Curved Space-Time and the Speed of Light

[AWA]

I don't know what you are trying to say here.

You said:"it is possible to have non-inertial frames where the coordinate velocity is not c." and : "the point is that you simply cannot get physically plausible velocities non-locally".
I was just trying to rephrase it my way. But not succesfully I guess.

 

[yuiop]

If 'proper length' is loosely defined as the length measured by an observer in their locally Minkowski frame, then there's an infinity of them. And it's not a very useful concept for this very reason. ...

There is an infinity of coordinate lengths of an object because it depends on the relative velocity of the observer, but "proper length" is usually defined as the length measured by an observer at rest with the object being measured and this is a single value that all observers can agree on. In SR the proper length of a non-accelerating object can be measured using short measuring rods laid end to end (ruler length) or by timing light signals (radar length).

It seems more meaningful to use operational definitions - like Einsteins clocks and rulers, to which we can add radar and lasers.

While the proper length measured by radar is equivalent to ruler length for an inertially moving object, the radar length of an accelerating object even in flat spacetime can vary depending upon which end you take the radar measurement from. The ruler measurement is not dependent on the location of the observer as long as the rulers are at rest with the object being measured. Ruler length remains a true indication of the proper length of an object even when it is accelerating.

I agree with your sentiments here. Also, the discussion here was previously about "physical length" (the "proper" came later and is wrong). "Physical length" is an even sloppier and less useful concept.

The "physical length" described here seems to be the length measured by radar, and even in flat spacetime one object has an infinite number of "physical lengths" depending on the relative speed of the observer. Why should it be the least bit surprising or worrisome that in curved spacetime one object has different "physical lengths" depending on the relative position of the observer?

What I am looking for is "intrinsic length". This is the length that an object must have even when it is a gravitational field and different observers at different ends of the object get different radar lengths. I guess the nearest you can get to the intrinsic length is the ruler length using infinitesimal measuring rods at rest with the object being measured. Physical length is not usually defined clearly in the textbooks, but usually equated with proper length. However, I guess the coordinate length is the nearest you can get to a definition of physical length because to any given observer the coordinate length appears to be the "physically real" length of the object in every way that he can measure it, but other observers will have a different opinion of what the physical length of the object is depending on their state of motion. What I am trying to get at, is that in a gravitational field an object might have an infinite amount of radar lengths depending on where you take the measurement my intuition is that the object has a single "intrinsic length" rather than a sort of quantum mechanical fuzzy superimposition of an infinite amount of observer dependent lengths.

So earlier when I said physical length, it was a bit sloppy and perhaps I should have said proper length or ruler length.

Just kicking some ideas around here

 

[Austin0]

While the proper length measured by radar is equivalent to ruler length for an inertially moving object, the radar length of an accelerating object even in flat spacetime can vary depending upon which end you take the radar measurement from. The ruler measurement is not dependent on the location of the observer as long as the rulers are at rest with the object being measured. Ruler length remains a true indication of the proper length of an object even when it is accelerating.

Just kicking some ideas around here

Hi kev Just a couple of questions. Assuming constant proper acceleration; What is the basis of the difference of measured radar lengths in an accelerating frame depending on which end the signals are sent from?
A) SImply the result of the acceleration during the propagation of the signals
or
B) The assumption of a dilation differential between the clocks in the front and back?


A related question stemming from your posting in another thread regarding radar ranging of the radial distance [ length] between two points at different G potentials.
In that case you stated ; based on the assumption of invariant c that the distance "up" would be different than the distance "down" due to the greater dilation of the clocks at the lower potential. This is clear enough.
My question is: does the assumption of a constant c mean that it is not possible to actually measure the speed of a light signal in this situation. It seems reasonable that this would be the case. That even if you could momentarily synch the respective clocks that the difference in periodicity between them would neccessarily result in different measured speeds up and down. But in case there are other factors I may be missing I thought I would check.
I.e. Is it possible to measure the radial speed of light up and down the well ? And if so how??
Thanks