If I’m informed correctly, Special Relativity does not presuppose any reason two bodies relative motion can’t be an infinitely precise value. And thus, their relative motion, time dilation and foreshortening are precisely related by the equations of SR. But consider the possibility that space and time are both quantized, perhaps at the units called the Planck length and Planck time. If two bodies had a relative motion of some exact number of Planck times per Planck length traveled (more or less a requirement of the assumption that spacetime is quantized), would the equations of SR return non-integer values for the time dilation and spacial foreshortening measured in Planck units? In other words, does space and time have to be infinitely divisible for the math to work?
So far, nobody’s even figured out how to make quantized spacetime consistent with quantized spacetime. We’re pretty sure that it happens somehow or another, even without us understanding how, but the details are anyone’s guess.
It should be emphasized, though, that “quantized” does not necessarily mean “in integer multiples of some smallest possible amount”. Charge is quantized, and it does work that way, and angular momentum is quantized, and it works in a way that sort of resembles that, but the energy in a bound state is also quantized, and it it doesn’t work in any way remotely resembling that.
What Chronos says is of course true. But note also that something traveling at 1 Planck length/Planck time is traveling at the speed of light, so it’s not as though something can be going at n Planck lengths/Planck time anyway. Well, other than n = 0 or 1.
It’s not widely thought that space and time need to be quantitized so that lengths/temporal intervals take on only integer multiples of certain values, however it is thought that an invariant scale may be desirable (e.g. a length that does not change between reference frames). Special relativity is not a good setting for an invariant scale, but there are variants which produce an invariant scale. For example adding a positive cosmological constant to empty space (de Sitter relativity) is a natural way to get a length whose value is not altered under a Lorentz boost.
Although, the length scale from the cosmological constant we’ve got is absolutely huge (one might even say cosmologically huge), and thus probably not suited for being a quantization length scale of any sort.
Does QM allow for singularities?
I am no expert in this, but I have read claims that Quantum Loop Gravity is consistent with Special Relativity and General Relativity.
I’m not sure all agree. I’m not sure of current standing of QLG in physics community. (As with String Theory, there has been no experimental confirmation. I’m not sure I understand its theoretical drawbacks, but there are some comments at the end of the wiki article.)
I guess there are problems proving that QLG is consistent with relativity. from the wiki above:
I guess it may be fair to say that LQG may be consistent with General Relativity. Maybe it’s easier to show it’s consistent with SR?
Which is specifically why I phrased it the other way around: number of Planck times required for each Planck length.
Well, that would only allow speeds of c, c/2, c/3, etc., and we’ve seen plenty of speeds that don’t match any of those. I suppose that you could have only speeds which are a rational fraction of c being allowed, but you’d need awfully big denominators for some of those fractions, and it’s tough to see how a theory could result in that.
And while you do occasionally see people proposing models of something-or-other that aren’t consistent with special relativity, they’re rare, and nobody takes them very seriously. Nor is it very hard to show that something is consistent with SR.
Whoops, so you did!
While I agree that this seems unlikely at best, it would seem naively to be inconsistent with special relativity, in that even if velocities were quantized to be a rational multiple of c, the length contraction and time dilation factors are not generally rational numbers.
That’s what I was trying (badly) to get across: if C is 10^43 Plank lengths every 10^43 Plank times, then just slightly below light speed would be (10^43)-1 Plank lengths, etc. Wasn’t there some attempt to detect quantization of spacetime by measuring gamma rays that had traveled billions of light-years from a distant quasar?
I will allow it.
Thank you … off to the store to buy some now …
What if [gobbledygook] spacetime is a Planck-length-grain gauge field lattice and the effects of relativity represent distortions in the lattice period (making the Planck value relative)[/gobbledygook]?
But Qadgop, you’ll lose all that tasty neutronium if you just let it go collapsing into black holes willy-nilly.
What does quantized mean?
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It means that some physical variable can only take on one of a set of discrete values, and can’t take any of the values in between. Charge, as mentioned, is the simplest example: You can have a charge on something equal to twice the charge of an electron, and you can have a charge equal to three times the charge of an electron, but you can’t have a charge equal to two and a half times the charge of an electron. So we say that charge is quantized.
A quantum leap, incidentally, is when a system changes from one of these discrete states to a different one, without going through any state in between (because there are no states in between). It’s most often used in reference to electrons in an atom changing energy levels.
I’m trying to see how that isn’t equivalent to the idea that quantization of a dimension means it comes only in integer multiples of a minimum value.
Are there examples unlike charge, where the dimension is quantized but takes values that are not integer multiples of a minimum value?
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Energy. for example, photons.
See Chronos, post #2.