Looking at this forum I notice physics can be discussed here. May I make some comments on Dr. Dick's thought experiment described at physicsforums.com:
Dr. Dick asks that the reader think of an experiment; the simpler it is the easier the math will be.
He suggests analyse it from any standard space-time frame of reference one finds convenient.
He says the experiment would involve a number of things travelling along trajectories in space-time. He says take arbitrary start and finish points for these trajectories.
He says each of these trajectories may be discussed in terms of a parameter along their length say for example "p".
He says that any given line in the experiment may be described by events which constitute that line; for any given p the space-time coordinates correspond to the collection of events (x,y,z,t)p.
He says these can be seen as continuous functions of p or as tabulated selection of a finite number of events; that either perspective is a reasonable representation of the space-time path of the thing of interest. He says do this for each thing in the experiment.
His "p" covers the whole line. So it is an invariant characteristic; like a pre-set bias that survives the whole length of the line.
How can a "p" have space-time co-ordinates?
I guess he is saying the "p" is the whole line (which is a sample of a trajectory so a "line element"?) and that "p" is defined by the interaction of x, y, z, and t over that line.
That is: the slice of t (time) covering the line and whatever juggling went on of x,y, and z during that time-slice would describe his fixed "p".
He says do this for each thing.
So you get a selection of samples where each projects a defining characteristic "p" that is unchanged throughout its own limited time-slice of x,y,z juggling.
He doesn't say if the various "p" s can overlap or share defining characteristics other than that they all supposedly share a fixed graph x,y,z,t.
He then says let us examine the paths of those entities of interest, each by itself, in the absence of the others. "The differential path length along the trajectory is exactly what is referred to as Einstein's invariant interval along the path of the thing being represented by that path. This fact is commonly used in high energy physics to determine the expected apparent path lengths (in x,y,z space) of particles with short half lives."
comments see next post...