Lee Smolin: Three roads to quantum gravity.

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Four principles.

Quantum theory changed the assumptions about the relation between observer and observed but retained Newton's view of space and time. General relativity changed the latter but not the former. So, Lee Smolin said, in the year 2000, of the search for the unifying theory of quantum gravity.

Three main groups research this, by way of string theory, which is mainly a development of quantum theory; or loop quantum gravity, based on general relativity with quantum modifications; and a third small group of originals. Smolin is hopeful that the three groups are converging to enhance each other's understanding.

String theory is introduced as the third road to quantum gravity. Having reviewed Brian Greene's book on The Elegant Universe, Ive said no more about it here.

Smolin outlines four principles as a basis for progress. First, consistency, with the definition of a universe, requires that 'there is nothing outside the universe'. So far, he agrees with his friend and colleague, Julian Barbour ( whose book is also reviewed on this site ). He agrees that time only makes sense in terms of change. But Smolin doesnt treat time as an illusion.
When we look into space we are looking back, also, in time. The light from further away comes from further back in the history of the universe.

Hence, Smolin's second principle: in the future we shall know more. Nothing can travel faster than light. But as time passes by, the spot-light, we are in, grows bigger. However, the spot-light is the limit to which we can see. This spot-light is different for different parts of the universe, depending on the time light has had to reach a given spot.
( The spot-lights are another word for the 'light-cones' familiar to readers of popular books on general relativity. )

No-one can have access to total knowledge about events in the universe. So, we cannot always say whether a thing is true or false, as Aristotle's classical logic assumes. New systems of logic, acknowledging only partial information, dependent on the observer's situation, reflect the nature of society. One of these systems, topos theory was found, by Fotini Markopoulou-Kalamara, to suit cosmology.

The quantum theory paradox of Schrödinger's cat, and so forth, make no sense in terms of classical logic or common sense. This is the 'super-position principle' that a cat in a box, subject to the chance of a fatal accident, is in superposed states of being alive and dead, until an observer opens the box. Then, the conventional interpretation goes, there is a 'collapse of the wave function' of superposed states, resulting in either of the definite states: dead or alive - but not both! ( Tho, this paradox begs the question of being 'half dead'. )

The paradox gives a vivid idea of the observer being outside the observed system. But combining quantum theory with cosmology means that the observer cannot be conceived as existing outside the system, when it is the whole universe.
The Wheeler-DeWitt equations suppose the quantum constraints on the universe. The author played a part in hitting upon their exact solutions, saying it took another ten years to find out what they meant.

Later, Smolin adds, like Douglas Adams' galactic hitch-hiker seeking the meaning of life:

So conventional quantum cosmology seems to be a theory in which we can formulate the answers, but not the questions.

He goes on that this is not surprising, since the whole universe is not within our purview like a quantum experiment in the laboratory. Context-dependent theories, such as Markopoulou's cosmological logic applied to quantum theory, provide a reason for observers' different points of view, from which the super-position paradox follows. One may observe a system, that includes another observer in a super-position of states. But that observer never so describes himself, remaining outside the system he describes.
And this is never precluded: the system observed can never be the totality of the universe, because of the light-speed limits on the size of the observable universe.

A slogan for this point of view is: 'One universe, seen by many observers, rather than many universes, seen by one mythical observer outside the universe'. And this is Smolin's third principle.

His fourth principle is: The universe is made of processes not things. Here he clearly differs from Julian Barbour. The world is not made up of a lot of static snap-shots put together like a movie. Taking the analogy further, he points out that real snap-shots decompose. Everything we observe is always changing more or less. In direct contrast to Barbour, Smolin speaks of 'the illusion of the frozen moment'.

Smolin says we learn about things, just as we do about people, from their stories, which are essentially about causes.

The fundamental idea in general relativity is that the causal structure of events can itself be influenced by those events...The laws that determine how the causal structure of the universe grows in time are called the Einstein equations. They are very complicated, but when there are big, slow-moving klutzes of matter around, like stars and planets, they become much simpler. Basically, what happens then is that the light cones tilt towards the matter... ( This is what is often described as the curvature, or distortion of the geometry of space and time. ) As a result matter tends to fall towards massive objects. This is...the gravitational force. If matter moves around, then waves travel through the causal structure and the light cones oscillate back and forth...These are the gravitational waves.

Nevertheless, Smolin says physicists tend to think there is a limit to the number of events in a process. And that space and time are not continuous but form into fundamental discrete units ( rather like the quantum, h, is such ). ( Barbour's 'snap-shot' reality may yet get a look in. )

Black hole thermo-dynamics.

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This is the first road to quantum gravity.

In accord with Einstein's equivalence principle, a space-ship can maintain a position out-side the event horizon of a black hole, with a force of acceleration matching the hole's force of gravitational attraction. The horizon is a 'curtain' of unseen photons that are just unable to escape the black hole. Hence the name: this curtain and everything behind it is a hidden region.

In general, wherever a light source cannot reach an observer, that is in a hidden region to that observer. Even far away from any black holes, a space-ship's acceleration will create a hidden region behind a horizon of photons that cannot be seen from the ship, because its acceleration has been enough to put them out of reach, even tho the ship itself cannot reach light speed.

Bill Unruh predicted that the energy source provided by the acceleration will activate the ship's particle detectors to register quantum fluctuations, in the vacuum of space, between electric and magnetic fields. By Heisenberg's uncertainty relation, both fields cannot be measured, in a region, as zero.

Another principle, that of quantum correlation, predicts the fluctuations will be random, which implies heat, detectable as a temperature proportional to the ship's acceleration. A pair of spontaneously created particles, like photons, within the limits allowed by the uncertainty relation, are, in effect a system, which can only be properly understood as a whole. A change in the condition of one photon, such as its polarisation, will affect the polarisation of the other, conserving the pair as a system, even tho they may have moved too far apart for a light signal to have been quick enough to effect this correlation.

The accelerating space-ship detects photons correlated with photons in its hidden region, denying their systemic information and, in effect, surrounding the ship with a random 'gas' of photons.
This is Unruh's law, the study of quantum gravity's first prediction.

The entropy of the gas is the measure of all the positions and motions of molecules in the gas. This measure is made in terms of information theory that counts in sequences of bits, as the number of answers to yes/no questions, like a digital computer. This information is missed when taking only temperature and density averages used in statistical mechanics or thermo-dynamics.

The photon gas randomness results from the missing information, in the accelerating space-ship's hidden region, which the entropy measures as exactly proportional to the area of the horizon boundary between the ship and its hidden region.
This is Bekenstein's law, the second prediction of quantum gravity.
'Bekenstein's bound' is a limit on the information that can be contained in any region. This finite capacity for information implies space is discrete, on the Planck scale.

Thermo-dynamics states an entropy law of the over-all increasing disorder of things, which gives a sense of time being irreversible. Black holes have this character, because nothing falling in one can ever get out. Consequently, Stephen Hawking showed, that, like entropy, the area of a black hole can never decrease.

In the case of black holes, the random photon gas is known as Hawking radiation, when pairs of virtual particles, created from the quantum fluctuations of space, are split near the event horizon. One partner may fall in the black hole, the other be shot off into space. The random radiation meant a black hole would give off ( very minimal ) heat, the result of missing information from black-holed partner particles, which showed a black hole could have entropy.

Hawking's law is a third prediction, that the temperature of a black hole is inversely proportional to its mass. Hawking radiation means a black hole will lose mass, therefore lose area, and lose entropy. The outside world should gain the entropy, so there is no over-all loss, contrary to thermo-dynamic law.

A black hole of the sun's mass would take ten, to the power of 57, times the fourteen billion year-age of our universe, to evaporate. So, the nature of the information trapped in the black hole, and possibly released by evaporation, is of decidedly theoretical interest.

The information lost in a black hole, is measured in discrete units of atoms and photons. But the measure of the black hole's entropy is in terms of the continous area of its horizon. The three roads to quantum gravity are converging on an atomised or quantised concept of space and time having fundamental units.

The Bekenstein surprise that information capacity of space is proportional to a region's area, and not its volume, makes one think of a holograph. This is a two dimensional picture that encodes three dimensions depending on which angle you look at it.
The weak holographic principle treats the surfaces of things as screens with finite capacities to channel information from observer to observer.

The last part of Smolin's book, on frontiers of knowledge, mentions several versions of a holographic principle, for which there are great hopes as a new founding principle of quantum gravity, as the ucertainty relation is for quantum mechanics, and the equivalence principle for general relativity.

Loop quantum gravity.

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The atomic nature of thermo-dynamics was not accepted in the nineteenth century. Einstein's 1905 paper explained Brownian motion in terms of collisions from the random motions of atoms or molecules. Another of his 1905 papers also explained light atomically in terms of light-quanta, carrying a unit of energy proportional to the light's frequency.
A theory of quantum gravity will likewise quantise space and time.

Chapters nine and ten are the core of Smolin's book, because they describe him working with many colleagues, the world over, to come to loop quantum gravity -- the second road. Because he is telling a story, this reader was given an illusion of understanding their progress, which clearly depends so much on professional co-operation.

With apologies, this amateur reviewer merely makes a few notes, by way of memoranda, hoping they are not too misleading.

Of the four known forces of nature, the strong force binds the three quark constituents of particles, like protons and neutrons, that themselves make up an atomic nucleus, whose cloud of electrons, in turn makes up an atom. Electrons are more or less easily stripped from atoms.

But energy directed at freeing quarks from protons only seems to add to the length of an apparent string, joining the quarks, without diminishing its strength. This 'quark confinement' has an analog in super-conductive metals at temperatures a few degrees above absolute zero. Normally, magnetic lines of force are continuous, tho the size of iron filings, put on paper around a magnet, show discrete lines. Only in a super-conductor are magnetic field lines quantised, carrying a whole number multiple of a basic unit of magnetic flux.

The electric force is closely related to the magnetic force. Together they comprise one of the four forces of nature. And the theory of the strong force was based on an analogy with electric charge, except that quarks are distinguished by having three distinct charges ( three 'colors' ).
( Quantum Chromo-dynamics, QCD, is the analgous theory to Quantum Electro-dynamics, QED. )

The color-electric lines of force, holding the color charges of quarks together, could become discrete like a line of magnetic flux in a super-conductor. The guess is that 'empty space is a color-electric superconductor'. The complete lack of electrical resistance found in super-conductivity is as if the temporary quantum fluctuations of energy in a vacuum also had large-scale effects.

The stretched 'strings', between quarks, have been thought basic entities, rather than justlines from force fields. Other physicists thought both points of view valid. One of the latter was Smolin after hearing of 'Wilson's loops'. Ken Wilson assumed a discrete space based on a grid or lattice, of units far smaller than a proton's diameter. Quarks could only be on the nodes and strings on the edges of the lattice.

Using simple rules, the three-color-electric field was described by the movement of discrete field lines along the discrete space. Given only one charge, like normal electricity, the field lines tended to lose their discreteness by joining to behave like continuous electric field lines. But, given three charges, as with quarks, the field lines always stayed discrete, no matter how big they got.

The next step would be to dispense with the grid, as a fixed back-ground, leaving only the 'quantised loops of electric flux' to characterise a discrete space. Building on the work of many colleagues, as always, the author's work included using Polyakov's expressions for the quantised loops of electric fields as the quantum states for a geometry of space-time given in a simplified version of the Wheeler-DeWitt equations.

It would not matter where these back-ground independent loops were in space. That would have no meaning, because space itself would be defined by the inter-relations of the loops, their intersections, knots, links and kinks.
The idea of discrete lines of force, taken from that in a super-conductor's magnetic field, quantised areas into discrete units, on the Planck scale, each carrying finite amounts of area; likewise for volume.

Loop states could be arranged in 'spin networks', previously derived by Roger Penrose, one of the originals, amongst the groups researching quantum gravity. The various lengths, of the joined lines in the net, are integers coming from quantum theory's allowed spin states of particles.
Arduous translation, of loop quantum gravity into spin networks, revealed:

...each spin network gives a possible quantum state for the geometry of space. The integers on each edge of a network correspond to units of area carried by that edge. Rather than carrying a certain amount of electric or magnetic flux, the lines of a spin network carry units of area. The nodes...correspond to quantised units of volume. The volume contained in a simple spin network, when measured in Planck units, is basically equal to the number of nodes of the network.

Theorems show 'that the spin network picture of quantum geometry... follows directly from combining the basic principles of quantum theory with those of relativity.'

'Connections have been discovered to... such as Alain Connes' non-commutative approach to geometry, Roger Penrose's twistor theory and string theory.'

Giovanni Amelino-Camelia suggested a test whether the geometry of space is discrete on the Planck scale. A photon's path should be deviated, from its expected classical path, by interference effects of its associated wave being scattered by the discrete nodes of the quantum geometry. Altho the effect is extremely small, it is cumulative and might be detectable over large fractions of the observable universe.

How probable would it be that this atomic structure of space yielded the Euclidean space we see? The universe under-went a phase transition, like a gas turning to liquid. The early plasma of photons 'froze' into matter. A smoothly featureless three-dimensional geometry resembles the crystalline atomic structure of a metal with its smooth surface. For the atoms of space to organise themselves over the cosmos, so highly, seems fantastically improbable.

( Reviewed briefly on this site's page on theories and methods of natural selection ) Lee Smolin's former book, The Life of the Cosmos, suggests a cosmological theory of natural selection of universes, to make the impossible seem inevitable.

Richard Lung.

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