How many Universes make a Multiverse?

According to a recent paper, published by Professor Andrei Linde and Dr Vitaly Vanchurin, both of the Department of Physics at Stanford University, there could be as many as 10^{10^10^7} universes in the cosmological – as distinct from quantum – Multiverse. See: http://arxiv.org/PS_cache/arxiv/pdf/0910/0910.1589v1.pdf.

Andrei Linde is the inventor of the model of cosmogenesis known as ‘cosmic inflation’, whereby, at the earliest instant of time t = (Għ/c³)^½ = 1.616 × 10^-35 s (the Planck time), the primitive Universe, which was initially super-dense, and ultra-hot, expanded in all directions at a velocity many times greater than the speed of light. This was possible solely because of the then enormous value of the cosmological constant, Λ.

The inflationary expansion continued until the Universe had cooled down sufficiently for the value of Λ to drop to where:

v ≤ c ≤ a(8πGρ/3 – kc²/a² + Λc²/3)^½ .

Here, the scale factor, a, which has the dimension, length, is taken to be numerically equal to 1. When Λ was equal to 10¹⁶⁰, ignoring the contributions of ordinary and dark matter (which would have braked the expansion, in any event), and given hyperbolic space (k = –1), v = (10⁶⁰c/1.732 – c) = 1.7309 × 10⁶⁸ ms^-1.

Clearly, there are very different régimes for high energy, high temperature, low energy, low temperature, physics. During the inflationary epoch, the ‘Big Bang’ (or ‘Big Whoosh’), there was one Universe, with one set of laws of physics, one set of initial conditions, and one, unified field of force, which united all four of the forces we know about today – gravity, electromagnetism, the weak and strong nuclear interactions.

However, after the cooling down, there was a breaking down, with the forces being split up into four, and the Universe becoming the Multiverse, being split up into myriads of separate universes (small ‘u’), of which our observable Universe is but one.

The other universes are too far away for us to see at present – they are beyond the particle horizon. However, as the Universe – our Universe – expands, the Big Bang recedes further and further into the past, becoming ever more distant from us in time and space. As it does so (and remember, from our POV, we are still at the centre of this great Sphere we call the Universe), more and more that was previously hidden becomes revealed to us – the Greek word for this process is apŏkalypsis, btw.

As they are beyond any possible communication range (with each other, not just with us) – ‘Einstein separated’, in the jargon – these separate universes can have different laws of physics. In some, the conditions will be perfectly suitable for life to arise, even conscious life, and so there will be observers. In others, the conditions will be altogether hostile for any kind of life at all, and so there will be none.

This takes care of the mystery of why our Universe is peculiarly advantageous for life, and for consciousness, at least to Professor Linde’s satisfaction. For the fact is that the laws of physics that apply here, and the values of the physical constants are remarkably well-attuned for life. If the value of the electromagnetic coupling constant, α, were the slightest bit different, for example, then organic chemistry, and thus our sort of life, the kind we know on Earth, including ourselves, would be completely impossible. For many other such instances, see Paul Davies’ book, The Accidental Universe, CUP, 1982.

Most scientists, like Linde and Vanchurin, invoke what is termed the ‘weak anthropic principle’ to account for this – namely that, the reason the Universe is so ordered is because, if it weren’t, we wouldn’t be here to observe it being that way. This is unanswerable, in a way, but also seems something of a cheating answer – a cheap debating point, rather than a genuine attempt to grapple with the mystery.

With lots of different universes available, life can play Russian roulette. In most of them, it takes the bullet, and never even gets started. In just a few, however, a very few – maybe only one in 10⁵⁰⁰, or less, it can get a foothold, because the conditions are right.

In fewer still, consciousness arises, and intelligent beings find themselves wondering why the Universe they are in is suitable for their kind of life, and ask if it is because it was created by a god, or God.

The problem with the Linde scenario is that, when you go back to the inflationary epoch, you go back to a period when there was just one Universe, and one set of physical laws, initial conditions, and only one physical force, as I said earlier.

So: where did they spring from? Let’s say that someone like the new Lucasian Professor of Mathematics at Cambridge, Professor Michael Green, who takes up his post on Sunday, 1^st November (my 53^rd Birthday!), see press release, University of Cambridge, a world-renowned pioneer and expert in Superstring Theory, comes up with the solution to how to unify quantum mechanics and the General Theory of Relativity, and how to put all four forces of nature, and the Higgs Field, and Professor Linde’s ‘inflaton field’ into one theory.

Even if you can manage to do that, you still haven’t accounted for where the mathematics came from in the first place. In pure mathematics, you get equations like this one (Euler’s identity):

e^iπ + 1 = 0.

Here, e is Euler’s number, 2.7818281828459…, i is the square root of –1, and π is Archimedes’ constant, 3.1415926535897932384… (being an Aspie has its compensations – I have an eidetic, or ‘photographic’, memory, and can recall numbers like these from memory. The golden mean, f, is 1.6180339887498948482…).

This is true (and has been proved to be true), because of the meaning of the symbols employed – it is logically true. The same does not apply in the case of statements in physics. They are not a priori truths. They are, at best, hypotheses, which are falsifiable (not verifiable) a posteriori.

Consequently, no theory in physics, no matter how good it is, or no matter how many times it is supported by observation or experiment, should ever be regarded as proved, still less as though it were Holy Writ.

More importantly, though, no physical theory should be regarded as a substitute for Holy Writ, or as a spurious means of ‘refuting’ it. Professor Linde cannot tell me, or anyone else where the laws of physics came from, or who wrote them, or who set the initial conditions, or the parameters of the equations that governed the behaviour of the forces in the very early Universe. Nor can he account for the fact that, at the very beginning, there was literally nothing – i.e., no thing – no matter, no energy, no space and no time, and then there was something, the Universe, the instant of the Big Bang.

Professor Linde is like all too many of his colleagues – he wants Creatio ex nihilo without a Creator.

As for the quantum Multiverse, each separate universe would have to have its own quantum Multiverse, increasing the total number of universes to infinity. The quantum Multiverse arises from the Everett-de Witt Interpretation of quantum mechanics. It is a realist, determinist approach which does away with the idea of ‘collapse of the wave function’ (or ‘state vector reduction’).

Instead, all the possibilities represented by the various probability amplitude waves are realised, in different ‘parallel universes’, or histories. Schrödinger’s Cat is both dead and alive – dead in one universe and alive in another.

However, the laws of quantum mechanics – and thus of physics, generally – must be the same in all of these universes, so each separate cosmological universe, with its own physical laws, must have its own, entirely separate, quantum Multiverse, assuming that the quantum Multiverse idea is correct.

Cosmological Coincidences.

Seen from Earth, the Universe is a great Sphere, centred on the Earth, with a radius stretching across the vast distance of inter-galactic space, all the way to the Big Bang, which is the Sphere’s circumference.

This Sphere is expanding as the Universe ages, so the circumference is becoming more distant in space the further back in time it becomes.

How old is the Universe? According to measurements carried out by the NASA Goddard Space Flight Center’s Wilkinson Microwave Anisotropy Probe (WMAP), the Universe is 13.73 billion years old.

The mass of the Universe, it turns out, can be calculated from an equation,

M = m_PL⁴/m_pm_nm_e = 8.79674 × 10⁵² kg ,

where m_PL is the Planck mass, (ħc/G)^½ = 2.1767 × 10^-8 kg, and m_p, etc., are the masses of the proton, neutron and electron, respectively.

It is a simple matter to check this. The Schwarzschild radius of the Universe (the radius the Universe would have, if it were an enormous black hole) is the same as its actual radius, on the condition that the value of something called the total density parameter, Ω_TOT, is exactly equal to 1.

This radius can be expressed as a time, so on that basis the age of the Universe should be equal to 2GM/c³ (given that the Schwarzschild radius, R = 2GM/c² = ct, with t being the age of the Universe).

A quick calculation suffices to show that, if the above equation for the mass is correct, then t = 4.357 × 10¹⁷ s, which is 13.8 billion years.

That’s pretty close to the WMAP figure, which has a degree of uncertainty of ±0.876%, or ±120,000,000 years (see: http://map.gsfc.nasa.gov/).

The question is, why is this equation right? What connection is there between the mass and age of the Universe and the masses of the sub-atomic particles, and the values of the Dirac constant, the speed of light in vacuo and the Newtonian gravitational constant?

One would expect to see some connection, at least between those last two and the the Universe’s mass. The ‘total density parameter’, which determines the large-scale geometry of space-time, is given by the Friedmann Equation:

H₀² = 8πGρ/3 – kc²/a² + Λc²/3 .

Here, H₀ is the Hubble parameter at the present epoch, G is the gravitational constant, ρ is the baryonic + dark matter density of the Universe, Λ is the cosmological constant, k is the space-time curvature parameter (–1 for Bolyai-Lobachevskian, or hyperbolic, space-time; 0 for Euclidean, or ‘flat’, space-time; and +1 for Riemannian, or spherical, space-time), and a is the scale factor, which is taken to be 1. The above is re-arranged, thus:

Ω_TOT = 8πGρ₀/3H₀² = Ω_B + Ω_D + Ω_Λ – Ω_k ,

where Ω_B is the ‘baryon’ (i.e., ordinary) matter density parameter of the Universe, Ω_D and Ω_Λ are the dark matter and ‘dark energy’ density parameters, respectively, and Ω_k is the space-time curvature density parameter.

The value of Ω_Λ is currently estimated to have a value of 0.72 – in other words, 72% of the mass of the Universe is thought to be comprised of dark energy, generated by the action of the cosmological constant. Some 23.3% of the remaining mass is dark matter, and 4.6% ordinary atoms (‘baryonic’ matter + electrons).

The critical density, ρ₀ (ordinary + dark matter + dark energy, less [negative] curvature density), is ~9.4 × 10^-27 kg m^-3, and the Hubble parameter is ~70.8 km s^-1 per megaparsec (a parsec is 3.2616 light years, or 3.0857 × 10¹³ km, so 1 megaparsec is 3.0857 × 10¹⁹ km, and H₀ = 2.2944 × 10^-18 s^-1; the reciprocal of H₀ is the Hubble time, τ₀, which is 13.82 billion years, roughly the age of the Universe; see: http://wmap.gsfc.nasa.gov/universe/uni_expansion.html).

Putting the numbers in above, we have:

Ω_TOT = 0.99817 = 0.72 + 0.233 + 0.046 – 0.00083 ,

which gives us the value of the space-time curvature density parameter, Ω_k = (-) 0.00083. If this is true, and if Ω_TOT < 1, then the curvature parameter k = –1, and space-time is Bolyai-Lobachevskian, i.e., open. With a positive non-zero value for Λ, its expansion is also accelerating over time, so that the past – the Big Bang – will retreat to infinity at a steadily increasing rate.

Long before then, the Sun will have died, as eventually all stars will die, and all black holes will evaporate, via Bekenstein-Hawking radiation.

It is a bleak prospect, but there are literally trillions of years to go before then, so there is really no point in worrying about it!

Of much more immediate concern is the fate of the Sun, which will become too hot for us, even without the greenhouse effect, in a few hundred million years from now. Of course, not only we not be here, but the human race might not be here – the dinosaurs, all the many different classes, genuses and species of them, lasted for hundreds of millions of years, and genus Homo has only been around for 2 million thus far. As for sub-species H. sapiens sapiens, we’re johnny-come-latelys, who have only been around for ~200,000 years, 0.0044% of the age of the Earth, or 0.00145% of the age of the Universe.

It is a sobering thought. However, as Blaise Pascal said, in the Pensées (1670, No.347), L’homme n’est qu’un roseau, le plus faible de la nature; mais c’est un roseau pensant. (‘Man is a reed, the weakest in nature; but he is a thinking reed.’)

Lockesley Hall.

'For I dipt into the future, far as human eye could see, Saw the Vision of the world, and all the wonder that would be;

Saw the heavens fill with commerce, argosies of magic sails, Pilots of the purple twilight, dropping down with costly bails;

Heard the heavens fill with shouting, and there rain'd a ghastly dew From the nations' airy navies grappling in the central blue;

Far along the world-wide whisper of the south-wind whistling warm, With the standards of the peoples plunging thro' the thunder-storm;

Till the war-drum throbb'd no longer, and the battle-flags were furl'd In the Parliament of man, the Federation of the world.

There the common sense of most shall hold a fretful realm in awe, And the kindly earth shall slumber, lapt in universal law.'

Alfred Tennyson wrote 'Lockesley Hall', the poem from which those lines are taken, in 1835, the year he turned 24. The first two lines quoted here appear on the dedicatory plaque of the Starship Voyager in the American TV Science Fiction series, Star Trek: Voyager. The phrase 'Parliament of man' inspired the title of Paul Kennedy's 2006 history of the UN, The Parliament of Man: the Past, Present and Future of the United Nations. I owe these facts to the anonymous author of the Wikipedia entry.

Was Tennyson a prophetic visionary? Nassim Nicholas Taleb rightly warns us about what he calls 'Black Swan' events, and his hero Sir Karl Popper rightly poured scorn on the idea of 'iron laws of history' in The Poverty of Historicism. (There is one iron law of history, at least, if no other - and that is that, sooner or later, all Empires - and all Civilisations - decline and fall.) Predictions, projections and forecasts are generally bunk. But maybe, just maybe Tennyson got it right here. It would be nice to think so.

I see nothing to be afraid of in a World Government or New World Order (NWO), and everything to be welcomed. That's why I'm in favour of the EU, and new security and co-operation agreements in Europe and Asia that would include the Russians, the Indians, the Pakistanis and the Chinese - all nuclear armed countries, with Pakistan having severe internal problems with Islamic extremist terrorism.

So the NWO isn't a conspiracy of Blacks, Jews, Freemasons, Catholics and Communists, or Knights Templars, Rosicrucians and Illuminati, or Little Green Men from Outer Space, or Demons and Antichrists, or the UN, the US Government, US Council on Foreign Relations, the Trilateral Commission, the Bilderberg Group, Uncle Tom Cobley and all. It's a good thing, and it can't happen too soon for me. Of course, being Catholic, disabled and gay, I'm probably in on the conspiracy, aren't I?

Not the New Age!

I should explain – should, perhaps, have already explained – that I am not a believer in the late Mr McKenna’s ideas, or in M Vallée’s, for that matter, and certainly not in Mr John Major Jenkins’s.

Like many other ‘New Agers’, apparently, Mr Jenkins is fascinated by the Mayans, and their Long Count Calendar in particular. This, it has been established, has a start time/date that corresponds to 0.00 GMT on the Gregorian Calendar’s Monday, 11^th August, 3114 BC (Julian Day Number 584282.5), and an end time/date that corresponds to the Winter Solstice in the Northern Hemisphere/Summer Solstice in the Southern Hemisphere of 2012 AD: to be precise, 11.11 (AM) GMT, on Friday, 21^st December, 2012 (Julian Day Number 2456282.9659722224).

According to Mr Jenkins, this end time/date corresponds to the end of the current Great, or Platonic, Year – the cycle of the precession of the equinoxes. He is simply wrong about that – it does not, in fact it isn’t due to end for another 600 years! (See: http://www.wwu.edu/depts/skywise/a101_precession.html). In fact, it is very unlikely that the Mayans knew about precession, and certainly not to the degree of precision required by Mr Jenkins’ theory (see: http://www.instituteofmayastudies.org/Milbrath2012.pdf).

He also argues that the Winter (or Summer, depending on which Hemisphere you’re in) Solstice Sun of 2012 will be passing through the exact centre of an area of the sky that corresponds to what we call the Galactic Dark Rift (or ‘Great Rift’), and that the Mayans knew that this would be the case. Susan Milbrath rightly points out that, in the absence of NASA’s high technology, that is, to say the least, highly improbable. In any event, it is not true – for the Sun was actually closer to the centre of the Dark Rift back in 1998 (see: http://en.wikipedia.org/wiki/2012_phenomenon).

The Great Rift consists of overlapping, non-luminous clouds of dust and gas located between the Solar System and the Sagittarius Arm of the Galaxy, about 100 parsecs (326.16 light years) from Earth. They are estimated to have a total mass equal to about 1 million Suns (1.9891 × 10³⁶ kg.

The Rift starts in the constellation Cygnus, passes through Aquila (‘The Eagle’), Ophiucus (‘The Serpent Bearer’), where it widens, Sagittarius (‘The Archer’), where it obscures the Galactic Centre (officially the powerful radio source, Sagittarius A*, almost certainly a super-massive black hole), before finally ending in Centaurus. See: http://en.wikipedia.org/wiki/Great_Rift_(astronomy).

The Milky Way was, according to Milbrath, perceived by the Maya as a cosmic serpent – a feathered or plumed one (K’uk’ulkan, in Yucatec) – which the Aztecs named Queztalco’atl (Classical Nahuatl: ‘feathered serpent’). It encompassed the World Tree, the Ceiba, which linked the heavens, the realm of the gods, the Earth, and Xibalba, the Underworld. The similarity to the Norse world picture is obvious, except that in the Norse case, the cosmic serpent, Jörmungandir (Niðhŏggr), apart from not being feathered, encompasses, not the heavenly realm, which in the Norse case is Asgard, but Middle Earth, Midgard, and lies at the foot of the World Ash Tree, Yggdrasill. (See: HR Ellis Davidson, God and Myths of Northern Europe, Penguin, 1964, pp.227, 234-5, 240; http://en.wikipedia.org/wiki/J%C3%B6rmungandr).

Another important feature of the Mayan cosmic serpent is that it swallows its own tail, like the Ouroboros (see: http://en.wikipedia.org/wiki/Ouroboros), that classic symbol of eternity and cyclic time, as does the Midgard Serpent – another interesting similarity, which almost makes one think there might be something in Jung’s idea of the Collective Unconscious after all.

The Great Dark Rift was also seen, by some Mayans at least, as the Xibalba be’, or ‘Dark Road’, which led to Xibalba, the Underworld (literally, ‘The Place of Fear’), ruled by twelve gods or demons, know as the Lords of Xibalba, chief of whom, according to the Popol Vuh, are Hun-Came (‘One-Death’) and Vucub-Came (‘Seven-Death’). The Orion Nebula is the physical location of Xibalba, according to Darren Aronofsky, although the K’iche’ Maya of Guatemala, who identify the Xibalba be’ as the Dark Rift, also claim that the entrance to Xibalba is to be found in a cave in the vicinity of Cobán, 219 km N of Guatemala City. Cave systems in Belize have also been identified as the entrance (see: http://en.wikipedia.org/wiki/Xibalba), just as Avernus, near Cumae, was the supposed entrance to the underworld of Roman mythology (by Virgil, e.g., in the Aeneid, see Aen. VI, 126f., ‘Facilis descensus Averni:/Noctes atque dies patet atri ianua Ditis;/Sed revocare gradum superasque evadere ad auras,/Hoc opus, hic labor est.’^[1]; http://en.wikipedia.org/wiki/Avernus).

For the Mayans, the Milky Way was not just the feathered serpent, K’uk’ulkan, but the Sac be’ or Zac be’ – The White Road. It is the White Road, not the Dark Road, that we should be focussing on, in trying to understand the Mayan cosmology and Mayan religious belief. The Xibalba be’ was the road to hell – Xibalba was a bad place, as not only the name, but the description in the Popol Vuh makes clear – the equivalent of the Greek Tartaros, the Norse Niflheim and the Christian Hell (see: Ellis Davidson, op.cit., p.235; Robert Graves, The Greek Myths, Vol.1, Penguin, 1960, pp.106, 112, 362-6; Vol.2, Penguin, 1960, pp.152-8, 409).

The anthropologist, Dr Steven Mizrach, of the Department of Sociology and Anthropology, Florida International University, Miami, argues in a paper entitled ‘The White Road of Yucatán. The Mayan Sacbe System Analyzed as an Information Web’, that K’uk’ulkan may have been a priest of a deity of the same name, who as the feathered serpent represents both the Earth – shedding his skin and regenerating – and Heaven – with his wings, carrying the élan vital of Heaven to Earth. Mizrach compares him to the Greek Hermes/Roman Mercury, the messenger-god and god of secret knowledge (as in ‘hermeneutics’, the science of interpreation, from Greek hermēneutikos; hermēneus, an interpreter; from Hermēs, the god; Hermetic Tradition, derived from the name, Hermēs Trismesgistos, ‘Thrice-Great Hermes’, pseudepigraphical author of the Corpus Hermeticum [prob. 2^nd/3^rd Cent. AD]) with his symbol of the caduceus, the staff bearing twin entwined snakes (which is also, incidentally, the symbol of Asklepios [Aesculapius], the Greek god of healing). See: http://www.fiu.edu/~mizrachs/white-roads.html.

To return, finally, to the Mayan Long Count Calendar. The Long Count was essentially, though not strictly, vigesimal, that is to say, it operated on a base-20 system. Twenty k’ins (days) made 1 uinal, or ‘month’. Eighteen of these make 1 tun. Twenty tuns make a k’atun, and twenty k’atuns equals 1 b’ak’tun = 20 × 18 × 20 × 20 = 144,000 days. Thirteen b’ak’tuns = 1,872,000 days, which is one Long Count Cycle, not counting the hours and minutes. That’s 5,125.2566735 Julian Years (a Julian Year is 365.25 days long, to take account of leap years).

How did the Mayans come up with this number, and why 13 b’ak’tuns, as opposed to say, 14, or 15, or some other number?

Well, one of the other calendars they used, the Tzolk’in, had a ‘year’ of 260 days, consisting of 20 named days combined with a repeating cycle of 13 days, which Spanish scholars dubbed the trecena (Spanish, trece, ‘thirteen’): 20 × 13 = 260. Vincent H Malström, of Dartmouth College, New Hampshire, US, in his paper, ‘Origin of the Mesoamerican 260-Day Calendar’, Science 181:939-41 (http://www.dartmouth.edu/~izapa/M-1.pdf), argues that this calendar arose among several Pre-Columbian Mesoamerican peoples (the Toltecs, Olmecs and Aztecs as well as the Mayans) from observations of the number of days between transits of the zenithal Sun in tropical latitudes, circa 15° N. It would have been easy to see on what two days the Sun did not cast a shadow from a particular stick or stone at noon, and count the number of days between them, quickly establishing that it comes to 260. The Tzolk’in Calendar was (and still is) used for religious and ceremonial purposes by the Mayans.

To convert from Tzolk’in to Long Count, it is only necessary to perform the following arithmetical calculation: 260 (= 13 × 20) × 20 × 20 × 18 = 1,872,000 days; but those are exactly the numbers that the Mayan Long Count uses, when multiplying k’ins, uinals, and so on.

It is fascinating to see how this cultural meme has arisen, but to blame the Maya for it is unfair and misleading. The Long Count end-date does not represent the Apocalypse, and those expecting to see Planet X/Nibiru slamming into the Earth that day, or the arrival/unveiling of the Antichrist, or the Dawning of the Age of Aquarius, or whatever, are likely to be disappointed. Some nutters think the Antichrist is already here – he’s Barack Obama (or Vladimir Putin, or whoever)!! With some of that, and some slightly more sensible, and non-racist, views, see: http://www.abovetopsecret.com/forum/thread457040/pg1.

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^[1] ‘The road to Hell is easy:/the black gates of Dis stand open night and day;/but to retrace one’s steps, and return to the upper air,/that is toil, that is labour.’