Of Particular Significance

# Chapter 6, Endnote 13

“Quark Number” — the total number of quarks minus the total number of anti-quarks, is observed to be conserved (i.e. preserved, unchanged) by all interactions known in nature. However, the story is not so simple.

### Why quark number need not always be conserved

Quark number divided by 3 is known as “Baryon Number”, which is a more commonly used term. Protons and neutrons are called “baryons” by physicists, as are any objects with three extra quarks in their interiors. (Anti-baryons have three extra anti-quarks.)

Electric charge is conserved/preserved too. Yet the conservation of electric charge is different from the conservation of quark number. An object with electric charge has electric field emanating from it, and wiggling an electric charge back and forth creates an electromagnetic wave (i.e. a radio wave, or a flash of visible light, depending on how rapidly the charge oscillates.) Consistent mathematics for the electric and magnetic field requires that conservation of electric charge be exact.

Quarks have electric charge, and also strong nuclear charge, known colloquially and misleadingly as “color” in the scientific lingo. That “color” charge is conserved for exactly the same reason as electric charge; any object with strong nuclear charge has non-zero gluon field (often called chromo-electric field) emanating from it, and so forth. Baryons, despite having quark number 3, have no net strong nuclear charge; it cancels out among the quarks. (For more detailed explanations of these statements, see first here, and then here.)

But while quarks also have quark number, there is no field associated with quark number. [Jargon: quark number is an example of what is known as a “global charge”, while electric charge and strong nuclear charge are known as “gauge charges”; their associated fields are known as “gauge fields.”] Wiggling a quark back and forth will generate both an electromagnetic wave and a chromo-electromagnetic wave in the gluon field, but no quark-number-field wave is created. Wiggling a neutron, which has quark number but no electric or color charge, creates no waves at all (well, none except unobservably tiny gravitational waves.) Correspondingly, there is no mathematics requiring quark number be conserved. Instead, its preservation appears to be an accident of the details of particle physics interactions; experiment shows that there’s nothing that obviously violates it, but mathematics shows that there’s nothing that necessarily protects it, either.

### Why we suspect quark number is not conserved

Moreover, in nature we find the universe full of protons and neutrons but largely bereft of anti-protons and anti-neutrons. This baryon asymmetry suggests (but does not prove) that baryon number, at some point in the distant past, was far from conserved — that something in the early moments of the universe created baryons faster than anti-baryons (or destroyed anti-baryons faster than baryons.) This left the world with more quarks than anti-quarks. (The other logical possibility is that, for some unknown reason, the universe was simply created with more baryons to start with.) So this makes physicists suspect that quark number isn’t exactly conserved, and that in special circumstances its lack of conservation can become dramatic.

Meanwhile, there’s another clue from the fact that the strong nuclear, weak nuclear and electromagnetic forces all have similar strength at distances more than a thousand times smaller than a proton. This has suggested the idea of “grand unification”, in which all three forces arise from a single type of force at an ultra-short distance; perhaps this one even unifies with gravity as well. The simplest theories of grand unification do indeed predict small rates of quark number violation. Such violation can allow a proton to decay to particles with no extra quarks in them (for example, a proton could decay to a pion and a positron.) Searches for proton decay have been carried out extensively, and the process is exceedingly rare. Based on current experiments, protons can exist for an average of at least 1036 years — far, far, far longer than the lifetime of the universe. At that rate, at most 100 of the protons in all the human bodies on Earth may have decayed in the past year.

Black holes give us another insight into the difference between conservation laws associated with fields (as in electric charge and gluon charge) compared to conservation laws with no such association. Suppose a proton falls into a black hole, increasing the black hole’s electric charge by 1 and increasing its quark number by 3. Before the proton fell into the black hole, the effect of its electric charge on the electric field extended away from it, on and on out into the universe, even light-years away. After the proton falls in, its effect on the electric field cannot disappear — it existed far from the black hole, and the black hole can’t reach out over gigantic distances to make it vanish. [A proof follows from Gauss’s law, described in the opening of this post and of this post.] Thus the electric field proves to us that the black hole has acquired the electric charge of the proton it swallowed.

No such argument applies to quark number; there is no field that extends out into the universe from the proton to prove it has quark number. And so when it falls into the black hole, all knowledge of the proton’s quark number is lost. There is no way to tell, from outside a black hole, whether the black hole has any net quark number or how much it might have.

Because of this, it is clear that if and when a black hole evaporates (as Hawking argued it could, if small enough or if left alone in a sufficiently cold room) the total electric charge of the particles into which it evaporates must be equal to the total electric charge of the particles that fell into it, while there need be no correlation between the quark number emitted as it evaporates and the quark number it absorbed over its lifetime. Black holes, and more generally quantum gravity, are believed to violate quark number, and indeed any type of conservation law not associated with a field.

Finally, there’s an even stranger clue buried in the arcane subtleties of quantum field theory. It turns out that the weak nuclear force itself actually violates the conservation of quark number! The rate at which it does so, in ordinary life, is ridiculously, insanely small. However, if the universe were sufficiently hot — and we think it probably was that hot during the Big Bang — then this violation can become large. In fact it may even, somehow, be responsible for the observed excess of baryons over anti-baryons; there are lots of speculations and research on this topic.

In sum, there are many reasons to expect that quark number is not exactly conserved, and that in certain circumstances (such as ultra-high temperatures) the conservation law may fail badly. That has no effect on daily life today, but its actions in the past may have made our lives possible in the present, for if the number of quarks and anti-quarks in the universe were equal — if there had been equal number of baryons and anti-baryons in the universe as it cooled — then the protons and neutrons in the universe would be billions of times fewer than they are, and galaxies, planets and living creatures might never have come to be.

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