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.
It’s partially that – when the universe cooled down sufficiently about 380,000 years after the big bang, during the so-called recombination 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, where a photon produces an electron and a positron.
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 e[sup]inθ[/sup], 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; 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.
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.