It seems to be a common perception of quantum theory that it predicts that everything is quantized. And that the theory of relativity means that everything is relative. Yet no one seems to believe that the theory of gravity say that everything is gravity.
Well, I’ve actually studied quantum theory, and “everything is quantized” is definitely not something that I learned. Is anyone willing to defend the idea that everything is quantized? For starters, imagine a square with sides of one length quantum each. How long is its diagonal? If I accelerate something with a rest mass of one mass quantum to .5c, what is its kinetic energy?
But the problem you’re gonna have with this question, though, is that “distance” becomes a fuzzy thing down at the quantum level, where everything is probability fields and uncertainty and stuff. When someone talks about the universe being quantized, they mean to say that energy comes in distinct units- which it has to, or the photo electric effect wouldn’t function, the black box would generate infinite amounts of heat, etc, etc.
space and time aren’t quantized, neither is the frequency of electromagnetic waves (these are just a few examples of things that people may mistakenly believe to be quanatized by quantum physics), all of them (as far as is observable) are continious in quantum physics.
While I would not defend (nor attack) the statement that “everything is quantized”, there are plenty of physicists who feel that space and/or time are likely quantized. I lean in that direction myself (IANAP). There are a couple of reasons that I can think of why you may not hear as much about this point of view.
First, because we have no observable evidence (yet) of the quantization of space, for example, physicists tend to go with the conservative position of working with what seems to be the case as we know it now.
Secondly, for the current capabilities of our experiments assuming continuity is a perfectly good approximation for our experimental results even if it is not actually true. Not to mention that the assumption of continuity greatly simplifies the maths. Doing calculations where everything is quantized would be a real bitch.
As for the length of the diagonal of a quantum cube, Maximum C pretty much covered that. IOW, I would challenge you to find a quantum ruler with a well defined length to measure your quantum diagonal.
MC- I might be wrong on the technical details of this, but I dont think space can possibly be continious. I recall The Elegant Universe discussing how thinking of space as continious leads to a breakdown in the theory of relativity, but if there is a “smallest” unit, this doesnt happen. Quantum Theory and Relativity marry happily.
But a lot of really smart people think space is quantized, though they can’t prove it yet. Give the relationship between space, time, and motion, that usually leads directly to the conlusion that time is quantized, but again this hasn’t been proven (in fact I think it would be impossible to prove a quantized time except as a corollary of a quantized space, but that’s just a WAG. I haven’t really spent much time brainstorming experimental designs.)
I think a more accurate way of saying it is that a lot of really smart people (in fact, I would guess that it’s the vast majority of physicists) think that something quantum mechanical happens to space and time (you do need to have both, and not just one). What exactly that “something” is happens to be rather up for debate, in large part because we’ve no experiments to tell us. But, for all we know, space and time might come in packets, like electromagnetic radiation does, but packets of arbitary size, also like electromagnetic radiation does (that is, you can choose any frequency you want for a photon, even though photons are quantum mechanical objects). The general implications of that seem to be, to me, that it needn’t be the case that space has discrete jumps, just that space does weird stuff at the smallest scales.
How can you state this with such certainty? As others have pointed out, there is good reason to think space is quantized, and this has been neither proven nor disproven.
Other than the theoretical implications (and of course any resulting practical science), if it’s not easily observed on our macro and slow speed level, does it really matter for most of our lives?
But if space is quantized, then none of our approximations are valid. Anything including limits (eg, pretty much all of calculus) is kaput, as are irrational numbers and the isometry of space-time.
If everything works out the same as if space weren’t quantized, then it seems to me that Occam’s Razor would say it’s not quantized.
Maximum C
Seems to me that a quantized universe would be more difficult to square with relativity, not less. Every Lorentz transformation would have to transform integers to integers.