Suppose we wish to quantize space into Planck Length units
(10^-32 meters)
and Planck interval units
(10^-44 seconds).
As a hypothertical observer travelling at99.9999etc% the speed of light, would the observer begin to “see” the individual
“chuncks” of space-time, or would relativistic distortion keep
such observations continuous and non-quantum?
(bump)
Chronos?
(Last chance bump)
ANYBODY?
A quantum observer is pretty much limited to a single interaction within any individual quantum space time location, so I don’t see how this can be answered with anything but “either yes or no.” Each iteration of that yes or no is random, by the definitions of quantum mechanics. Coming back to macrocosmic scales is just an averaging of probability, not a determination of the individual phenomena.
It is entirely likely, though that I don’t understand the question, since I certainly don‘t understand the answer. 
Well, if you ask anybody, I guess that includes me.
In the traveler’s frame of reference, the size of the “chunks” would remain the same by the principle of relativity. For a stationary observer the uncertainty in the Planck scale dimensions for the traveler would be greatly magnified.
This sounds like the sort of topic that MIGHT be covered by Stephen Wolfram’s new book.
I’ll bite. If an observer were going sufficiently fast, 0.99999999etc. c, he would observe the entire universe in a single Planck Interval and relativistic contraction would compress the entire universe to a single Planck Length.
All of you folks are talking about 0.999999etc *C for a velocity…
I’ve always thought that 0.999999etc. (as in, '9’s forever) was equal to one.
In other words, is our observer traveling at a definite velocity (less than C), or is the observer’s velocity limited to C?
Not that I can offer any insight into the answer, of course, I just would like clarification of the question.
askol
askol, when we say that, we don’t mean an infinite number of 9’s. We just mean a large number of 9’s. How many 9’s? However many it takes to make our statement true. For instance, by my calculations, to compress the Universe into a Planck length, you’d need a γ of roughly 10[sup]58[/sup], which means you’d need a speed of roughly (1-10[sup]-116[/sup])c. So in Truth Seeker’s example, there should be about 116 9’s.
Concerning the OP, I don’t think you can just go and quantize spacetime. Maybe I misunderstand the question, though.
Achenar’s calculation suggests this is the maximum meaningful speed for any massive particle. (Though I can envision some complications regarding the actual “size” of the universe.) How massive a particle could be accelerated to this speed using all the energy in the universe? If this comes out to be something fundamental like the Planck Mass (~10[sup]-5[/sup] grams) . . .
BTW, we, of course, do not have that accurate an estimate of the actual amount of energy in the universe. I’d be pretty impressed, though, if it came out to be correct within a couple of order of magnitude.