Here’s a debate to bore the masses. In this thread Xeno’s paradox is being evaluated. Xeno’s paradox assumes that space and time are continuous. This tenet is congruent with general relativity. The proponents of other specialized disciplines, e.g., superstring theory, maintain that time and space are discrete. This tenet is congruent with quantum mechanics. (Just so people understand the nature of this “discretion”, the Planck length is 1.60605(10) x 10[sup]-35[/sup]m and the Planck time is 5.39056(34) x 10[sup]-44[/sup]s). General relativity and quantum mechanics are incompatable. So which is it? Are space and time discrete, continuous, or something else?
Unfortunately, the chosen parameters (Planck ranges) are what they are because our paradigm fails to describe the conduct of reality in a consistent fashion. What we need is a new paradigm. (That being fundamental in the nature of paradigms, of course, to always be needing a new one.)
The function of forces within the ranges of superstring theory can only be described in theoretical models. Direct observations (providing evidence supporting predictions made by those models) have been equivocal, until very recently, and still have only limited acceptance as reliably predictive. It seems we need bigger accelerators, and more powerful computers. (That being fundamental to their natures as well.)
One thing seems abundantly clear. Peeking over the Creator’s shoulder is . . . expensive.
Tris
“If we are going to stick to this damned quantum-jumping, then I regret that I ever had anything to do with quantum theory.” ~ Erwin Schrodinger ~
[pet peeve]
ARGH! You know, we hear all the time that GR and QM are incompatible. The people who tell us these things are… string theorists, who obviously have a vested interest in making people believe this statement, because it’s how they get their funding. It is not yet known whether the naive quantum mechanical theory of gravity (which is based on quantizing GR) is wrong; all that’s known about it is that the conventional methods for solving the equations won’t work, and we don’t have any good ideas about how to do things differently.
[/pet peeve]
That being said, I would argue that space and time are most likely to be quantized. It can’t be proven to be so, of course, but quantum mechanics gives us ridiculously accurate answers for the way things work for three of the four forces (electromagnetic, strong, and weak), and aesthetically, it seems rather unreasonable to suggest that there is no correct quantum mechanical description of the fourth force (gravitation). Any QM version of gravity will have to be consistent with GR on the scales where QM isn’t important, and if it is to do this, spacetime must be discrete. So spacetime is probably quantized.
Of course, this argument relies basically on aesthetic principles, and it could be incorrect. That said, a dirty little secret of modern theoretical physics is that most of it begins from principles of symmetry and aesthetics, and most of it seems to be right.
I believe that the original theory of atoms (literally Greek for “non-dividible”) was proposed to eliminate the paradoxes caused by presuming space was infinitely dividible.
I guess I agree with the quantum physicists who claim space/time to be granular. My gut feel is that everything is quantized.
They say that a distance less than the Planck length is meaningless, and that sounds a lot like a limit to me.
I also find appealing for some reason that human science has figured out the resolution of the universe, like it were a PC graphic mode or something mundane. I just think it’s neat.
PErsonally I suspect that some group of elementary school students 1000 years from now will be giggling over the “primitive” and “wierd” theories we have today for most physical phenomenon. Perhaps I am negative, but it seems that such is the march of scientific progress.
By the by, did anyone catch it that a recent study in PHYSICAL REVIEW LETTERS suggest that the speed of light has changed over the (billions of) years.
avalongod,, there was just a thread about that yesterday. Personally, I’m waiting to actually read the paper as opposed to hearing a Reuters summary, which is probably hopelessly inaccurate anyway.
Well, I should probably let this thread continue to fall like a turd from a vulture like it is, but I won’t.
Tris, long time no see. It’s good to see you again.
That is precisely what I believe. GR and QM are incompatible. That is a fact and not the nefarious workings of string theorists. String theorists are actually attempting to resolve the problem with a new paradigm, g8rguy. The question is, what’s the next step? Physics continually improves upon itself. Nothing is actually lost. It is simply refined. Here there is a dichotomy. Are space and time quantized or continuous? Logically it would follow that a new paradigm would serve to incorporate the premises of both GR and QM. Would this be something similar to wave-partical duality or something along the lines of continuity at a sub Plank length/time? Perhaps this is too much ungrounded postulation, but there may be something on a metaphysical level to offer insight.
Ahhhh…the most powerful force in the universe.
And Tris, your sig is just too appropriate here.
Lumpy, the Greek postulation of the atom did not prove the infinite divisibility of matter.
Oh, I quite understand that string theorists are attempting to resolve the incompatibility of QM and GR with a new paradigm. The problem is that there’s nothing inherently wrong with the existing one, aside from this little technical detail that quantum gravity is not perturbatively renormalizable. What this means is that the techniques that are around for solving the equations of quantum field theories can’t be applied very far. You can, IIRC (and I’ll check on this) solve them to low order and make testable predictions; I am not aware that these predictions have actually been tested because we don’t really know where to test them yet.
String theory postulates an (ever increasing) number of extra dimensions of miniscule size; I see no reason to adopt this viewpoint largely because it actually makes the theoretical problems worse until you do some other hokey stuff to bring these problems under control. They expect to have complete, exact solutions in (IIRC) 1-6 years now, except that they still have to define the problem. (unless there’s been a breakthrough in the last few months that I am unaware of).
In other words, being strictly precise, QM and GR must be unified in some framework or another, whether than be quantum gravity, string theory, or some other alternative. This framework will almost inevitably require quantization of spacetime, with QM recovered on one scale and GR recovered on another. But to say that the solution MUST be string theory is strictly wrong.
And no, QM and GR are NOT incompatible in that the only problem with quantum gravity is that it’s not perturbatively renormalizable.
Um, I didn’t.
Uh… true. Sorry. Methinks I got carried away.
slinks off sheepishly
Not that I’ve ever read. I seem to recall one with 11 dimensions and one with 26. (well, “one” is wrong because there are Tpes to the string theories).
In fact, one of the neatest things about string theories is that they are only consistent inside a specific number of dimensions.
Then you must hate quantum mechanics which works of huge-dimensional artificial spaces which are, essentially, limitless.
It is only wrong if string theory is wrong. Since it is possible it is right, anyone who claims it must be right is simply not supporting his arguments with facts.
Yes, quite. It used to be 10, actually, IIRC, and while I’m no expert on the history of string theory, the idea of extra dimensions is not a new one, and earlier in the century, there were 5D, 6D, etc models as well. But at some point, people decided on 11. Then 26 came up. There are some inklings that all five types of 11D string theory are connected into M theory. But while it’s been fairly stable for a while, there has been a lot of confusion about this. I’ve heard string theorists speculating (hopefully in jest) about negative, fractional, or imaginary numbers of dimensions as well. I think CalTech needs to set up a hotline so you can call them and they’ll tell you the current dimension of spacetime.
Entirely the opposite! In strict point of fact, QM is what I do for a living. The point, though, is that in QM, we have solutions of a problem in mathematical spaces; the simple fact that there are 6 coordinates for the hydrogen atom, so that we need a 6D wave function, doesn’t imply that the hydrogen atom exists in 6 physical dimensions, it merely means that the solution lies in a 6D Hilbert space. The hydrogen atom quite happily floats around in three spatial dimensions.
Contrast this to string theory, which proposes extra REAL PHYSICAL dimensions. That they are inaccessible is beside the point; adding physical dimensions at will only makes the problems one sees in quantum gravity worse. The way string theory ultimately gets around this is by postulating new forms of interactions (often, for example, the kind that are frowned upon is conventional field theory as being unphysical) that get rid of the problem.
Largely because of Occam’s Razor, I see no reason to do this when the only demonstrated shortcoming of quantizing GR is that it’s not perturbatively renormalizable. (This means, broadly speaking, that if you try to calculate something with Feynman diagrams for QG, you’ll get X + infinity - infinity + infinity - infinity … Note that if you reorganize your calculation properly, it’s entirely possible that you end up with getting, say, 42. In something like QED, you also get X + inf - inf + inf - inf. The difference is that you can play a shell game called renormalization and get the infinities to cancel out, leaving the interesting parts. In quantum gravity, this can’t be done the same way, but I am aware of no proof that it can’t be done at all.)
Conceded.
As far as the ten-dimensional/eleven-dimensional thing I believe there was always eleven, but people only referred to them as 10-D because of the 10 spatial dimensions, much like we use 3-D to mean, well, 4-D. Heh.
Uh, er, I did say “artificial” meaning, “not real.” Never-the-less, you’ll find some people are of the opinion that even if String Theory does “come true” that doesn’t mean that the universe is really 26D, merely that that is the only way we can describe it. :shrug: Damn philosophical interpretations of mathematics.
Hilbert spaces were exactly what I was thinking of when I said that, however. 
Interesting were your comments on renormalization. You don’t feel that that’s “cheating”?
Yes, I understood that. My point was simply that what standard QM postulates is strictly understood to be artificial (like, if I wanted to write a function that says where g8rguy and erislover are at the same time, I’d need more than 3 variables), where AFAIK string theory seriously postulates more physical dimensions, and I don’t see any good reason to do that unless you can’t make things work elsewise. This doesn’t mean that they’re wrong, of course, but adding lots of perhaps unnecessary complexity inclines me to believe that maybe they are.
Oh God, don’t even get me started on that! I mean, fine, yes, I believe QM works, and works exceedingly well. But I HATE some of the philosophical interpretations of it. Hate hate hate them.
Well, yes and no. I do feel that renormalization is kind of cheating, BUT:
a) it works.
b) the way it works is by noting that the parameters of the theory (i.e. the bare mass of an electron) needn’t be the same as what you actually measure, and I’d say that this is true.
c) it may be that if you solved the equations exactly, you wouldn’t have to cheat via renormalization anyway.
Interesting stuff. The way that QED gets solved is perturbation theory (basically, a certain type of series expansion), and actually… the series may or may not converge. It’s just that if you had infinite patience and infinite ability with algebra and calculus (drawing Feynman diagrams is easy; interpreting them gets to be very hard very fast), you ought to be able to get several hundred significant figures out of it before having to worry about convergence issues, and hey, if I can give you an answer accurate to 1 part in 10[sup]100[/sup]…
Well, in QED, you can renormalize order by order; in QG, you can’t do this, so QG isn’t perturbatively renormalizable. HOWEVER, the entire scheme is only an approximate way to solve the equations anyway, so what’s the big deal about not being able to make it work? I mean, okay, so if I try the simplest way I know to approximately solve the equations, I fail. I don’t see this as being a criticism of the theory as a whole, however.
QM says that time and space are quantized? That’s funny, I recall integrating and differentiating over those dimensions. Just how can you differentiate with respect to time if time is quantized? Just because a theory is called “Quantum” Mechanics doesn’t mean that it claims that everything is quantized, any more than “Heat” Mechanics claims that everything is heat. I really doubt that space and time are quantized, seeing as how that would go against pretty much every current idea of how the universe works. For starters, it would require an absolute frame of reference. And that’s just for starters.
Not to mention our spelling. Sorry, couldn’t resist.
Well, I believe the reason people claim that space and time are most likely quantized is that logically, the metric will be the quantum field for gravity (whether this be through string theory or some other means). If the metric is quantized, then doesn’t it automatically follow that spacetime is also quantized?
The reason, of course, that you can integrate or differentiate QM equations even if spacetime is discrete is that the scales of quantization would be so low as to be unimportant in normal QM applications. Hence, we could treat what’s really a Riemann sum as an integral, and what’s really a finite difference as a derivative.
We normally ignore relativity in doing basic QM, we normally ignore QM in macroscopic applications, so I see no reason that we shouldn’t be able to neglect a discretization of spacetime on size scales where spacetime is essentially continuous. I suppose what we’d end up with is an answer that’s correct in the limit that the Planck scales go to zero, just like we recover Newtonian physics in the limits of zero velocity and Planck’s constant being zero.