# Why does the Universe have a net charge of zero?

1. Aug 29, 2010

### seagull68

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?). But these two processes happened at different times in the early Universe as well as many other decays and reactions with quarks and leptons etc. in between. It all seems very convenient that the number of protons and electrons balance...

My tutor is not much help because this is a general science intro course, this isn't her speciality and outside the course requirements anyway, so any info is appreciated. Especially if I've got totally the wrong end of the stick!

Thanks

2. Aug 29, 2010

### mathman

Your question in a sense reflects one of the unanswered questions of cosmology, i.e. why is there any matter at all?

3. Aug 29, 2010

### BillSaltLake

Creation of excess lone protons directly from a neutral scource (or excess lone electrons directly) is considered impossible in any lab experiment done at present (charge conservation violation). If physical laws were the same at t = one microsec and later, then it would have also been impossible during those two pair production episodes.
However, the creation of excess neutrons (over antineutrons) is allowed (violates no conservation principles) and may have have happened around t = one microsec. If so, most neutrons soon decayed into an electron and proton (& a neutrino). Hence, an exactly equal # of charges now.

4. Aug 30, 2010

### Chalnoth

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 [URL [Broken] 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.

Last edited by a moderator: May 4, 2017
5. Aug 30, 2010

Uhm.
By the way.
Silly question.
Is the net charge of universe really zero? How can we now?

6. Aug 30, 2010

### Chalnoth

Any significant charge imbalance would lead to electrostatic repulsion overwhelming gravitational attraction. The electrostatic repulsion would have the exact same long-distance behavior as gravity, except with an opposite sign, and would thus lead to gravity appearing weaker when we compare observations of the strength of gravity in larger systems (solar system, galaxies) vs. smaller systems we observe here on Earth where we have the charge distribution under control. And no, by the way, a small electrostatic repulsion term wouldn't explain dark energy.

Of course, this doesn't mean that our universe is exactly electrically neutral. But it does say that any deviations from that are minuscule indeed, and if they exist, are likely due to where exactly you draw the boundary to our universe.