I was shooting the breeze with a co-worker about quantum physics, which neither of us really know anything. But, I had a question; if there is a minimum quantum “distance” of finite size, does that mean there is a finite number of other “spaces” that are adjacent to it. i.e., can something like a photon only travel from where it is to a finite number of other places?
I was thinking about sphere packing, where in 3-dimensions a sphere can have no more than 12 other spheres of identical size touching it. In other dimensions you have more or less.
I think that all depends on how many dimensions are really down there at the Planck scale. And also the shape of those dimensions (or space itself?). But, I dunno… I’m with you on the ignorance level.
Also fairly ignorant about this stuff, but I would say you can’t really say how a photon gets from point A to point B, Heisenberg’s uncertainty principle and all that. You can say a photon travels every possible route from point A to point B (with some being more likely than others), and collapses onto one when measured (the thinking behind Feynman diagrams, IIRC) or say that a photon exists in a probability wave function, where you can only specify the probability of a photon existing at a certain location. As for actually moving over these really small distances, I would think that the quantum fuzziness would be such that you get teleportation (quantum tunneling?), flitterings into and out of existence, etc., so you couldn’t say: “If a photon is at position (x0,y0,z0) it has these certain positions it can travel to.”
To my knowledge, there’s no limit in how things move that has to correlate to these lengths, it’s just that it is impossible to get information more accurate than 1 Planck Length. I think of it like an analog-to-digital conversion. Color in the real world has an infinite variety, but an 8-bit color scheme has to classify all of those in only 256 levels. When the difference between two colors is too small, you become unable to detect the difference.
It’s also worth pointing out that a proton is 10^20 Planck units, which means even subatomic particles are unfathomably enormous compared to a Planck unit. If a Plank unit was a millimeter, a proton would be 950,000 light years across (much larger than our galaxy).
There’s some small length scale (perhaps the Planck length, but not necessarily) at which our current understanding of physics no longer suffices and you need to understand quantum gravity to know what happens. Since we don’t understand quantum gravity, at this point the answer to questions like “Is space ultimately discrete?” would be a big “who knows?” I can tell you that at the level governed by ordinary quantum mechanics, we can still treat position as a continuous parameter.
It’s also important to remember, as otorophile eluded to, that a particle doesn’t have a well-defined position except at the precise moment we measure its position, and moreover in the real world we can never measure its position with perfect precision, and even if we could then it would be impossible to know its momentum (or, more precisely, it would be in a state where it no longer had a well-defined momentum).
If you move one PL north and the one PL east, you are now 1.4 PL northeast. Then you move one PL SW towards your original position and then you are at less than one PL from it. How does that work? How can space be discrete?
Only by being anisotropic, at least when we take “discrete” in the sense whose consequences you just pointed out. Which is a mess of a thing indeed, and why I think most lay-discussion of Planck length is probably horribly confused. But I don’t know anything about what the real significance of Planck length is, so I never know what to say when it comes up. Still, when tim314 says that position is still treated as a continuous parameter in ordinary quantum mechanics, I am set at ease that I was correct to be dubious (of the things non-experts tend to say about Planck length).
To add to what tim314 said: even in the realm of quantum field theory (which is the “upgraded” version of quantum mechanics that describes the highest energies and smallest scales), one still treats position as a continuous quantity. And the theory matches the relevant experimental data rather well, suggesting that there is at present no evidence for discrete space.
(And, hi again, SDMB. I’ve been, well, busy this past half-year.)
To reiterate, we don’t really know what happens at the Planck scale. But there are some situations in quantum mechanics that are weird in roughly the way you describe.
For instance, there is a fundamental unit for angular momentum. We call it “h-bar” (although it’s normally written as h with a horizontal line through the middle). And there are some particles for which if you measure any component of their angular momentum vector, you should get only two possible values, namely positive h-bar/2 and negative h-bar/2. (Note that the component of angular momentum can thus only change by a whole unit of h-bar.)
But say you have a particle where the angular momentum vector is aligned with the z-axis, so that if you measure the z-component of angular momentum you get + h-bar/2. What do you get if you measure the x-component? Common sense tells us it should be zero, but quantum mechanics tells us you can only get + h-bar/2 or - h-bar/2.
The answer is you measure + h-bar/2 half the time, and you measure - h-bar/2 half the time. What can I tell you? Sometimes QM is weird.
Of course, if space is discrete at the Planck level, it’d hardly be a surprise that we don’t see any evidence of it yet, at the scales we are able to probe.
But in general, for most questions relating to most of the Planck scales, the only answer we can give as yet is “I dunno”.
Welcome back, Pasta! To be honest I’ve been a bit too busy myself lately to notice anyone else’s absence, but it’s good to have you around all the same.
Believe it or not, your absence had been noted. It is good to have you back. You are one of those people with the ability to bring complicated matters to layman levels.
Which leads to another interesting question: if at the Planck scale space and time can be reduced to discrete quantum units…linear measurements…could angular measurements also be quantized, to avoid the 1.4 PL situation?
