Is the Changing Clock Rate in Relativity Directionally Dependent?

[yogi]

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.

 

[JesseM]

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.

 

[yogi]

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 Earth's oblateness they run at the same speed, but that is incidental).

 

[Hurkyl]

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.

 

[JesseM]

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.

 

[yogi]

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.

 

[yogi]

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?

 

[JesseM]

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.

 

[Hurkyl]

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]

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.

 

[yogi]

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]

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]

we can presume that during the travel time the clock that is put in motion runs slower.

No, because you can't decide which 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

 

[yogi]

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]

...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?

 

[JesseM]

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?

 

[yogi]

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.

 

[yogi]

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?

 

[yogi]

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.

 

[JesseM]

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}.

 

[robphy]

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]

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.

 

[yogi]

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]

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 realized 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]

What is time?

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 ?

 

[Ich]

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.

 

[JesseM]

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.

 

[yogi]

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 let's 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.

 

[yogi]

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]

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

To 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.

 

[yogi]

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]

- 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;
https://www.physicsforums.com/showthread.php?t=106600

 

[robphy]

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.

 

[JesseM]

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.

 

[yogi]

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

 

[yogi]

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.

 

[Ich]

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]

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.

 

[yogi]

RandallB - its not that I won't 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 that's the problem - too late - too many beers

 

[yogi]

ich - i want to consider your post 37 more before responding

Thanks

yogi

 

[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]

RandallB - its not that I won't 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 that's 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 anyone 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.

 

[Janus]

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]

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?

 

[Ich]

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]

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.

 

[Hurkyl]

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.

 

[yogi]

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 let's 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?

 

[yogi]

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.

 

[Hurkyl]

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.