seagull68 said:
Hi all,
Just studying the early life of the Universe so here is what I know that I think is relevant to my question - protons were built from the imbalance of quark/anti-quark annihilation and a matching number of electrons were left over after lepton/anti-lepton annihilation imbalance (surely not the same imbalance?).
It's not really all that mysterious. There exists an asymmetry in the laws of physics which caused the matter/anti-matter imbalance, but the symmetry that leads to conservation of charge is absolute. These are different symmetries, and as a result we have no reason to expect the breaking of the symmetry that leads to matter/anti-matter imbalance would also break the symmetry that relates to conservation of charge.
My more detailed answer is below.
The symmetry that leads to charge conservation turns out to be that physical law doesn't depend upon the complex phase angle of the underlying matter. This works through theorem[/url], where we find that whenever there is something about physical law that is such that if we make a change to the system, it doesn't change the behavior of the system, then that means that there exists a conserved quantity. For instance, if the laws of physics are such that I move from one place to another, but the behavior of whatever system I am studying remains the same, then momentum is conserved. If I observe some system, wait some amount of time, and observe the same sort of system again, and the behavior remains the same, then energy is conserved.
We understand these as having basis in fundamental law because if I take the exact same configuration of matter and change its location it in either time or space, the behavior of the system must remain identical (side comment: things get a bit more complex when we talk about General Relativity, but for any small-scale interaction this simple analysis is good enough, and there is an analog in GR as well).
The phase angle symmetry perhaps requires a bit more explaining. Basically, in quantum mechanics, all matter is made of waves, whether you're talking about an electron, a proton, a photon, or a person. Everything is described by what we call a wave function (frequently using the Greek character \Psi). One of the properties of this wave function is that it is
complex. That is, numerically, it is composed of a real part and an imaginary part. The complex phase angle is the angle between the two.
In other words, it's a statement that the "real part" of the wave function is somewhat arbitrary: we can pick any axis we want and call that axis the "real part", it just depends upon how we define things in terms of the underlying behavior. One might consider it analogous to the situation in real space where there is no unique direction that we identify as "forward/backward". Which direction of motion this indicates depends upon which way we are facing, but there is no difference in fundamental law between the "forward/backward" direction and the "left/right" direction. Similarly, if we take a quantum mechanical system, and add some complex phase angle to all of its parts, nothing about the behavior of the system changes.
From what we understand, this appears to be a fundamental law, and it turns out that this results in the conservation of electric charge. To see exactly
why is a whole other ballgame, but suffice it to say that this is a well-known proof in quantum mechanics.
By contrast, the symmetry that corresponds to conservation of the balance between matter/anti-matter is what is known as the "CP" symmetry. This is a combination of parity and charge inversion. That is, if this symmetry is obeyed, and I take a system, swap all of the electric charges (that is, replace the matter with anti-matter), and then also exchange left with right, then if CP symmetry is obeyed the system will act exactly as it did before. It turns out that this is
almost the case. For every electromagnetic, gravitational, or strong nuclear force interaction, CP symmetry is obeyed exactly, so far as we can tell. The weak nuclear force, however, does not. This means that nearly every interaction we ever observe obeys the CP symmetry, but we have observed a few interactions that do not. You can read up a bit more here:
http://en.wikipedia.org/wiki/CP_violation
If this symmetry is violated, then the amount of matter/anti-matter in the universe changes with time. That's exactly what must have happened in our early universe, however the conditions under which we've seen it violated so far don't violate CP symmetry enough to explain the observed imbalance between matter/anti-matter.