The solution to a conundrum.

Yesterday, BBC2 broadcast a fascinating Horizon programme on one of my favourite subjects – black holes.  A parade of physicists (theoretical and experimental) and astronomers were put before us to talk about them, and why the thing that lies in their very centre presents such problems for modern physics.

            Einstein’s General Theory of Relativity is very good at accounting for gravity, and what happens on the large scale; quantum mechanics is very good at describing atoms and sub-atomic particles, and what goes on at the very small scale.  With black holes, we know there is a connection of some sort between the two theories, and between them and thermodynamics, because of the phenomenon of Hawking radiation (which, saving Hawking’s status among physicists, should really be called Bekenstein-Hawking radiation, because Jacob Bekenstein worked out the formula for it first, in 1972, whereas Hawking came up with it in 1975^[1]) and because inside a black hole, at its very centre, is a thing called a ‘space-time singularity’.

            What is a space-time singularity?  It is what existed at the very, very beginning of the Universe, and why we can describe our Universe as if it were an enormous black hole.  It is, in effect, a Euclidean point, of zero dimension and extension, but one that has mass, and therefore density and pressure – both infinite – and infinite energy density.  It is, to the theoretical physicists, a surd in the equations of the General Theory of Relativity, and one they can’t cope with.

            When they try to deal with it by quantising it, to create a Quantum Theory of Gravity, they get still more infinities.  Such a theory is not, in the technical jargon, ‘renormalisable’.  They get infinities in ordinary quantum field theory, too, but by a piece of mathematical sleight-of-hand called renormalisation^[2], they can get rid of them.  Neither the great British theoretician, Paul Dirac, nor the American physicist, Richard Feynman were particularly happy about this conjuring trick, but they could see no alternative.

            Sir Roger Penrose has pointed out that, in order for our Universe to have the level of order we perceive, and in order for it to be capable of supporting organic chemistry and therefore life, what emerged from the space-time singularity had to be selected from the thermodynamic phase space of all possible Universes to a very high degree of precision.  If the number of baryons (protons and neutrons) in the Universe is of the order of 10⁸⁰, and the cosmic background radiation is 2.7 K, then the current entropy per baryon is

 

S/N  = ( k log_eV)/ N  =  10⁸ ,

 

meaning there are roughly 10⁸ photons for every baryon (k here is measured in ‘natural units’, and is thus equal to 1; N = 10⁸⁰; log_eV = 10⁸⁸; V = e^{10^88}).  Penrose calculates that, when one takes into account the black holes in all the galaxies, for a closed (Riemannian) Universe, the total volume, V, of phase space that the Creator had to aim for in creating the Universe out of the original space-time singularity, given an entropy per baryon at the ‘Big Crunch’ of 10⁴³ in natural units, this would mean a total entropy of 10⁸⁰ × 10⁴³ = 10¹²³, and a phase space volume of 10^{10^123} (or, to be more accurate, e^{10^123}).  As Penrose says, in order to produce a Universe resembling the one in which we live, God had to aim for an absurdly tiny volume of the phase space of all possible universes – about 1/e^{10^123} – of the entire volume, a number one could not write down in the ordinary denary notation, even if one employed all the particles in the Universe on which to write each single digit^[3].

            What neither Penrose nor any of the scientists interviewed on the Horizon programme can deal with is the idea that infinity, or the infinitesimal, might have a rôle in physics – and the very last thing they can deal with is the idea of God.  Penrose actually talks of ‘the Creator’, rather than God, and he is not serious in referring to Him.  Je n’avais-pas eu besoin de cette hypothèse.  They have tried to create a unified ‘theory of everything’ (‘TOE’), in the form of Kaluza-Klein Theory, N=8 Supergravity, String Theory, Superstring Theory, M-Theory, Quantum Loop Gravity, and E8 Polytope Theory, all of which have failed.  (This would undoubtedly be denied by the theoretical physicists who continue to waste their careers pursuing them, but the fact is they are simply going around in ever-decreasing circles.)

Electro-weak theory has been a partial success, in that it has managed to unify electromagnetism with the weak interaction.  Quantum chromodynamics is a reasonably successful account of the strong nuclear force, but there are several GUTs (‘Grand Unified Theories’) on the market, which attempt to unify electromagnetism, the weak force and the strong force, and no candidate has yet found universal favour and sufficient experimental support to count as the theory of the three forces other than gravity.  The Standard Model accounts for the various particles and forces, but it is ad hoc, and relies on the Higgs Field and the Higgs Boson to provide all the various particles with their mass.  The latter may be detected by the Large Hadron Collider at CERN in Geneva when it is finally over its teething problems.

Why am I so confident that the TOE-pursuing physicists are wasting their time?  Because they are trying to explain the inexplicable.  They are trying to extend physics where physics does not belong, and where theology and metaphysics take over.  A space-time singularity is not a surd in the equations, but an irreducible and inescapable reality.  The Big Bang singularity was the very moment of creation.  At cosmic time t = 0, spatial extension in all three dimensions, x, y and z was 0, and all the mass in the Universe – all 8.79674 × 10⁵² kg of it – was concentrated in a Euclidean point.

The rest-energy of this mass is Mc² = 7.906 × 10⁶⁹ J, a truly staggering number.  However, at cosmic epoch t = 0, when you convert this into action, which is energy × time, you get 0.  It is only when the jump is made from t = 0 to t = the Planck time, (Għ/c³)^½ = 1.616 × 10^-35 s that there is a non-zero quantity of action,

 

_S  =  1.277648 × 10³⁵ Js .

 

This is perfectly consistent with the Feynman path integral approach to quantum mechanics and quantum field theory.  Of course, the implication is, that there was one enormous jump in the amount of action (in the physical sense) in a very, very short space of time!  Divide s by h and one gets 1.928 × 10⁶⁸, an enormous number, which is the equivalent of 10⁵⁶ photons, each with a frequency of 1.928 THz (infra-red light, or radiated heat)^[4].  The Big Bang was very hot indeed (about 10³² K, see: http://www.astro.ucla.edu/~wright/BBhistory.html)!

            Yet this won’t satisfy the physicists.  Why not?  Because they will want a set of equations telling them how to get rid of the Big Bang singularity altogether and allowing them to supply a complete, atheistic, naturalistic explanation of the Universe and its laws.  That they cannot have.  It simply isn’t on offer.  There is no such explanation, because the Universe was created by a Creator God from nothing.  There was a point in eternity (not time) when there wasn’t even a space-time singularity, because there was no mass-energy to be squeezed into that Euclidean point.

            Einstein’s dream of a final theory is just that – a dream.  His dream, and that of the British mathematician WK Clifford, and of Galileo Galilei before him, and Pythagoras and his followers before him, of reducing physics to geometry, is pure fantasy.  (There are mathematicians who want to reduce geometry to topology and thence to algebra!)

            The Austrian-American mathematician and physicist Kurt Gödel probably spelt the end to this dream in 1931, when he published the work proving his two incompleteness theorems^[5].  Gödel proved that, in any formal system capable of generating propositions of arithmetic, it is the case that (a) for any consistent, effectively generated theory capable of proving certain basic arithmetical truths, there is at least one statement that is true, but not provable, in the theory; and (b) for any formal theory including basic arithmetical truths and also certain truths about formal provability, the theory would include a statement of its own consistency if and only if it were inconsistent.

            Any physical theory must, of its very nature, be mathematical, and – obviously – logically consistent.  While it may not be provable, it must, at least, be empirically disprovable, if the late Sir Karl Popper is any guide to the methodology of the natural sciences.  Applying Gödel’s two incompleteness theorems to all theories in physics, there must be some equations generated by such theories that are either insoluble, or if soluble, are not provably true, which amounts to the same thing (i.e., one might be able to come up with an answer, or several possible answers, but have no way of knowing if it was the right one, or which was the right one).

            It is therefore quite impossible for a TOE to specify the values of all the physical constants, determine the laws of physics, the relative and absolute strengths of the four physical forces, and the initial thermodynamic properties of the Universe, all with a unique, self-consistent and mathematically provable set of equations.  There are just too many different parameters involved, as we have already seen.

Even if it were possible for such a theory to exist, which I am very far from allowing, that still wouldn’t prove that God did not exist, nor would it obviate the need to postulate a Creator.  For one would still have to ask, where did this set of equations come from – who (or conceivably, what) decided to set the Universe up on that basis?  Where did the matter and energy come from, where the space and time?

There are none so blind as those who will not see.  It is a sad reflection on so many of our scientists that they will do anything rather than admit the possibility of a God.

 

***

    

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^[1] The equation is S = 2πm²(kG/ħc) for a spherically symmetrical black hole, where S is the entropy, m is the mass, k is Boltzmann’s constant, G is the Newtonian constant of gravitation, ħ is the Dirac constant (Planck’s constant over 2π) and c is the speed of light in vacuo.  See: Penrose, R. (1989), The Emperor’s New Mind, London: Vintage, pp.441-3.  The absolute temperature of the black hole is then T = ħc³/8πkGm, and the power output is given by P = ħc⁶/15,360πG²m².  See: http://en.wikipedia.org/wiki/Hawking_radiation.  The super-massive black hole at the centre of our Galaxy has a mass equal to 4 million Suns (see: http://news.bbc.co.uk/1/hi/7774287.stm), and as the Sun has a mass of 1.9891 × 10³⁰ kg (332,900 Earth masses; see: http://en.wikipedia.org/wiki/Sun), this means that its power output is 5.629 × 10^-42 W.  Its temperature is 1.524 ×10^-14 K, a very small amount above absolute zero, the lowest possible temperature.

^[2] Normalisation entails the use of a normalising constant, which is a constant which, when multiplied by an everywhere non-negative function makes the area under its graph equal to 1.  The Boltzmann distribution requires one (see: http://en.wikipedia.org/wiki/Normalizing_constant).  Renormalisation arises out of the need to avoid infinities stemming from particle or virtual particle self-interactions, point charges, and so on.  See: http://en.wikipedia.org/wiki/Renormalization.

^[3] Penrose, op.cit., pp.444-6.

^[4] THz = Teraherz, 10¹² Hz (= s^-1).

^[5] Gödel, K (1931), Über formal unentscheidbare Sätze der Principia Mathematica und verwandter Systeme, I.  Monatshefte für Mathematik und Physik 38:173-98.

Theodicy.

‘That I may assert Eternal Providence/And justifie the ways of God to men.’ So Milton declares his aim in writing Paradise Lost (Bk.1, ll.25-6).

Theodicy is a compound of two Greek words – theos, God, and dikē, justice. The ‘theodicy question’ is the attempt to answer the question that is often put by people who have become atheists because of something terrible that has happened, either to them, or to someone they loved. ‘If God is good and all-powerful, why does He allow so much suffering and so many terrible things to happen in the world?’

This question is very often couched in directly personal terms. ‘If God is so good, why did He let my wife/husband/son/daughter die of cancer?’

The people concerned don’t usually have any problem with the idea of God’s omnipotence. It is automatically assumed that, if God exists, then He is all-powerful. What they question is His moral status – His goodness. And given that God is supposed to be good per definitionem, they regard the absence of goodness they perceive as conclusive disproof of His existence.

What all such people fail to understand, however, is that God is not in the business of ensuring that everyone’s life runs absolutely smoothly and pain-free. Nor Has He organised the Universe to ensure that no-one ever dies, or gets sick, or injured in an accident, or as a result of some natural event, like an earthquake, or a flood.

To create a complete pain, suffering and death-free world for us to live in would require so much intervention in the natural order on His part, that the natural order would, in effect, disappear, and the divine, supernatural order be visible to plain sight. There would, in consequence, be no room for faith.

With no room for faith, there would be room for free will; and without free will, there can be no love, because love, in order to be genuine love, must be given freely, and from the heart.

Above all, God wants us to freely love Him, because He is love (1 John 4:8). So free will is not an optional extra: it is essential. Without free will, we would, in any event, be like zombies or robots, with no more moral responsibility for our actions than a computer has for its actions.

The 18^th Century French philosopher, François-Marie Arouet de Voltaire (1694-1778), ridiculed Leibnitz’s idea that ‘all was for the best in the best of all possible worlds’ in his famous satire, Candide, and it is understandable, in many ways, why he and others should have felt compelled to do so – just as it is understandable why the Jews of Auschwitz should have felt justified in putting their God on trial (if the story described by Elie Wiesel in The Trial of God has any truth in it, that is; sc., the excellent BBC2 TV play by Frank Cottrell Boyce, based on the book, broadcast in September 2008, God on Trial, starring Anthony Sher, Stephen Dillane, Rupert Graves and Jack Shepherd).

Many of the terrible things that happen in this world are not the fault of God, but of Man. All too often, we exercise our free will to inflict death, injury and needless harm on our fellow human beings – physically, psychologically and in other ways, simply to gratify our own ends.

Many more ills, that are not the result of malign human acts, are the result of human omissions, neglect and negligence, or just sheer human stupidity. ‘Against stupidity, the gods themselves contend in vain’ (Friedrich von Schiller, Die Jungfrau von Orleans, III, vi).

So, whereas it might be understandable – and even pardonable – for Voltaire and the Auschwitz Jews to criticise Leibnitz’s theology and God Himself, respectively (particularly the latter, given their truly terrible circumstances), neither criticism is justified.

For, in spite of all appearances to the contrary, all really is for the best in this, the best of all possible worlds – which may not say very much for the alternative possibilities, but we have already seen, in earlier postings, that the Universe is fine-tuned for life generally, and intelligent life here on Earth in particular.

This would suggest that the other alternatives might not even support life! In wishing the world to be other than it is, we would do well to be careful what we wish for – not that our loving Father would grant any of His children anything that would harm them.

He does however, permit them to harm themselves – precisely because He wants them to be free, and has endowed them with free will. So, if they end up killing themselves with a drugs overdose, or by driving their car while drunk, or by committing suicide, then – although that will undoubtedly grieve Him – He will allow it, because free will matters, and He will not abrogate it just for our convenience.

There is, in other words, no divine equivalent of the ‘Nanny State’. We remain in control of ourselves, and therefore responsible for what we do, both to ourselves and to those around us; and we are responsible for ourselves, too.

Perhaps it is time we shifted the focus away from theodicy onto anthropodicy (Greek: anthrōpos, ‘man’; dikē, ‘justice’). That sound to me like a far more interesting question!

***

Creationism versus Darwinism.

The opinion researchers Ipsos-Mori have just completed an Opinion Poll on behalf of the British Council, of a sample of 11,768 people aged 18+, in 10 different countries – Argentina, China, Egypt, Spain, India, Mexico, Russia, South Africa, the UK and the USA.

The poll asked the surveyed adults to say whether they had heard of Charles Darwin and knew of his work on evolution, and asked their opinion about whether (a) Darwin’s theory of evolution should be taught in schools on its own; or (b) in conjunction with creationism and/or ‘intelligent design’. Only 7000 members of the sample had actually heard of Darwin in the first place! (See: http://news.bbc.co.uk/1/hi/education/8322781.stm.)

Of the British adults surveyed (973 members, 8.268% of sample), 54% said they wanted evolution taught alongside creationism and intelligent design. In the US, of the 991 people who took part in the survey (8.421% of sample), some 51% agreed that evolution should be taught alongside creationism and intelligent design.

This figure rose to 68% in Argentina. Worldwide, 43% said evolution should be taught alongside other views, while 20% said only evolution should be taught (see: http://www.google.com/hostednews/ukpress/article/ALeqM5jNch2zlhAbeuVngLrvT2C0szGfOQ.)

I have had my own run-in with creationists. In fact, I was told by one recently that, if I did not believe that the world was created in six days (meaning, in six periods of twenty-four hours – I checked that that was what he meant) 6000 years ago, then I was destined to spend eternity in the flames of Hell, for not believing the Word of God.

I told the man who said this (a civil engineer by profession, a Dr Farid Abou-Rahme, see: http://www.bcseweb.org.uk/index.php/Main/FaridAbouRahme) that, if so, I was in good company, and preferred the idea of going to Hell with Richard Dawkins and Stephen Hawking than to Paradise with him. I also told him precisely where he could stick his Bible.

Divine intervention is not a requirement for evolutionary speciation by means of natural selection of random mutations. Divine Providence cannot be ruled out of Earth’s biological history – the Chicxulub asteroid impact 65 million years ago that wiped the dinosaurs out, and allowed the mammals to take their place, may have been no more than a happy accident, from our point of view – but on the other hand, it may have been the hand of God at work. However, if it cannot be ruled out, neither can it be ruled in. Whether or not you believe in a God – that is a matter of choice – of individual faith.

Does the existence of the Universe require God for an explanation? If there is only one Universe, and only one set of physical laws and parameters and was only one set of initial conditions, then yes, because the weak anthropic principle is not a sufficient explanation of the fact that they are so finely adjusted to the requirements of organic chemistry and biology, and the strong anthropic principle is, in Barrow and Tipler’s reformulation, merely a re-statement of the classic Design Argument of St Thomas Aquinas and William Paley (see: http://en.wikipedia.org/wiki/Anthropic_principle; and http://en.wikipedia.org/wiki/Design_argument).

However, if, on the other hand, there is a cosmological Multiverse – not like Linde’s and Vanchurin’s – but with an infinite number of universes, all existing in parallel, in an infinitely extended higher dimension, with each having its own, quantum multiverse – then the answer may be no.

If the laws and parameters of physics are different on each separate ‘brane’ – i.e., in each separate universe, the question is, do they need to be the same at the ‘Big Bang’ stage – when the four forces of nature: gravity, electromagnetism, the weak and strong nuclear interactions; were one, unified force?

If the answer to that is ‘yes’, then there is no escape from theism – God is still there, and He has not become a deus otiosus or a deus absconditus. If you can explain away the fine-tuning of our particular universe for carbon-based life, and for observers, in terms of the weak anthropic principle and observer self-selection effects, then how do you explain away the physics that allows those self-selection effects to arise in the first place?

Even if the laws of the ultra-high energy, ultra-high temperature and pressure physics that prevailed in the very early Universe were extremely general, you would still have to explain how they got there, and where they came from. Where did the mass and energy come from? Who or what ‘decided’ on the physical parameters and initial conditions?

This, of course, assumes that we are dealing with one – and only one – Big Bang. Now let’s assume that each separate universe, or ‘brane’, of the Multiverse had its own Big Bang, and therefore has its own laws of physics at ultra-high, as well as much lower, temperatures. Consequently, there are an infinite number of different sets of laws of physics, physical constants, and initial conditions. That still leaves the question of where did the mass and energy come from.

The Heisenberg Uncertainty Principle allows a quantum system to ‘borrow’ energy for a given amount of time and then pay it back, by the equation:

ħ = ∆E.∆t .

Thus, the electromagnetic interaction between two charged particles is mediated by the exchange between them of a ‘virtual’ photon, which ‘borrows’ energy equal to hν (Planck’s constant × its frequency) for a time t = 1/2πν.

For a universe, the amount of time that the energy needs to be borrowed for is enormous, and one would think that the amount of energy required would be enormous, too – but in fact, it can sum to something close to zero.

This is because gravitational energy, which is trying to pull all the matter and energy in the universe back into a singularity (a Euclidean point, of zero extension and dimension) can be treated as negative, and subtracted from the kinetic energy of the Big Bang itself, which is, of course, pushing everything in the universe further apart, and the energy of the cosmological constant repulsion force, which is doing the same thing. There is also heat energy in the universe, which diminishes as the cosmos cools down.

This idea still pre-supposes, however, that there is something for the universe (whichever universe it happens to be) to borrow energy from. The ‘quantum vacuum’ has to pre-exist from all eternity, and it is the quantum vacuum that proclaims Fiat lux.

It won’t do, will it? Try as hard as I can, I cannot come up with a convincing argument – one that convinces me, at any rate – that atheism is true. You can squeeze Him out of biology, but you cannot squeeze Him out of cosmology. I don’t believe in the cosmological Multiverse, on the grounds, quite simply, of Occam’s Razor: Entia non sunt multiplicandur quærens necessitatem^[1].

As far as the quantum multiverse is concerned, it seems to me that the Copenhagen Interpretation is more likely to be valid than the Everett de-Witt Interpretation, and I prefer its emphasis on the rôle of the Observer, in any event. The quantum multiverse also seems to me to be ruled out by Occam’s Razor, and by the principle – central to quantum mechanics – that unobservables, or things that are not even indirectly observable, are of no significance for physics (or empirical science, generally).

Kierkegaard said that ‘subjectivity is the truth’. I disagree, but not to the extent of flatly contradicting him. I prefer, rather, to say, ‘intersubjectivity is the truth.’ Nor do I agree with the likes of Richard Rorty or Hilary Putnam that ‘there is no such thing as “truth”’.

God is still needed for the Creatio ex nihilo; He (I use the masculine pronoun purely for convenience – I do not imply that God is, in fact, male – or female, for that matter, and certainly not neuter) had to pre-exist from all eternity in order to create the matter and energy of the Universe, and establish the laws and constants of physics and initial conditions required for carbon-based life and, eventually, observers to emerge at the appropriate times.

This is, of course, the Barrow-Tipler Strong Anthropic Principle (SAP), or revived/revised Design (or Teleological) Argument.

The appropriate time, in the case of Observers, is given by:

t = 2GM/c³ = 2ħ²/Gm_pm_nm_ec = (3.3825 × 10³⁸) × (ħ/m_ec² = 1.288 × 10^-21 s)

= 4.35666 × 10¹⁷ s = 13.8 billion years .

Here, the expression ħ/m_ec² represents the angular Compton period of the electron. M is the Mass of the observable Universe (8.79674 × 10⁵² kg). The 3.3825 × 10³⁸ is close to Dirac’s large number (actually ħc/Gm_p² = 1.69358 × 10³⁸), which is the reciprocal of the gravitational coupling constant, 5.90465 × 10^-39.

As can easily be seen, this is the present age of the Universe, as determined by the Wilkinson Microwave Anistropy Probe (WMAP).

Anatomically modern humans, the sub-species Homo sapiens sapiens, first emerged in Africa some 500,000 years ago (see: http://en.wikipedia.org/wiki/Human). This is 0.003623% of the total age of the Universe. We have had the scientific knowledge and technological capability to launch space probes only in the last fifty-two years, since the launch of Sputnik 1, on 4^th October 1957. That is 0.0000003768% of the age of the Universe. A space probe as sophisticated as WMAP could only be launched within the last ten years – in fact, on 30^th June, 2001, nearly 8 years 4 months ago. Eight years is 0.00000005797% of the age of the Universe, so it was just 0.00000005797% of the age of the Universe ago that we became capable of measuring the age of the Universe.

Perhaps that means that we have at long last come of age – or maybe just entered adolescence.

***

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^[1] ‘Do not multiply entities beyond necessity.’

Middle Eastern Apocalypse, 2009?

Today’s (Sunday, 25^th October) BBC News Online carries a story about Israeli police arresting stone-throwing Palestinian demonstrators outside the Al-Alqsa Mosque on Temple Mount in Jerusalem.

So, what else is new, you might ask. What is new, and disturbing, is that the demonstration was provoked by rumours that have been circulating in the Arab communities throughout the Middle East that Jewish extremists are plotting to destroy the Dome of the Rock (the Masjid Qubbat as-Sahkrah, or Kipat Hasela^[1], in Hebrew, see: http://en.wikipedia.org/wiki/Dome_of_the_Rock) and/or the Al-Aqsa Mosque itself, together known as Al-Haram al-Sharif, ‘The Noble Sanctuary’, in order to make space to rebuild the Temple, and re-instute the Temple sacrifices, which were halted when the Romans under Titus destroyed the Second Temple in 70 AD, following the First Jewish Revolt of 66-70. (See the account of Flavius Josephus [37-c.100 AD], The Jewish Wars, VI, 249-60, trans. & ed., William Whiston,

http://old.perseus.tufts.edu/cgi-bin/ptext?doc=Perseus%3Atext%3A1999.01.0148;query=whiston%20chapter%3D%2394;layout=;loc=6.177.)

That these rumours are being stoked up by enemies of peace on the Arab side is certain. That they are not without foundation is, unfortunately, also certain. For there are indeed Jewish extremists who have been wanting to do precisely as outlined above ever since the Israelis seized East Jerusalem from Jordanian control in the Six Day War in 1967. It was only the intervention of the then Israeli Defence Minister, Moshe Dayan, that prevented members of the Israeli Defence Force (IDF) from dynamiting the Dome of the Rock then. (See: http://www.acpr.org.il/English-Nativ/06-issue/medad-6.htm.)

These extremists are supported by so-called ‘Christian Zionists’, such as David ben-Ariel, and Dispensationalist Evangelicals, such as Hal Lindsey and Tim LaHaye, all three of whom may safely be characterised as American Christian fundamentalists, well to the right of the political spectrum.

‘Google’ the term ‘Third Temple’, and this is what you will come up with: David ben-Ariel’s ’Blog (see link above); the website of the Temple Mount and Land of Israel Faithful Movement, http://www.templemountfaithful.org/ (‘Our goal is the building of the Third Temple on the Temple Mount in Jerusalem in our lifetime in accordance with the Word of G-d and all the Hebrew prophets and the liberation of the Temple Mount from Arab (Islamic) occupation so that it may be consecrated to the Name of G-d^[2]); and http://thirdtemple.org/, a vitriolic anti-Muslim site featuring the Dutch politician Geert Wilder’s film, Fitna, which portrays the Qu’ran as a ‘fascist’ book, and all Muslims as extremists, and a piece by a Spanish journalist which reads, in part, ‘we [Europeans] killed six million Jews and replaced them with 20 million Muslims. In Auschwitz we burned a culture, thought, creativity, talent. … under the pretense of tolerance, and because we wanted to prove to ourselves that we were cured of… racism, we opened our gates to 20 million Muslims, who brought us stupidity and ignorance, religious extremism and lack of tolerance, crime and poverty due to an unwillingness to work and support their families with pride’.

The Muslims I know are neither stupid nor ignorant, they are extremely hard working, have never been in trouble with the law, and no-one could further from the description of intolerant religious extremist. On the contrary, they are as moderate as the average middle-of-the-road Anglican.

Just who is the intolerant religious extremist here? Is it someone who can work in a shop or restaurant and happily serve their customers alcohol, even though they can’t drink alcohol themselves, or is it someone who rants about all Muslims as if every single Muslim man, woman and child in Europe was a stupid, ignorant, intolerant, religiously extremist layabout and social security scrounger-cum-criminal?

This is not true of the vast majority of European Muslims, of whom it was estimated in 2006 there are 13 million, not 20 million (see: http://fra.europa.eu/fraWebsite/attachments/Manifestations_EN.pdf). On the contrary, they are more likely to be the victims of crime and ethnic and religious discrimination, as the recent BBC Panorama undercover investigation on a housing estate, Broadmead, on the outskirts of Bristol, showed (see: http://www.bbc.co.uk/iplayer/episode/b00nfr2h/Panorama_Undercover_Hate_on_the_Doorstep/).

At a time when the Israeli Government, led by Benjamin Netanyahu, is refusing to halt its settlement building in the Occupied Territories, or even to consider dismantling its controversial Security Fence (or ‘Peace Barrier’, as they prefer to call it), and at a time when the Palestinian National Authority of Mahmoud Abbas is only in control of parts of the West Bank, with Gaza being controlled by the rejectionist group Hamas, any talk of a new intifada, or Palestinian uprising, sparked by rumours of threats to the Haram al-Sharif, is – to say the least – inflammatory.

That said, what the Israeli authorities should be doing is making it abundantly clear to their own extremist factions that talk of destroying the Dome of the Rock, and building a Third Temple in its place, must remain talk, and that any moves to act upon it will not be tolerated.

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^[1] Alternatively, Hashtiyah, the word referring to the ‘Foundation Stone’ (Arabic: Sahkrah or Tzachra, depending on transliteration used.) This is the site of Abraham’s offer of sacrifice of his son, Isaac (Gen.22:1-14), or, in Muslim tradition, Ishmael (Qu’ran: Sura 37:101-110).

^[2] Devout Orthodox and Ultra-Orthodox Jews may not pronounce the Sacred Name of their God, the Tetragrammaton (YHWH, or Yahweh), and will not even use the word ‘God’; hence, ‘G-d’.

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.