PeterDonis said:
...However, you should be careful in specifying exactly what this argument proves. It proves that any event on the third observer's worldline that has sent a light signal which has been received by some other observer, must "exist" (because it's been observed)...
Wait a minute--you've just left out the most important part: Brown and Blue share the same simultaneous 3-D space at an event where each one occupies a different 3-D cross-section of the 4-D universe. Further, Brown's simultaneous space includes one 3-D cross-section of the 4-dimensional Light Brown body, and Blue's simultaneous space includes a different 3-D cross-section of the 4-dimensional Light Brown.
PeterDonis said:
...It does *not* prove that the *entire* worldline of the third observer, including its extrapolation to "future" events that have not yet sent light signals to anyone, must "exist".
I take it from the way you stated this that you at least acknowledge that we have established that Light Brown, as a minimum, has been shown to exist at two events along his world line, one being simultaneous with Brown and the other being simultaneous with Blue while Brown and Blue share their intersection event.
In the interest of brevity I just indicated that by extending the experiment we could establish the same Light Brown existence for any arbitrary point along his world line--or with sufficient tedium (perhaps with the use of mathematical induction) we could establish the existence of Light Brown at a continuum of points along the world line, i.e., a 4-dimensional object.
PeterDonis said:
...But many of the claims you have made about the "block universe" strongly suggest, at the very least, that you are making the latter claim, which is not justified by your argument. That's why you have gotten pushback from several people here, including me.
Of course that is the claim I have made. A push-back is not unexpected.
And of course a stronger argument could be made, providing more explicit data, adding more and more observers with different Lorentz boosts, all intersecting in a way that shares one point from their respective inertial frames of reference.
The experiment can be further embellished by establishing an array of objects, spaced at specified distances from the Brown observer and all at rest in Brown's frame of reference (each accompanied by a clock, computer based controls system with appropriate algorithms for sending transmissions of various kinds of on-board information--two-way distance, computations, time marked videos, etc.).
Yet another array of objects can be sent out at the same velocities, programmed to travel to selected rest frame objects, then return to the Brown observer (all the while computing, storing and transmitting data).
Finally an array of objects travel at different velocities and finally all intersect at a specified event along with the Brown observer (similar to the above experiment).
Experiments could be conducted over and over again over a period of many years (although the distances and velocities do not have to be extreme--after all, experimenters have carried clocks on airplanes to verify time dilation).
If you give it some thought, you can probably come up with a better battery of experiments than I have proposed. I think you can see intuitively, without putting in specific numbers, that the outcome of these kinds of experiments would provide very strong evidence of 4-dimensional objects.