To simplify the mathematics, the cosmological principle assumes that on a cosmic scale the distribution of matter and energy is approximately uniform.
Einstein's general theory of relativity replaces the Newtonian concept of gravitational force with matter exerting geometrical distortions on space and time.
A universe which has a positive curvature of a sphere is finite in spatial extent. A universe which has the negative curvature of a saddle is infinite in extent.
A flat universe like a tabletop may be either finite or infinite in extent.
Greene says a uniform presence of matter generally curves space-time but can leave zero space curvature.
The curvature of space depends on the density of matter and energy. There did not appear to be enough for more than negative curvature of space. Then the behaviour of galaxies suggested there must be more energy than was visible, short of modifying the laws of motion.
Hence a supposed "dark energy" suffusing space. This harks back to the idea of a cosmological constant. Einstein found that a positive constant produced a repulsive gravity, that counteracted normal attractive gravity.
Building on this principle, Greene later explains (to my confusion) why Inflationary theory of the Big Bang strongly implies an infinite multiverse.
Thru Inflation, the universe bears the signature of its quantum scale origins. Unlike the determinist measurements of classical physics, the quantum state has the jitters, being subject to random fluctuations. The consequences of a super-small quantum origin have been predicted and found to a surprising experimental accuracy in tiny ripples measured in the cosmic microwave background radiation, a sort of faded flash to the Big Bang.
Ultimately it is the random deviations from a completely uniform distribution of energy and matter which gravity has gradually worked upon on the cosmic scale to separate into larger clumps, the stars and clusters of stars.
From what little I could make out, Inflationary theory seems to be tied up with the idea of a compact region of differing energy potentials. At some points, in keeping with random quantum fluctuations, they seem to have realised their potential like stones rolling downhill.
These kinetic energies are likened to bubble universes, much like holes forming in a Swiss cheese.
This is the expanding Inflationary multi-verse. Tho these are bubble universes, Greene explains how they may be likened to an infinite universe. It has to do with the relative measurement of time, familiar since Einstein's special and general relativity, by which observers cease to share the same time, either when relative motion is significant compared to light speed or when gravity is strong, as in bending a light ray moving close to a solar mass.
Observers may coordinate their times according to a shared measure of energy density or mass density. That is because, at any given time, the universe has a fairly uniform density, which becomes steadily more diffuse with the universal spatial expansion.
Reminiscent of Einstein's famous thought experiment of the two observers inside and outside an accelerating lift, there is now an observer outside the bubble universe as well as inside. According to Greene, "what appears as endless time to an outsider appears as endless space, at each moment of time, to one insider."
Current evidence suggests a small positive cosmological constant, for a universe that seems to be increasing its rate of expansion.
The astronomical evidence, taking into account the estimated dark energy, suggests the universe has zero curvature. It is not known whether this is finite or infinite.
Greene says that since the universe is extremely big any way, you may not think it matters -- but “you should.”
Einstein's special theory of relativity postulates that nothing can move faster than light. Light bounds our observational universe in a cosmic horizon, analogous to the global horizon that we cannot see over.
In an expanding universe, different regions, with their own cosmic horizons, become so separated that they could not possibly influence each other.
All of these independent regions can consist of only a finite number of particles of matter or energy. And they are subject to only a finite number of possible re-configurations.
Greene stresses that "anything but measurements with perfect resolution reduces the number of possibilities from infinite to finite."
This is not merely a technical temporary limitation. This is a limitation in principle, according to the uncertainty principle, which specifies how much the gain in resolving the quantum scale measurement of one property is at the expense of another property.
To measure a particle’s position with complete precision would require infinite energy, which no particle can be given.
In an infinite universe, the consequence, of an infinite number of re-shuffles of a finite number of particles, is that eventually all of those independent regions will undergo more or less exact repetition.
Greene postulates the reductionist view, common among physicists, that knowing the full arrangement of physical particles fully describes reality.
This is what Francis
Crick called The Astonishing Hypothesis. Namely that consciousness is an
emergent property of the evolution of the brain.
In other words, we cannot explain it, we just give it a mysterious
characterisation, like emergence, and take it as given. But this attitude is
what the philosopher, Robert Nozick, was getting at the young Brian Greene
about, as Greene re-tells near the end of the book.
The assumption is one of materialistic determinism or that body determines mind. But what of mind over matter? What of the influence of faith, that medicine is pleased to call the placebo effect?
Treating a correlation as a one-way cause must be regarded as suspect. A critic has said, it is like assuming that when a television "dies" that is all there is to it, overlooking that it is just a receiver for a signal, not the signal itself.
Such an unsuspected consciousness "signal" might be labeled unhelpfully paranormal or psychic or spiritualist etc but is no more fantastic or implausible than - indeed seems rather complementary to - some physicists suggestion that the world is no more than the projection, as it were, of a computer simulation, discussed in the same chapter as Nozick's philosophy. The world as computer simulation re-opens the way for mind, if doing the computing from a hidden reality.
This leads me to suspect that the physics of materialist determinism (matter over mind) is at odds with the physics of the world as computer simulation (mind over matter) short of some more balanced assessment of the inter-relation between mind and matter.
In the penultimate chapter on creating universes and simulating reality, Greene cites the research into computer simulation of the brain and the prospect for artificially realising emergent consciousness with the acceleration of computing power.
While the objective creation of a new cosmos evidently needs energies beyond humanitys grasp for the forseeable future, the subjective creation of a new cosmos in any robotic consciousness seems a not too distant possibility.
Of course, every new birth into consciousness is a new subjective universe in the multiverse of human and other life forms.
We cannot traverse individual universes in a multiverse any more than individual consciousnesses.
But Greene is surely right in believing we may infer the existence of other universes in a conjectured multiverse, just as we avoid solipsism by infering individual consciousness other than our own.
However that may be, physics may find that reductionism has severe limitations.
Take for instance the conclusion of "infinite copies of you and everyone and everything". Well, we don't have to imagine an infinite journey thru the cosmos for this.
Twins are already exact copies.Despite their remarkable psychological affinities, as far as I know, they do not share the same consciousness. Nor, would I guess, any doppelgangers from here or the other ends of an infinite universe. Moving the same model of body, like driving the same model of car, does not make you the same person.
Are we not missing something here? Like a common quality of consciousness that different life-forms filter variously like so many specialised sensory instruments.
I suppose I'm saying that it is a common consciousness that unites life but different bodies that divide it, even if they are physically identical.
The Hidden Reality gives a summary update of The Elegant Universe (also reviewed on this site) and The Fabric Of The Cosmos, on string theory.
The 19th-century mathematics made an axiomatic modification that was the first revolution in geometry since Euclid's classic text. Riemann's geometry of curvature made general relativity possible.
In the late 20th century, physics led mathematics, when string theory generalised the classic geometry of zero dimensional dots, used to describe elementary particles, into a geometry of one-dimensional strings.
The over-coming of certain mathematical obstacles allowed and encouraged strings themselves to be generalised into higher dimensional membranes.
Our own three dimensional universe could be considered as just one membrane among many floating in higher dimensional space.
It has been speculated that these membrane universes might more or less collide. A gentle collision with our membrane universe and another might leave an astronomically observable signature.
Less happily, more violent collisions might induce what is being called facetiously Big Splat. On this basis, a possible mechanism for a never-ending cyclic creation has been worked out, one avoiding the progressive disorder and collapse known as the second law of thermodynamics.
The Calabi-Yau spaces of higher dimensions stitched in to the observable three dimensions lead to a stupendous number of possible universes, such that it would be much easier to locate a particular grain of sand on a beach than to find the particular higher dimensional space that would characterise our own universe.
String theorists have tried to show that this superfluity can be accounted for in terms of a theory of eternal Inflation. It seems to have something to do with extending the Swiss cheese model of the multi-verse, so that bubble universes cascade into ever more bubbles.
This runaway multiverse involves a mountainous energy multiverse with different valleys, for the extra dimensions different forms, where quantum tunnelling can take place to lower energy levels indefinitely creating bubble universes within bubble universes.
This review is just a sketch caricature of admittedly extravagant speculation. To get the proper explanation, you have to read the book, which does indulge in some soul-searching about whether all this untested abstraction is really science.
Some hopes for theoretical hints are pinned on the large hadron collider experiments at CERN.
Not only string theory and Inflationary cosmology have invoked multiverses. Quantum theory has also resulted in a Many-Worlds scenario.
Greene discusses the Copenhagen interpretation of a collapse of probabilities, generated by Schrodinger’s equation of the evolution of a particle property like position in space and time, into a certain measurement, which when repeated confirms the equation’s predicted odds.
Neils Bohr drew a line between microscopic and macroscopic objects. But experiments have shown the Schrodinger equation’s probabilistic (and increasingly difficult) measure to hold for ever increasing collections of particles, without any supposed collapse into one definitive measure of where the object actually is.
Everett’s proposal sought to get round the ad hoc nature of the Copenhageninterpretation. But it raised ad hoc problems of its own. Suppose the Schrodinger equation simply describes the evolution of many worlds represented by the different peaks of a wavefunction, with one observer or measurer becoming many, for each peak or spike, tho each of the experimenters proliferating selves are unaware of the others in their many worlds.
The probability of observing a given particle position measurement, say, is determined by the height of the wave spike. This probability weighting of some observations over others undermines the Many Worlds view that all the possibilities are equally real, and that our worlds observer is no more real than other observers in other worlds of possibility.
An Oxford UK suggestion is that the wavefuntion probabilities are just the odds that one out of any number of possible worlds will be the one you turn-up, for any given measurement.
Gary Zukav, in The Dancing Wu Li Masters, notes that the basic quandry of quantum mechanics is that a single foton may interfere with itself.
This is a reference to the double-slit experiment. Here one foton at a time can be fired to pass thru either of two closely placed slits such that they arrive at a foto-sensitive target.
If one of the slits is blocked, you'll get a fog of strikes on the side in line with the open slit. And conversely if only the other slit is left open. If both slits are left open, there is not an undifferentiated mass of strikes on both sides of the target. Instead, there is a series of bright vertical bars alternating with vertical dark regions. These resemble the crests and trofs in waves, in this case light waves.
A member of the above-mentioned Oxford group, David Deutsch, in The Fabric Of Reality, argues that the interference effect is evidence of the existence of another foton, we cannot see, and therefore indicating another world impinging on our own. The single foton, that the experimenter fires and that goes thru one of the slits, is accompanied by a sort of ghost foton that goes thru the other slit. But the interference effect is reckoned to be just as sure as when two stones are dropped into a pond and their radiating ripples bump into each other.
I also recommend “Quantum Enigma” by Bruce Rosenblum and Fred Kuttner. It is an ever so polite renunciation by veteran physicists (one of them met Einstein as a grand old man) of the doctrine of “Shut up and calculate,” in order to more fully expose the outrageous implications of quantum theory. I must admit I hadnt realised just how extra-ordinary it really is.
Greene’s chapter nine on Black Holes and Holograms starts with a brilliantly simple introduction on the relation of entropy to information, before going on to the conservation of information apparently lost in black holes.
Hawking radiation, from the black holes surface area, is where the information is encoded from an object passing the event-horizons point of no return.
That is from an outsiders point of view, seeing a gravitationally attracted observer sizzled on the event horizon.
The faller inside would not notice any such spontaneous combustion but the outside observer would only observe this too late to catch up with the inside observer, to confront him with a paradox.
The holographic principle expresses this reduction of information from three to two dimensions. This principle was couched in terms of Maldecana’s revelation of a duality between string theory (as bulk physics in three dimensions) and a specific kind of quantum field theory (as the boundary physics in two dimensions).
From Maldecana's
result, it turns out that the math of string theory can facilitate
intractable calculations in the quantum theory, which have a direct bearing
on experimental observations.
Indirectly, at least, string theory has come of age as experimental
science.
The Maldecana holographic result has led to speculation about a whole
universe of three dimensional space having a parallel universe on its
two-dimensional boundary – whatever that means, as Leonard Susskind would
say.
(Tho this notion resonates with some of my recklessly ill-informed guesses on
cosmology, on my web page: Light speed by time as fourth dimension of
space.
An Event-horizon Universe. An hour-glass universe.)
Brian Greene says that he avoids the free will debate. The physicists emphasis on multiverse at the expense of multi-choice seems to stem from David Hume's dualism between facts and values, rather than Immanuel Kant’s rejoineder in terms of a unified graduation between the natural sciences and the moral sciences.
Since the 1970s, I have been more or less vaguely aware that theories of physics, most obviously special and general relativity and quantum theory, seem to have corresponding methods of observational choice.
The more general the
method of choice, the more comprehensive the tests that physical theory may
be subjected to.
Election science is a mathematics and experiments of ethics.
Mathematically, I guess “electics” would be another facilitative duality for physics.
And experimentally,
if the method of choice, the electoral method, is generalised to provide
broader observational frames of reference, then their operation is in effect
creating new universes of observation, by which this universe is more
multiverse than it otherwise would have been.
(That argument reminds me of the reasoning from fuzzy logic.)
At least as important would be the strict standards
of honesty imparted to electoral method, so sadly lacking in politics - and
so destabilising of society, because of the greater power for disaster from
an honest science in the hands of a dishonest politics.
CP Snow partly highlighted this, when he talked of The Two Cultures, tho HG
Wells anticipated the problem more starkly.
In case it be thought that I am being merely moralistic, consider the crudely inefficient voting systems used by most so-called democracies. Consider the current referendum for the alternative vote in the United Kingdom and the stupefying level of debate, especially from the opposition to progress from the illiterate least choice of an x-vote to counting 1, 2, 3, etc order of choice for candidates.
The explosion of scientific exploration,
characterised in this book, stupefying in its potential, is in grotesque
contrast to the stupefying atavism of politics. This imbalance is likely to
capsize society, if not corrected. The Establishment reaction against
democratic progress, from its most crude and primitive form, is inevitably an
attack on the progressive mandate of science from taking its nine-to-five
honesty outside office hours.
As HG Wells said: Civilisation is a race between education and
catastrophe.
Richard
Lung.
19; 20 April 2011.