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Sunday, 6 September 2009

The Big Bang Conspiracy & Baryogenesis

Did you know that those amazing maps of the so-called Cosmic Microwave Background were produced by a webcam placed inside a painted sphere in a studio in Pasadena? Just another put-up job like the moon landings!

No? You mean you actually think the Big Bang - or something rather like it - actually occurred about 13.7 billion years ago?

Good - we can proceed.

The conspiracy I was actually alluding to was that of the scientific writers and science popularisers who state blandly that in order for everything we see in the universe to be ordinary matter - as opposed to a mixture of matter and anti-matter) the universe had to have been created with a slight excess of protons over anti-protons from the very beginning; "slight" being here about one in a billion, i.e. for every 1,000,000,000 anti-protons there were, there were 1,000,000,001 protons. [My preferred "popularisation" of this issue is given at the end]

The "reason" for this "necessary" excess is that particles and their antiparticles annihilate: if the numbers had been exactly equal there would be no matter at all, just radiation, since every particle would have had a corresponding anti-particle to annihilate with.

The problem is that it is obvious after a moment's thought that there is another possibility - and one which is actually more coherent than positing the slight imbalance referred to above ex nihilo: we know that (yes we do, don't quibble) there are symmetries in physics and that symmetries are often broken, so why not assume that the numbers of particles and anti-particles were in fact equal at t~=0 and that the ratio then drifted away from 1:1 owing to some broken symmetry?

Ever since that thought occurred to me (as a solution to the problem of Baryogenesis - i.e. where all the baryons - things like protons and neutrons - came from, how and in what proportions, etc.) I had wondered "Well, why not?"

Well, you can go this way. In fact Andre Sakharov worked it all out in 1967 - but being then in the Soviet Union his work wasn't seen for quite some time, and it was left to Susskind and Dimopoulos to independently suggest exactly the same thing to the West in about a decade later.

Having subsequently read up on Sakharov's work, I rather thought, OK... it can work that way, but I didn't really see how neatly and simply it could be put together until I saw Susskind's Lecture 6 on Cosmology - thank you Stanford and Prof. Susskind for putting your excellent lectures on YouTube, and thank you to whichever student asked precisely the question I wanted to ask.

I'll try to restate his answer here, and add one tiny observation of my own on why the alternative (the magic of an ab initio imbalance in numbers) is in fact doubly improbable...

Caveat - if we were to do properly we would, like surgeons of old, very quickly be up to our knees in the full gore of particle physics, quantum mechanics and relativity, so following Susskind's lead I'll just talk about electrons and protons and neglect the fermion/boson, hadron/baryon/lepton/etc. distinctions, and all the other gristly bits.

All you really need to know to get the hang of this is:
  1. E=mc2, and
  2. the mass of the proton (mp) is about 2000 times the mass of the electron (me)
E=mc2 is from Einstein's Special Relativity and says in essence that from certain quantity of energy you can create a certain quantity of mass - e.g. a high energy photon can turn spontaneously into particles - and vice versa.

Once upon a time the universe was very small, and thus rather a lot hotter than it is now. In fact the temperature increases without limit as you approach t = 0 (this is the problem for modern physics: how to get rid of such unpleasant infinities by some clever theory that subsumes both general relativity and quantum mechanics) .

Temperature being just a measure of energy, it's not too hard to see that when things are hot enough, light (which is just energy in the form of photons) can create pairs of electrons and anti-electrons (they come in pairs because electrical charge has to be conserved). And when things are even hotter - remember, mp is 2000x me, so it takes 2000x as much energy to create a proton as an electron - even more energetic photons can create protons and anti-protons.

OK, the stage is set... Fiat lux! It's started - space and time are now up and running and the microscopic fireball is seething. For a while after Fiat Lux there is just FLUX as mass and energy inter-convert, but as the universe expands, the fire cools. Now it just so happens that the expansion at the relevant time is relatively slow - sufficiently slow in fact for the fireball to be in thermodynamic equilibrium, which means that reactions have time to "go to completion"... in other words, if there are 1,000,000,001 protons and 1,000,000,000 anti-protons, there is sufficient time form them each to find their anti-particle and annihilate.

If there were an initial imbalance in the number of protons and anti-protons, the period in which energy and mass inter-converted would not have affected the imbalance because every photon that became particles would become a pair of particles (charge conservation)... adding equal numbers of protons and anti-protons, or if the reaction went the other way, removing a matching pair.

But, the universe is expanding, and as it expands it cools and there suddenly comes a time at which the photons cool to the point at which they don't have enough energy to make protons & anti-protons any more; they can still create lighter particle pairs for a while, but that will stop too eventually. The same thing will occur for the electrons and positrons as happened for the protons & anti-protons - they will annihilate until either there are none left or the remainder of an initial imbalance is revealed.

And there's the odd thing: the universe is electrically neutral - the numbers of electrons and protons match perfectly. Now, if by fiat there was an imbalance in the number of protons & anti-protons, it takes another fiat to create a perfectly matching imbalance of electrons and positrons.

The most logical inference is that some process is creating equal numbers of electrons and protons, indeed we may suppose that at some extremely high energy photons can create not particles and their anti-particles but any pair of particles as long as charge is conserved. The only problem with this is that there is no such process in the enormously successful Standard Model - which is why most physicists agree that there is physics beyond the Standard Model to be discovered.

The Standard Model does not "allow"an electron and a proton to be created from photons because that would violate the so-called law of baryon number conservation. Protons have a baryon number of +1, and anti-protons have a baryon number of -1, so it a pair is created the baryon number doesn't change, but if an electron and a proton were created the baryon number would increase by 1. But this "law" is just an empirical observation thus far: we have just never seen baryon number change in any of our particle accelerators - or other experiments (such as filling giant tanks with water and watching to see if any protons decay - anything that can be created can be destroyed; we haven't seen that either and the half-life of the proton is now estimated to be at least 6.6x1033 years... which is about a trillion trillion times the age of the universe)

Supersymmetry is I believe the extension considered to be the solution to the problem as it contains processes that allow the individual baryon (and lepton) number to change... as long as the baryon-lepton number total doesn't.

There's a nice review paper on baryogenesis on arXiv here (it's for experts... I just look at the pictures...)

And the preferred "popularisation" of the Big Bang baryogenesis issue is: Given the observed facts that the universe if made of matter and not a matter/anti-matter mix and that there are about a billion photons for every proton we can see, at some point very, very early in the history of the universe not only were there about a billion and one protons for every billion anti-protons, there were also a billion and one electrons for every billion positrons, and rather than call this a monstrous coincidence of not only ratios but absolute numbers, it is preferable to consider this as evidence for new physics that would allow the so-called "law" of baryon number conservation to be broken at sufficiently high energies and for electrons and protons to have been created together and equally in slight preference to positron and anti-proton creation.

Watch the lecture - it's better than a blog posting.

Fiat Stuff - et Stuff Erat.