Brian Cox

Ohhhhh... so it's about the amount of energy needed to get somewhere. And that's not just "intuitive", its' actually mathematically correct?

One thing the cox "lecture for the stars" or whatever, helped me finally understand is they say "all electrons everywhere are connected". I don't really *get* it, but at least it doesn't sound as out of the ass as it did before. all electrons, everywhere must operate as a different energy level (this is the part I didn't get -- why??) so if i change the energy level of one, the entire universe's must shift, at least fractionally, in response.

i'm not sure I "buy" it, cause why must everything, everywhere hum at a different frequency, but at least it has a theory i can say "ah." to. rather than just hearing Al-Khalili say "QM is freaky, every election is connected to every other one - communicating" which just sounded way too magical and wooie.

I suppose you could say it's about the energy. I wouldn't quote me on that, but it's probably a fair thing to say. If you speed up close to the speed of light you need to apply more and more energy - eventually to move at the speed of light you either need infinite energy or ZERO mass (like photons, although Cox likes to explain it as photons must travel at the speed of light because they have no mass). So by the above token of "now" being something that extends from us at the speed of light, to get anywhere "now" you need infinite energy - to get anywhere in "a bit from now" you need finite energy. And using less energy is means its easier to get there from here.

As for electrons, I wouldn't worry too much about the "connected to the whole universe" thing if you can't quite get it. It takes you to interesting conjectures like the thought that there's only really one electron and it's moving back and forward through time along different paths and that is what makes the universe - crazy, unfalsifiable, but interesting nonetheless. The exclusion principle makes more sense if you just consider energy levels around an isolated atom and that they fill up one by one... BUT there's no such thing as an isolated atom. If you actually look at the equations that govern what an electron's wavefunction is like, it actually never reaches zero anywhere (apart from nodes, but those don't count for this), it actually goes on to infinity.

Now, in the Copenhagen interpretation of quantum mechanics, which just says that this wave stuff is just a probability distribution, this means that an object could, just randomly, jump anywhere - and you saw Jonathan Ross try to work that out for the diamond. The further away, the less likely it is to do so because that function tails off so much. If you go by the visualization I tend to use because I work in chemistry and not particle physics, which is that the wave is electron density, then that means the electron is more like a distributed cloud that doesn't really end at all, it just thins out to zero density only at infinite distance. So the electrons in my fingers hovering a few centimetres above the keys on this laptop are still actually touching the electrons on the keys. And worse still, they're also touching you - albeit very very gently :P. You know that whole "not touching can't get angry!" move? Quantum physics says otherwise. So yeah, while you might only think it makes sense when you isolate an atom and look at the energy levels in isolation, in the real world they really do extend to infinity and take into account all the electrons in the universe.

That's not as big a leap as you might think. Imagine we have the electron around a hydrogen atom (and it's the only atom in the universe), then we have one energy level. Next add another hydrogen and an oxygen. Now we have just under a dozen of them, all interacting in a water molecule, which is the only molecule in this hypothetical universe. Now add another water molecule and you wouldn't have much trouble thinking that perhaps one molecule interacts with the other - indeed they do because there's an electrostatic interaction among other things. But then add another molecule, then another, and another... they all still interact, with the interactions gradually getting weaker with distance but never actually to ZERO. In fact, in solids there's an approximation called wp:band theory that does just this and models all the interacting electrons as continuous bands of energy rather than discrete energy levels (for simplicity), precisely because they all interact on some level and pack tightly to form what looks like a continuum - the individual levels are still there in reality, of course, but we'd be damned if we can separate them out easily. While band structure is just a model for working with a solid, but the principle behind it actually applies to the entire universe, all the electrons are interacting in some way, however small. They're all jostling for their place in this great big band of energy because no two can occupy the same space.

As for why they can't occupy the same space, that's just a Law of Nature. I can tell you that if it didn't exist that the universe would simply collapse in on itself and nothing interesting would happen, but that doesn't explain "why" as such.

It fully makes sense that you can't occupy the same space, if only cause that one makes sense in our real world. My cat wants to sleep on my bed - I move for her. But i'm not sure why that means they all must have slightly different energy levels. energy is space?

Also, i *think* either one of the BBC horizin shows, or even BC himself on his talk tried to explain the one electron thing. those are moments when I just shake my head, and wonder how insane physicists are.

Well, bosons can occupy the same quantum state. That's how lasers can build up their intensity. And also how deuterium behaves very differently to hydrogen (protium) - as do the main isotopes of helium, where only one exhibits superfluidity.

That's not really the same as "same space", though. Different atomic orbitals overlap significantly in space, but won't necessarily have the same state or energy.

Louis CK puts it best: "Because if it wasn't, there'd be giant ants with top hats dancing around. There's no room for all that shit."