I Determining a stationary point of reference to base all absolute motion

[PeterDonis]

The theory of relativity predicts that the craft with the fastest clock will be one that is at rest with respect to us.

If we only take into account special relativity, i.e., if we assume that spacetime is flat, then that will be true, yes. More precisely, it will be true relative to us. But some other observer moving relative to us will say that his clock runs fastest, and our clock runs slower. Such comparisons of clock rates are always relative. (More precisely, they are always relative if we restrict ourselves to objects that always move inertially, i.e., zero proper acceleration. If we allow nonzero proper acceleration, we can get clock comparisons that both observers will agree on.)

But if we take into account general relativity, i.e., gravity, i.e., if we allow spacetime to be curved, then we can no longer make the general statement you make. Clocks higher up in a gravity well than us might run faster even if they are moving with respect to us. And note that, when we take gravity wells into account, we can get clock comparisons that are invariant, i.e., both observers agree on which clock is running faster, even if we restrict to only inertial motion.

But there will never be a clock that runs "the fastest of all" in any absolute sense. Even taking into account gravity wells, no matter what clock we pick, we will always be able to find one that runs faster. (And the same is true for running slow--there is no clock that runs "the slowest of all" in any absolute sense either.) So the thing the OP is trying to postulate simply does not exist at all.

 

[tsslieberman]

As I understand this experiment, we launch a space craft. Or a series of space craft, each with a different speed. We let each craft coast at its selected speed. They are all equipped with clocks.

From our vantage point at rest in a comfy chair at our home base we watch those clocks, paying close attention to the tick rates. Importantly, we correct our measurements for speed of light delays -- the Doppler effect.

We look for the craft whose [adjusted for Doppler] tick rate is the fastest of all of them. That one will identify our candidate "absolute frame of reference".

The theory of relativity predicts that the craft with the fastest clock will be one that is at rest with respect to us. That the "absolute frame" is our own inertial rest frame.

It predicts that the same will hold for anyone else who runs the same test. They will find that the "absolute frame" is their own inertial rest frame. If this seems strange, you will probably need to learn about the relativity of simultaneity before things make sense.

The point of a thought experiment is to apply the laws of a theory and see what that theory predicts. It is a way to explore the consequences of a theory. Special relativity predicts as above that there is no uniquely identifiable absolute inertial frame. Any inertial frame will do just as well as any other.

Thank you. I appreciate the thoughtful response.

 

[tsslieberman]

Thank you. I appreciate the thoughtful response.

 

[Dale]

if we launched a spacecraft that had propulsion and kept moving that craft to a point where it’s relative time, as compared to a clock on earth, ran the fastest, would that not indicate that it would be a stationary point?

No, that would only indicate that it is at rest relative to earth.

 

[PeterDonis]

No, that would only indicate that it is at rest relative to earth.

With the caveats I gave in post #51.

 

[Dale]

Clocks higher up in a gravity well than us might run faster even if they are moving with respect to us.

With the caveats I gave in post #51.

I think your caveats are going too far. If a clock higher up but moving runs faster then a clock just as high and at rest will run even faster than that. The fastest relative to earth will still be a clock at rest wrt earth, even in GR.

A better caveat would be that in curved spacetime there is no unique way to compare velocities at separate events. But I don’t think that caveat is worthwhile here.

 

[PeterDonis]

I think your caveats are going too far.

I agree that, if we are talking about a single gravity well and we pick a given altitude, the fastest clock at that altitude, relative to a clock at rest on the (non-rotating) gravitating body, will be the one at rest relative to the gravitating body.

However, this sense of "fastest" is still relative, and the caveats I gave still apply: a clock at rest relative to the gravitating body at a given altitude will not be faster than all moving clocks, only moving clocks whose altitude is not high enough above the at rest clock to compensate for the slowdown due to their speed.

In any event, the OP is trying to use "fastest" in an absolute sense, and there is no "fastest" clock in that sense. Pick any altitude you like, and find the fastest clock at that altitude, i.e., the one at rest relative to the gravitating body. You can still find a clock at a higher altitude that is faster still. And there is no highest altitude; space goes out to infinity. So it is impossible to find an absolute fastest clock--no matter what clock you pick, you will be able to find another one that is faster.

 

[Herman Trivilino]

Oh, I thought that if I traveled at near light speed, time would progress faster.

But you are already traveling at near light speed relative to, say, a beam of protons in the LHC.

Speed is not a property of the object that's moving. Different frames of reference will measure different speeds for the same object.

There is no experiment you can do to distinguish between a state of rest and a state of uniform motion. That's an idea first articulated by Galileo. (He described it quite eloquently in layman's terms, discussing what it's like to be enclosed in the hull of a moving ship on a calm sea. I encourage you to do a google search, it's a great read.) It was Newton's First Law. It was Einstein's First Postulate. In the hierarchy of physical law it now forms the Principle of Relativity.