1 Edgar L. Owen | In an SR universe do all inertial clocks run at the same (proper time) rate | Monday 14 October 2019 |
2 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Tuesday 15 October 2019 |
3 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Wednesday 16 October 2019 |
4 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Friday 18 October 2019 |
5 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Friday 18 October 2019 |
6 jrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Saturday 19 October 2019 |
7 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Saturday 19 October 2019 |
8 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Monday 21 October 2019 |
9 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Monday 21 October 2019 |
10 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Tuesday 22 October 2019 |
11 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Thursday 24 October 2019 |
12 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Friday 25 October 2019 |
13 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Saturday 26 October 2019 |
14 tjrob137 | Re :In an SR universe do all inertial clocks run at the same (proper time) rate | Sunday 27 October 2019 |
In an SR universe do all inertial clocks run at the same (proper time) rate
23 posts by 9 authors
https://groups.google.com/forum/#!topic/sci.physics.relativity/Zc_2yeUUe5M
keywords = SR, inertial clocks
Now imagine one clock changes its motion a couple of times so its worldline between two arbitrary events is no longer the shortest possible (as it would have been for an inertial clock). Thus its PROPER TIME to traverse this worldline will be shorter.
Now will the PROPER TIME interval (NOT the various coordinate time intervals calculated by different observers, which will be different) this clock took to traverse its bent worldline be calculated as identical (invariant) by all inertial observers? And if not WHY?
Thanks, Edgar
> | Imagine an SR universe full of inertial clocks with various constant velocities relative to each other. Do all these inertial clocks run at the same (PROPER time) rate? |
All clocks advance by one second for every elapsed second of their proper time. This OUGHT to be obvious, because that is what those words mean. Note this is so regardless of how they might move or where they might be located.
> | If so why can't we consider this single inertial proper time rate as the standard clock rate of the SR universe? |
We can and do. Not only for an "SR universe" (whatever that might mean), but also in the universe we inhabit.
1 second here is the same as 1 second over there -- 9,192,631,770 cycles of the Cs133 ground-state hyperfine transition. One second on earth's surface is the same as one second on a GPS satellite; but when we compare the two there is a difference -- it is due to different paths through spacetime, not different clock tick rates.
> | Now imagine one clock changes its motion a couple of times so its worldline between two arbitrary events is no longer the shortest possible (as it would have been for an inertial clock). Thus its PROPER TIME to traverse this worldline will be shorter. |
Sure. The elapsed proper time along a path between two specified points depends on the path. The clocks following those paths, of course, always tick at their usual rate (advancing one second per 9,192,631,770 cycles of the Cs133 ground-state hyperfine transition, for a Cs atom co-located and co-moving with the clock).
> | Now will the PROPER TIME interval (NOT the various coordinate time intervals calculated by different observers, which will be different) this clock took to traverse its bent worldline be calculated as identical (invariant) by all inertial observers? |
Yes. Elapsed proper time is an invariant. That is, the elapsed proper time along a path is a specific integral of the metric over the path; any coordinates can be used to compute the integral, because all choices obtain the same result -- that's what "invariant" means in this context.
Tom Roberts
> | Tom, OK, so what I think you are saying is that the amount of time (aging) lost by the traveling twin doesn't depend on him leaving and returning to earth and comparing clocks there. |
Hmmm. If that is the physical situation being discussed, then it does depend on that. DUH!
But similar results apply anywhere in the universe, when phrased properly. Which this isn't.
As rotchm said: Not "lost". Just didn't gain as much.
> | If he took a trip with the same geometry anywhere else including empty space he would lose the same amount of time on that trip as well relative to all inertial clocks in the universe, not just a clock on earth. |
This is rather garbled, with several implicit assumptions not in evidence.
What we can say is:
Tom Roberts
> | 1. We know that all inertial clocks in an SR universe (no gravity) run at the same PROPER TIME RATE (but not coordinate time rates which obviously depend on their relative motions). |
Yes, in this sense:
Note this holds without excluding gravity.
> | 2. However a NON-INERTIAL clock will run at a slower PROPER TIME RATE |
Nope. Non-inertial clocks also tick at their normal rate, as above.
The internal "clock" that regulates the decay of muons has been observed to "tick" at its normal rate for muons in a storage ring, experiencing a truly enormous proper acceleration of 10^18 g.
> | 3. Now the non-inertial clock runs at only ONE (its own) proper time rate. Since all other (inertial) clocks are running at the same rate as each other, there must be one and only one PROPER TIME rate at which the single non-inertial clock is running relative to all THE IDENTICAL PROPER TIME RATES of all inertial clocks. |
This is just plain nonsense. Your words describe things that cannot be observed or measured (see below).
> | The question is how to determine that relative rate? |
Yes. In fact, it simply is not possible to directly compare the tick rates of two clocks, unless they are co-located and co-moving. Anything else requires either: a) signals between the clocks, or b) comparison of elapsed proper times rather than tick rates.
One of the major lessons of 20th century physics is:
While generally associated with quantum mechanics, this applies to all aspects of physics.
Tom Roberts
> | But you still don't get the main point here, that proper time rates can be compared. |
HOW????
You'll find that they cannot be directly compared unless the clocks are co-located and co-moving. In any case you MUST specify the method of comparison in sufficient detail that the physical situation can be analyzed.
Tom Roberts
> | One way to compare proper times without being �co-located and co-moving� is what I suggested before. Observer B continually broadcasts a signal with his current clock reading. A receives one such signal giving B�s clock reading as bt�. A subtracts the transit time of that signal from his own current clock reading giving a time of at� on his own past clock. He now knows that his clock read at� when B�s clock read bt�. After a pause A repeats this and finds that his clock read at�� when B�s clock read bt��. |
THINK about what you said.
A is comparing his own clock to SIGNALS from B. That is not a comparison of clock tick rates, no matter how much you would like it to be.
> | [... further nonsense based on that error] |
Tom Roberts
> | All your objections are just measurement accuracy problems, |
No, they are FUNDAMENTAL errors in your thinking.
> | Astronomers measure distances and light transit times to varying degrees of accuracy all the time, |
Sure. In the world we inhabit. And to do that they ASSUME the validity of SR/GR (which, of course, is fully justified experimentally). THEY are not trying to test or explore relativity, they are USING it to learn about the cosmos.
> | so measuring the transit time of a light beam |
is undefined in a GEDANKEN, until you explain how to determine it. If you bothered to think about HOW to determine that transit time, you'll find you need to assume what you are trying to prove (whatever that is), or must assume the validity of SR.
> | And what kind of nonsense is "the method compares signals not proper times " Duh! |
It is just plain English: comparing this clock to signals from that clock does NOT compare their proper times, it compares a clock to some signals. DUH!
> | That's how proper times are compared. |
Only by people who cannot read simple English, and who don't understand the real issues involved.
> | My method is a valid way to compare proper times |
No, it isn't. It compares a clock to some SIGNALS.
As I have said repeatedly: when using signals like that you MUST account for the effects of the physical situation on those signals. Do that and you find it accounts for any differences, so you must conclude that each clock ticks at its normal rate.
For comparing/measuring clock tick rates using signals, you must disentangle the tick rates from the Doppler effect. You seem completely unaware of this. The result will necessarily depend on your assumption of how Doppler works.
Tom Roberts
> | No one has said it is impossible to compare proper times. |
Yes, I have said it is not possible to DIRECTLY compare the proper times of two clocks, unless they are co-located and co-moving. This is just awareness of the physical situation(s) when they are not co-located or not co-moving.
You can compare SIGNALS from one clock with the other (as Owen repeatedly does), or you can ASSUME the validity of SR and make several different kinds of comparisons, but none of these are DIRECT comparisons -- you must ASSUME some aspect of the physical situation behaves as SR predicts, and then correct for it.
Some people think that after such corrections they are comparing the proper times of the clocks. I don't -- my usage of the language does not stretch that far. Of course after such corrections one always finds that each clock advances its proper time at one second per second, so this is not very useful because nothing new is learned.
Tom Roberts
> | I see the problem now. |
No, you don't.
The problem is YOURS. You will NEVER understand this until you a) specify the physical situation more precisely, and b) STUDY relativity. It is ABSOLUTELY USELESS to just make stuff up, pretend it is true, and post nonsense to the net.
> | Each proper clock has a distinct rate in its own frame depending on its relativistic circumstances. |
Except the tick rate of a clock measured in its own rest frame does NOT depend "on its relativistic circumstances" (whatever that means). I KNOW this because every clock advances by 1 second for every 9,192,631,770 cycles of the ground state hyperfine transition of co-located and co-moving Cs133 atoms, within its specified accuracy.
> | Clocks near black holes run slower, the traveling twin�s clock runs slower. |
Nope. When COMPARED to other clocks using signals, the signals may arrive more slowly. But that is NOT measuring the proper time of the clock, it is measuring SIGNALS from the clock.
If you correct for the effects of the physical situation on those signals, you learn nothing new because you conclude that the clock advances by 1 second for every 9,192,631,770 cycles of co-located and co-moving Cs133 atoms, within its specified accuracy.
> | The twin�s clock conclusively demonstrates proper times run at different rates |
NONSENSE. There is another possibility that you ignore: they traveled different paths through spacetime, and the paths have different elapsed proper times.
> | [... further nonsense] |
Tom Roberts
> | In physics when we speak of clocks we are generally actually talking about the local rate of time where the clock is located rather than the physical mechanism. |
But "time is what clocks measure" [Einstein and others].
This is fully justified, because in every experiment that involves time, it is measured by clocks.
> | The clock near the black hole is the same as on earth, |
Yes.
> | but the local rate of time near a black hole is very much slower than on earth due to its geometry. |
No! NO! NO!!!
I keep telling you this and you keep ignoring it: Clocks everywhere and everywhen ALWAYS advance at their normal rate (advancing 1 second for every 9,192,631,770 cycles of co-located and co-moving Cs133 atoms, within its specified accuracy). So "tine" also advances at its normal rate.
It is only COMPARISONS OF CLOCKS' TICK RATES where differences arise. And they are invariably due to the effects of the physical situation on SIGNALS between clocks, and not the tick rates themselves.
I repeat: you will NEVER understand this until you: a) specify the physical situations more precisely, and b) STUDY relativity. It is ABSOLUTELY USELESS to just make stuff up, pretend it is true, and post nonsense to the net.
Tom Roberts
> | [...] velocity through time. |
That is an oxymoron. Complete nonsense.
You are making up your own meanings of words commonly used in physics. You cannot expect to communicate with others when you do that.
Tom Roberts
> | Indeed we do seem to have a basic disagreement over terminology. |
Yes. YOU clearly do not know what some very basic terms actually mean.
> | My understanding is that the time I read on my own clock is my proper time. |
Yes. Provided the clock remains right with you (i.e. co-located and co-moving with you).
> | The time I read or compute on a moving clock is a coordinate time. |
Nope. Not even close.
Coordinate time is the time coordinate of a specified coordinate system. There can be many coordinate systems, and thus many coordinate times. It has NOTHING to do with any proper time, except that if some time coordinate is specified to be determined by a certain clock, then that coordinate time is equal to that clock's proper time.
If you are moving inertially, and you construct a set of inertial coordinates in which you are at rest, then the coordinate time of your coordinate system will be equal to your proper time. If there is another clock moving relative to your coordinate system then you can calculate what its proper time should be, for any value of your coordinate time; your calculation of its proper time will advance by a factor 1/gamma compared to the advancing of your coordinate time.
Such calculations have been observed to agree with actual moving clocks, many, many times, and to high accuracy.
Remarkably, if that other clock is moving inertially, and an observer with it constructs inertial coordinates in which she (it) is at rest, she will calculate that your proper time will advance by a factor 1/gamma compared to the advancing of her coordinate time. This is a basic example of Lorentz invariance, and also demonstrates that this is a geometrical projection, not any sort of "physical change" in the clocks.
Tom Roberts
> | I'm expressing the well known theorem mentioned by Einstein, Brian Greene and numerous other physicists that everything in the universe moves at constant velocity c, where that velocity is the vector sum of its spatial and temporal velocity. |
That's no theorem, and describing it that way involves bending the meanings of words so much that the whole description is useless. In particular, "velocity in the time direction" is meaningless (because velocity is DEFINED as a spatial distance divided by a temporal interval).
This is merely a fanciful description of the fact that any timelike object's 4-velocity always has norm c. This includes Brian Green, who is writing for a popular audience and has "dumbed down" his writing; I doubt Einstein ever described it that way.
> | I say: The time I read or compute on a moving clock is a coordinate time. |
This is wrong. The time a clock displays is ALWAYS its proper time -- THAT'S WHAT THE WORDS MEAN.
Coordinate time is ALWAYS the time coordinate of some coordinate system -- THAT'S WHAT THE WORDS MEAN.
> | under your conditions my coordinate time would be equal to my proper time - but why would anyone even bother except to confuse the issue? |
This is not "confusing the issue", this is using words in their normal way. Here's the key: proper time is only defined along an object's (clock's) worldline. Coordinate time is defined throughout the region in which the coordinates are valid.
In particular, it simply is not possible to directly compare the proper times of two clocks unless they are co-located and co-moving. But if you are moving inertially, and construct an inertial coordinate system using your clock for its coordinate time, then you can compare the proper time of a clock moving relative to your coordinates to the COORDINATE time you constructed (which involves disseminating it throughout the entire region of your coordinates, not just on your worldline).
> | I said if I read a time on a clock MOVING relative to me, that's a coordinate time. |
This is wrong -- see above for why.
> | Yeuro, Again it may just be your screwed up terminology |
His terminology is not "screwed up", YOURS is.
> | [to yeurohenry] If you�d just said it as I did it would have been clear. |
No. If he said it as you did then it would be WRONG.
For reference, I repeat:
You seem to have confused yourself because a given observer can carry a clock displaying her proper time, and she can ALSO construct a system of coordinates using her own clock to define the time coordinate. This last, of course, requires her to disseminate the time coordinate throughout the region of the coordinate system -- that is straightforward if and only if those coordinates are an inertial frame.
Tom Roberts
> | [to yeurohenry] Anyway enough of this. You'll never understand and I'm wasting my time... |
Finally you said something that is clearly correct. Yeurohenry already understands SR, but will indeed never understand what you are trying to say, because what you are saying is muddled and wrong. Ditto for me.
You are indeed wasting your time. You need to STUDY. Just making stuff up, pretending it is true, and posting nonsense to the net is CLEARLY a waste of your time.
Tom Roberts
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