. Uh, why does this mean it's not "permissible" to shift into another frame? That's the whole point, that different frames disagree about whether a given set of clocks is running at a uniform rate. But all frames will agree on all physical questions like what two clocks will read at the moment they meet at a single location in space. You need to define what you mean by "permissible", when physicists use this term all it means is that you can use the same laws of physics in another frame and all your predictions about physical questions will still be accurate (that's why it's not 'permissible' to use the ordinary rules of SR for inertial frames in a non-inertial coordinate systems, because you would make wrong predictions if you did this). Given Lorentz-invariant laws, this is automatically going to be true for all inertial frames.
Also, the GPS clocks are programmed to adjust themselves so that they tick at a constant rate in the frame of the earth. My other point was that this is a completely arbitrary choice made by the designers, you could just as well design the orbiting GPS clocks to adjust themselves so that they tick at a constant rate in the frame of an inertial observer moving at 0.99c relative to the earth. Would you then say it is not "permissible" to analyze these clocks in the rest frame of the earth, since they would not be running at a uniform rate in the earth's frame?
pervect
Jan22-06, 06:22 PM
pervect - your post 104 - I see no ambiguity either - don't know where you could have acquired the idea that i did - in fact it is what I have been trying to get across - earlier I drew an analogy to GR - the clock at the greater G potential runs faster - that clock at a lower potential runs slower - things are not reciprocal in GR nor are they in SR when only one clock has been accelerated into orbit
Fine with me. Actually I think I need to tighten this up a little bit. The round trip time for light signals between two obserers is something that can be measured - A sends a signal #1 to B, B sends a signal #2 to A on recipt of A's signal. A measures the interval on his clock between the sending of the signal #1 and the receiving of signal #2 as the "round-trip time".
If this round-trip time is always constant, we can always compare the rate of two clocks unambiguously.
We may need to demand that the round-trip time is constant for both A and B before we can compare rates, but I think it is true that if A's round trip time is constant, so is B's. I'm relying on my intuition a bit here, though.
Of course A and B don't necessarily have to agree on the value of the round-trip time (and in general they won't) - they just have to agree that it's constant.
but there is no experiment that tests the transforms completely
The transforms are mathematical things, not physical things -- there cannot be an experiment that tests them at all.
RandallB
Jan23-06, 09:05 AM
The satellite clocks will not be seen as running at a uniform rate in another frame in motion wrt to the non-rotating earth centered reference frame.This statement alone stands as a claim the Einstein’s version of relativity is broken so quit complaining.
What I’d wish you’d do tell us what your trying to do in your posts, they seem to flip from one objective to a the other.
Are you:
A) trying to convince others that the standard view of SR (and extending into GR as well) is somehow wrong or incomplete. And your 'LR-like' view or something else must be better.
OR
B) sincerely trying to learn SR completely, to filling the gaps of information about it, that leave you unable to see concepts in books you’ve had for 10 years.
For the sake of all those that are trying to respond to you, be clear on this; are you arguing a point of view; or trying to learn something. And please refrain on saying “yes & no” or “both”, do one or the other.
I have no agenda Randall - my interest in SR goes back many years - likely before you were born - I pose questions that come to mind - if those questions lead to a different view ...one I have overlooked - great. Usually what happens on these boards is an attack - either I don't understand it or I am not qualified to question it - but for a few posters, the attitude is always one of condesention.
If anyone thinks it is easy to synchronize GPS satellite clocks in some frame than the non-rotating earth centered system -I would like to see how you would go about doing it.
Hurkyl - The transforms relate time and distances - they are not abstract mathematical artifact - these are physical things - my point is with you and Jesse - the mathematical relationships (LT) have been confirmed in certain experiments - but those experiments do not test the fundamental premise upon which Einstein's derivation was based - perhaps w/o complete justification, I do have a stong conviction that the spacetime interval is invarient.
pervect - i would agree that any interrogation must depend upon the constancy of the round trip time - and since the GPS clock will always be found to be running at a uniform rate relative to the ground station - we have a convincing demonstration of the constancy of c - at least in the earth centered frame
Jesse - your post 110 - last Paragraph: Transforming to another frame - what I have been trying to discuss was the non reciprocal reality of time dilation in certain experiments - if we have a GPS clock that was originally at the top of the tower and launched into orbit from there with no velocity correction - we have a situation where the ground clocks run consistently fast wrt to the GPS satellite clock and the GPS satellite clock always runs slow wrt to the ground clocks and we can verify this non symmetrical situation by interrogating the GPS clock with radio signals - that is the experiment. To inquire as to transforming to a frame in high speed motion wrt to the earth simply subverts the objective. Such a transformation of course is possible, but you have missed the whole point -we are now back in a situation where whatever is measured is apparent - the two frames have not been synchronized - Einstein only makes a prediction about real time dilation when one of two originally synchronized clocks is accelerated to a uniform velocity wrt the other. This is the subject of the thread - which i would like to explore further.
If anyone thinks it is easy to synchronize GPS satellite clocks in some frame than the non-rotating earth centered system -I would like to see how you would go about doing it. If the satellites can figure out their velocity relative to the center-of-earth frame and adjust their clock rates accordingly, it is trivial to figure out their velocity relative to any other inertial frame and adjust their clock rates to be constant in that frame instead. Do you doubt that if I know my velocity in earth's frame and I know the earth's velocity in frame X, I can easily figure out my velocity in frame X, and from this figure out how much my clocks would be slowed down in frame X?
Jesse - your post 110 - last Paragraph: Transforming to another frame - what I have been trying to discuss was the non reciprocal reality of time dilation in certain experiments More ill-defined terminology...what does "non-reciprocal" mean in yogi-speak? Surely you don't mean "non-reciprocal in the way the laws of physics work in different frames", do you? Please address the main part of post 110 and not the last paragraph, where I explained that "Lorentz-invariance" is simply a mathematical property of certain equations, and that given laws of physics whose equations in our own inertial frame have this property, it is automatically going to be true that the laws of physics will obey the same equations in all other inertial frames. Do you deny this or not??? if we have a GPS clock that was originally at the top of the tower and launched into orbit from there with no velocity correction - we have a situation where the ground clocks run consistently fast wrt to the GPS satellite clock and the GPS satellite clock always runs slow wrt to the ground clocks and we can verify this non symmetrical situation by interrogating the GPS clock with radio signals - that is the experiment. It is symmetric in how the laws of physics work in different inertial frames, which is all that most physicists would mean by "symmetric" in the context of special relativity. If you have your own idiosyncratic definition of "symmetrical", please present it.
Do you agree that if the GPS clock is orbiting the earth at a constant speed in the center-of-the-earth frame, that means that in other inertial frames the speed of the GPS clock is not constant? (This would be just as true in Newtonian mechanics as in relativity, of course.) Do you agree that if each inertial frame assumes the same relationship between instantaneous speed in that frame and instantaneous rate of ticking (ie that if the clock is moving at speed v in that frame it will be slowed down by a factor of \sqrt{1 - v^2/c^2}), then different inertial frames will disagree about the relative rate of the tower clock and the orbiting clock at a given moment (with 'given moment' meaning something different in different frames too, due to different definitions of simultaneity), yet they will all make the same prediction about how far behind the orbiting clock will be at the moment it completes an orbit and reunites with the tower clock at a single point in space? Please, please give me direct answers to this question, when I ask you questions in my posts they are not meant to be rhetorical, and it's incredibly frustrating when I ask you questions that I hope will help pin down your nebulous comments and you just ignore them and comment on a single statement in my post. To inquire as to transforming to a frame in high speed motion wrt to the earth simply subverts the objective. Such a transformation of course is possible, but you have missed the whole point -we are now back in a situation where whatever is measured is apparent - the two frames have not been synchronized - Einstein only makes a prediction about real time dilation when one of two originally synchronized clocks is accelerated to a uniform velocity wrt the other. This is the subject of the thread - which i would like to explore further. There could only be a "real time dilation" in the sense that all frames would agree on how much time elapsed on two clocks between two points in time in a case where the clocks started at the same location and ended at the same location. Einstein would certainly never say that in a case where two clocks started at separate locations and then one accelerated towards another, there is any "real" (frame-independent) truth about which clock was ticking faster or slower. Different frames would disagree about this, and there is no physical reason to prefer one frame's analysis to another. If you disagree with this, then it's important that we first see if you agree with my statements above that any laws of physics which have the mathematical property of Lorentz-invariance will automatically work the same way in all different frames, and whether you also agree that all frames will make the same prediction about all physical questions like what two clocks will read at a moment when they are at a single location in space. If you don't agree with this, then you're expressing some basic ignorance about purely mathematical issues in relativity which needs to be corrected. If you do agree with this, yet still feel that there is some other reason to "prefer" one frame's analysis of the situation to another's, you need to explain what sort of aesthetic criteria you are using here to prefer one over the other despite the fact that all will see the same laws of physics and make the same physical predictions. And if you also want to continue to defend the absurd proposition that Einstein would agree with you about preferring one frame's analysis over another's, you need to provide the quotes that you think support this interpretation.
Hurkyl - The transforms relate time and distances
No they don't!
The transforms relate (inertial) coordinate systems, which most certainly are "abstract mathematical artifact".
E.g., IIRC, Einstein made a big deal about showing how to construct what he called an inertial reference frame, via a hypothetical network of clocks, each of them "at rest" with a given inertial observer, and "synchronized" with his clock. I put those terms in quotes because those are also terms in need of construction.
If coordinate systems were physical things, Einstein would have just said "measure it".
RandallB
Jan24-06, 09:37 AM
I have no agenda Randall - my interest in SR goes back many years - I pose questions that come to mind - if those questions lead to a different view ...one I have overlooked - great. Usually what happens on these boards is an attack - either I don't understand it or I am not qualified to question it - but for a few posters, the attitude is always one of condesention.Fine – I’ll let your condescension towards me pass as a result of the above.
I understand I don’t have the “pro” tag, banner or ribbon of the mentors & advisors on this board - so you don’t have to take my encouragements to heart.
As to reciprocal views being relative – Based on how you pose those questions as conclusions, from the frame of reference of many trying to respond, it can often be seen as attacks on SR as they know it to be. So that part seems to be the same from both views.
No they don't!
The transforms relate (inertial) coordinate systems, which most certainly are "abstract mathematical artifact".
I guess I should qualify this...
The transforms do relate coordiante position, and coordinate time, so in some sense they can be said to relate times and distances.
But my point still stands -- coordinate position and coordinate time are derived from coordinates, which are not physical things.
Case in point: the Julian and Gregorian calendars are not the same -- they1 assign different time coordinates to events. Would you say that the transformation between these calendars is a physical thing?
1: I'm assuming any usual2 method of identifying spatial position. A calendar, by itself, is unable to assign time coordinates to almost every event!
2: Notice I said usual, and nothing such as "intrinsic" or "determined by reality" -- it's a convention we use as humans. And it's even changed over time, such as when time zones were instituted, and when calendars were changed!
pervect
Jan24-06, 10:51 PM
Randall - you are obviously going to have a difficult time undertanding the Gravity" book you borrowed - you are having a difficult time with my several statements to the effect that the resolution of the question doesn't involve anything but SR - first you accuse me of saying Relativity is Broken - title of another post - they you allege I am making a claim about GR - my reference to GR is strictly an analogy - nothing to do with it other than the fact that SR has in common with GR the fact that in some experiments things are not reciprocal.
Since I've had some run-ins with RandallB in the past, I didn't and don't consider it an enjoyable use of my time to respond to his response.
Hopefully the point I wanted to make has been made, though.
Pervect - I appreciate your comments and frequently read your posts although a cannot always make a sensible response. See Below
Pervect - I appreciate your comments and frequently read your posts although often cannot make a worthwhile response.
I do recall at one time in another thread you made a statement that the time discrepancy is physically explainable - but then the direction of the thread veered off along other lines as is often the case - so i wasn't able to get back to the subject
In my previous posts on this thread I have tried to target the situation Einstein created when he combined the relationships that were obtained from observations in another frame - specifically to my way of thinking there is a quantum jump from the notion of two observers in relative motion drawing identical conclusions about lengths and clock rates in the other frame - as opposed to the idea that one of two synchronized clocks put in motion will run slower than the one that was not moved. There is a real loss of time between the clocks when they are later compared - in other words, did Einstein get the right answer for the wrong reason - or by intuition. He does not attempt to justify or even rationalize this - it works to explain the experiments - but it doesn't follow from the initial postulates of SR - in one sense it seems to require its own special postulate and - i guess what i am saying is that something is missing.
So to pick up the thread - it seems there is a discontinuity in the development of the notion of real time dilation - for example if we explore what Einstein asserts in part 4 we could imagine the following scenerio - we plan a trip to Altair but first we draw a line connecting the earth and Altair and at the center point of this line we place a clock C - we also place a clock E on the earth and a clock A on Altair. All are initially synchronized. Now from the center point (location of clock C) we draw a large circle that intersects both the earth and altare. This is the trajectory the spaceship will follow. The spaceship has a clock R also initially synced with A, E and C. The spaceship is quickly accelerated to its crusing velocity v wrt earth and steered to maintain a uniform velocity tangent to the circular path it will follow during the entire voyage (there will of course need to be some lateral thrust to correctly follow the path - this radial acceleration however does not enter into the accumulated time on clock R because acceleration per se does not affect clock rates as has been determined many times in centrifuge experiments). Einstein tells us that the R clock will read less than the A clock when R passes by A, and that it makes no difference what path is followed so long as the velocity remains constant - this is simply the first half of the twin thing - and since the second half is dynamically the same as the first half, half the time is lost in arriving at Altair and half is lost on the return trip.
The three clocks A, E and C remain in sync since they are not moved - if the gamma factor is 0.5 the R clock should read half that of the A clock at the time R passes A - during the return trip the R clock will again lose the same amount of time - so it will read half the E clock time when R returns to earth.
The issue is whether in real time dilation experiments there is symmetry - either the R clock runs at the same rate as A,C and E or it runs at a different rate - and if it runs at a different rate how does it know physically at what rate to move its hands. We can interrogte the R clock from C at each and every mile along the way just as we can interrogate the GPS clock from the earth tower. We know from GPS data, unless a GPS clock is corrected for its velocity relative to the tower clock, the earth clock and the satellite clock will run at different rates at all times while they are in relative motion.
A possible query is whether the R clock is a good reference frame - true it has slight radial component - but not one that would influence its rate in a measurable manner - so if we assume R is at rest in an approximate inertial platform - would we expect measurements made in the spaceship frame using R to determine the rate of time passage on clocks , C, E and A to be the same as measurments made by C, E and A to measure R. In other words, if we sent interrogation radio signals from R to C, what conclusion could R arrive at from the signals received from C
lets take it a step further - we will have C send out interrogation signals every hour - they are received by tansceiver on the spaceship and they immediately transmit the time reading on clock R - now we presume c is constant and we have defined the radial distance to be always constant - so we know the over and back time is always the same - so after each transmission is received by C, C should be able to say that R is always running at 1/2 the rate of C (for gamma = 0.5). In a like manner, R can send interrogations to C and R should be able to determine from what it receives from C that C is running at double the rate of R.
If this really occurs - then do we not have a reference frame problem - if there is an intrinsic difference in the rate of uniformly moving clocks - it cannot be said that two clocks meeting in empty space with uniform relative motion will each judge the other clock to be reciprocally slow as measured by a local clock at rest. How does one distinguish between two clocks meeting in empty space and R flying by A after several thousand years of travel in deep space?
Let's take it one step further: let's have R periodically send interrogations to E. (instead of to C)
Everything stated below is as seen by R.
(I'm using units in which the distance between A and E is 2, and c = 1)
I've written a program to run this experiment -- R is sending a signal every 0.01 units of time. E receives the signal and immediately broadcasts its time. R receives the return signal. R then takes the average of the send & receive times, by his clock, and compares it with the transmitted E-time.
R-time : E-time
---------
0.0 : 0.0
0.073 : 0.037
0.141 : 0.074
0.202 : 0.111
0.256 : 0.149
...
1.8 : 3.585
1.81 : 3.616
1.82 : 3.647
1.83 : 3.678
1.84 : 3.708
...
3.602 : 7.242
3.607 : 7.245
3.612 : 7.247
3.618 : 7.25
3.623 : 7.253
3.645 : 7.264
The first group is, of course, as R is leaving Earth.
The second group is when R passes Altair. (at 1.813 R-time)
The third group is when R passes by Earth again. (at 3.628 R-time)
Compare the rates of the R and E clocks by this reckoning:
As R leaves Earth, R-time is running twice as fast as E-time.
As R passes by Earth again, R-time is once again running twice as fast as E-time.
In other words, it is exactly what one would expect from "reciprocosity".
Also, note that R is passing by Altair that E-time is running three times as fast as R-time. (As opposed to C-time, which is only running twice as fast as R-time)
Hurkyl - Thanks for your interest and the time taken. Your approach is however, what I endeavored to avoid - I cannot help but feel that to find an explanation in the symmetry of the transforms is a bootstrap argument - it leads to a nummerical solution (albeit a correct one as far as the numbers go) but what is missing is an appreciation of what is really going on in the moving frame. Treating the clock frames of R and E as equal casuses a shift from apparant observations to an actual time dilation - I am not sure Einstein was not guilty of the same methodology - What I tried to do was set up the simpliest scenerio possible - with a central clock C that is always the same distance from R ....the three clocks in the earth-Altare (ECA clocks) frame will always read the same - so if you are getting different relationships between R and E at different points in the journey - they can only be apparent because the C clock always runs at a constant rate and since the R clock is following a circle - it too must run at the same rate for the entire trip - so any statements to the effect that the R clock observes E to be running fast at the beginning and ending, and slow in the middle, must of necessity be apparent. What I am trying to do is disect the problem by proposing the simpliest geometry possible ... one which is free from any challenges that could be raised as to changing conditions (e.g., accelerations, turn around stress etc) as is frequently done depending upon how the twin paradox is rationalized to a non-paradox). Run your programe using only signals between C and R and vice versa - if you arrive at a time discrepancy when R returns to E, tell where and when the R clock runs fast wrt to C and where it runs slow.
I didn't use the transforms at all, actually.
I did the entire problem in the coordinates of the ECA-rest frame. I placed Earth at spatial coordinates (1, 0), and Altair at spatial coordinates (-1, 0).
Since R travels with uniform speed in a circle (as measured by the ECA frame -- most inertial frames would disagree on both counts), its worldline has to look something like:
r(s) = <ks, cos s, sin s>
for some k. (The parameters are time, x, y) You gave the condition that the rate of the R-clock should be one-half that of its ECA-time coordinate. I used that to solve for k, and then I reparametrized the worldline by R's proper time:
\vec{r}(\tau) = \langle 2 \tau, \cos (\tau \sqrt{3}), \sin (\tau \sqrt{3}) \rangle
So, I'm now armed with the knowledge of how to find the ships ECA-coordinates if I know what R's clock reads.
Using this, if I decree that the ship emits a signal at R-time \tau, I could determine the ships ECA-coordinates when the signal is emitted. I can then compute when the signal arrives on Earth. I then numerically solve for the R-time \tau' when R receives Earth's reply.
That is how I generated the chart.
I certainly agree that if I add a C-column via the above methodology, the C-times will always read exactly twice that of the R-times.
I also certainly disagree that the problem is free of acceleration. :tongue: While the ship may be accelerating gently, we are also looking at the problem over very large scales -- small * large = indeterminate, so we cannot brush away the effects of acceleration as being irrelevant.
If this really occurs - then do we not have a reference frame problem - if there is an intrinsic difference in the rate of uniformly moving clocks Why do you think your example shows an intrinsic difference in the rate of uniformly moving clocks"? "Uniformly moving" means uniform velocity, not just uniform speed, so R doesn't qualify.
Any thoughts on the questions I asked in my previous post?
I think one of the important lessons that was learned from Einstein is that a concept is only relevant if we can determine it experimentally.
The big, overarching point is that you cannot talk about what time something happened way over there -- what you can talk about are the results of some sort of "timing experiment".
One way to give meaning to a phrase like "E observes that R's clock is running half as fast as his own" is to say that E is continually performing timing experiments to assign E-times to the readouts of R's clock. The results of these experiments yield E-times that are increasing twice as fast as the R-times to which they're assigned.
It is somewhat of a miracle (or more accurately, an assumption) that it is possible for E to perform this timing experiment on C, and find that the assigned E-times are equal to the readouts on C's clock. And conversely, that C performs this timing experiment on E to find that the assigned C-times are equal to the readouts on E's clock. The concept of a reference frame is an abstraction of this miracle.
When R performs this timing experiment on E's clock, and finds that the result is not that the assigned R-times are always half as much as E's clock, it shouldn't be a surprise.
All it means is that the amazing string of coincidences that allowed some of these experiments to agree with each other have finally come to an end. There's no inherent reason to think that any of these coincidences could be possible! In fact, according to GR, they are not: they can only be approximately possible on small scales. (Okay, I should point out that my confidence in this very last sentence isn't nearly as much as the rest of my post)
Jesse - Hurkyl Let me address part of what you have both said - it has to do with the propriety of R as a reference frame - here i will again direct you to Einstein's statement (1905 Part 4) - that it doesn't make any difference what path is followed - the equation for the time difference only concerns the relative velocity v between the clock that remains at rest after sync and the clock that is put in motion - I interpret this to mean that the moving clock (in our case R) could zig zag all over the place as long as its heading velocity remains v - if we believe Einstein's statement then should we not be able to disregard any radial acceleration that R incurs during the round trip flight - we all agree (I think) that we get the right answer by considering only C and R, and when we do that we arrive at the same result as Hurkyl gets using the chart methodology - so if arriving at the right numbers is the primary object - either approach is of equal utility.
Now if we follow hurkyl's logic that we will see R running at half the assigned C rate if we continue to use timing experiments between R and C at all points of the path, and vice versa, can we not conclude that the spaceship is a good inertial frame - it shouldnt really make a difference in the outcome if the path were comprised of many straight segments that approximate the circle and the readings were always taken at the midpoint of the seqments - we wouldn't really expect the total time difference between a circular path and a segmented path to be any different so long as the total distance traveled was the same - what I am trying to do is eliminate any affect of acceleration.
Now I do not see that this experiment leads to the notion of a universal time - but if both R and C run at the same speed at all times as a necessary consequence that they are not being acted upon by any forces or factors that would change the rate at which they run - then we do have a condition where they run at different rates as judged by each other - but unlike apparent time dilation - R judges C as fast and C judges R as slow ...in other words, they are running at intrinsically different rates, The question that follows is whether its permissible to ignor this difference when using the LT or some other methodolgy to make measurements in a ralativly moving frame. Again are we getting the right numerical answer for the wrong reason. Does not R have to take into account that it is running slow wrt to C when setting up its local clocks to make mesaurements in C's frame - for example let us say that prior to launch someone fiddles with the R clock so it doesn't keep the same time as C before launch - we would not expect that R would be able to get correct results when it is used to measure E and A rates.. More later
Jesse - I assume you were asking about the questions posed in your post 120 which referred to your Epistle posted in 110. If I have given the impression that I have any doubt about physical experiments producing different results in different frames - I did not intent to - Nor am I taking issue with the lorentz group of symmetries as a mathematical principle, although it is not always easy to see what is being conserved.
At this juncture however, I cannot say whether such mathematical constructs always represent the real world - we use them as though they were God given - just as we once used Newtonian mechanics w/o question.
Jesse - Hurkyl Let me address part of what you have both said - it has to do with the propriety of R as a reference frame - here i will again direct you to Einstein's statement (1905 Part 4) - that it doesn't make any difference what path is followed - the equation for the time difference only concerns the relative velocity v between the clock that remains at rest after sync and the clock that is put in motion - I interpret this to mean that the moving clock (in our case R) could zig zag all over the place as long as its heading velocity remains v - if we believe Einstein's statement then should we not be able to disregard any radial acceleration that R incurs during the round trip flight Are you referring to this part of section 4 of the 1905 paper? It is at once apparent that this result still holds good if the clock moves from A to B in any polygonal line, and also when the points A and B coincide.
If we assume that the result proved for a polygonal line is also valid for a continuously curved line, we arrive at this result: If one of two synchronous clocks at A is moved in a closed curve with constant velocity until it returns to A, the journey lasting t seconds, then by the clock which has remained at rest the travelled clock on its arrival at A will be 1/2*tv^2/c^2 second slow. Thence we conclude that a balance-clock7 at the equator must go more slowly, by a very small amount, than a precisely similar clock situated at one of the poles under otherwise identical conditions. If you're saying that this justifies treating the circular-moving clock as having its own rest frame, you misunderstand what he was saying there. Einstein was saying that time dilation as seen in an inertial reference frame is dependent only on velocity in that frame. So if something moves on a curved path at constant speed as seen in an inertial frame, you can calculate the time elapsed just by multiplying the coordinate time in that frame by \sqrt{1 - v^2/c^2}. But Einstein is not claiming there that the object moving on the curved path itself has its own rest frame where the usual rules of relativity apply; these rules only apply in frames "in uniform translatory motion", ie no acceleration (and changing direction always involves acceleration). Now if we follow hurkyl's logic that we will see R running at half the assigned C rate if we continue to use timing experiments between R and C at all points of the path, and vice versa, can we not conclude that the spaceship is a good inertial frame - it shouldnt really make a difference in the outcome if the path were comprised of many straight segments that approximate the circle and the readings were always taken at the midpoint of the seqments But making the path into a series of straight line segments wouldn't help either, because R would not have a single inertial rest frame throughout the journey, it would have a series of different inertial rest frames. This is just like the twin paradox, where for convenience you usually assume that the travelling twin's path is just made up of two straight line segments. Now I do not see that this experiment leads to the notion of a universal time - but if both R and C run at the same speed at all times as a necessary consequence that they are not being acted upon by any forces or factors that would change the rate at which they run - then we do have a condition where they run at different rates as judged by each other - but unlike apparent time dilation - R judges C as fast and C judges R as slow Usually in the context of relativity, when people say things like "A judges B to be running slow" they just mean that in the inertial frame where A is at rest, B is running slow. But again, R does not have a single inertial rest frame throughout the journey. It is certainly true that in any frame where R is momentarily at rest, then in that frame C will be running slower than R at that moment, but then that frame will see R's velocity change throughout the journey and at some point it will have to see R running slower than C. And again, there is no physical reason to prefer one inertial frame's description of the whole situation to another's, so you cannot say that R was running slower than C at every moment, you can only say that R's average rate of ticking over an entire orbit was slower than C's (this will be true in every inertial frame). Again are we getting the right numerical answer for the wrong reason. WHY do you think it is wrong? You keep objecting to the idea that every frame is equally valid but you never spell out any reasons, and you seem to have agreed in your last post that as long as all the laws of physics have equations with the mathematical property of lorentz-invariance, this insures that every inertial frame will see the same laws of physics and will make the same predictions about all physical questions like what two clocks read at the moment they meet. If you agree with this, it seems that you must agree that no inertial frame's analysis is physically preferred over any other's, so all you're left with is some kind of aesthetic preference for one frame's description over all others, no different than someone who prefers cartesian coordinates to polar coordinates.
in other words, they are running at intrinsically different rates
Well I have two responses:
(1) R interrogating C and R interrogating E are exactly the same experiment. What do you find so special about the former experiment that allows you to justify calling it "intrinsic" and the latter "apparent"?
(2) There is no "intrinsic" difference. The observer on R, using the R-clock to measure all relevant times, still finds that his heart is beating at 120 bpm, still finds that middle A is 440 Hz, still finds that the half-life of a pion is 26 ns, et cetera.
it shouldnt really make a difference in the outcome if the path were comprised of many straight segments that approximate the circle and the readings were always taken at the midpoint of the seqments
But making the path into a series of straight line segments wouldn't help either, because R would not have a single inertial rest frame throughout the journey, it would have a series of different inertial rest frames.
In order to predict what C's (or E's or A's) clock reads in the inertial frame that R happens to be instantaneously at rest in, at any point along R's path, you need to perform a series of Lorentz transformations, from one straight segment to the next in yogi's approximation. Then, ideally, you would take the limit as the number of segments increases towards infinity and their length each approaches zero. Mathematically, this is of course an integral. But yogi's example is a two-(space)-dimensional problem so you need to use a two-dimensional version of the Lorentz transformation. :yuck:
In order to predict what C's (or E's or A's) clock reads in the inertial frame that R happens to be instantaneously at rest in, at any point along R's path, you need to perform a series of Lorentz transformations, from one straight segment to the next in yogi's approximation. Then, ideally, you would take the limit as the number of segments increases towards infinity and their length each approaches zero. Mathematically, this is of course an integral. But yogi's example is a two-(space)-dimensional problem so you need to use a two-dimensional version of the Lorentz transformation. :yuck: Well, if the speed as a function of time is v(t), the integral would be \int_{t_0}^{t_1} \sqrt{1 - v(t)^2/c^2} \, dt regardless of how many dimensions the problem is, no? Anyway, yogi specified that R was moving at a constant speed in the rest frame of the other clocks, and in any frame where speed is constant you shouldn't need to do an integral.
My use of the word intrinsic is of course undefined in SR - - it is not the observed time - it is the difference between what two clocks that are in uniform relative motion will determine to have accrued on each clock when they are compared in the same frame. Let us proceed to use R and E as Hurkyl has chosen to illustrate - as long as they are in relative motion, we make measurements and get different results because relative velocity and distances are changing But what is being measured is a distortion - If R quickly stops halfway to Altare and interrogation signals are sent from E to R and from R to E - what do they report - after comparison R has fallen behind E by 1/2 - the comparison is being made in the same frame and there is no doubt that they have been physically running a different rate. But the result would be no different if we made the same inquiry while R is moving. But we must ask the question "What does your clock read" and not set up a Lorentz grid or some other formalism that can only lead to a distorted answer as to how fast time appears to be moving in the other frame. We can make this determination at any point we wish during the trip - and by asking the question: "What does your clock read" rather than: "how fast does time appear to be passing while we are in relative motion" we arrive at the correct physical reality....at all times during the voyage, proper time in the R frame accrues twice as fast as it does in the E, C, A frame. The result would be no different if R is in an orbit around some great attractor which C happended to be the center of - and it is no different on any other experiment - the invariance of the interval assures us that it is the high speed pion and not the earth clock that runs slow - real time dilation is a one way thing.
Jesse - yes I was referring to the polygonal line statement - and i agree Einstein did not go further - what I am saying that every motion has some curvature most likely - but it does not show up in the results - why because acceleration per se does not affect clock rates - as i have said about 50 times. So the slight curvature is of no moment - if you were on that spaceship with such a low curvature you would feel perfectly justified in claiming yourself to be on an inertial platform (you could even straighten it out if you desired, as you passed A - it wouln't make any difference - when you attempted to use your slowly running clock to try to make measurments of the A clock as you passed by ...you would get the wrong answer - because the proper rate of the A clock in the A frame and the proper rate of the R clock in the spaceship frame is different by a factor of 2 whether you momentarily straighten out the spaceship path or not.
My use of the word intrinsic is of course undefined in SR - - it is not the observed time - it is the difference between what two clocks that are in uniform relative motion will determine to have accrued on each clock when they are compared in the same frame. Let us proceed to use R and E as Hurkyl has chosen to illustrate - as long as they are in relative motion, we make measurements and get different results because relative velocity and distances are changing But what is being measured is a distortion - If R quickly stops halfway to Altare and interrogation signals are sent from E to R and from R to E - what do they report - after comparison R has fallen behind E by 1/2 Only if R "stops" in the inertial frame that E is at rest. But what if both R and E "stop" in some other inertial frame? If R has only made 1/4 of a full circle, I'm not sure if all inertial frames will agree that its average rate of ticking was slower than E (they would definitely agree on this if it made a full circle), and in any case it certainly won't be true that all frames agree that its average rate of ticking was 1/2 of E's. So what if, at the moment R has made it halfway to Altare both R and E stop in some inertial frame where R's average rate of ticking was 3/4 that of E's--in this case when they compare non-doppler-shifted signals, they will indeed find that during the journey R only elapsed 3/4 the time of E. Why should the comparison after both clocks "stop" in this frame be considered any less real than the comparison after R "stops" in the rest frame of E? But we must ask the question "What does your clock read" and not set up a Lorentz grid or some other formalism that can only lead to a distorted answer as to how fast time appears to be moving in the other frame. We can make this determination at any point we wish during the trip - and by asking the question: "What does your clock read" rather than: "how fast does time appear to be passing while we are in relative motion" we arrive at the correct physical reality....at all times during the voyage, proper time in the R frame accrues twice as fast as it does in the E, C, A frame. The result would be no different if R is in an orbit around some great attractor which C happended to be the center of - and it is no different on any other experiment - the invariance of the interval assures us that it is the high speed pion and not the earth clock that runs slow - real time dilation is a one way thing. Well, see above, there is no reason to consider the time comparison in E's frame any more of a "physical reality" than the time comparison in any other. No matter what frame you choose, if both clocks "stop" in that frame then when they compare non-doppler shifted signals they will conclude that one clock is behind by exactly the amount that frame's coordinate system would predict.
Let me ask you this, if you had an object moving inertially at 0.99c relative to the earth and another object travelling in a circle at constant speed in the first object's rest frame, then would you consider the earth-frame's analysis of this problem to be "distorted"? Note that if the circular-moving object came to rest relative to the inertial one, and in their new rest frame they agreed that the circular-moving one had elapsed 1/2 the time of the inertial one, in the earth-frame the signals between them would still appear to be extremely doppler-shifted since one object is moving towards the other's signals at 0.99c while the second is moving away from the first one's signals at 0.99c. So we would not conclude that the circular-moving one had elapsed 1/2 the time of the other, you only get that conclusion if you assume that the relative velocity between each object and their signals is c, which is not true in our frame.
Only if R "stops" in the inertial frame that E is at rest. But what if both R and E "stop" in some other inertial frame? If R has only made 1/4 of a full circle, I'm not sure if all inertial frames will agree that its average rate of ticking was slower than E (they would definitely agree on this if it made a full circle)
I think you have a hang up on the necessity of a round trip - there is a physical thing going on - 1/8 of a circle is as good as a half which is as good as 3/4 which is as good as a whole. Look at the physical reality of what is actually taking place - there is no way that any of the clocks can change the rate at which time progresses in their own frame after R reaches crusing velocity - the A, C and E clocks remain in the same frame from beginning to end, the R clock rides on a spaceship that changes direction at a continuous rate but the tangent velocity remainst constant (there is no energy added or subtracted to or from the spaceship) What could possibly cause R to run a different rate at different parts of the voyage. if you prefer we can consider R tied to C by a long teather - there is unchanging continuity during the journey
Think about each clock as being powered by a frictionless flywheel which has been cranked up to speed and geared to drive the hands of the clock - it spins on for years at the same rate - when the R clock is launced, the angular momentum of the flywheel should not change (or perhaps you think it does - if so how and why) In any event - if it does not change, the hands should keep moving at the same pace as those of E, C and A - but SR tells us that the hands now go slower - something physical has occurred - this is the crux of the SR puzzle.
Jesse - As to some of your other questions - go back again to Part 4 - Einstein puts both clocks in the same frame and then moves one - when you introduce other moving frames you will again be mixing real time events with apparent measurments - we can only have two frames if we are going to follow Einsteins scenerio - obviously if we ever come to an agreement on something then we could extrapolate to other situations - in fact that was what I tried to do in my original statement of this thread -i then shifted to the orbiting GPS clocks and then the big voyage centered on clock C to make it easy to illustrate how REAL values could not be any other way - obviously I did not do such a good job - so I will restate what i am convinced to be correct - namely - it doesn't make any difference if the R clock travels in a circle or in orbit in a G field (freely floating fame) or a straight line or a polygonal path - the reality of the situation is that the clock which is accelerated to reach a constant magnitude velocity after initial synchronization will run at a constant slower rate than the one which remains fixed - we can only find out by how much if we ask the question - what does the moving clock read when interrogated - we can pose this question at any time during the travel period or we can ask it when the moving clock is brought to rest in the same frame from which it was launched - if we try to predict the results in third frames - it obscures the issue.
I think you have a hang up on the necessity of a round trip Only because that's the only case where all frames will agree on the time elapsed on both clocks. there is a physical thing going on - 1/8 of a circle is as good as a half which is as good as 3/4 which is as good as a whole. But with less than a full circle, there is no reason to prefer one frame over another. If you disagree, what reason do you think there is? Look at the physical reality of what is actually taking place - there is no way that any of the clocks can change the rate at which time progresses in their own frame after R reaches crusing velocity - the A, C and E clocks remain in the same frame from beginning to end, the R clock rides on a spaceship that changes direction at a continuous rate but the tangent velocity remainst constant (there is no energy added or subtracted to or from the spaceship) The tangent speed remains constant in C's rest frame, but the tangent velocity does not, because velocity is a vector, and the tangent velocity vector points in different directions as R moves along the circle. And in a frame where C is not at rest, the tangent speed isn't constant either. What could possibly cause R to run a different rate at different parts of the voyage. The fact that its speed is changing (in some frame other than the rest frame of A, C and E), and rate of clock ticking depends on speed.
Again, yogi, you didn't address my questions. When I ask you questions, can you please not just ignore them? Do you agree that if R and C both "stop" in some other frame other than C's original rest frame, and afterwards they compare their times using radio signals, they will get a different answer to how much R fell behind then if R "stopped" in C's original rest frame and they compared times with radio signals? And what about the question about the clock that is moving at 0.99c in the earth's frame, with another clock moving in a circle relative to the first--is the earth-frame's perspective on this situation an incorrect one, according to you?Think about each clock as being powered by a frictionless flywheel which has been cranked up to speed and geared to drive the hands of the clock - it spins on for years at the same rate - when the R clock is launced, the angular momentum of the flywheel should not change (or perhaps you think it does - if so how and why) In any event - if it does not change, the hands should keep moving at the same pace as those of E, C and A - but SR tells us that the hands now go slower - something physical has occurred - this is the crux of the SR puzzle. Again, as long as the laws of nature obey equations which have the mathematical property of lorentz-invariance, then it's inevitable you'll get relativistic phenomena like time dilation. For example, since Maxwell's laws of electromagnetism have this property, if you built a "clock" which could be understood totally in terms of electromagnetic laws--say, a charge which oscillates back and forth at a regular rate, which can occur in EM--then it's necessarily going to be true that if are moving inertially and this clock moves away from you and then comes back, it will have elapsed less time than yours. No need to have a specific theory of relativity, this is guaranteed to happen just based on the equations of electromagnetism, and would have to be true even if you believed in an ether theory which obeyed the same equations in the rest frame of the ether.
Anyway, if you admit your own intuitions tell you a clock should not change its rate just because it moves, but you can see these intuitions are somehow incorrect, then why do you feel so comfortable trusting your intuitions about which reference frame's perspective is the "correct" one and which frame's is "distorted"?
Jesse - As to some of your other questions - go back again to Part 4 - Einstein puts both clocks in the same frame and then moves one - when you introduce other moving frames you will again be mixing real time events with apparent measurments What is a "real time event" and what is an "apparent measurement"? we can only have two frames if we are going to follow Einsteins scenerio No, his scenario is only that you have two clocks at rest relative to each other, and then one accelerates towards the other. He chooses to analyze this situation in the frame where they are originally at rest, but this is not part of the "scenario", it is fundamentally no different from a choice of where to place the origin of the coordinate axes or a choice of whether to use cartesian or polar coordinates. the reality of the situation is that the clock which is accelerated to reach a constant magnitude velocity after initial synchronization will run at a constant slower rate than the one which remains fixed But for an object moving in a circle, "constant magnitude velocity" itself depends on your reference frame. Likewise, "initial synchronization" of separated clocks also depends on your choice of reference frame. These things are entirely coordinate-dependent, there is no rational reason to treat one frame's view of them as more valid then another's, so your own preferences can only be aesthetic ones.
But we must ask the question "What does your clock read" and not set up a Lorentz grid or some other formalism that can only lead to a distorted answer as to how fast time appears to be moving in the other frame.
Aha! You have confessed to belief in absolute time. :tongue2: You have now unequivocally confirmed my suspicion that you are selecting one reference frame to be the preferred frame, and that all other reference frames are considered to be "distorted".
This is exactly what it means for one to consider time to be "absolute", or "universal", or such.
The question is why should that particular frame be preferred? It is just as much as "formalism" as any other reference frame.
Why isn't, say, the Andromedra frame the preferred one? (In which ECA are all moving) Can you write down an experiment that would prove the ECA is the preferred frame, whereas the Andromeda frame is not?
(No)
Hyrkyl - There may be many preferred frames in a particular experiment if we define preferred frame as a frame where we can determine reality at all times - For example lets take the case where we have our spaceship tethered to C and halfway out on the rope we add another clock - say J. Now J moves at half the speed of R. J moves at a constant velocity wrt to C. J is a preferred frame in the sense that it will always measure the R clock to be running at 1/4 the speed of light - each and every time it interrogates R and C it will find that the time lapsed on R is 1/2 that of C. In theory we can have an infinite number of these types of frames - all strung out along the rope joining R and C.
When Einstein made the shift from observational results to real time dilation in part 4 he implicitly made the rest frame a preferred frame - this is the bases of the twin thing and every other counterintuitive aspect of SR - if SR were nothing but an abstract theory of how things appear distorted in moving frames it would be of little use - in actuality, I see no justification for Einstein combining the equations as he did to arrive at the conclusion that one clock gets physically ahead of the other - it would seem that he should have said: The traveling clock appears to run behind the at-rest clock from the perspective of the at-rest clock and the at-rest clock appears to run behind the traveling clock when judged from the moving clock, and that both clocks read the same when the traveling clock is stopped so that it is at rest in the original frame. But he didn't say that - he went out on a limb and predicted a physical result that has fueled a 100 year debate. Actual time dilation does not follow from the mathematics - it is in fact a new postulate - couched in the mathematics of apparent observations, but not a logical consequence thereof. Einstein created a preferred frame thought experiment which results in the answer he had arrived at by intuition - as he said in one of his biographies - he had worked on the problem off and on for ten years - but it was always with me ... gradually I began to suspect time as the culprit. in actuality, Einstein turned a problem into a postulate. To get real time dilation, one frame had to be different from the other. If you choose to call it preferred - fine with me.
Jesse: "But with less than a full circle, there is no reason to prefer one frame over another. If you disagree, what reason do you think there is? "
There is every reason - because the C point I have chosen always gives the same value for the rate of the moving clock R. This is the same reason we choose the non rotating earth centered reference system for GPS. The R clock should not change the pace at which it logs time during the voyage - the C clock measures this rate - i suppose you will say this is just its a convenience. True. Any clock on the ACE frame could be used to send and receive signals to R and as long as they ask the question "what does your clock read" we have an experiment that
comports with Einsteins 2 frame scenario. A third frame passing the whole experiment would raise the further issue - were the clocks in teh new frame ever properly synchronized in the ACE frame - that situation is undefined in Einsteins scenario
Hyrkyl - There may be many preferred frames in a particular experiment if we define preferred frame as a frame where we can determine reality at all times - For example lets take the case where we have our spaceship tethered to C and halfway out on the rope we add another clock - say J. Now J moves at half the speed of R. J moves at a constant velocity wrt to C. J is a preferred frame in the sense that it will always measure the R clock to be running at 1/4 the speed of light J is not a frame in the first place. And how can J "measure" the speed of the R clock at all, without using some coordinate system? Presumably you just mean how fast J will see R ticking using light signals, but all inertial frames will make the same prediction about this, so it makes no sense to treat this as evidence for a "preferred frame". When Einstein made the shift from observational results to real time dilation in part 4 he implicitly made the rest frame a preferred frame No he didn't, because he'd get the same answer if he analyzed the situation in some other inertial frame. Actual time dilation does not follow from the mathematics Yes it does. Given laws whose equations have the mathematical property of Lorentz-invariance (which, remember, is not a statement about relativity at all, it's just a purely mathematical property of certain equations, like saying a given equation is a 'polynomial'), it is logically impossible that clocks obeying these laws would fail to show genuine time dilation as in the twin paradox. Do you agree with this or not?
There is every reason - because the C point I have chosen always gives the same value for the rate of the moving clock R. What do you mean "gives the same value"? Are you talking about how fast C sees the signals are coming in from R? You should know the difference between statements about how fast signals come in and how fast a clock is actually ticking in a given frame--because of doppler shifts, the two are not necessarily identical. And do you agree that all inertial frames will predict the same thing about how fast C sees the signals coming in from R? If so, isn't it obviously nonsense to say that something which all frames predict is evidence that one frame should be preferred? This is the same reason we choose the non rotating earth centered reference system for GPS. No it isn't. We choose that reference system because it's the most convenient if we want to have a universal time system for people on earth. And I think the GPS system could easily be adapted to deal with situations like a satellite in an elliptical orbit, where the signals from the satellite would not be coming in at a constant rate as seen by an observer at the center of the earth. A third frame passing the whole experiment would raise the further issue - were the clocks in teh new frame ever properly synchronized in the ACE frame - that situation is undefined in Einsteins scenerio What do you mean "undefined"? If you know what the clocks read at a given moment in another frame, it is perfectly straightforward to figure out whether they are synchronized in the ACE rest frame--you just use the Lorentz transform, which Einstein had already derived earlier. Just like if you know the coordinates of A,C, and E in some coordinate system where they do not all lie along the same coordinate axis, it is perfectly straightforward to figure out if A would lie along the x-axis in a coordinate system where C and E did.
Jesse I take issue with your reasoning on every point - you avoid the obvious conclusion that R and J cannot be inertial frames because of the slight curvature - no matter how small - that is a cop out. You keep asserting the transforms as controlling - but the issue is how they are to be applied - where is the symmetry - there is no sysmmetry between two frames in motion unless every experiment carried out in one frame gives the sames result when carried out in the other - but that is a yet to be proved assertion - assume R moves straight way toward A rather than in a circle - things are exactly the same - R is now a good reference frame even by your narrow standards - but when R interrogates C or A or E by asking the question "what does your clock read" he will find R is running slow by Gamma
A convenient aspect of the circular path is that C and R can not only use "What does your clock read" to determine relative rates - but either can signal the other using reflected light signals - if both R and C are equipped with a reflecting mirror - every time R bounces a signal off of C it will require "k" seconds to return back to R as measured on R's clock. But whenever C sends a signal to R it will return in "2k" seconds as measured by the C clock - if we do this enough times even you might conclude that the two clocks are running at intrinsically different uniform proper rates.
here is another heuristic experiment - let us launch a second spaceship from A headed in the opposite direction along the same circle and at the same velocity v - The second spaceship carries a clock Q. These two space ships pass at pi/2 and each uses the formalism of SR to conclude that the other clock is running slow - C of course will determine that each clock is running slow wrt to C by the same amount - so C will conclude that the actual clock rate of Q and R is the same. We will stipulate that Q and R straighen their orbits for a brief interlude while carrying out the experiment -
We next assume that Q is launched to (1/2)v rather than V so when the clocks meet after momentarily straightening their orbits - in the neighborhood of 135 degrees - will Q measure R to be running slow by the same amount that R measures Q to be running slow ?
Jesse I take issue with your reasoning on every point - you avoid the obvious conclusion that R and J cannot be inertial frames because of the slight curvature - no matter how small - that is a cop out. How is it a "cop out" when it's what the math tells you must be true, given the equations of the laws of physics? If you want to dispute that certain equations (Maxwell's laws of electromagnetism, for example) actually agree with experiment, fine, but if you somehow argue that conclusions which follow automatically from these equations are wrong, then you are in complete crackpot territory, akin to someone who accepts that a curve has the function y = x^2 but refuses to accept that its derivative is dy/dx = 2x. You keep asserting the transforms as controlling - but the issue is how they are to be applied - where is the symmetry - there is no sysmmetry between two frames in motion unless every experiment carried out in one frame gives the sames result when carried out in the other - but that is a yet to be proved assertion There is a symmetry if it can be proven mathematically that, given laws of physics that obey certain equations in one frame, the equations must be the same in other frames related to the first frame by the Lorentz transform. I thought you had already admitted this was true in your post #135: If I have given the impression that I have any doubt about physical experiments producing different results in different frames - I did not intent to - Nor am I taking issue with the lorentz group of symmetries as a mathematical principle, although it is not always easy to see what is being conserved. Now, do you agree or disagree that, given laws of nature whose equations have the mathematical property of lorentz-invariance when expressed in one inertial coordinate system, it is logically impossible that the laws of physics could fail to work the same way in other inertial coordinate systems related to one first one by the Lorentz transform? Please give a clear and unambiguous answer to this question. Since you have a tendency to not respond to direct questions from me whenever I write long posts answering your points in detail, I'm going to leave off responding to any more of your post for now and wait for an answer to this question.
Jesse. As to Galilean invariance - it would be very surprising if this were ever proved false - As to lorentz invariance - the issue arises as to "What constitutes a physical experiment within the inertial frame - Einstein took the position that passing light should be measured to have the same velocity in every frame - lorentz took the view that light always travels at c relative to the ether - both men were attempting to explain the nearly null results of MMx. I recently cited the CBR as an example of the fact that different inertial frames will get different results as to this phenomena - you came back with something to the effect that it wasn't an experment performed w/i the frame (can't remember what post or exactly what you said) But why could not the same argument be made wrt to passing light. Before relying too heavily upon the arithmetic, it would be nice to have some experiments conducted in a gravity free environment. Transforms are only as good as the conditions under which they are created - specifically the veracity of the assumptions and postulates. This thead calls attention to the fact that Einstein arrives at real time dilation only after he imposes strict initial conditions upon the two clocks. Your interpretation of the situation as you have championed in the past is that the accompanying frame of each clock (after the moved clock has reached a unifom relative velocity) as as good an inertial frame as the other. You rely dogmatically upon the transforms - but alas - it is the transforms and their application to the case at hand that is in question
Anyway I appreciate your confining your comments to one specific point
yogi, you're missing the point of my question. I'm not asking whether you think Galilei-invariance and Lorentz-invariance are ever going to be proven false experimentally (but why do you say of Galilei-invariance 'it would be very surprising if this were ever proved false'? Any law that is known to be lorentz-invariant, like Maxwell's laws of electromagnetism, must already violate Galilei-invariance). I'm asking whether, given laws whose equations have this mathematical property of lorentz-invariance when written in some inertial frame, you agree that it is logically impossible that these laws could fail to have the same equations when written in any other coordinate system related to the first by a lorentz transform. In other words, if you accept for the sake of the argument that a given clock can be understood wholly in terms of laws which are known to be lorentz-invariant such as Maxwell's laws, would you agree it automatically follows from this that the clock will obey the same laws in all the other frames generated by the Lorentz transform? You are free to accept this but to doubt that actual physical clocks actually do obey lorentz-symmetric laws, of course, this question is just about whether you agree that if they do, then there can be no further doubt about the laws working the same way in every inertial frame.
Note that when you analyze situations like Einstein's thought-experiment or the A,C,E,R scenario, you seem to grant for the sake of the argument that all the clocks in this scenario will slow down by the amount predicted by relativity in whatever frame you choose to analyze the problem, which is why I find it completely puzzling that you go on to question whether the laws work the same way in every frame even in your hypothetical scenario where you seem to be assuming for the sake of argument that the laws work the way relativity says they should in the frame where you have chosen to analyze the problem. If you want to question whether relativity makes correct predictions in any frame, that would be one thing, but once you have granted that relativity makes correct predictions in one frame that means it is logically impossible that the observed laws could fail to work the same way in other frames related to the first by the lorentz transform.
There may be many preferred frames in a particular experiment if we define preferred frame as a frame where we can determine reality at all times
Which, of course, begs the question of what we mean by "determine reality".
You assume a very special (and very nonrelativistic condition that "reality" has the property that there is a single, "real" way to compare the rates of any two clocks, and that this comparison has nice properties. (such as if A is faster than B, and B is faster than C, then A is faster than C)
I'll state it again: you are assuming absolute time.
And I'll state again the problem of absolute time: given all the laws of physics we currently know, we cannot even in principle figure out how to "determine reality". There does not exist an experiment that can confirm the hypothesis that the ECA-frame makes "real" measurements, and can deny that the Andromeda-centered frame does not.
This is why people question just how "real" the nonrelativistic view of reality is.
For example lets take the case where we have our spaceship tethered to C and halfway out on the rope we add another clock - say J. Now J moves at half the speed of R. J moves at a constant velocity wrt to C. J is a preferred frame in the sense that it will always measure the R clock to be running at 1/4 the speed of light
How do you figure that?
First off, as Jesse said, J is not a frame. :tongue:
Secondly, why would R appear to be moving at all?
When Einstein made the shift from observational results to real time dilation in part 4 he implicitly made the rest frame a preferred frame
I have no idea what part 4 means, but I can still strongly suspect you have this wrong. When one does problems, it is usually most efficient to set up a choice of coordinates that simplifies the problem, and do the problem in those coordinates. This choice of coordinates is no more preferred than the choice of x and y-axes you might make when trying to solve a high-school geometry problem.
if SR were nothing but an abstract theory of how things appear distorted in moving frames it would be of little use
Wrong. If we take this interpretation of SR, it is still extremely useful, since distortions are all we can ever measure, even in principle. Therefore, it would be extremely practical to have the correct theory of distorted measurements.
To get real time dilation, one frame had to be different from the other.
To get real time dilation, you first must have a definition of what the phrase "real time dilation" means. :tongue2: (Well, you need a practical definition, one that can be determined by experiment. But to begin, I'll settle for any definition at all)
Hyrkyl
I am not assuming absolute time - I am reasserting as Einstein did, an unambiguous relationship between the rate of two clocks in uniform relative motion where they have been previously synchronized in the same frame and only one has been put into motion
If the Andromeda centered frame is not moving wrt to the ECA frame, it can make real measurements as to the rate of R, although not as conveniently as C. If it is moving wrt to the ECA frame it will make apparent measurments as to both distances and time
If you do not consider either J or R a frame - I say to both of you - you are hiding behind a slight curvature which doesn't affect the clock rates in order to avoid certain conclusions - To avoid that foxhole, I said do the same experiment with R traveling straight from E to A - you will get the same result - for Gamma = 0.5 the R clock will read 1/2 the C, E and A clocks upon arrival at A, and if it turns around and travels straight back to E at the same velocity (e.g., it slingshots back due to the gravity field of Altair) it will read again 1/2 that of clocks ECA.
Do you really want to stand on the statment: "Secondly, why would R appear to be moving at all?" I suppose you mean relative to J -
"I have no idea what part 4 means,"
That is what this is all about
]
I am not assuming absolute time - I am reasserting as Einstein did, an unambiguous relationship between the rate of two clocks in uniform relative motion where they have been previously synchronized in the same frame and only one has been put into motion Einstein asserted no such thing, and you will find no quote in his paper that implies anything like this. He simply chose to analyze the two-clock problem in the frame where they were initially synchronized and at rest, but he made no suggestion that the problem could not equally well be analyzed in any other inertial frame. "I have no idea what part 4 means,"
That is what this is all about Perhaps Hurkyl just didn't know what you meant by "part 4", ie that you meant part 4 of Einstein's original 1905 paper (http://www.fourmilab.ch/etexts/einstein/specrel/www/) (you didn't specify this in your post), not that he had seen part 4 of the paper and failed to understand it.
Jesse - I am not avoiding your post - I drafted a response - but I wanted to think about it - so I removed it. It got me wondering about something you said.
Hurkyl - You asked for a defiition of real time dilation - rather that put into words - I will go back to the example I described previously - while R is pursuing its path on the tether - C sends signals to R. The over and back distance is always the same - and we take as fact in the experiment that light travels at the same velocity c in both directions - C notes the time the signal was sent and the time it is refected from a mirror attached to R - we will say it is 10 seconds as recorded by the C clock. R sends similar signals to C and they are reflected back to R. The time recorded on the R clock is 5 seconds (you can debate this if you like - but for the purpose of defining Real time dilation, if the return time is 5 seconds we can say R runs at a rate of 1/2 that of C). There are no variables - the over and back distance is the same for both R and Cs transmissions - and they do not have to be correlated - any time R bounces a radar signal off of C it takes 5 seconds to return as measured on R clock ---any time C bounces a radar signal off of R it takes 10 seconds to return as measured on the C clock.
Yogi's Rule: Two clocks in relative motion that maintain the same separation distance will exhibit real time dilation if reflected signals sent from one to the other require different times as measured by the clocks where the signal originated
Jesse - Just so you two are on the same page - do you agree that Einstein concluded that one clock was physically ahead of the other when they were compared - if you two havn't got past that point - there is no point in further discussion - either yes or no will do.
Jesse - Hurkyl is perfectly capable of telling what he meant - he doesn't need help - Do you do anything other than post on these boards??
Einstein asserted no such thing, and you will find no quote in his paper that implies anything like this. He simply chose to analyze the two-clock problem in the frame where they were initially synchronized and at rest, but he made no suggestion that the problem could not equally well be analyzed in any other inertial frame.
Ok - if you go ahead and analyse it in the moving frame - what will you get - will you get the same result that the moving clock is behind the clock in the stationary frame - lets see what you come up with
Jesse - Just so you two are on the same page - do you agree that Einstein concluded that one clock was physically ahead of the other when they were compared - if you two havn't got past that point - there is no point in further discussion - either yes or no will do. Yes! I have said over and over again that every inertial frame will make the same prediction about all physical questions like what two clocks read when they meet, and if this isn't completely obvious to you, then you need more practice analyzing the same situation in different frames. Just as an exercise, would you like to try transforming Einstein's problem into another frame to see how it works out? EDIT: I hadn't seen your last post suggesting this when I wrote that...
Jesse - Hurkyl is perfectly capable of telling what he meant - he doesn't need help - Do you do anything other than post on these boards?? No need to be snarky. And if Hurkyl didn't already know that you were talking about Einstein's 1905 paper, your one-line response wouldn't clarify things for him, so that comment was as much for him as you.
Ok - if you go ahead and analyse it in the moving frame - what will you get - will you get the same result that the moving clock is behind the clock in the stationary frame - lets see what you come up with OK, Einstein does not give any specific numbers in his problem, but let's say that in the original rest frame of the two clocks, they are 12 light-seconds apart, with the clock 1 at position x=0 and clock 2 at position x=12 l.s. Assume they are also synchronized in this frame. Then when clock 1 reads time t=0 seconds, it accelerates instantaneously to a velocity of 0.6c in the direction of clock 2, and travels at this velocity until it reaches clock 1 at t=12/0.6=20 seconds in the coordinates of this frame. At the moment they meet, clock 2 will of course read 20 seconds since this is its rest frame, but clock 1 will have been ticking at \sqrt{1 - 0.6^2} = 0.8 the normal rate, so it will only have ticked 0.8*20 = 16 seconds. Thus when they meet, clock 1 reads 16 seconds and clock 2 reads 20 seconds, according to this frame's prediction.
So, let's consider the coordinates of the following 4 events as seen in this frame:
EVENT A -- clock 1 reads 0 seconds and accelerates: x=0 l.s., t=0 s
EVENT B -- clock 2 reads 0 seconds: x=12 l.s., t=0 s
EVENT C -- clock 2 reads 7.2 seconds: x=12 l.s., t=7.2 seconds (the reason I picked this event will become apparent later)
EVENT D -- clock 1 and clock 2 meet, with clock 1 reading 16 s and clock 2 reading 20 seconds: x=12 l.s, t=20 s
In this frame, events A and B are simultaneous, because they both happen at the same coordinate time, while C is not simultaneous with either of them.
But now, let's transform events A, B, and C into an inertial frame moving at 0.6c relative to the first one, in the same direction that clock 1 moves afte accelerating. In this case the Lorentz transform for finding the coordinates of events in this frame would be:
x' = 1.25*(x - 0.6c*t)
t' = 1.25*(t - 0.6*x/c)
So, the coordinates of event A would be: x'=0 l.s., t'=0 s
The coordinates of event B would be: x'=15 l.s., t'=-9 s
And the coordinates of event C would be: x'=9.6 l.s., t'=0 s
So you can see that in this frame, it is events A and C that are simultaneous, while event B happened prior to both of them--in other words, at the "same moment" that clock 1 read "0 seconds" and accelerated towards clock 2, clock 2 was reading 7.2 seconds (that was the definition of event C, remember) and was at a distance of 9.6 l.s. away in this frame. And once clock 1 accelerates, it is at rest in this frame, while clock 2 is moving towards it at 0.6c. So in this frame, we conclude that it will take 9.6/0.6 = 16 seconds for clock 2 to reach clock 1 (and if you map event D into this frame using the Lorentz transform, you find it does indeed have coordinates x'=0 l.s., t'=16 s in this frame).
Now, if we assume the laws of physics work exactly the same in this frame as in all other frames, then since clock 1 is at rest in this frame it should be ticking at a normal rate, so it should have elapsed 16 seconds between the time it comes to rest and the time the two clocks meet; but since clock 2 is moving at 0.6c in this frame, it should be slowed down by a factor of 0.8, meaning it will have elapsed only 16*0.8 = 12.8 seconds between the moment clock 1 accelerates and the time they meet. But we already figured out that the time of clock 1 accelerating was simultaneous with the event of clock 2 reading 7.2 seconds in this frame (ie they were not synchronized to begin with), so it should read 7.2 + 12.8 seconds = 20 seconds when they meet.
So, to sum up: in the first frame, both clocks read a time of 0 when clock 1 accelerates, and it takes 20 seconds of coordinate time for them to meet, so that the slowed-down clock 1 only reads 16 seconds while the at-rest clock 2 reads 20 seconds when they meet. But in the second frame, clock 1 reads 0 but clock 2 reads 7.2 seconds at the moment clock 1 accelerates, and it takes 16 seconds of coordinate time for them to meet, so clock 1 elapses 16 seconds while the slowed-down clock 2 only elapses 12.8 seconds, meaning that it reads 7.2+12.8 = 20 seconds when they meet. So in both frames you predict that clock 1 reads 16 seconds and clock 2 reads 20 seconds when they meet, even though the two frames disagree about which was running slower as they approached each other, and they also disagree about simultaneity (ie what clock 2 read 'at the same moment' that clock 1 accelerated).
I am not assuming absolute time
Yes you are (or at least you are assuming something logically equivalent to absolute time), and you did it yet again in this very post when you said:
"If the Andromeda centered frame is not moving wrt to the ECA frame, it can make real measurements as to the rate of R, although not as conveniently as C. If it is moving wrt to the ECA frame it will make apparent measurments as to both distances and time"
Now that I know the paper to which we're all referring, allow me to remind you that Einstein is in no way suggesting that any frame is truely stationary.
In the opening paragraph of section one, he states:
"Let us take a system of co-ordinates in which the equations of Newtonian mechanics hold good. In order to render our presentation more precise and to distinguish this system of co-ordinates verbally from others which will be introduced hereafter, we call it the ``stationary system.''"
Emphasis mine. The ``stationary system'' of his paper is simply a co-ordinate choice in which Newton's laws are valid to a first approximation. He merely wants to use the phrase as a convenient way to refer to the co-ordinate system whose coordinates he wants to label with x, y, z, and t. He even puts "stationary" in quotes at the beginning of the next few sections to remind us that he's not talking about anything truly stationary.
In no way is the stationary frame to be construed as being "special". To wit, you could simply choose any other frame you like in which Newton's laws are valid to a first approximation, and "the stationary system" now refers to the new choice throughout the entire paper.
I gotta go; I'll make a further response later.
So in both frames you predict that clock 1 reads 16 seconds and clock 2 reads 20 seconds when they meet, even though the two frames disagree about which was running slower as they approached each other, and they also disagree about simultaneity (ie what clock 2 read 'at the same moment' that clock 1 accelerated).
Quite right Jesse - good show. You can analyse the problem in either frame - and if properly done, the answers should agree, which they do - somehow you led me to believe during one of our earlier debates that you did not concur with actual time difference in the one way trip i.e., I got the impression you were saying - from the #1 clock perspective, #2 would be found to be in arrears when the meet whereas from #2 perspective, #1 would have logged less time.
Hurkyl - Einstein used the word stationary - and we all know what was meant - it did not convey the idea of absolute rest
When I say you can use the moving Andromeda frame to make your analysis, you will be doing the same thing Jesse just did - which I have said before, will get you the right answer - all the apparent lengths and times combine to yield the same time difference. You can say the time for a clock to travel from here to Alpha at Gamma factor of 0.5 is shortened because the distance is half (Rindlers approach) or you can say that the traveler is halfway ahead on the time clock when he starts (an analysis I received from you). These methods all lead to a correct result.
I am not assuming absolute time.
Maybe not by your definition of "absolute".
But you certainly are assuming something closer to "absolute time" than the "relative time" used in Relativity.
What you seem to be calling "relative time" is limited to only a certain aspect of the full picture painted in Relativity.
It is as if you were treating time like the directions North and South. Two observers can be relatively postioned with respect to each other by varying degrees, But both will agree which is the most Northernly.
In Relativity, time is more like Left and Right. Two observers relatively positioned to each other, depending on how they are facing, may not agree as to who is to the right. Both may equally claim that they are on the right, and both can be correct.
So if we are in agreement that the coordinate frame of EAC is not preferred in the sense of an absolute rest frame - it is a frame where radar samplings can be made from C to R and from R to C at every point along the path of R to verify the difference in the clock rates.
R and C are identical clocks - the only difference is that R has been accelerated - thereafter R runs at a slower rate than before - any problems with this statement
So if we are in agreement that the coordinate frame of EAC is not preferred in the sense of an absolute rest frame - it is a frame where radar samplings can be made from C to R and from R to C at every point along the path of R to verify the difference in the clock rates. What do you mean when you say "it is a frame where radar samplings can be made"? If you agree that all frames make the same physical predictions, then all frames should predict the same thing about what a particular clock will read when a particular signal reaches it, so the radar samplings aren't associated with any one frame. Of course, when any observer uses the raw data from clock-readings to try to calculate the rate at which the signals were "actually" emitted (taking into account doppler shift), he has to pick a particular reference frame for figuring out how far the signal had to travel, making the assumption that the signals travel at c in that frame, and calculations based on different frames will give different answers.R and C are identical clocks - the only difference is that R has been accelerated - thereafter R runs at a slower rate than before - any problems with this statement Yes, there's a problem. Although R's average rate over an entire orbit will be slower than C in all inertial frames, it is not true that R's rate will be slower than C at every moment in all inertial frames, so if you accept that any frame's analysis of the situation is equally valid, you can't say "thereafter R runs at a slower rate than before". Also, if you combined the raw data from the radar signals and clock-readings with the assumption about light moving at c in some frame, along with that frame's answer to how far the emitter was when the signal was sent, then this analysis of the data will agree with the abstract calculation of how this frame should expect R's ticking rate to vary. Again, there is nothing about sending radar signals that will force you to prefer one inertial frame over another.
Janus - whether time is absolute on some cosmic scale is yet to be proven - but it is not part of the premise of this thread - we start with a reference to Einstein 1905 part 4 - and we follow the arithmetic to arrive at Einstein's conclusion that as between the stationary frame and the moving frame, the clock which moves loses time relative to the stationary clock - that is all ...what I always wind up doing on this board is defending the notion that the moving clock (the one that got accelerated at the start of the journey is always losing time at every point in the trip) This is the source of the twin thing - turnaround does not create the problem - turnaround is only incidental in the sense that it provides a convenient place to compare readings back at the origin. Einstein makes it very clear, on the one way trip, the clocks will read different when they meet each other after following any pologonal path or whether the moving clock returns to its origin.
we start with a reference to Einstein 1905 part 4 - and we follow the arithmetic to arrive at Einstein's conclusion that as between the stationary frame and the moving frame, the clock which moves loses time relative to the stationary clock Einstein doesn't even talk about a "moving frame" in that problem, he just analyzes everything from a single frame, the one he calls the "stationary frame". Don't confuse frames with actual physical clocks! And Einstein does not conclude the accelerated clock "loses time", he just concludes it's behind when they meet. But every frame agrees it's behind when they meet, even frames that say the other clock lost time (see my earlier analysis, where in the second frame the accelerated clock ticked forward 16 seconds while the inertial clock only ticked forward 12.8 seconds--wouldn't you agree that in this frame it's the inertial clock that 'loses time'?)
Well, much of what I was going to say now seems irrelevant, so I will skip ahead.
Hurkyl - Einstein used the word stationary - and we all know what was meant - it did not convey the idea of absolute rest
Okay -- so the question is why are you conveying the idea of absolute rest?
You continually pick out the ECA measurements as being "real", and everything else merely apparent. This conveys many absolute ideas:
Absolute time - Since using the ECA-frame is the only way to make "real" measurements, this gives us an absolute standard of time: the duration measured by ECA-clocks. All other durations one might measure are merely "apparent".
Absolute distance - Since using the ECA-frame is the only way to make "real" measurements, they give us an absolute standard of distance: that which is measured by ECA-rulers. All other distances are merely "apparent".
Absolute rest - Since using the ECA-frame is the only way to make "real" measurements, this gives us an absolute standard of rest: something is at rest if and only if its position remains constant according to ECA-rulers. All other notions of rest are merely "apparent". (Actually, this could be defined as saying that the absolute distance travelled by an object is zero)
Absolute simultaneity - Since using the ECA-frame is the only way to make "real" measurements, they give us an absolute standard of simultaneity: two events are simultaneous if and only if ECA-clocks say they happened at the same ECA-time. All other notions of simultaneity are merely "apparent". (Actually, this could be defined as saying the absolute duration between events is zero)
Need I go on?
This is the source of the twin thing - turnaround does not create the problem - turnaround is only incidental in the sense that it provides a convenient place to compare readings back at the origin.
The twin paradox is the following (invalid) series of statements. (but with more or less detail, depending on the arguer)
(1) The earthbound twin has an inertial reference frame in which he's stationary.
(2) The spacebound twin is always moving in the earthbound twin's frame.
(3) Therefore, the spacebound twin's clock is always running slower than the earthbound twin's clock, as measured by the earthbound twin's frame.
(4) Therefore, when they meet, the spacebound twin's clock will read less than the earthbound twin's clock.
(5) The spacebound twin has an inertial reference frame in which he's stationary.
(6) The earthbound twin is always moving in the spacebound twin's frame.
(7) Therefore, the earthbound twin's clock is always running slower than the spacebound twin's clock, as measured by the spacebound twin's frame.
(8) Therefore, when they meet, the earthbound twin's clock will read less than the spacebound twin's clock.
(9) This is a contradiction.
If you think the twin paradox is anything other than the above argument, then you are not talking about the twin paradox -- you are talking about some other thing that involves a similar setup.
The turnaround is crucial to the refutation of the twin paradox, because it is the reason statement (5) is wrong. The spacebound twin is moving in a noninertial manner during the turnaround, and that is the only reason why he cannot have an inertial frame in which he's stationary. If you could somehow get rid of the turnaround, the argument would be rock-solid, and we'd have a true contradiction on our hands.
Jesse - you can make it hard and do the analysis from any frame - but it obscures the physics - its a great mathematical exercise - but what is the point - its not necessary to resort to averages - we know the instantaneous rate of R wrt to C at all times - and that is the reality revealed by the experiment - a clock accelerated to a velocity v wrt to another clock will run at a uniform slower rate - you want to derail the obvious simplicity of the experiment and the conclusion that follows.
Jersse "(see my earlier analysis, where in the second frame the accelerated clock ticked forward 16 seconds while the inertial clock only ticked forward 12.8 seconds--wouldn't you agree that in this frame it's the inertial clock that 'loses time'?)"
No - this is exactly why making measurements from moving frames distorts reality
Hurkyl - I disagree with your narrow interpretation of the Twin thing. Einstein generated the controversery when he said the moving clock will be behind the clock in the stationary frame when it travels any polygonal path even when it returns to its starting point. In my example R moves at a uniform rate following a giant circle and returns to the start - this path could be a geodesic - if you object to it being an inertial system - but the reading on the R clock will be the same when it returns to E.
Two more points Hurkyl - you can avoid the change in frame using an inbound triplet to transfer the outbout voyagers reading to and you can avoid it by having the vehicle trajectory be an ecentric ellipse that slingshots around a strong gravitational source - this is free float inertial frame according to Wheeler so there is no change in reference frame
Hurkyl: "You continually pick out the ECA measurements as being "real", and everything else merely apparent. This conveys many absolute ideas:
Absolute time - Since using the ECA-frame is the only way to make "real" measurements, this gives us an absolute standard of time: the duration measured by ECA-clocks. All other durations one might measure are merely "apparent".
In the ECA the proper time and proper distances are those measured by clocks E,C and A and proper distance is that measured between C and R
What we do not say is that these are absolute in the cosmological sense - they are the bases for the conclusion that the experiment measures a uniform rate difference between proper time C and proper time of R
Jesse - you can make it hard and do the analysis from any frame - but it obscures the physics - its a great mathematical exercise Why do you think one frame's analysis is "the physics" while one is a "mathematical exercise"? You keep talking like this but you never give any actual arguments why we should agree with you. Is it simply because Einstein described the problem in the original rest frame of the two clocks? If he had instead started out by saying "suppose we have two clocks moving together inertially at 0.6c at a distance of 9.6 light seconds apart, with the front clock 7.2 seconds behind the back clock, then the front clock comes to rest while the back clock continues to move towards it at 0.6c", would you then consider this the "real physics" of the situation simply because this was the way the problem was initially described, with it being merely a "mathematical exercise" to transform this description into a frame where the two clocks were initially at rest? If not, please explain what your criteria are for deciding what frame represents the 'real physics', since it's a mystery to the rest of us. Jersse "(see my earlier analysis, where in the second frame the accelerated clock ticked forward 16 seconds while the inertial clock only ticked forward 12.8 seconds--wouldn't you agree that in this frame it's the inertial clock that 'loses time'?)"
No - this is exactly why making measurements from moving frames distorts reality Moving with respect to what? Is your criterion just that if the situation we are analyzing involves some objects which are initially at rest with respect to each other, their rest frame represents the "real physics" and all other frames are distortions?
OK Jesse - fair enough - The situation I have proposed is that which relates the rate of two different clocks - each moving in a different frame (I always mentally attach a frame to a clock and vice versa) So in the ECA frame we have a reference were nothing has changed physically (except you might say a temporal change has taken place as the clocks have aged during the experiment) but there is no spatial movement of any clock E,C or A. R which was originally synchronized at rest wrt to E C and A has experienced an acceleration and thereafter it runs at a uniform rate relativeto E,C and A which is different than the rate of E,C or A. What physical law operates to relate the clock rate of R to the acceleration it has experienced? Alternatively - what physical law operates to connect the velocity of R wrt C to the clock rate difference between C and R.
I suppose you will say there is nothing physical - its simply a consequence of the LT and the postulates of SR or whatever theory that yields the same results. Still, there is a curious energy relationship between the CEA frame and the R clock that corresponds to effective time dilation in a G field - so maybe physical factors are in some way at work. For me, the purpose of examining the subject is fulfilled in finding a convenient geometry - you may not find the ECA-R thought experiment of value - I consider it a useful framework
Ok yogi, I think I understand what you intend to say: R and C are at rest in equally valid inertial frames, so you don´t have to turn around as in the classical twin paradox (as Hurkyl stated), and the only thing different in both frames is that one is initially accelerated. So that must somehow be the reason for the difference in clock rates.
Assuming that I understood you correctly, I can point out the errors in your argumentation:
1. C is at rest in a global IF, but R is not. Maybe you think that the difference is negligible as you can think of the radius getting infinitely large and the inward acceleration infinitely small. But that is not true: You could set up a giant local IF but it´s extension is always confined to a region significantly smaller than the radius of the movement and a timespan significantly smaller than the time of circulation. C is necessarily always outside these bounds: the situation is not symmetric.
2. You can handle the situation in SR by dividing R´s orbit into arbitrarily many straight lines with accordingly small angles between them. The result is that R and C "see" each other go slow during the straight movement, and that R "sees" C jump ahead in time at each transition between straight lines. There is no difference to the classical twin paradox, besides that in the limit where the straight lines get infinitely small, the net effect is R´s clock going slower than C´s as "seen" in both frames.
3. The initial acceleration has nothing to do with this effect. The reason is that R is not in an inertial frame which enables him to adjust the direction of his motion in such a way that it is always perpendiculat to the distance C-R. The lorentz transformation then correctly shows C´s clock going faster.
Note that R could also move on the surface of a sphere with center C. As long as he keeps the magnitude of his velocity constant wrt C, he could accelerate and go loops and whatever ad nauseam, the result stays the same. Initial acceleration has just as little impact.
OK Jesse - fair enough - The situation I have proposed is that which relates the rate of two different clocks - each moving in a different frame (I always mentally attach a frame to a clock and vice versa) So in the ECA frame we have a reference were nothing has changed physically (except you might say a temporal change has taken place as the clocks have aged during the experiment) but there is no spatial movement of any clock E,C or A. R which was originally synchronized at rest wrt to E C and A has experienced an acceleration and thereafter it runs at a uniform rate relativeto E,C and A which is different than the rate of E,C or A. What physical law operates to relate the clock rate of R to the acceleration it has experienced? Alternatively - what physical law operates to connect the velocity of R wrt C to the clock rate difference between C and R.
I suppose you will say there is nothing physical - its simply a consequence of the LT and the postulates of SR or whatever theory that yields the same results. Still, there is a curious energy relationship between the CEA frame and the R clock that corresponds to effective time dilation in a G field - so maybe physical factors are in some way at work. For me, the purpose of examining the subject is fulfilled in finding a convenient geometry - you may not find the ECA-R thought experiment of value - I consider it a useful framework You didn't really answer my question--what criteria are you using to decide that the ECA frame is the "physical" one here? The fact that all clocks run at a uniform rate in this frame? The fact that E, C, and A are at rest in this frame (and that R was originally too, perhaps?) And can you also explain how the same criteria lead you to conclude that the "stationary frame" in Einstein's thought-experiment is the only physical one? Or do you not have any set of universally-applicable criteria for deciding which frame is the physical one in any situation, and it's just a sort of case-by-case, "know it when I see it" sort of thing?
Jesse - didn't mean to convey that one frame is physical - or more physical -- what I was trying to structure is a way to evaluate the underlying cause that appears as a physical difference (clocks running at intrinsically different rates) - physics is basically a study of relationships - we make experiments and from those we deduce that two charges repell each other with a certain force - but we don't have a good concept of what charge is - where it comes from etc - physics deals with relationships for the most part
So I am interested in the relationship between the situation when all clocks were at rest in the same frame and later when one has been but into motion. The ECA is not a better physical frame and it is not privileged with regard to the universe at large - but the relationship that evolves by considering the R clock to be following a circular path centered on C is useful - It is a springboard for making a prediction which you will no doubt challenge - namely, that any clock given a linear acceleration wrt to an inertial frame will run at an intrinsically lower rate at all times when compared to any clock in the inertial frame which has not been accelerated.
I await your encyclical
Jesse - didn't mean to convey that one frame is physical - or more physical Then what exactly did you mean when you said "you can make it hard and do the analysis from any frame - but it obscures the physics - its a great mathematical exercise"? Were you not saying that one frame's analysis is "the physics" while the other frame's analysis is a mere "mathematical exercise"? -- what I was trying to structure is a way to evaluate the underlying cause that appears as a physical difference (clocks running at intrinsically different rates) - physics is basically a study of relationships - we make experiments and from those we deduce that two charges repell each other with a certain force - but we don't have a good concept of what charge is - where it comes from etc - physics deals with relationships for the most part
So I am interested in the relationship between the situation when all clocks were at rest in the same frame and later when one has been but into motion. The ECA is not a better physical frame and it is not privileged with regard to the universe at large - but the relationship that evolves by considering the R clock to be following a circular path centered on C is useful - It is a springboard for making a prediction which you will no doubt challenge - namely, that any clock given a linear acceleration wrt to an inertial frame will run at an intrinsically lower rate at all times when compared to any clock in the inertial frame which has not been accelerated.
I await your encyclical How can you on the one hand say that no frame's analysis is more physical or real than any other's, and yet on the other hand say that a clock that's accelerated will always run at an "intrinsically lower rate" when there are perfectly good inertial frames where the acceleration caused the clock to lower its velocity and therefore caused its rate of ticking to speed up? How are these two statements of yours not obviously mutually contradictory?
Jesse says: "How can you on the one hand say that no frame's analysis is more physical or real than any other's, and yet on the other hand say that a clock that's accelerated will always run at an "intrinsically lower rate" when there are perfectly good inertial frames where the acceleration caused the clock to lower its velocity and therefore caused its rate of ticking to speed up? How are these two statements of yours not obviously mutually contradictory?"
That is one of the things I have been pondering - let me try this on you - mind you this idea is only in its infancy - but what if the clock rate change is somehow directionally dependent - for example - the ECA frame is taken to be an inertial frame - it would make no difference in which direction the acceleration of R proceeded as to the initial boost - any direction would have the same result - but to return - the acceleration would have to be opposite - and when it arrived back at ECA it would run at the original rate - its similar to the G potential - I raise a clock to a height above the earth - in doing so I have done work against the G field - at the new potential it runs faster - to get back to the original rate everything is reversed. Both involve energy changes - at this point i cannot say it will provide a consistent result in every case - perhaps worth more thought -
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