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Washoe
07-22-2011, 03:15 PM
Be forewarned that I will issue a fatwa on the first person who says “when a daddy electron and a mommy electron love each other very much…”

But seriously—I’m having a hard time putting together a cogent picture of how this works. Let’s say that 30 neutrons and 30 protons get together and agree to form the nucleus of a zinc atom. Where do the electrons come from? Are electrons floating freely all around us, and the nucleus acts as a magnet or trap for the electrons, analogous to a strip of fly paper suspended in a swarm of flies? Wiki has this article on the Dirac sea (http://en.wikipedia.org/wiki/Dirac_sea) which appears to indicate that this is indeed the case. Are they moving when they float freely? How fast? And the most burning question of all, at least to my enfeebled mind, is how is it that the charge on an electron is exactly the right strength to both counter the charge on the proton and ensure a 1:1 correspondence of the number of protons to number of electrons in the atom? Seems like a hell of a coincidence to me.

Chronos
07-22-2011, 03:44 PM
In your example, where are the neutrons and protons coming from?

Washoe
07-22-2011, 03:51 PM
Yeah, I think I maybe see what you’re driving at. But for now let’s just say that they magically appear out of nowhere.

Shagnasty
07-22-2011, 03:58 PM
My friend is a proton so I just asked him where electrons come from. He said that the stork brings them. When I asked him if that is really true, he said yes, he is positive.

Washoe
07-22-2011, 04:09 PM
Great. It’s already degenerated into a nucleon jokefest. :( You should all be thrown in jail for making bad puns, but I’m not sure what the charge would be.

Uncertain
07-22-2011, 04:18 PM
Neutrons decay, emitting an electron and becoming a proton, fairly rapidly (half-life about 20 min.). Perhaps that's a partial answer to your question.

Indistinguishable
07-22-2011, 04:37 PM
Yeah, I think I maybe see what you’re driving at. But for now let’s just say that they magically appear out of nowhere.
Then the electrons can magically appear out of nowhere as well...

It's not impossible to have a bundle of protons and neutrons without corresponding electrons. That's just a positively charged ion... If there were electrons around to be attracted to it, they'd, well, be attracted to it, but otherwise, so far as I'm aware, there's nothing forcing electrons to be created for this purpose. Were you under the impression that they would be?

[Disclaimer: I don't know what I'm talking about.]

Giraffe
07-22-2011, 04:49 PM
But seriously—I’m having a hard time putting together a cogent picture of how this works. Let’s say that 30 neutrons and 30 protons get together and agree to form the nucleus of a zinc atom. Where do the electrons come from? Are electrons floating freely all around us, and the nucleus acts as a magnet or trap for the electrons, analogous to a strip of fly paper suspended in a swarm of flies? Wiki has this article on the Dirac sea (http://en.wikipedia.org/wiki/Dirac_sea) which appears to indicate that this is indeed the case. Are they moving when they float freely? How fast? And the most burning question of all, at least to my enfeebled mind, is how is it that the charge on an electron is exactly the right strength to both counter the charge on the proton and ensure a 1:1 correspondence of the number of protons to number of electrons in the atom? Seems like a hell of a coincidence to me.

The example you're describing is what happens in extremely high temperature plasmas -- atoms become fully ionized, i.e. all electrons gain enough energy (through collisions with other particles) to escape the pull of the atom, leaving behind just the nucleus. So then you indeed clusters of protons and neutrons in a gas of free electrons. But those electrons came from somewhere, they aren't just hanging around, waiting to make atoms with free nuclei. (Ignore the Dirac Sea thing -- that was just a hypothesis that doesn't actually make a lot of sense.)

The nucleus does act like a magnet for free electrons: a fully stripped ion is very attractive to electrons, which is why you only see fully stripped ions in very high temperature plasmas. Any cooler, and at least some of the electrons would either stay bound or immediately rebind to the nuclei. Remember, electrons fill energy levels in order of lowest energy to highest (1s, 2s, 2p,...). So the highest energy electrons (valence electrons) may not take much energy to dislodge (this in fact happens all the time in your body at room temperature), but the more electrons you remove, the harder the next one is to get loose.

As for the incredibly convenient symmetry of electrons and protons having the same charge, that's not a random coincidence. Particle creation has to obey quite a few symmetry and conservation relations, one of which is charge conservation -- you can't turn energy into mass without a net charge of zero.

Indistinguishable
07-22-2011, 04:52 PM
And the most burning question of all, at least to my enfeebled mind, is how is it that the charge on an electron is exactly the right strength to both counter the charge on the proton and ensure a 1:1 correspondence of the number of protons to number of electrons in the atom? Seems like a hell of a coincidence to me.
(Bolding mine)

What do you mean "both"? If the charge on the electron is the same strength as the charge on the proton, then you get a 1 : 1 correspondence when the charge is all countered; these aren't two separate conditions, so far as I can see. So the "coincidence" is just that protons and electrons have the same magnitude of charge. Which doesn't seem so surprising for me; the symmetry seems more reasonable than having them be close but slightly different or whatever... Indeed, given that charge is quantized, it seems to me no surprise that we would see exactly equal charge strengths in various particles; it just means they have the same discrete multiple of the charge quantum.

paperbackwriter
07-22-2011, 04:58 PM
Great. It’s already degenerated into a nucleon jokefest. :( You should all be thrown in jail for making bad puns, but I’m not sure what the charge would be.

It's obvious, isn't it? 1.602176565(35)×10−19 coulombs (http://en.wikipedia.org/wiki/Electron_charge), of course.

Washoe
07-22-2011, 05:12 PM
Then the electrons can magically appear out of nowhere as well...

Well, basically I was giving nucleons the “privilege of pre-existence” just because they stand still and the electrons go zipping around them. It just seemed intuitively picturesque to have the electrons flying around loose until forced to behave by the presence of a nucleus. So am I to understand that everything was paired up from the git go—when all the hydrogen in the universe was created everything matched up perfectly and everybody got picked for the soccer team—there were no loose particles left floating around?

tellyworth
07-22-2011, 06:23 PM
Neutrons decay, emitting an electron and becoming a proton, fairly rapidly (half-life about 20 min.).

That's only strictly true of free neutrons, right?

Khadaji
07-22-2011, 06:56 PM
I'm not supposed to say but ... I make 'em in my back yard at night. Please don't tell anyone.

leahcim
07-22-2011, 07:17 PM
That's only strictly true of free neutrons, right?

True.

The best explanation I've heard of why neutrons are stable in the nucleus is because the decay of a neutron creates a proton, which will be co-located with the rest of the protons in the nucleus. But because of the Pauli Exclusion Principle, this new proton will need to be in a different state than the protons already there. The protons already in the nucleus generally occupy all of the lowest energy states, so the new proton would have to occupy a higher energy state than all the others. This extra energy requirement means the energy of the decayed state is now higher than the energy of the undecayed state so it doesn't decay.

Dr. Strangelove
07-22-2011, 07:51 PM
Indeed, given that charge is quantized, it seems to me no surprise that we would see exactly equal charge strengths in various particles; it just means they have the same discrete multiple of the charge quantum.

Okay, but why is charge quantized? It was certainly surprising at the time this was discovered by Millikan. And why isn't the case that protons have, say, 1,037 units of charge and electrons 1,038 units?

In fact, one could argue that the charge on an electron isn't really the true elementary charge; quarks come in multiples of 1/3 the elementary charge. You'll never see a free quark but bound ones sure seem to exist, so it seems reasonable to say that e/3 is the true charge.

A proton has two up quarks and a down which add to e, but did it "have" to end up this way? I guess it probably did, but I'd also guess that you'd need to have a very serious understanding of quantum mechanics and the standard model to know why. Same goes for the electron.

Indistinguishable
07-22-2011, 08:13 PM
Hey, I'm not saying it has to be this way. I'm just saying, I don't find it particularly mind-blowing a coincidence. Yeah, the proton has 4 - 1 quantums of charge and the electron has -3 quantums of charge and thus they match. You could imagine things having been different, of course, but it doesn't make me go "Whoa! What're the chances of that exact a match?!". It just makes me think that if I had a more serious understanding of quantum mechanics and the standard model, the "coincidence" would dissipate even further. (Not fully, never fully; we could always imagine the physical laws having been different. But to the point where it seems to arise naturally from a fairly non-contrived system of rules)

Chronos
07-22-2011, 10:07 PM
Okay, but why is charge quantized?Well, for one thing, if it's possible to have magnetic monopoles (and all indications we have are that it is, albeit extremely difficult), then charge quantization follows from angular momentum quantization, which is about the most fundamental thing in quantum mechanics.

To clarify: Electromagnetic fields can carry momentum, and can also, under the right circumstances, have angular momentum. If you take a point electric charge and a point magnetic monopole, and calculate the electric and magnetic fields generated by them, and then add up the angular momentum due to those fields, over all of space, you'll find that it's nonzero, and is proportional to the product of the two charges (though it does not depend at all on the distance between the particles). Like any angular momentum, this angular momentum in the fields must be quantized. But since it's proportional to the product of the charges, this means that electric charge and magnetic charge must also be quantized.

Note that since we've never (well, aside from that one time at Stanford, but ignore that) observed a magnetic monopole to measure its charge, this doesn't actually tell us what the quantization must be (other than, obviously, being an integral factor of the electron charge). It could, for all we know, be the case that an electron is exactly 927 charge quanta, or the like, in which case magnetic monopoles must have a charge 927 times larger than we think. But given that nobody (or at least, nobody not at Stanford) has ever observed anything that wasn't an integral multiple of the electron charge, it's simplest to just assume that that's the quantum.

leahcim
07-22-2011, 10:32 PM
Okay, but why is charge quantized? It was certainly surprising at the time this was discovered by Millikan. And why isn't the case that protons have, say, 1,037 units of charge and electrons 1,038 units?

In Kaluza-Klein theory, a compact fifth dimension (compact meaning that if you travel a small distance in that direction you come back to where you started) is added to the standard four and tries to extend general relativity on that background. It turns out that you can recover gravity and electromagnetism from that framework if you posit that the electromagnetic charge is proportional to momentum in this new dimension you've added.

Applying quantum mechanics to this framework, you now have wavefunctions over this compact dimension with momentum in that direction (and therefore charge) proportional to the frequency in that direction. Since the dimension is compact, the wavefunctions are essentially standing waves in that direction, and standing waves have quantized frequency. So momentum in that direction is quantized. So charge is quantized. And there ya go.

Kaluza-Klein is no longer the cutting edge theory, but it was the first of the "Hey, let's add some compact dimensions to the universe to see what happens" theories, and later theories incorporate similar ideas.

Indistinguishable
07-22-2011, 11:50 PM
But given that nobody (or at least, nobody not at Stanford) has ever observed anything that wasn't an integral multiple of the electron charge, it's simplest to just assume that that's the quantum.
I thought quarks had charge 1/3 and 2/3 times the electron charge?

Chronos
07-23-2011, 01:38 AM
And nobody's ever observed an isolated quark. The only way that quarks are ever observed is in composite particles with a total charge an integer multiple of the electron's.

Indistinguishable
07-23-2011, 01:40 AM
Ah, I didn't realize that. Is it supposed to be even theoretically impossible for quarks to stand alone?

JWT Kottekoe
07-23-2011, 02:01 AM
Ah, I didn't realize that. Is it supposed to be even theoretically impossible for quarks to stand alone?

Yes, that's called "quark confinement". The quantum chromodynamic force that binds quarks in a proton, neutron, or other strongly interacting particle gets stronger as the quarks are separated (unlike gravity, more like a rubber band). If you pull too far, there is enough potential energy to cause the rubber band to break, creating two new quarks, which snap back like the ends of the two halves of the rubber band. The quantum chromodynamic analog of electric charge is called "color", which comes in three kinds and the theory predicts that any isolated particle must be colorless, which happens in a proton when the colors of the three quarks add up to "white" or in a meson, where the two quarks have opposite colors.

Half Man Half Wit
07-23-2011, 05:15 AM
So am I to understand that everything was paired up from the git go—when all the hydrogen in the universe was created everything matched up perfectly and everybody got picked for the soccer team—there were no loose particles left floating around?
It's partially that -- when the universe cooled down sufficiently about 380,000 years after the big bang, during the so-called recombination (http://en.wikipedia.org/wiki/Recombination_%28cosmology%29) period, it became energetically favourable for electrons, protons, and sometimes neutrons to hook up, generating the first stable atoms -- mainly hydrogen, but also some slightly heavier elements, like helium and a bit of lithium. These later clumped together under their own gravity, forming the first stars, which started the cycle of heavy element production.

But of course, electrons can be 'produced' even today: the vacuum is permeated by quantum fields, one of which is the electron field; an electron (or positron) is simply a quantized excitation of this field, and thus, can be produced under sufficient conditions, as in pair production (http://en.wikipedia.org/wiki/Pair_production), where a photon produces an electron and a positron.

Okay, but why is charge quantized?
To give yet another answer, in physics, symmetries of a system are always associated with conserved quantities -- spatial translation symmetry, i.e. the fact that physics works the same 'here' as it does 'over there', gives rise to the conservation of momentum, rotational symmetry -- physics doesn't change when you rotate the entire system -- gives rise to the conservation of angular momentum, etc.

Electromagnetism exhibits a somewhat abstract, 'internal' symmetry (internal symmetry stands here as opposed to spacetime symmetry, which are things like the translations and rotations above; one might imagine a certain structure attached to each spacetime point, or 'internal' to it, that exhibits this symmetry), which is an invariance under certain transformations -- basically, rotations of a circle of unit radius. This gives rise to the conserved quantity 'charge'. Its quantization follows from a somewhat more technical argument -- glibly, one might say that it's simply quantized because we're doing quantum mechanics. Basically, it comes from the fact that these symmetry transformations can be realized in different ways, and these ways are 'labelled' by an integer, which gives the units of charge -- mathematically, one represents these transformations by a quantity such as einθ, where i is the complex unit, θ describes an angle of rotation, and n is the integer in question. (Wolfram|Alpha is helpful in visualizing this (http://www.wolframalpha.com/input/?i=exp%28i*1*45*pi%2F180%29); try to stick in different values for 'n' and 'θ', i.e the first and second positions in the exponential; θ must be given in radians, i.e. rotation by k degrees = k*pi/180 (for n = 1); observe that for higher n, the little red dot rotates faster around the origin -- this is related to how strongly a particle interacts with an electromagnetic field).

Indistinguishable has made several good posts explaining the connection between rotations, complex numbers, and exponentials on this board, but I'm unsure which one to point too in particular...

That both proton and electron have the same charge is coincidental, in a sense, in this picture, but it is sort of natural if you think of both as 'fundamental' (or at least, 'almost fundamental') particles, who get the smallest n possible (this leaves out the quark issue, of course). There are theories unifying the electromagnetic with the nuclear interactions, so-called grand unified theories, in which this makes somewhat more sense, but we don't know if any of these applies yet.

This relates to what leahcim above said in that the compact fifth dimension is circular -- the difference being that in Kaluza-Klein theories, the symmetry is a spacetime symmetry (translation along the fifth dimension), which means that you can find transformations that combine or mix it with other spacetime symmetries, which I believe is what is responsible for some of the problems with these theories.

leahcim
07-23-2011, 01:10 PM
Ah, I didn't realize that. Is it supposed to be even theoretically impossible for quarks to stand alone?

Not at room temperature anyway. Maybe in a Quark-Gluon Plasma (http://en.wikipedia.org/wiki/Quark%E2%80%93gluon_plasma).

Autolycus
07-25-2011, 02:10 AM
Not at room temperature anyway. Maybe in a Quark-Gluon Plasma (http://en.wikipedia.org/wiki/Quark%E2%80%93gluon_plasma).

I have a TV like that. The picture's a bit bright but I like it.

***

So yeah, first electrons, now quarks. Can we talk about leptons next, or would that be strange?

****

Quark is a fun word. Quark quark quark.