Is There a Total Electric Charge for the Universe?

[humanino]

Dear cosmologists,

how do we know the total electric charge of the Universe ? For instance the matter-antimatter asymmetry was a part in (say) 10 billions. But gravity is 40 order of magnitude less intense than electromagnetism, so I need an asymmetry 30 orders of magnitude less for electrical repulsion to just balance gravitational attraction. Even if we now have the same number of protons and electrons, there is no measurement (say) 50 significant digits for the equality of their charge. If their electric charge would differ by such a tiny amount, would not I expect 10% deviation in the global expansion rate ?

 

[Haelfix]

Its usually assumed to be charge neutral eg zero but that's a bit shaky, even if almost everyone believes in it.

One cute way of seeing it where the statement is exactly true. In a closed FRW universe, let's say you have some positive charge somewhere, and you draw lines of force emmanating from the charge. Since the topology of the closed universe is a 3 sphere, you can see that the force lines will want to wrap around the sphere and move to an antipodal point, where there must be a negative charge in order to preserve the shape.

Now, as for the flat or open case, well you start getting into particle physics and we can talk about baryon number conservation, CP conservation and perhaps more importantly the fact that the vacuum typically spits out both a particle and an antiparticle or at the very least a positively charged particle and an negatively charged particle.

Since we think that the universe's particle content comes from reheating after inflation, its hard to imagine the reheating physics somehow violating charge conservation (even if it must violate the matter-antimatter symmetry, perhaps via baryo or leptogenesis)

 

[humanino]

Thank you for your answer.

In a closed FRW universe, let's say you have some positive charge somewhere, and you draw lines of force emmanating from the charge. Since the topology of the closed universe is a 3 sphere, you can see that the force lines will want to wrap around the sphere and move to an antipodal point, where there must be a negative charge in order to preserve the shape.

So can I interpret that by saying that a single non-balanced charge in FRW universe will disrupt it !?

Since we think that the universe's particle content comes from reheating after inflation, its hard to imagine the reheating physics somehow violating charge conservation (even if it must violate the matter-antimatter symmetry, perhaps via baryo or leptogenesis)

Yes, I realize that if the initial state is perfectly chargeless, it entails violation of conservation of the EM current. So there are two possibilities by which it could arise : either such a violation beyond the standard model, but the experimental constraints to make sure it does not happen seem to me to be out of reach. The other possibility is just that the initial state had a charge. After all, it had angular momentum, and it was almost washed out by inflation, but not completely, and I am after something tiny.

I'd be interested either in references in the literature (which I failed to find), or if you have ideas for what an experimentalist could look for

 

[Haelfix]

The experimental numbers on the matter-antimatter symmetry violation must be beyond the standard model physics. You roughly need a rate something like ~ 4 to 10^11 protons to antiprotons+protons for instance.

The general gist is that you have to satisfy the Sakharov conditions. For current experimental bounds for a variety of different models, you should peruse a review article on baryogenesis and leptogenesis, there are a lot of them on arxiv and its a major field of research.

What numbers exactly are you looking for?

 

[humanino]

What numbers exactly are you looking for?

I was comparing this ~10^-10 to what I would need for electric charge asymmetry to just cancel gravity, and it seems to me something of the order 10^40 would suffice. I end up thinking I already have, from the observed dynamics, an upper bound at say 10^-50, but I have never seen that stated anywhere.

Of course, on the back of mind is the consequences a non-vanishing charge asymmetry on the putative cosmological constant

 

[Chalnoth]

Well, these sorts of tiny asymmetries in charge would be picked up by tests of the equivalence principle (basically, small charge asymmetries for protons/electrons would look like slightly different gravitational interactions for protons versus neutrons). But I think it's easy to see how these charges must be exactly equal if we just accept that electric charge is an exactly conserved quantity.

 

[deepak_poondi]

While it is true that electric charge repulsion has to be offset by 10^40 to balance gravitational attraction, is there any evidence of citing and tracking "dimensional" charge in this real universe ? While real charge can leave this universe, an equivalent amount of "dimensional" charge returns back to this universe at a "dimensional" time equivalent to the value of the charge that disappeared. However, when this "dimensional" charge returns it becomes real. But western literature argues against charge conservation in the univere which lends one to speculate if anybody has cited and tracked "dimensional" charge in this universe...

Can "dimensional" charge be generated by subatomic off-center particle collisions ?

 

[Chalnoth]

While it is true that electric charge repulsion has to be offset by 10^40 to balance gravitational attraction, is there any evidence of citing and tracking "dimensional" charge in this real universe ? While real charge can leave this universe, an equivalent amount of "dimensional" charge returns back to this universe at a "dimensional" time equivalent to the value of the charge that disappeared. However, when this "dimensional" charge returns it becomes real. But western literature argues against charge conservation in the univere which lends one to speculate if anybody has cited and tracked "dimensional" charge in this universe...

Can "dimensional" charge be generated by subatomic off-center particle collisions ?

What are you talking about?

 

[Chronos]

Electrical charges in the universe necessarily cancel out. The universe must be electrically neutral unless you are bold enough to spin the crackpot phyics wheel. Give it some thought.

 

[IsometricPion]

Models of the early universe eventually require the difference between baryon number and lepton number to be conserved (By eventually, I mean within some orders of magnitude of the time of the post-inflatory reheating period. It is conserved in all of the known interactions.) So it comes down to the charges on baryons and leptons being equal, since the stable charged versions of each are the proton and the electron, respectively, the following link may be useful.

http://pdg.lbl.gov/2010/listings/rpp2010-list-p.pdf" -This URL links to the Particle Data Groups entry on the proton. Of interest is the bound on the difference in charge between the proton and the electron, the value they give is: <1.0x10^-21 (from the neutrality of matter, specifically neutrons which are assumed to have a charge equal to the sum of the proton's and the electron's). I am sure the source of that value discusses the considerations that went into obtaining the bound.

 

[bcrowell]

One cute way of seeing it where the statement is exactly true. In a closed FRW universe, let's say you have some positive charge somewhere, and you draw lines of force emmanating from the charge. Since the topology of the closed universe is a 3 sphere, you can see that the force lines will want to wrap around the sphere and move to an antipodal point, where there must be a negative charge in order to preserve the shape.

Misner, Thorne, and Wheeler discuss this on p. 458.

To keep from getting tied up in knots by issues like these, let's talk about a variable F defined as (the number of protons per cubic megaparsec)(q_p)+(the number of electrons per cubic megaparsec)(q_e)+..., where the ... represents other species of charged particles. It's possible that the ... is fundamentally ill-defined (the MTW argument suggests that it is), but let's assume it's not. In the present-day universe, the ... is clearly unimportant.

Electrical charges in the universe necessarily cancel out. The universe must be electrically neutral unless you are bold enough to spin the crackpot phyics wheel. Give it some thought.

This isn't a logical argument, and it seems to show that you haven't read humanino's posts 1 and 3 carefully.

I'll try to spell out the possibilities raised in humanino's 1 and 3 in a little more detail.

In a homogeneous cosmology, F has to be constant over a slice of constant t, where t is the time measured by an observer moving with the Hubble flow. There are really three different possibilities that could lead to a nonzero F. (1) There was F=0 before some time t_0, and then at t_0 some charge-nonconserving process happened that made F nonzero. (2) |q_p| \ne |q_e|. (3) F is constant for all t on the manifold, and happens to be nonzero.

Possibility #1 would require physics beyond the standard model, and since there is no hint of such a thing at any energy we've explored, t_0 would have to be a very early time. Nonconservation of charge is very difficult to fit into the fundamental theories of physics. It's not compatible with what we think we know about gauge theories. It's also not compatible with general relativity, where charge is conserved in all processes, including the formation, collision, and evaporation of black holes.

Possibility #2 is also probably very difficult to shoehorn into QFT, but I'm not enough of an expert to know.

#3 doesn't require any new physics and seems perfectly plausible to me.

If their electric charge would differ by such a tiny amount, would not I expect 10% deviation in the global expansion rate ?

This is talking about what I referred to as #2 above, but I don't think it matters which mechanism we're talking about. I suspect that the standard cosmological observables (CMB, supernova redshifts, nuclear abundances) can't constrain F empirically. If you assume a homogeneous cosmology, then a nonzero net charge has an effect on cosmological expansion that is probably indistinguishable from rescaling the gravitational constant G on very large scales, compared to its value as determined by Cavendish experiments. But we would have absolutely no way of detecting such a thing, because we have no way of accurately determining the average mass-density \rho of the universe. We do know that the universe is very nearly spatially flat, but if you allow F to be nonzero, I think you can accommodate the observed flatness simply by imposing some constraint relating F to \rho.

I suspect that the best empirical bound on F would come from the transparency of the interstellar medium. If the interstellar medium had a nonzero charge, wouldn't it scatter and absorb light? The types of observations that would put a bound on F would probably be similar to the ones that rule out the "electric universe" kook theory, so it might be productive to google for stuff about that.

 

[tom.stoer]

For gauge symmetries like U(1) in QED and SU(3) in QCD one can derive the corresponding Gauss law. Promoting this to an operator during quantization one can derive a constraint equation like

G^a(x)|\psi\rangle = 0

for physical states (a is a label in the adjoint rep. of the gauge group). Integrating this equation results in a constraint for vanishing charge

Q^a|\psi\rangle = 0

That means that electric charge must vanish and that the universe must be a color-singulet state.

This argument depends on integrating the Gauss law operator and therefore it depends on the boundary conditions (surface terms). The derivation is made using the canonical formalism and is restricted to a global topology like M⁴ = R * M³ ="time" * M³

In order to old strictly speaking M³ must be compact. For M³ with non-empty boundary surca eterms are allowed, for non-compact M³ there is (afaik) no purely kinematical reason to have vanishing total charge but I guess that non-vanishing total charge would create background fields which should be suppressed dynamically.

 

[zonde]

I'd be interested either in references in the literature (which I failed to find), or if you have ideas for what an experimentalist could look for

I have seen this in Independent Research:
https://www.physicsforums.com/showthread.php?t=87097"

But I want to say that unbalanced charge seems to have inconsistencies.
If we distribute infinite number of preserved unbalanced charges inside infinite space we get infinite field everywhere. It's like http://en.wikipedia.org/wiki/Olbers%27_paradox" only for charge.
So we have to have opposite charge too to speak meaningfully about field of that charge.
Or as an alternative we can assume that particular charge was not there forever. But in this case we would have problems applying mathematical formalism to this case as we require conserved quantity for math to be applicable. So we would need some other quantity to fill the role of conserved quantity.

 

[Haelfix]

Bcrowell. The reason your point 3 is extremely difficult to work is several fold.

First.

Inflation will wipe out most of the initial charge asymmetry to ludicrously small values, makign it effectively irrelevant. If on the other hand you insist and put in an enormous initial asymmetry such that it persists after say 60 efolds, you really have to massively finetune the model in order to create the observed amount of anisotropies in the CMB thereafter. The problem is, it is extremely difficult to even create the proper conditions for inflation to even begin, under those circumstances.

If on the other hand you choose to ignore inflation dynamics, you still have a bound due to equivalence principle tests, as was mentioned ealrier.

Thus it seems likely that if there is charge asymmetry in the universe, it arises from dynamics and not initial conditions. Now, there are a few things you could consider --throwing caution to the wind-- under that guise that aren't completely incompatible with known physics. For instance, exotic GUT physics or theories that generate a large amount of nontrivial topology in cosmology. But in general the phenomenological terms necessary will always be higher dimensional operators, and thus highly suppressed. It also implies a nonzero mass for the photon (which also has pretty large bounds).

So I wouldn't say its impossible to have some amount of charge nonconservation, its just highly nonminimal and ridiculously unlikely (unless we are really missing something fundamental)

 

[tom.stoer]

So I wouldn't say its impossible to have some amount of charge nonconservation, its just highly nonminimal and ridiculously unlikely (unless we are really missing something fundamental)

It is impossible as it violates gauge symmetry!

 

[Haelfix]

The gauge invariance of QED would be lost of course, and you would need to use a Proca term for the photon. However, that's not necessarily the end of the game. As we can certainly give mass to gauge bosons through other means. There is a long literature studying models with exactly that property (and experimental limits)

A cursory glance at the literature does show a few exotic models and interactions that have been studied with charge nonconservation as well (again typically occurring with coefficients that are highly unnatural). Again, I'm not saying its likely, just that it is a game you can play.

 

[tom.stoer]

I do not say that one must introduce a mass-term to break gauge invariance but that a modification of the equation Q|phys> = 0 breaksgauge invariance generated by G(x). That's not the same.

I agree that one might be able to complete such a program formally, but I doubt that it makes sense physically.