Main Question or Discussion Point
How does special relativity affect a quantized spacetime? Specifically, how can time and space be quantized the same way for all observers?
I guess there is no mainstream answer to this.Specifically, how can time and space be quantized the same way for all observers?
There IS a mainstream answer, and it's that it's not consistent with special relativity.I guess there is no mainstream answer to this.
That would depend on what you mean by a quantized spacetime. For instance, talking about LQG, it is just a popular misconception that LQG divides spacetime up into little chunks .How does special relativity affect a quantized spacetime? ...
Yes regarding chunks I see your point, but I guess the way I see it the notion of "quantized spacetime" is not unambigous in what I think of as "mainstream". This was what I meant. And if you suggested that there IS a mainstream sense, that in turn is inconsistent, then that still feeds the question on howto resolve it.There IS a mainstream answer, and it's that it's not consistent with special relativity.
A minimum length implies a breakdown of Lorentz Invariance at that scale. The reason is easy to see---in who's frame are you quantizing space? If I quantize space in my frame, and you come running by me really fast, then you see that my little chunk of quantized space is smaller by a factor of gamma. So "smallest chunk of spacetime" is a relative notion in special relativity.
I'm not sure I understand your question, if you have a question. LQG is a quantization of geometry which among other things is consistent with SR as far as we know. It does not involve thinking of space as consisting of little chunks That is not what "quantizing" geometry means.What I mean by 'the same to all observers' is that it should not depend on your velocity...
Does string/M-theory satisfy all 5? thxRegge calculus is sort of the historical forebear to the whole atom of space idea. You can retain lorentz invariance provided that there is enough residual symmetry left over in the marginal operators, not unlike textbook lattice gravity.
The problem really is getting these five (not necessarily independant) conditions to mix:
1) Lorentz invariance or at least lorentz breaking effects but only up to very small factors (which is very constraining and hard to do)
2) Flat spacetime in at least some sort of limit (as opposed to crumpled up phases)
3) Manageable entropy densities (as opposed to planckian entropy^4, which leads to ridiculous cosmologies)
5) Existence of a continuum limit.
All treatments known to date end up sacrificing 1 or 2 conditions, depending on the context.
Heh heh. In this case Savant, I would have to say that Haelfix knows a good deal more than you about it, so it seems odd for you to flatly contradict him without offering any link to peer-review literature. What technical article have you read about LQG, where it is defined? A simple one is Rovelli Upadhya LQG Primer. Look it up on arxiv. You will see that LQG is defined on a continuum representing spacetime. The operators representing geometric measurment have discrete spectrum, not the same thing as having a spacetime made of discrete bits. Please go back and read my post on this.LQG is definitely discrete
I agree with you about LQG, certainly. But sometimes I'm not sure what you mean by the words you use, Haelfix. Could you explain what you mean by saying that CDT is a "discrete theory"....LGQ is not really a discrete theory either. CDT is though!
in string theory, what are its predictions for a Planck-sized string accelerating toward c? Is string theory committed to infinitely continuous sub-planckian distances and time? In string theory, is spacetime classically smooth at arbitrary small distances?ST is not a discretization theory (atom of space idea) so it doesn't apply. Incidentally, LGQ is not really a discrete theory either. CDT is though!
I'm not talking about strings. Can we please stop dragging other theories into this?I'm not the best one to ask about that sort of question, im sure a stheorist could explain it better and with more authority.
From what I gather the question becomes illdefined. If you start probing the string (either via scattering or dumping energy into the free string) eventually past a certain point (not necessarily the planck scale, but thereabouts) you no longer are probing strings, but rather blackholes (b/c all that energy density eventually pushes the system past its Schwarschild radius). At that point, transplanckian physics is no longer well described by string theory, but becomes quasi classical again (eg GR.. scattering of blackholes and so forth).
In a certain sense, thats kinda what you want. It makes good sense that the degrees of freedom of a QG theory when pushed to the extreme breaking point eventually lose their significance b/c you can no longer ask questions about them since they lie behind horizons.
As for whether or not the spacetime is smooth. Well again, the question is a little fuzzy and only makes sense in certain limits. The metric is only part of the degrees of freedom of the whole (as yet to be understood) shebang, in fact its presumably not fundamental and therefore emergent. The main (string/brane) d.o.f as well as the precise nature of the moduli should in principle contribute to its dynamics, but like all emergent systems the technical details becomes really challenging. Still, since those d.o.f are decidedly quantum and fuzzy its a little hard to say with a straight face that spacetime is 'smooth'.. Its only 'smooth' when we make it so (by hand) as a sort of initial condition for calculational tractability.
Hi Savant, now I am beginning to make better sense of what you are asking about. Your question seems to make sense in a particular context of Loop Quantum Gravity. You indicate that by citing a Smolin book and by saying not to drag in string. If we can just limit things to a specific theory like LQG, then we can get clear more easily.I'm not talking about strings. Can we please stop dragging other theories into this?