Electrons orbiting an atomic nucleus exist in a quantum probabilistic location. Are the actual measurements of that location infinite?

The strange behavior at the quantum level produces the rock that Dr. Johnson kicks when he refutes Bishop Berkeley.

In a Woody Allen movie, a young, frightened Woody couldn’t do his homework, because the Universe was expanding. His mother’s answer: “What is it your business?”

I’m not a physicist but I love the topic, and I don’t fully understand your question. What do your mean by “how much infinity can a finite mind handle before it simply explodes”? Also, infinity factorial is still just the same concept as infinity, right? Are you saying something like since space can be infinitely divided, there are an infinite number of possible places for an electron to be, despite having some sort of maximal constraints?

@ETpro Your mind may be finite, but mine isn’t!

@dpworkin Ha! Thanks for a great non-answer. :-)

@cockswain Yes.

@davidbetterman Then stare deeply into my eyes…

So….I’m lost. I mean, if all space can be infinitely subdivided, but “things” inhabit certain areas at certain times, what is the question now?

@ETpro I’m quite frank about not having an answer. That doesn’t mean I don’t enjoy thinking about it. I’m convinced, as perhaps Einstein was (though for him it worked out rather pathetically), that one day we will find the sheer orderliness in the froth.

@ETpro Okay, I’m staring…staring…staring…OMIGAWD!!!!!

The word quantum implies quantization. Though this has more to do with the states of an electron rather than the number of possible locations. The possible states do constrain an electron’s location, energy level, and spin so although the possible 4D locations are infinite (provided space and time isn’t quantized—some believe this) they are constrained.

That is the weird thing about subdivision. Many a philosopher has toiled with this idea.

measurements are finite but the infinite is always moving and can’t be measured,
and, Energy cannot be Created or Destroyed, but can be changed.
What you are talking as a reference point is all on the physical plane. The infinite, if it took up any space it would be a manifestation on the physical plane, but in reality it is not what it appears to be. the infinite is the soul of the physical universe, but is beyond physical form, and takes up no space.
in other words the infinite cannot be seen through a microscope and cannot be understood through thought.

@babaji What do you mean the infinite takes up no space? How did you figure this out?

I take it you’re referring to Feynman’s “sum over histories” formulation for quantum theory. As I understand it, this hasn’t yet been made fully rigorous mathematics. For the moment, it is a useful heuristic for physicists (as Dirac’s delta “function” used to be before it was reinterpreted as a distribution or measure). But it isn’t the only one you can use. Nick Herbert’s book Quantum Reality lists four equivalent formulations: matrix mechanics, wave mechanics, Dirac transformation, and sum-over-histories. I know that he missed one, the phase space formulation.

this is too complicate. my infinite mind has reached its limits…...(BOOM!!)

I actually don’t have a problem with the concept of infinity that is written out in the context of your question. For example, infinity is used all the time in math integrals and although it’s been years since I’ve actually done a math integral, I had no problem back when I was taking advanced calculus.

Another somewhat related concept is the one of a singularity. Asking the question “what is the diameter of a black hole”? is meaningless because to measure a diameter, you’d have to communicate the measurement, and since you can’t communicate the measurement, for all intents and purposes, the black hole is a single point. That’s a difficult concept to wrap my head around, but I accept that black holes exist so I just nod and move on.

Similarily, you look at a finite distance, say a meter. You can divide the meter up into 100 subsegments (cm), 1000 subsegments, and so on . You can divide the meter down to an infinite amount of subsegments. But does that mean the meter is infinite? No.

That’s how I resolve the apparent conflict.

“God does not play dice” just because it appears probabilistic to us (the observer) does not mean there are not deterministic processes driving it from an angle we can’t see or detect (yet).

Uhmm, well, you see… it goes… oh nevermind

@Shuttle128 That’s where I was heading with this thought. If the location is truly quantized but electrons move, them must then move in step functions instantaneously from one position in space to another. I think things like energy levels and spin are all that are quantized. I’m just not ready for the weirdness involved if they lurch through infinitely fast small steps. BTW, Google’s quote for the day was, “This is one of those views which are so absolutely absurd that only very learned men could possibly adopt them.”—Bertrand Russell

@babaji You’re probably right.

@hiphiphopflipflapflop Yes, and if Feynman is right, then the multiverse is one REALLY big set.

@Rarebear I somehow have no trouble conceiving of a infinite number of divisions within a finite thing, because there, infiinite is just a mathematical abstraction. What toasts my noodle is thinking about projecting a line out in both directions infinitely long. That doesn’t like it could be, and yet at least as a thought experiment it must be.

@ARE_you_kidding_me I thought it made a catchy book title, but since we can’t prove that there even is a God, how can we be certain that God does not play dice?

Oh, I see what you’re getting at now. So if you look at the electron probability cloud around a nucleus, there is a statistically finite possibility, however unlikely, that an electron around a particular nucleus could be located across a galaxy, or even across the universe.

Feynman would tell you to stop being so philosawfigal and get on with your business.

@hiphiphopflipflapflop He would be right. :-)