Can We Observe Our Own Past Through Reflected Light?

[JesseM]

1. If there is no naturally preferred frame reference (which I agree with), why would physicists need to use the term "preferred" in this sense"?

Because older theories imagined there was a preferred frame (aether theories of electromagnetism, for example), so they are usually making a pedagogical point about how relativity dispenses with the idea of any preferred frame. Also, there's always the faint possibility that future experiments will show relativity is wrong and bring back the idea of a physically preferred frame.

2. I'm not saying there is a basis for a for an absolute frame of reference. Mach's principle suggests there might be as an explanation for the 'force" of acceleration.

Relativity doesn't respect Mach's principle in this sense, in relativity an observer could decide if he was accelerating even if he was the only object in the universe. So, again, are you just arguing that there might be an absolute frame if relativity turns out to be wrong?

3. Exactly. A coordinate system needs fixed "landmarks". I'm not aware of any basis for such a system for entire universe in the traditional sense of space-time coordinates.

You don't need actual physical landmarks, you just need a well-defined hypothetical procedure which would allow you to create such landmarks, like the hypothetical in SR of filling the entire universe with a network of rigid rulers at rest with respect to one another, and clocks at every ruler-marking. Once you have figured out what the laws of physics should look like in such a hypothetical system, in the real universe you can figure out approximately where objects would be relative to such a hypothetical system by using things like delays for radar signals to bounce back or the amount of light you receive from certain astrophysical standard candles.

However, a coordinate system based on acceleration as a vector quantity might be possible. All inertial frames moving at the same velocity in the same direction (if that could be defined) would be defined by the same set of coordinates.

I don't understand what you mean here at all. How would "acceleration as a vector quantity" allow you to assign x,y,z,t coordinates to specific events?

 

[DrGreg]

I think some of the confusion in this thread is over different interpretations over the word "acceleration". Like almost everything in relativity, acceleration is a relative concept. It is $d^2\textbf{x}/dt^2$, but that depends on what coordinate system you choose to measure x and t in.

In special relativity (i.e. in the absence of gravity) all inertial observers agree whether something is accelerating or not. But they disagree over the magnitude of the acceleration of an accelerating object. So even in special relativity, a non-zero acceleration must specify which frame it is being measured in. However, there is the notion of proper acceleration, which is what an accelerometer measures and what an inertial observer measures if the object is momentarily at rest relative to the observer.

In general relativity, with gravity, (or even in a non-inertial frame without gravity), you are free to choose any coordinate system you like, so everyone disagrees about acceleration, even zero acceleration. Nevertheless, there is still proper acceleration (where now "inertial" should be reinterpreted as "free-falling"). So any free-falling object undergoes zero proper acceleration, but its acceleration in some other coordinate system may be non-zero.

That explains why there has been some disagreement in this thread over whether something is accelerating or not. Some people meant "proper acceleration" and others meant general "coordinate acceleration".