Relativity and The Stopped Clock Paradox

[James S Saint]

What did I say about "distractive argumentation"?

At some point from Einstein's POV;
Clock1 = 11.072
Clock2 = 15.690So the question becomes;
For what time t1 and other clock time t1+4.6184 separated by 6.928 μls would there be an x location from which to observe the difference of 4.6184 μs?

x' = γ(x-tβ)

x' = 1.1547(x - t1/2) ;for clock1
x’ = 1.1547((x+6.928) - (t1+4.6184)/2) ;for clock2

(x-t1/2) = ((x+6.928) - ( t1+4.6184)/2)
(x) = x + 6.928 - ( t1+4.6184)/2 + t1/2
at this point x drops out meaning that any distance will do.

6.928 = ( t1+4.6184)/2 + t1/2
2*6.928 = ( t1+4.6184) + t1
2*t1 = 2*6.928 - 4.6184
t1 = 6.928 - 4.6184/2
= 4.6188

So at any location x, as long as t1 = 4.6188, the proper difference in time can be observed by Einstein at the button press.

-----------------------------------

The distance of 6 μls was irrelevant.

But you could never convince me that because I said that the train was traveling rather than saying that the station was traveling, the distance between the station and train would be different. Again if it had been 2 rockets coming toward each other, due to symmetry, neither can claim ownership of the distance.

I am curious of one detail though. Is length contraction the same for objects moving away as it is for object moving toward? The equations would imply that it is, but sometimes that sort of thing just gets left out as presumption much like the t=0=t' concern.

{..and I meant that the original had 4 timing paths, not 4 clocks.}

 

[darkhorror]

The distance of 6 μls was irrelevant.

But you could never convince me that because I said that the train was traveling rather than saying that the station was traveling, the distance between the station and train would be different. Again if it had been 2 rockets coming toward each other, due to symmetry, neither can claim ownership of the distance.

I am curious of one detail though. Is length contraction the same for objects moving away as it is for object moving toward? The equations would imply that it is, but sometimes that sort of thing just gets left out as presumption much like the t=0=t' concern.

{..and I meant that the original had 4 timing paths, not 4 clocks.}

Did you read what I wrote?

What you are saying is that you don't believe in length contraction. If the train is 100 meters long in the train's frame of reference, do you think that the train is also 100 meter's in the stations frame of reference if the train is moving at .5c in that frame of reference?

 

[James S Saint]

Did you read what I wrote?

What you are saying is that you don't believe in length contraction. If the train is 100 meters long in the train's frame of reference, do you think that the train is also 100 meter's in the stations frame of reference if the train is moving at .5c in that frame of reference?

No. That is a different issue. The length perceived in any frame within that frame will be dilated from how it is perceived from the other frame. But the distance between the moving object of one and the moving object of the other must be equal.

 

[darkhorror]

How about this if on Earth we see a star 100 light years away from Earth in Earth's frame of reference. Then let's say there is a spaceship moving at .5c towards that star, how far is the star and the Earth away from each other in the ships frame of reference?

 

[James S Saint]

And now I see what the simplification error I made was.

If Einstein must see clock1 at 4.6184 at button press time. And the light coming from it telling the stationmaster to press the button had to be 4.6184 - 3.464 = 1.1544.

So in the station’s frame clock1 had to be reading 10 when it sent the message and in Einstein’s frame that same clock1 had to be reading 1.1544.

Lorenz would suggest that Einstein’s POV would require that a clock in the station’s frame that reads 10 in that frame, must be reading 8.666 in Einstein’s frame, not 1.544.

 

[ghwellsjr]

No. That is a different issue. The length perceived in any frame within that frame will be dilated from how it is perceived from the other frame. But the distance between the moving object of one and the moving object of the other must be equal.

Are you aware that your claim is in opposition to Special Relativity?

 

[PeterDonis]

Lorenz would suggest that Einstein’s POV would require that a clock in the station’s frame that reads 10 in that frame, must be reading 8.666 in Einstein’s frame, not 1.544.

No, Lorentz (sp.) would not suggest that. If a clock physically reads "10" at a particular event (meaning the LEDs on its face display the digits "10", or the equivalent depending on the type of clock), then that is a direct physical observable, an invariant which will be the same in *all* frames. Einstein's frame may assign a different *time coordinate* to the event at which the LEDs on the clock's face read 10, but that is a different thing. You continue to miss this point and it appears to me to be a primary source of your confusion.

 

[James S Saint]

At some point from Einstein's POV;
Clock1 = 11.072
Clock2 = 15.690So the question becomes;
For what time t1 and other clock time t1+4.6184 separated by 6.928 μls would there be an x location from which to observe the difference of 4.6184 μs?

x' = γ(x-tβ)

x' = 1.1547(x - t1/2) ;for clock1
x’ = 1.1547((x+6.928) - (t1+4.6184)/2) ;for clock2

(x-t1/2) = ((x+6.928) - ( t1+4.6184)/2)
(x) = x + 6.928 - ( t1+4.6184)/2 + t1/2
at this point x drops out meaning that any distance will do.

6.928 = ( t1+4.6184)/2 + t1/2
2*6.928 = ( t1+4.6184) + t1
2*t1 = 2*6.928 - 4.6184
t1 = 6.928 - 4.6184/2
= 4.6188

So at any location x, as long as t1 = 4.6188, the proper difference in time can be observed by Einstein at the button press.

Can anyone point to the exact error in that post?

 

[James S Saint]

No, Lorentz (sp.) would not suggest that. If a clock physically reads "10" at a particular event (meaning the LEDs on its face display the digits "10", or the equivalent depending on the type of clock), then that is a direct physical observable, an invariant which will be the same in *all* frames. Einstein's frame may assign a different *time coordinate* to the event at which the LEDs on the clock's face read 10, but that is a different thing. You continue to miss this point and it appears to me to be a primary source of your confusion.

This is just an issue of the language we each are using. Everything is "physical".

 

[PeterDonis]

This is just an issue of the language we each are using. Everything is "physical".

You appear to be claiming that, at one and the same event, a clock can be reading "10" to one observer but something different to another. That is not an "issue of language": it is a contradiction in terms. The actual observed reading of a clock (the actual digits displayed on its face, or the equivalent) at a particular event is a direct physical observable, and must be the same for everyone.

 

[James S Saint]

You appear to be claiming that, at one and the same event, a clock can be reading "10" to one observer but something different to another.

"seen as reading differently" from Einstein's POV.
That is how we got the relativity of simultaneity.

and must be the same for everyone.

It can't be observed as the same by everyone. That is the whole point to relativity and especially to relativity of simultaneity.

 

[James S Saint]

I can't believe I have been spelling "sync" as "sink" and got somehow talked into spelling Lorentz as "Lorenz"... brain just getting too worn out. :(

 

[ghwellsjr]

You appear to be claiming that, at one and the same event, a clock can be reading "10" to one observer but something different to another.

"seen as reading differently" from Einstein's POV.
That is how we got the relativity of simultaneity.

and must be the same for everyone.

It can't be observed as the same by everyone. That is the whole point to relativity and especially to relativity of simultaneity.

James, you need to learn something now that I tried to teach you way back in post #12 but you flat out rejected in post #14 and I tried to clarify for you in post #17. There is no point in continuing any discussion with you with regard to Special Relativity until you understand what coordinate time is.

There is no clock that two different people see as having different times on them. Einstein has his own set of clocks and the stationmaster has his own set of clocks. At any given moment at every possible location, there are two clocks colocated, one for Einstein and one for the stationmaster. These two clocks almost always have two different times on them. That is what Relativity of Simultaneity is related to. The Lorentz Transform allows you to pick a clock at any location at any time in one frame (say one of the stationmaster's) and see which clock and what time is on it in another frame (say Einstein's).

Please reread posts #12 and #17 and study the first two sections of Einstein's 1905 paper until you grasp how Einstein constructs a Frame of Reference. If you have any questions about this, please ask--discussing anything else truly will be "distractive argumentation".

 

[PeterDonis]

"seen as reading differently" from Einstein's POV.
That is how we got the relativity of simultaneity.

It can't be observed as the same by everyone. That is the whole point to relativity and especially to relativity of simultaneity.

See ghwellsjr's comment. The actual reading displayed by a particular clock is not "seen as reading differently"; it *is* "observed as the same by everyone". The "time from Einstein's POV" refers to a *different* clock (or set of clocks) moving on a different worldline (or worldlines).

 

[James S Saint]

Well, I have to say that this is getting interesting... in a somewhat depressing way.

I really didn't expect to have to defend fundamental relativity concerns on this forum.

I have asked 2 questions that have been ignored in favor of directing me to go learn to think like Einstein (and thus perhaps make all of the same mistakes) rather than my more direct and simple algebra. I have read many of Einstein's papers but that was years ago when I was more tolerant of having to interpret what someone is trying to say when they wrote something despite the superficial appearances. It is a bit like reading the Bible in that you have to realize what the authors at that time in their situation intended to be saying rather than the more literalist presumptions that ignore writing styles and symbolic language usage of the era.

It seems that there are 2 fundamental complaints preventing me from getting the answers to my simple questions.

PeterDonis seems to not understand that a moving observer at a different point in space will not see the same time on a clock that a non-moving observer would see. He seems to think that the time it takes for light to travel to an observer has no effect on what the observer will see. It surprises me a bit that grwellsjr seems to agree. Einstein has written papers on that issue (not that he should have needed to), most notably his 1920 paper concerning Relativity of Simultaneity (Ref: Relativity: The Special and General Theory. Chap IX. The Relativity of Simultaneity).

Granted if we can't even agree on that issue, there is little point in discussing anything concerning relativity at all. Without that one issue, there would be no relativity concerns at all.

The other complaint seems to be that if I would only workout the math in the far, far more complex and obfuscated way using "coordinate clocks", rather than my simple algebra, I would get the "right" answer. Frankly, to me math is math and the simpler the better. There is nothing magic about relativity. It doesn't need any special worshipful symbols or rituals. And if such is somehow required, then that would be a clear indication of it being fallacious. When math has to be done in only some particular way to get the "right" answer and not done any other way, it could only be because that "right" answer isn't.

All of that is just me ignoring the good probability that you each have misunderstood what Einstein was saying in the first place (especially considering the "observation" issue and the "6 μls" issue).

I have asked 2 questions;
1) can you point out any error in the relatively simple math posts.
2) on a side note, is it commonly understood that length contraction is irrespective of direction of motion?

I don't feel that this is really the thread to be arguing over fundamental relativity issues. I feel like I have proposed a calculus issue to discuss and we are arguing basic arithmetic.

 

[PeterDonis]

PeterDonis seems to not understand that a moving observer at a different point in space will not see the same time on a clock that a non-moving observer would see. He seems to think that the time it takes for light to travel to an observer has no effect on what the observer will see.

Wow. Either you are extremely confused or you are using words in a very different way than ghwellsjr and I are. I think some more precise definition of terms is in order.

In an earlier post I gave labels to a number of events in the scenario in question. Take one of them, say event A, where the stop-clock "closest to Einstein" reads 10, and emits a light signal showing that reading. That light signal then travels to event B, where the station-master sees it and presses the button.

What I have been saying is this:

(1) The statement "the stop-clock at event A reads 10" is an invariant statement; it is true for all observers.

(2) The station-master at event B, when he receives the light signal from event A, "sees" that the stop-clock read 10 when that signal was emitted--i.e., at event A.

Now consider another observer, call him Bob, who is moving relative to the station-master, but who just happens to be passing the station-master precisely at event B--that is, at precisely the instant that the station-master sees the light signal from event A. The following is then also true:

(3) Bob *also* "sees" that the stop-clock read 10 when the light signal was emitted from event A.

Note two things: first, the station-master and the other observer both "see" the *same* time on the stop-clock, even though they are in relative motion; second, both the station-master and the other observer are at a different point in space from the stop-clock, yet they agree on what the stop-clock's reading was at event A.

Now consider still *another* observer, Fred, who is moving at the same speed as Bob relative to the station-master but is separated in space from Bob, such that he passes the station-master some time *after* event B. Fred will receive the light signal from event A at some *other* event than B--so when he receives it, he will be separated in space from Bob, the station-master, *and* the stop-clock. And yet:

(4) Fred *also* "sees" that the stop-clock read 10 when the light signal was emitted from event A.

All of these statements seem to me to be obviously true. Do you agree?

1) can you point out any error in the relatively simple math posts.

I don't see the point, since I'm not even sure how you are using words yet.

2) on a side note, is it commonly understood that length contraction is irrespective of direction of motion?

If you mean "length contraction occurs in the direction of motion, but not transverse to that direction, regardless of which direction the motion is in", then yes.

 

[James S Saint]

What I have been saying is this:

(1) The statement "the stop-clock at event A reads 10" is an invariant statement; it is true for all observers.

That one statement is a "show-stopper". It is defiant of relativity and as long as you believe that statement, there is no point in going further. You are declaring an "absolute truth" frame of reference. If this was a philosophy forum, I could stand on your side and we could possibly go far. But as far as the world of relativity, that statement is heresy.

UP to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train traveling along the rails with the constant velocity v and in the direction indicated in Fig. 1. People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment. As a natural consequence, however, the following question arises: 1
Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? We shall show directly that the answer must be in the negative.

FIG. 1.

2
When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A —> B of the embankment. But the events A and B also correspond to positions A and B on the train. Let M' be the mid-point of the distance A —> B on the traveling train. Just when the flashes 1 of lightning occur, this point M' naturally coincides with the point M, but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M’ in the train did not possesses this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A. We thus arrive at the important result: 3
Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity). Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event. 4
Now before the advent of the theory of relativity it had always tacitly been assumed in physics that the statement of time had an absolute significance, i.e. that it is independent of the state of motion of the body of reference. But we have just seen that this assumption is incompatible with the most natural definition of simultaneity; if we discard this assumption, then the conflict between the law of the propagation of light in vacuo and the principle of relativity (developed in Section VII) disappears.

 

[PeterDonis]

That one statement is a "show-stopper". It is defiant of relativity and as long as you believe that statement, there is no point in going further.

Wow again. Apparently it's option 1: you are extremely confused.

Read my statement again, very carefully:

The statement "the stop-clock at event A reads 10" is an invariant statement; it is true for all observers.

What am I saying? I am saying that "the stop-clock at event A reads 10" is a statement about a direct physical observable. It is a statement similar to the following statement that could be made about the scenario from Einstein that you quote: "Lightning strikes at event A". In other words, the stop-clock reading 10 is a direct observable like a lightning strike. An event, like "event A", is *defined* by what direct physical observable (a particular stop-clock reading, "10", or a lightning strike) happens there.

Note also that my statement above (and in fact all of the statements in my previous post) say absolutely *nothing* about "absolute time". Every single statement referred to direct physical observables at specific events. *None* of them were statements about how "times" at spatially separated events are related. (I never said "what time it was" according to the station-master, or Bob, or Fred, at event B, or any other event; I only said what they "saw" from the light signal that was emitted at event A.)

In summary: direct physical observables *must* be invariants, the same for all observers: otherwise we could not do physics. Saying that different observers in different states of motion can disagree about what the stop-clock reads at event A is like saying that different observers in different states of motion can disagree about whether or not lightning struck at event A.

Different observers in different states of motion *can* (and will) disagree about whether two different events are *simultaneous*; that's what Einstein's scenario is all about. So different observers in different states of motion will disagree about whether the lightning strikes at A and B are simultaneous. Similarly, different observers in different states of motion in your scenario (such as the station-master and Einstein) will disagree about whether, say, the events that I labeled "A" and "D" are simultaneous. But they will *not* disagree about what happens at those events; both will agree that stop-clock #1 reads 10 at event A, and stop-clock #2 reads 10 at event D. For them to disagree about that, once again, would be like the observer on the train disagreeing with the observer on the embankment about whether lightning struck at events A and B.

 

[James S Saint]

What am I saying? I am saying that "the stop-clock at event A reads 10" is a statement about a direct physical observable.

That doesn't exist.
No one "directly observes" anything...ever. There is no such thing. And that is what relativity is all about.

In reference to relativity of simultaneity;
Two clocks that are "in sync" can only be observed to be in sync by someone standing in one particular spot. Anyone else cannot testify by "direct observation" that those clocks are in sync. That is what his paper and that last post was about.

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa

Clocks in sync are "simultaneous events" with each tic.

My clock1 and clock2 are ONLY simultaneous/"in sync" to the stationmaster.

 

[James S Saint]

Well, I partially take that back.
There is a zy plane intersecting the stationmaster wherein the clocks would be in sync, but not reading the same as what the stationmaster sees at the same moment that the stationmaster sees them. Anyone else in that plane would be out of sync with the stationmaster's purview.

 

[James S Saint]

(2) The station-master at event B, when he receives the light signal from event A, "sees" that the stop-clock read 10 when that signal was emitted--i.e., at event A.

That statement reveals the problem.
Event B occurred after the clock already passed 10.
4 μs later, the stationmaster "sees" the "10".
At that point, the clock is already at 14 per station POV.
He doesn't "see" the clock. He sees the light from the clock later.
His observation isn't "direct", but delayed.

When I am calculating "Einstein's" POV, I am calculating the time difference between the station POV of the clocks plus the time delay for the light to get to the stationmaster as per Einstein's relatively slower time rate of .866 and the distance contraction of .866 both due to the speed of travel.

Anyone on the train MUST see the 2 clocks out of sync if the stationmaster sees them IN sync.
I calculated how much out of sync they must be from the purview of anyone on the train.

 

[darkhorror]

That doesn't exist.
No one "directly observes" anything...ever. There is no such thing. And that is what relativity is all about.

In reference to relativity of simultaneity;
Two clocks that are "in sync" can only be observed to be in sync by someone standing in one particular spot. Anyone else cannot testify by "direct observation" that those clocks are in sync. That is what his paper and that last post was about.

Clocks in sync are "simultaneous events" with each tic.

My clock1 and clock2 are ONLY simultaneous/"in sync" to the stationmaster.

The clocks being in sync or out of sync is totally different from what he is saying.

The even that the clock is at 10 when he hit's the button is a single event. Just like when the clock's stop and read 18. Are you trying to imply that a will read a number higher than 18 when it stops or read a number lower than 18 when it stops?

The problem I see you having is that you are trying to use equations before you understand the basics or why things work that way. Then you are trying to use the equations to get the answer that you think you should be getting rather than what you actually should be getting.


and with statements like this

But you could never convince me that because I said that the train was traveling rather than saying that the station was traveling, the distance between the station and train would be different. Again if it had been 2 rockets coming toward each other, due to symmetry, neither can claim ownership of the distance.

Do you want to learn or do you already know it all, thus can never be convinced of something? As I already explained it over and over and you continue to ignore it.

 

[PeterDonis]

No one "directly observes" anything...ever. There is no such thing. And that is what relativity is all about.

You appear to have repeatedly failed to read what I actually wrote, and you keep responding with vague general statements instead of responding to the specifics of what I actually said.

Also, you are contradicting yourself, since you then go on to say:

Two clocks that are "in sync" can only be observed to be in sync by someone standing in one particular spot. Anyone else cannot testify by "direct observation" that those clocks are in sync. That is what his paper and that last post was about.

If someone standing in a particular spot *can* testify "by direct observation" that two clocks are "in sync", then it can't possibly be true that "no one directly observes anything".

My clock1 and clock2 are ONLY simultaneous/"in sync" to the stationmaster.

For your particular, idiosyncratic definition of "simultaneous", yes, this is true. But that's not the standard definition. Nor is it very useful, since it precludes any use of reference frames, which require extending a definition of "simultaneity" beyond the one particular spot where light rays from two particular simultaneous events meet.

In any case, it's irrelevant to what I've been saying, as you would realize if you had actually read my previous post, where I explicitly said that I wasn't saying anything about simultaneity; I was only making assertions about what actually happened at particular events, like lightning strikes or clocks having particular readings.

That statement reveals the problem.
Event B occurred after the clock already passed 10.
4 μs later, the stationmaster "sees" the "10".
At that point, the clock is already at 14 per station POV.
He doesn't "see" the clock. He sees the light from the clock later.
His observation isn't "direct", but delayed.

With your particular definition of "direct", yes, this is true. So what? I wasn't saying anything about that. I was only saying that the station master "sees" the "10" when the light ray from event A arrives at event B. There is also the further obvious point that, since the station master "sees" the "10", he can therefore infer that, at event A, when the light signal was emitted, the stop-clock read 10.

What you have utterly failed to address is my additional point, that Bob, the observer who is just passing the station master at event B, also "sees" the "10", because he sees the exact same light signal from event A at the exact same event. Which means that two observers, in relative motion, both agree that, at event A, the stop-clock read 10. Because they can both make the same inference from the same light signal.

When I am calculating "Einstein's" POV, I am calculating the time difference between the station POV of the clocks plus the time delay for the light to get to the stationmaster as per Einstein's relatively slower time rate of .866 and the distance contraction of .866 both due to the speed of travel.

Which may or may not be correct, depending on what you are trying to calculate from Einstein's POV. But we haven't got that far yet; we are still trying to nail down the meaning of much simpler statements like "the stop-clock read 10 at event A".

Anyone on the train MUST see the 2 clocks out of sync if the stationmaster sees them IN sync.

Let me re-state this more precisely: "Light rays from the event where stop clock #1 read 10 (event A) will reach someone on the train at a different event than light rays from the event where stop clock #2 read 10 (event D)." This is in contrast to: "Light rays from event A will reach the station master at the *same* event (event B) as light rays from event D."

I agree that the above statements as I have rephrased them are true.

I calculated how much out of sync they must be from the purview of anyone on the train.

Let's assume that your calculations are correct. (I haven't reviewed them in detail, as I said before; I don't see the point until we have much more basic things nailed down.) What do they tell us? They tell us the proper time elapsed, for an observer on the train, between receiving light rays from event A and light rays from event D. But you appear to be claiming that, because that proper time elapsed is nonzero, the observer on the train will somehow see a *different* light signal from event A (one that shows the stop-clock reading something other than 10) than all the other observers who see the light signal from event A (and similarly for event D). That is nonsense, and that is what I have been saying is wrong. The light signal from event A carries the information that the stop-clock read 10 at event A; and it carries that *same* information to every observer that sees that light signal, regardless of their state of motion, and regardless of the proper time, for the observer, when they see the signal.

 

[James S Saint]

As I stated before, this is obviously a language issue (obvious enough to me anyway). With many people, logic can't be resolved as long as language stands in the way. I am not one of those. But certainly arguments will continue as long as language is in the way.

So never mind and thanks anyway.

 

[Mentz114]

As I stated before, this is obviously a language issue (obvious enough to me anyway). With many people, logic can't be resolved as long as language stands in the way. I am not one of those. But certainly arguments will continue as long as language is in the way.

So never mind and thanks anyway.

Oh, don't go away - this has been great fun.

 

[ghwellsjr]

James, I want to make sure I understand what you are saying. Suppose we add another observer, a switchman, and put him 6 μls from the first clock, the same location that Einstein is at when the stationmaster presses the button. What time will the switchman see on the two stop-clocks at the moment the stationmaster presses the button? What time will Einstein see on the two stop-clocks at that same moment?

 

[PeterDonis]

As I stated before, this is obviously a language issue (obvious enough to me anyway). With many people, logic can't be resolved as long as language stands in the way. I am not one of those.

Hmm. I agree there is a language problem here, but I suspect we disagree about which one of us is the source of the problem.