1 In an SR universe do all inertial clocks run at the same (proper time) rate

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

2 In an SR universe do all 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.

But one must be clear: when I say "a clock's tick rate" I am discussing ONLY the clock. If you want to discuss how some particular observer or coordinate system will measure its tick rate, that is something else.

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

3 In an SR universe do all inertial clocks run at the same (proper time) rate

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:

The elapsed proper time over a (timelike) path depends on the path.

Tom Roberts

4 In an SR universe do all inertial clocks run at the same (proper time) rate

Yes, in this sense:

A clock ticks at its normal (usual) rate when it advances by 1 second for every 9,192,631,770 cycles of the hyperfine ground-state transition of co-located and co-moving Cs133 atoms.

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.

So experiments can test the predictions of SR and GR, which include predictions of how those signals and elapsed proper timed behave. But don't deceive yourself into thinking they "compare clocks' tick rates". Rather, they necessarily test all aspects of the physical situation.
For instance, in any comparison of clocks using signals, one finds that the predicted effects on measuring those signals account for the entire observation, so the clocks are indeed ticking at their normal rates.

Your attempts to discuss "the proper time rates of all clocks" is nonsense, because it is physically unrealizable.

One of the major lessons of 20th century physics is:

Don't attempt to discuss things that cannot be measured.

While generally associated with quantum mechanics, this applies to all aspects of physics.

Tom Roberts

5 In an SR universe do all inertial clocks run at the same (proper time) rate

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.

(See my recent post for more detail.)

Tom Roberts

6 In an SR universe do all inertial clocks run at the same (proper time) rate

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.

Also: you did not state how A determines "the transit time of that signal". But that does not affect your basic error.

>	[... further nonsense based on that error]

Tom Roberts

7 In an SR universe do all inertial clocks run at the same (proper time) rate

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.

Testing relativity is the province of physics, not astronomy.

>	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.

If you were really comparing proper times, you would not need to worry about Doppler. But you aren't, and you DO.

Tom Roberts

8 In an SR universe do all inertial clocks run at the same (proper time) rate

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

9 In an SR universe do all inertial clocks run at the same (proper time) rate

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.

Hint: If it didn't, it would not be a standard clock.

>	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 traveling twin is a DIFFERENT physical situation, with a DIFFERENT explanation, because the twin paradox compares elapsed proper times, not tick rates.

>	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

10 In an SR universe do all inertial clocks run at the same (proper time) rate

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.

Differences also arise when one compares the elapsed proper times of clocks that travel over different paths through spacetime. Not because they "tick at different rates", but rather because different paths can have different path lengths, which for timelike paths is elapsed proper time.

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

11 In an SR universe do all inertial clocks run at the same (proper time) rate

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

12 In an SR universe do all inertial clocks run at the same (proper time) rate

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.

Note you cannot compare your proper time to the proper time of that other clock. But you CAN compare your coordinate time to the proper time of that other clock. (This is only useful if your coordinates are inertial, unless you are very careful and make no mistakes in the complicated physical measurements and intricate math.)

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

13 In an SR universe do all inertial clocks run at the same (proper time) rate

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.