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 (m_p) is about 2000 times the mass of the electron (m_e)

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, m_p is 2000x m_e, 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.

Hoist with Zeno's Petard

[Metaphor Warning: this posting exists in a superposition of metaphorically analogous similes, or analogous metaphorical similes, or... and?]

So - Zeno's Petard? Well, he could have described a shock wave instead of an arrow... if he'd known about explosives... allow me to allow myself a little creative licence.

Anyway, a new problem has arisen, and the problem is that instead of preventing you from being hoist into the air (because the shock wave can never arrive) the Quantum Zeno Effect turns out to have a sting in its tail (though the venom may turn out to be its own antidote - as we shall see later).

Lawrence Krauss has just put up a rather large "Oops?" sign in his latest paper - where he raises the concern that whereas the universe was ticking along nicely, even if it was potentially in a metastable false vacuum, we may have just buggered it up by noticing the fact. All bets are off - our nice little temporarily stable universe may now be a teensy-weensy bit wobblier.

It's like this... The Quantum Zeno Effect tells us that for small t, the probability of decay is proportional to t squared and if we can't quite bring decay (radioactive, quality of TV programming, moral, etc.) to a complete halt, we can at least slow it down by Obsessive Observation (TM) [Tools: Geiger counter, The Ghost of Mary Whitehouse, and, er, The Ghost of Mary Whitehouse]

Normally decay processes are exponential. Example: a while back a Northern Rock share was worth £12, then it became £6, then £3 - anything that halves at regular intervals is undergoing exponential decay. (I can't bear to provide a link.)

But - and here's the fly in the quantum cosmic ointment - for large t, the decay becomes slow again (a Power Law) - meaning apparently that if the decay hasn't happened by then it's really not likely to decay at all.

But, I hear you cry, that's a good thing! It is indeed - if we are living in a wobbly universe. Or it was, until some idiot went and observed the universe before it has reached the transition point (actually I'm not sure that the timing was that important) from Exponential to Power Law because at that point his observation reset everything (trust a bloke to start fiddling with (qu)bits of fundamental existence) - and we are back on the slippery slope of Exponential decay again.

Oh dear, as I seem to find myself exclaiming more and more these days (as in, "Oh dear. Where are my slippers," or "Oh dear, I've snagged my nice new cardigan,", or even "Oh Dear!The Windows Vista Update - KB938797 if you want to know - that Microsoft recommended for my PC is not, in fact, valid for my PC", etcetera, etcetera, etcetera.)

It may not all end in tears, but (oops - didn't plan this one, honestly) it could all end in tears, rips, splits and general cosmic hyperactivity disorder as the false vacuum (have I explained that one yet? No? Ah.) collapses to a new all time low of vacuity (c.f. UK government data protection assurances (random but relevant link), Northern Rock share valuation, usw.) and Life the Universe and Everything goes "Poof!".

Now I'm in a bit of a quandary as to what to recommend. Live long and prosper but get overrun in the end, or accept that everyone dies young (good or bad - remember to tell the kids "Only the good die young" at the same time you tell them Santa keeps a list of Naughty and Nice) cosmologically speaking.

However, getting back in the saddle of my tame French ovine, if we have indeed put an observational spanner in the cosmic works, we have the answer in hand: the Quantum Zeno Effect, the cause of the problem in the first place.

Whoever made that ill-advised observation of some remote supernova and noticed that the universe is accelerating "outwards" - thereby effecting the observation of a false vacuum - should be glued to his telescope and forced to keep watching... and his children... and his children's children... and his children's children's children (etcetera, etcetera, etcetera ad infinitum - if we want there to be one) to make sure that it doesn't decay. Seems fair to me.

However, two other considerations to take into account.

a) Death of Universe = No Invasion of the Boltzmann Brains (not a bad thing, IYAM)

and (more fundamentally)

b) How in the name of Dick Emery can one part of a quantum system "observe" another part of a quantum system in such a way as to affect the decay probability of the system as a whole?

Answer that if you can! Personally - Oh dear, I really should stop thinking about such things - I'm now more concerned about The Boltzmann Brains From Another Universe observing ours (universe that is) - that really could upset the cosmo-quantum apple-cart and dump several unattractively large flies in our collective soup (ah... you are wondering now, "Did he say ointment or soup earlier?"). The BBFAU may already have observed us - or done so long ago - and it's all over bar the shouting.

Or just perhaps, the plethora of BB's in the multiverse ensures that we are always observed, and thus safe for the foreseeable future.

What was that old Chinese curse? May you live in interesting times.

Here's hoping we live through these interesting times... personally I'm planning to stick around.

Watch me.

[PS A False Vacuum - one which talks about you behind your back]
[PPS If the Quantum Zeno Effect is both doom and salvation doesn't it just cancel itself out, or does it mean it's all kindofuncertain in a satisfyingly-quantum-sort-of-way? Over to you Nicey]

Black Holes, Galaxies & Stars

Now that much of the inferred population of the universe's black holes has been found the overall picture seems to be like this.

In their youth, galaxies form stars and black holes together as the primordial gas and subsequently added dust (you don't get dust until the first generation of supernovae have gone pop and spilled their heavier elements - "metals" in astronomical terminology). The black holes at the centres of galaxies grow until they become quasars and the intensity of their own radiation holds back the very material they need to grow further, which leads to the general observation that central black holes are typically about 0.2% of galaxy mass (I think that's the right figure).

[Side note - now we have found the hidden population of black holes, we can infer something about quasar structure by comparing the numbers we can see directly with those we see indirectly through the infra-red etc. from surrounding dust.]

If this picture is broadly correct, then there should be a typical upper mass-limit for organically grown black holes.

My conclusion from all this: central black holes of greater mass should be indicative of galactic mergers and the mass of such holes might even be a proxy for the number of mergers that have occurred in the course of a particular galaxy;s history (complicated of course by the original size of the galaxy cluster etc.). It is interesting to consider that, whilst the specifics would always remain vague (barring identification of specific sub-populations of stars by e.g. velocity, age, etc. - we can do this for the Milky Way, and have found the remnants of several mergers this way, but it becomes increasingly difficult the further away a target galaxy is), one might be able to infer something about the original sizes of clusters, super-clusters etc. in the early universe from present day observations; or, running the logic in reverse, the more we learn about early cosmological structure, the more we may be able to infer about the dynamics of galactic mergers.

Just a thought. Just more Stuff.

Boltzmann Brains - Problem? What Problem?

(You might want to read this post first... or you may not)

Don Page probably gets more headlines for his "ladies and gentlemen, the universe will shortly be ending so please finish up your drinks and put the paper bags provided earlier over your heads..." announcements ( as in "Is Our Universe Likely to Decay within 20 Billion Years"), but James Hartle and Mark Srednicki have a saner approach.

To recap (very loosely) the story so far.

We are not special, we are typical - if we're not, how can our observations be typical of the universe, how can we know anything, doesn't our very existence tell us something about the universe? (Copernican Principle, Anthropic Principles)

Sometime soon (soon in the cosmological sense of umptillion years being a lot less than an infinite number of years) the universe will be crawling with Boltzmann Brains just popping into existence, making an observation or (or two?) and pushing off again into the vacuum, without so much as a "by your leave".

And then we will be utterly insignificant in the grand scheme of things, and hence not typical at all and can't possibly be learning anything sensible about the universe.

But, since clearly we are significant and know loads of stuff (and Stuff, I hasten to add), it follows that we can't be about to be invaded by Boltzmann Brains and hence that the universe will end shortly because that's the only way to stop them taking over.

[It would spoil the story to admit that there are other ways to deal with them pesky Brains... but there are, e.g. ..."Repelling the Invasion of the Boltzmann Brains" by S Carlip]

(And may I add as an aside how very short-sighted some physicists can be - even if they do have a way with catchy titles for their papers? What about some preventative measures? Surely it's not too late to take action! A Department of Home World/Galaxy/Universe Defense for example, the e-petition I mentioned in the previous post? Oh, what I wouldn't give to hear Dubya pronounce "These Bolts-men folk are un-American! We must fight their statistical evil!")

The argument up for ridicule is basically: if we are to remain typical we need to pull the plug quickly (or get cloning) - before we become atypical.

Of course it's complete tosh, the fundamental problem being "What do you mean by Typical?" and here Hartle and Srednicki have done a far better job than I ever could in their paper Are We Typical?.

I was going to waffle on about the fact that at least one observer (e.g. the first) has to be atypical, and that "being" is entirely different from "being randomly selected from a population of observers", and that since we see time as having an arrow ["Time flies like an arrow; fruit flies like a banana"] we should perhaps, at best, think of ourselves as typical observers of the now - Temporal Typicality as an eternal assumption probably leading to a Steady State theory (which seems unlikely).

Hartle & Srednicki's paper says it all very clearly and only needs the tiniest bit of maths (in the form of Bayesian Probability) to follow. They basically say that there is no basis other than prejudice (ideas that one likes or dislikes because they lead somewhere interesting) in the selection of the prior probabilities used in the Bayesian calculations; by all means assume what you like, but be clear about it and recognise that the choice is not scientific.

They also deal neatly with the whole Typicality thing: we are typical of what? Of things weighing between 10kg and 100kg? Of things with ten toes? And point out how silly assumptions can lead to equally silly conclusions.

Read it. It's worth it.

Conclusion: so what? Even if the universe will shortly be hosting The Great Boltzmann Brain Ball it doesn't affect us at all.

So, unless Boltzmann Brains are improbably more probable than they would seem to be a priori (in which case I suspect we have a different kind of problem) there's nothing to worry about.

Phew! I can sleep soundly now.

Ugh! What was that grey squishy thing I just sat on?

Boltzmann Brains

Yesterday I decided to write about the serious problem of Boltzmann Brains*; I knew it would be a long post as it would have to take in - at least passingly -

• What a Boltzmann Brain is
• What the Anthropic Principles are
• The Copernican Principle
• Quantum Mechanics
• Bayesian Probability
  
• Physical Cosmology
• Consciousness

and several other major topics.

However, in the course of doing some basic research - including reading various fascinating but obscure papers on one or more of the above (with such wonderful titles as "Repelling the Invasion of the Boltzmann Brains") - I became a little distracted by other things as The Sleeping Beauty Problem, Bertrand's Paradox, The Doomsday Argument - and Mike The Headless Chicken and it might take a little longer than I expected... There is Stuff and there is Deep Stuff - this is the latter.

Maybe I should do it in pieces?

Please return to this page again on 22nd August 1,000,0000,000,002,007 - or thereabouts - for an update.

What do you mean you already have?

*If you think the government should take action now to deal with the problem of Boltzmann Brains, why not start an e-petition? (My first attempt at this, to urge the PM to answer questions in a "more business-like manner", has so far attracted 7 signatories - so maybe I haven't quite tapped into the zeitgeist...)