Relativity and The Stopped Clock Paradox

James S Saint

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.

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

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

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
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

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:

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".

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.

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.

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".

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.

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

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

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.