The possible positions of an electron is more or less infinite. See, an electron’s “positon” is a probabilistic energy state. The grade-school concept of discrete little electrons orbiting a nice, round atom is totally incorrect, albeit useful. Since the electron has no actual mass or position, only a probability of so much energy being in a certain position, it exists in an infinte number of locations simultaneously.
This may or may not be limited by the Plank length, however, and even the plank length specifies that below that limit, nothing exists in the way we define “existance”.
Right, but you can represent numbers in the natural world. As you said, you can see an apple, and earth, a galaxy, or detect an atom, an electron, a photon, or even a quark.
How can you detect an infinity. I don’t need to tell you that infinity is not a number, and as Lib points out, it can be represented as such in mathematics, but it’s not a real number – rational, irrational or otherwise.
Is that circle round? Does the ratio of its circumference to it’s diameter equal pi? In pure geometry it does, but in reality it’s always an approximate.
You can have one apple, but not infinite apples (or an infinite apple). Can we have an infinite anything?
that’s the rest mass. equivocally it’s also 0.511MeV in terms of energy.
smiling bandit’s talking about heisenburg uncertainty where the locust of possible locations of an electron around a nucleus result in a cloud. Granted, the positions of the electron are infinite theoretically, it doesn’t prove the existence of infinity as the OP would dictate. You’re still modeling the positions discretely and yes theoretically there are an infinite number of places the electron can be, but it is the same as saying there are an infinite number of locations to exist in my house.
Sorry, this is hard to explain. The damn thing is so small its very existence is sort of a matter of probabilities. It is a particle, and therefore has mass, but it’s also just energy at the same time, and therefore doesn’t. It mean, it has mass, but that mass may or may not exist at any given point.
This is an aspect of phsyics which I dont’ totally understand. I’m not wholly convinced anybody does, but there are a alot of people who understand it better than me. If anyone here does (and I’m sure there are) please correct me if I’m wrong about some things.
Well, as pancakes3 mentions, it’s a matter of potential possible positions. So the particle/waveform is not in any one position, but in all of them, with a certain probability of any one position, at a given time.
Yes, but that specific position/state doesn’t exist until the electron waveform is collapsed. Until then, it might in any position at all, and is somewhat is all of them at once.
Err… would you believe… Yes? To both. At once. There could be one electron, ever, in the whole universe, which is simultanously in all neccessary positions everywhere. Or, there could be many electrons, each with a probability of being in a certain place at a certain time, if you like.
Anyway, going back to the OP specifically, there’s no easy way to observe an infinity. Even if an infinite amount of, say, bubblegum surrounded the universe, we could not actually observe it all at once. We lack that capacity. We could posit that an infite amount exists, but never prove it directly. By definition, nothing infinite can ever be measured or observed. We cannot measure it, because all we can measure with are numbers, and we can always add +1 to anything we’ve measured in that manner.
I think I see what you’re saying. I just posted this quote in another thread, but it’s applicable here as well: “The atoms or the elementary particles are not real; they form a world of potentialities and possibilities rather than one of things or facts.” Werner Heisenberg
And another quote, my favorite from a scientist: “Something unknown is doing we don’t know what.” Arthur Eddington
While this may be strongly conjectured, it’s far from certain, and definitely not ‘indicated by measurement’ – between the relevant energies and what we can now (well, could now) produce at the LHC are still about 15 orders of magnitude.
It’s true that you can’t probe lengths beneath the Planck scale, on account of every attempt to do so just leaving you with a very small and very hot black hole, but that in itself doesn’t prove a quantised space-time.
Infinity does pop up in nature sometimes though, like the infinite amount of acceleration required to reach the speed of light, or the infinite amount of time it would take for something from our point of view to fall into a black hole. But these aren’t really “real” infinities. To actually observe something fall into a black hole, we’d have to wait an infinite amount of time, and so the experiment would never end, and we’d never get a real measurement. It’s just shorthand for defining a very large number compared to all the other measurements in a problem.
Actually, I checked with someone and no, it appears electron orbital states are not infinite, since the Plank length limit means they will not, in fact, be infinte, although the possibilities are ridiculously huge.
One infinity which does and must exist, however, is the disatnce from the Event Horizon to the center of a Black Hole. by analyzing the redshift of light from around a Black Hole, we can deduce what happened to the light which did not escape. Well, as it turns out, the only possible explanation for the redshiting observed is that it must be extending over an infinite distance.
Of course, as I said, it’s impossible to actually observe this directly.
Even weirder thought: If you crossed the line of the Event Horizon, in some sense you’d never actually die, as you would spend an infinite amount of time being sucked into the central singularity. In another sense, you’d be instantaneously shredded and your atomic energy sucked God-knows-where.
You would die in normal (local) time. Particles do not take an infinite amount of time to fall into a black hole, it only looks like they do because of the enormous redshift.
