Cosmology

Nature vol. 440, 27th April 2006

Since Newton the description of physical systems has been divided into two parts, first the configuration of a system at a particular time and second the dynamical laws governing its development. When either of these are judged to be finely tuned, it is seen as an indication of some underlying mechanism that produces the fine tuning that is observed.

The concept of entropy or disorder gives the likelihood of a particular configuration. With a gas, a high entropy configuration means even distribution over an allowed area. If we find a low entropy configuration into one part of the allowed area, we look for what is causing this.

The entropy of the universe is lower than it could be, which in itself demands an explanation. The early universe was in a state of very low entropy, which is thus even more in need of explanation. Further to this is there is apparent fine tuning of the energy levels of the forces of nature.

The most likely type of universe is one in thermal equilibrium, because the universe is old, and matter naturally trends towards thermal equilibrium. However, the existing universe has relatively low entropy, and the early universe had very low entropy. The later universe is predicted to have high entropy. This expresses the second law of thermodynamics, which predicts that entropy stays level or increases, but never decreases in a closed system such as the universe. The puzzle is why this trend is so, despite the apparent time-reversibility built into the equations of physics.

One favoured explanation for the low entropy of the early universe is the theory of inflation in which a tiny area of space expands very rapidly and smoothes out the early universe in the process. There is no observational evidence for inflation, and the only justification for the theory is to explain the apparent fine tuning of initial conditions.

However, Roger Penrose has argued against the idea of inflation as an explanation of the early universe. He claims that the patch of space from which inflationary space springs would itself have to have very low entropy, so the fine tuning problem remains, even though inflation does succeed in explaining the thermal equilibrium of the background radiation left over from the Big Bang. Penrose thinks that new physics is required to explain the conditions of the early universe

Another way to deal with the problem is the proposal that so-called baby universes broke off during the inflationary phase. These would have an initial low entropy and given a sufficiently huge number of such universes, there should eventually be one that has laws of nature such as those in our own universe, which allow intelligent life to evolve and observe the resulting universe.

The snags with this proposal are lack of observational evidence, and the absence of a description of how a large number of baby universes actually arise from the inflationary phase. Many of the baby universes are expected to contain different laws of physics, another hard-to-test concept involving effectively new physics. This appears to require new physics, much as Penrose does, so the two approaches are on the same footing in this respect.





The Cosmic Origins of Time’s Arrow

Sean Carroll

Caltech

Scientific American, June 2008

In discussing the problem of time, Carroll’s article ranges over the more general problems of cosmology. The author starts by pointing out the fundamental contradiction between the laws of physics, which make no distinction between past and future, and the observed time asymmetry between the hot, dense past of the Big Bang and the cooler, less dense conditions of the present era. For the purposes of everyday experience and classical physics, the asymmetry of time is apparent in the second law of thermodynamics, which states that the entropy of a closed system can only stay the same or increase, but never decrease.

Entropy is loosely defined as disorder, but more accurately as the number of different arrangements of atoms that give rise to a particular macroscopic state, and thus a state that is more likely to arise over time than one which is produced by fewer possible configurations. Thus, relatively few configurations give rise to an egg as opposed to a huge number of configurations that give rise to various different versions of a broken egg. Alternatively, if we think of entropy in turns of the throw of a pair of dice, the score of 7 has a higher entropy than the score of 2, because there are 3 chances of scoring 7, but only one chance of scoring 2.

Entropy is often described in terms of dispersal, such as the dispersal of cream in a cup of coffee or of gas molecules in a vessel. However, these are instances where gravity is not a major factor. Where gravity is a factor, the trend of entropy is towards clumping rather than dispersal, and there will be relatively few configurations that allow particles to remain dispersed. However, if sufficient time is allowed gravitational clumpings will fall into black holes, and these in turn will evaporate over a very long period of time, giving the final state of our universe as nearly empty space, which is thus the eventual state of maximum entropy given a very long period of time.

Carroll points out that it easy to see why entropy will rise in the future, but very difficult to understand why it was very low in the early universe. The thermal equilibrium of the radiation left over from the Big Bang is sometimes argued to indicate a state of high entropy in the early universe, but in fact the lack of gravitational clumping indicates very low entropy, with many more possible configurations of microstates that would have given rise to gravitational clumping than to the state which actually existed in the early universe. Thus, if the Big Bang is viewed as having arisen from a chance fluctuation there is a hugely greater chance of ending up with high entropy than very low entropy. The author stresses that the real challenge is to find an explanation for the low entropy in the early universe.

Carroll moves on to discuss the idea of a period of very rapid inflation of the volume of space during the early life of the universe. This works quite well in explaining the thermal equilibrium of the observed background radiation. It is less successful in terms of entropy. Roger Penrose and other physicists have indicated that the entropy before the inflationary period would have to be even lower than after the inflationary period. It has been argued that because the universe was very small before the inflationary period, there would be very few microstates and therefore the chance occurrence of a low entropy state would not be that surprising, but Carroll points that despite its small size this very early universe would have the same number of microstates as the modern universe. Of the possible arrangements of microstates in the pre-inflationary universe, only a tiny proportion would be of the special kind needed to produce inflation.

Carroll’s own suggestion is that the universe was initially in the highest possible entropy state, which is empty space. Empty space is subject to quantum fluctuations, and given a sufficiently large number of fluctuations, one of these could eventually produce the initial low entropy state necessary for inflation. At this stage, the view is normally that the inflationary phase itself spawns a huge number of baby universes, one of which has the extremely fine-tuned laws of physics that are necessary for a universe that can support living organisms.

Carroll, however, also points out an important snag to the whole idea of universes produced from quantum fluctuations. We know nothing about any laws that might govern this process, and as it stands it is just as likely for such quantum fluctuations to project fully formed matter such as galaxies and stars into this and other universes, something which has never been observed. This in turn makes it more likely that if the universe was produced from a fluctuation, it was a one off, or at least an infrequent event, in which case we are left with the problem of low entropy, and possibly also that of the fine-tuning of the laws of physics.





The Trouble with Physics

Lee Smolin

Smolin begins by looking at the insights and the problems of the two main theories of modern physics, relativity and quantum theory. Einstein showed that spacetime is not a fixed absolute background, or a rigid theatre within which life is acted out, but instead that it is dynamic in response to changes in matter. In particular, general relativity described the functioning of gravity as the curvature of spacetime in response to massive objects. The geometry of spacetime is not fixed, but changes as a consequence of the movement of matter.

Relativity was satisfactory for describing gravity and the behaviour of the universe on large scales where the behaviour of individual particles could be ignored, while quantum theory was satisfactory for describing the behaviour of particles at a scale where gravity could be ignored. Problems however arise in situations such as black holes and the Big Bang where matter is compressed down to a scale that is normally described by the quantum.

General relativity implies that matter would be infinitely compressed at the singularity of a black hole, but quantum theory does not allow infinite compression, with the vacuum itself always comprising virtual photons fluctuating in and out of existence, a constant fluctuation between 0 and 1.

A problem with reality
Quantum theory has from its beginning contained a problem as to whether it described reality or was only a mathematical abstraction. Traditionally science is supposed to give an account of reality as it would be without any human observers, the tree in the forest when there are no humans in the forest, or the moon in the night sky before there were human observers, or even a moon circling an uninhabited alien planet. The idea of a real world that exists independently of observers is supported by the fact that the early universe could not support life. This would have had to wait at least until the first generation of stars began to explode in super nova, and thus disperse the heavier atoms such as carbon and oxygen that are considered essential for life.

But the orthodox version of quantum theory, derived from Neils Bohr and known as the Copenhagen interpretation, did not allow for such realism. The system is the result of observation by instruments and human observers. Until it is observed it is only a mathematical abstraction representing a probability wave for where a particle might be found, or alternatively a superposition of all the possible locations the particle might have when an observation is made. This view has to some extent been superseded by the modern idea of decoherence in which the wave form of the system becomes a particle when there is sufficient interaction with the environment. In both cases, the process of choice of position is often referred to as the collapse of the wave function.

The Copenhagen notion of the wave form being a mathematical abstraction persists because it seems to dispose of the problem of quantum non-locality. A thought experiment by Einstein in 1935 demonstrated that two quantum particles could be related in such a way that wherever they were subsequently located in the universe an observation, or wave function collapse, which decides some property of one particle, would instantaneously produce some correlated change in a quantum property of the other particle, despite being out of range of a signal travelling at the speed of light.

Einstein objected to the randomness inherent in quantum theory, and proposed this thought experiment to demonstrate that quantum theory was flawed, but a much later real experiment by Alain Aspect in 1982 demonstrated that such correlations existed for quantum particles. This contradicts the notion of causality, the notion of the world working by bits of stuff or possibly energy bumping into one another, a notion shared by both classical physics and common sense. The Copenhagen proposition that the wave form of the quanta exists only as mathematical abstractions rather than physical realities gets round this problem by giving the quanta no real existence until a measurement is made.

The geometry of spacetime
Smolin’s concern is to find a theory that unites relativity and quantum theory. The geometry of spacetime is not fixed, but changes as a consequence of the movement of matter. Geometry describes the relationships of lines or edges, areas and volumes with respect to space. In the case of the geometry of spacetime, it is necessary to to get away from the schoolroom idea of geometry as something fixed and rigid. Here the physics governs how the geometry changes. Smolin takes this to be a fundamental principle as to how physics should work. The laws of physics govern how the geometry of space evolves. Thus the equations of general relativity govern the curvature of space by massive objects. The physical law has to be worked out first, independently of the spacetime background. Smolin’s prime criticism of recent grand unification theories and string theory is that they are not background independent, they treat spacetime as a freestanding stage for their activities. But spacetime emerges from the laws rather than providing a stage for them to act on.

In contrast to the other forces of nature, which have been shown to be intermediated by force carrying particles, the intermediation of the gravitational force or quantum gravity remains elusive. To understand quantum gravity would involve removing the conflicts between relativity and quantum theory, since in relativity gravity is an aspect of spacetime geometry.

String theory
From the 1980s string theory emerged as, an at least initially, promising candidate to reconcile relativity and quantum theory. Its problems emerged as time went by. It was impractical to test string theory experimentally, which conventionally should have ruled it out as a scientific theory. String theory required supersymmetry, as versions of string theory that lacked this were not stable. However, supersymmetry required higher dimensions beyond the three normal spatial dimensions and this resulted in a huge number of possible versions of string theory. The theory was background dependent and each possible fixed background produced a different version of the theory. All versions of string theory predicted extra particles, not so far observed in nature. They also predicted extra forces, also not so far observed. The problem of a huge number of solutions was that it was almost impossible to falsify the theory, which is the equivalent of not being a scientific theory at all. With such a large number of theories almost any observation could be reconciled with one or more of the possible theories.

The situation for string theory became more difficult with the discovery of dark energy in 1998. Dark energy is known about through its impact on the expansion of the universe, after observation of super novae in other galaxies indicated that contrary to expectation the expansion of the universe was accelerating. This could be explained by the existence of dark energy. It is not known what it actually is, although it is most often thought to equate to the cosmological constant, which is now known to be positive.

The idea for a cosmological constant goes back to Einstein, who realised that general relativity allowed a value for the energy density of empty space. This energy density would be the same for all observers throughout spacetime. The effect of positive energy density is to cause the universe to expand. In the first place, Einstein used it to offset the contractionary pull of gravity, so as to predict a static unchanging universe, which he and other scientists of the early 20^th century assumed to be the case. Shortly afterwards, Hubble demonstrated that universe was expanding, and the cosmological constant came into its own in order to explain what drove this expansion.

String theory had not predicted dark energy or a positive cosmological constant, and it was difficult to describe how strings would relate to the resulting background spacetime. The string theorists solution was to stop trying to get rid of the numerous solutions to string theory that had been considered a problem until now and to accept the idea of a so-called landscape of theories. This made string theory consistent with the positive cosmological constant.

The landscape of numerous solutions is suggested to be possible because of a proposed multiverse resulting from a period of inflation just after the Big Bang. The idea that the universe went through a phase of very rapid expansion just after Big Bang has considerable support, because it is a plausible explanation for the thermal equilibrium of the microwave background radiation left over from the Big Bang.

Some physicists have taken this a step further with the concept of eternal inflation. It is proposed that during inflation a possibly huge number of bubbles formed and that these broke of as separate universes. Our universe is supposed to be one of these existing alongside a multiverse of other universes. There does not appear to be any evidence for this proposal or any way of falsifying it. However, it has attracted considerable support, because it is a way of explaining the fine tuning of the universe.

Fine tuning refers to the fact that if the electromagnetic and gravitational force or the nuclear forces were one part in billions different from what they are, the universe would not be in a form that could support organic life. If the eternal inflation/multiverse idea is accepted, it is possible that the many solutions of string theory equate to the many universes that were spun off in the eternal inflation phase, with only one of these needing to equate to our own universe. One snag with this theory is that it still leaves the early universe with low entropy, and in fact a Big Bang with inflation is argued to require an even low entropy than one without, and this low entropy just by itself represents an incredible degree of fine tuning.

Smolin says that the reason why the multiverse idea has strong support in much of the scientific community, is that given the fine tuning problem, the multiverse appears the only alternative to the hypothesis of an intelligent designer. Smolin, however, argues that both alternatives are untestable, and that scientists should consider the possibility of an as yet unknown mechanism that would be testable. Penrose has also argued that physicists should look to possible new physics to explain the condition of the early universe.

Smolin further criticises the use of the anthropic principle to justify the multiverse. The anthropic principle states that the universe is the way it is, because if it wasn’t, intelligent life would not be here to observe it. The analogy is that we evolved on Earth rather than Jupiter, because Earth is a biofriendly planet, and there is therefore nothing surprising about our location. Smolin says that it would only be surprising if there was only one planet in the universe and that was biofriendly, while we know that there are many planets, and it would not be surprising if a good number prove to be biofriendly. However, we do not know whether there are one or many universes and there are no testable predictions that can resolve this for us. To add to these problems some of the more recent data from the cosmic microwave background radiation is not consistent with inflation, although it is admitted that this data may not give a full picture.

Smolin argues that string theory, like quantum field theory, is only an approximation. He admits that it has some successes. The vibrations of strings correspond to the graviton, the hypothetical particle of the gravitational force. If supersymmetry is included, the quarks and electrons that make up matter as distinct from energy also emerge. The strings are a simple entity that describe all the forces and particles of nature and their interaction. Smolin identifies the chief weakness of string theory as the fact that because it is not background independent, spacetime does not emerge from it in the way that it emerges from general relativity. Strings operate against the fixed background of classical physics, but Einstein showed nearly a century ago that spacetime was a dynamic background responding to matter.

Alernatives to string theory
In the latter part of his book, Smolin discusses alternatives to string theory. Smolin suggests that the over numerous solutions found in string theory might be the solutions to some deeper and as yet unknown theory. This would replace a huge number of string theories with a huge number of solutions to a single fundamental theory. Existing string theories are dependent on individual fixed spacetime geometries, but the fundamental theory would not depend on a spacetime geometry, but would determine its spacetime geometry.

Smolin claims that the most successful approaches to quantum gravity involve three basic ideas, that space is an emergent property, that is based on something that is discrete rather than continuous, and that causality is fundamental to this. Smolin is an advocate of loop quantum gravity. This theory is based on the idea of describing a field in terms of its field lines. The field lines are viewed as describing the geometry of space. This quantum geometry is viewed as being a graph. Quantum spacetime is a sequence of events allowing the graph to evolve. Areas and volumes come in discrete units. There is a suggestion that knots and links in the network code for particles. Different ways of knotting or braiding the network are suggested to be different elementary particles. When coupled to the standard model of particle physics there are no infinities. When applied to black holes and the Big Bang there is suggestion that singularities are eliminated. In the case of the Big Bang, this implies that there might be something before the Big Bang. Usually, both string theory and loop quantum gravity have difficulty in coming up with testable predictions. However, loop quantum gravity has now made predictions for quantum gravity effects that might be seen in future observations of the microwave background radiation.

The trouble with physics
The last part of this book comprises an attack on the way in which science is now structured and practised. Problems here are blamed for string theory remaining dominant despite its failings, and for the disappointing progress in physics over recent decades. Smolin contrasts the experimental confirmation as it existed for physics in the 1970s with the lack of testability in the now dominant string theory. He also contrasts the reflective and philosophical style of research in early relativity research, which has continued into loop quantum gravity, with the more aggressive and competitive style of elementary particle research. He also makes an implied criticism of US research, saying that the US dominance of science has led to an emphasis on application rather than fundamental theories. He suggests that this latter style has predominated in string theory, and that it is a style that is not suitable to the development of new fundamental theories. The standard model was developed in this way, but it was closely constrained by experiment. Without the possibility for experimentation, it is suggested that string theory in particular has become fashion driven. Smolin argues that there used to be more variety in foundational research, but since 1990 only one university has been investing in research other than string theory in this field. He criticises science for having become too heirarchical. Young entrants have to compete to be well thought of by older scientists, because of an over production of potential researchers. This entrenches the ideas of the older generation, and represses new ideas amongst younger scientists. At the same time the power of administrators has grown at the expense of the judgement of practising scientists. This encourages reliance on mechanistic ways of judging new applicants, such as citations or funding which itself tends to reflect acceptance by mainstream supporters of older ideas, rather than an ability to innovate. He also suggests that too much attention is given to status, with good ideas from lower status academics automatically rejected, rather than assessed on their merits. Smolin also criticises the modern structure for discouraging those scientists, who were interested in the larger questions, and by implication more likely to innovate and also to stick with ideas that interested them.





Multiverses: description, uniqueness, testing