Monday, April 30, 2007

Resolving the Big Bang

Sean Carroll wrote a bizarre essay arguing against the cosmological principle and against many sane ideas we have about the beginning of the Universe, while trying to oversell many less sane ideas. Because I think that many comments about these issues are based on basic and widespread misunderstandings, let me try to re-analyze these questions.

Cosmological principle

The cosmological principle says that the Universe is homogeneous and isotropic at large distance scales. Of course, this principle isn't a religious dogma we received from the heavens. It's an assumption about the Cosmos. Do we know it's true? Well, even though it can't be obvious a priori, the answer is Yes. Observations show that the visible Universe is homogeneous and isotropic at distances longer than 300 megaparsecs or so.

Does it mean that the Universe has satisfied the cosmological principle in the past? Once again, the answer is not obvious but it is Yes. Why? Well, it's because the inhomogeneities increase with time. In the past, they were smaller. This statement may be supported by particular calculations as well as observations. For example, the cosmic microwave background that was created 300,000 years after the Big Bang is much more uniform than the distribution of galaxies in the present Universe.

Can we extrapolate this statement to the very beginning? Well, we can extrapolate it to an arbitrary moment in the past in which classical general relativity coupled to other objects was a good zeroth approximation of reality. This certainly includes later stages of the inflationary era. In fact, during inflation, the Universe was as homogeneous as you can get because it was essentially empty. Inflation has the remarkable ability to turn the rules of the game upside down. Inflation makes the Universe more uniform. Do we know this is the case? Well, we know it theoretically and obviously, it is not easy to test it by direct experiments. But as long as we agree about the definition of the word "inflation", we should agree that it tends to make the space empty.




The same conclusion also implies that the Universe could have been very inhomogeneous and complicated before the inflation and it wouldn't destroy its future. But was it? The second law of thermodynamics makes entropy increase with time. At the beginning, the entropy of the Universe had to be much lower than it is today. Although we can't construct a rigorous proof, the extremely small Universe should simply be describable by a small number of degrees of freedom. As long as this Universe has a geometric description, they can be connected with overall uniform features of space or the first few spherical harmonics. There is simply not enough room for more information. The low amount of information is thus either equivalent to a largely uniform Universe, or to a Universe described non-geometrically.

Causality, before, and outside

In the second paragraph, Sean claims that it is pure moonshine to say that there was nothing before the Big Bang and nothing outside the Universe or to say that the distant points are behind each other's horizons. Well, I don't see any moonshine here. Comments about moonshine are pure, uniform fog. Because different questions often have different answers, a rational thinker must avoid general clichés about moonshine and, unlike Sean, he must answer these questions separately.

As long as we accept the picture of the Universe that started from a tiny size (and I will discuss other pictures below), there was nothing before the Big Bang. The spacetime geometry simply doesn't allow us to extrapolate before the first moment. Asking what was before the Big Bang is equivalent to asking what is closer to the center of Earth than the center of Earth. Well, the answer is nothing. There is nothing paradoxical about this answer even though many people, especially laymen, would like to argue that there is a paradox here.

Was there something outside the Universe? Well, it depends on your definition of the Universe. If the Universe means everything there is, which is my preferred definition, there can't be anything outside the Universe, by definition. We often use the description of a curved Universe in which a membrane is embedded in a higher-dimensional space. But when this trick is meant to be just a pedagogical tool to teach conventional 4D general relativity, it is important to realize that the space "outside" the membrane is just a misleading relic of the analogy, not a true property of our spacetime.

If you use the word Universe to define just a brane or similar object embedded in a higher-dimensional space or its generalizations, then there can be things outside your Universe. But whether these things are allowed (compatible with known facts) is a question that can be studied scientifically - by theory and, speculatively, also by experiments. Again, it is certainly not moonshine.

Are different, distant points behind each other's horizons? Well, if you truncate the Universe at age of 1 minute or any other moment that is still described by the Big Bang cosmology, the answer is definitely Yes. Although the answer is a result of a calculation, this part of the Big Bang cosmology has been verified experimentally, too. On the other hand, the uniform cosmic microwave temperature indicates that different points of our Universe had to be in causal contact i.e. their past light cones should overlap, after all. Inflation is the most natural framework that allows such a causal contact and/or thermal exchange. As long as causal spacetime geometry continues to hold, at least approximately, something like inflation is in fact necessary.

Alternatively, the very childhood of the Universe could be described by a set of non-geometric ideas that don't care about causality and locality.

Adding pre-history

In the scientific, minimalist picture, the Universe started as a small seed that was itself expanded by inflation. Before the inflation, the only thing we can find is the creation from "nothing". Such a creation, if it follows some laws, almost certainly follows laws based on the ideas of Hartle and Hawking or their generalizations. It is likely that the full laws of quantum gravity, i.e. string theory with all of its strings, branes, extra dimensions, dynamical dimensions, topology change, microscopic black holes, non-commutative geometry, and other concepts, must be taken into account to derive something solid about the pre-inflationary Universe.

I think that completely different, additional eras of the life of the Universe in which it was large are extremely unlikely fantasies. They are not needed to explain anything in the observed data, most of them are in a subtle tension with the second law of thermodynamics, and all of them fail to solve the question of the initial conditions because they just move the enigma further into the past. This black list includes entries such as
  • big bounce: a contraction preceded our expansion in a symmetric fashion
  • pre-Big-Bang cosmology: there was a large, cold, flat Universe that shrank in order to start to expand again
  • cyclic or ekypyrotic Universe: the number of contraction-expansion cycles was in fact extremely large
  • and, to a large extent, eternal inflation: our Universe was created as a bubble in a much larger multiverse and we should track its ancestry for many generations and study the existence of completely different Universes who were grandfathers of ours

Unlike ordinary inflation, these theories don't solve any problems of the well-established framework of the Big Bang cosmology. They're not theories that are meant to explain data or problems with previous theories: they're just meant to add something new that is not needed and something that is not mathematically robust. I don't like this kind of theories.

Also, neither of them can be shown to be inevitable by solid calculations. There are so many of them exactly because neither of them is well motivated. It is virtually guaranteed that we won't have any experimental evidence for any of these scenarios in the next few millenia. Will we ever have any theoretical evidence for them? I don't think so.

But even if we will, the derivation of one of these scenarios from a solid underlying theory - probably string theory - will be much more important than the random guess that has predicted its validity. If someone proved the validity of one of these theories kind of rigorously tomorrow, I would still think that it would have been a complete coincidence that someone else has guessed the answer in advance.

Note that I listed four examples. The average probability of one of them to be right is at most 25%. Be sure that the actual probability is way smaller, with the exception of the eternal inflation. I assign this theory a probability of 10%, somewhat less than 20% I gave to the statement that the anthropic explanation will remain the only explanation of the smallness of the cosmological constant.

Imagine that you want to describe your origin. You will end up with the egg. Would you think that the egg was created by shrinking an elephant, or infinitely many times oscillating donkey? Maybe you would but you would be wrong. The egg was never large. The only other interesting events in the past are connected with your parents - your ancestors are analogous to eternal inflation. But operationally speaking, starting with the fertilized egg and continuing with the conventional evolution explains everything about physics of yourself. ;-)

To summarize: Occam's razor was exactly designed to remove speculations of these kinds. We shouldn't be inventing new structures that are not needed for an explanation of any data and that are not needed to explain any theoretical discrepancy.

Dirty games with the arrow of time

Sean also discusses some theories where the arrow of time is spontaneously reverted. I think that these speculations are mad, stupid, and I won't honor them with too a long response except for saying that a fixed arrow of time is an inevitable component of any picture of reality based on special relativity that is compatible with any semi-realistic macroscopic physics. The arrow can't be reverted, and the idea that it can be suddenly reverted is not useful to explain anything about the Universe. The likelihood that the arrow of time gets flipped is much lower than the probability that Jesus Christ is born from a virgin, and if Sean thinks otherwise, he only reveals his deep exo-religious bias.

Sean argues that the "right" expectation would be that the entropy should be increasing into the past. Obviously, it doesn't. In the whole Universe, the macroscopic entropy was always increasing in the same direction as it is today, namely from the past to the future. Isn't it enough to show that Sean's speculations that it should have been the other way around are just wrong? They are circularly based on the wrong conclusion he wants to derive, namely that the entropy of the Big Bang should be "naturally" high.

Of course that we know that it is bogus. There exists no rational method based on science and verified theories and/or principles that would imply that the entropy should be higher in the past. The entropy of the young Universe is low and there is nothing wrong whatsoever with this picture.

Any argument meant to show that something is wrong here is an artifact of sloppy and dogmatic thinking, thinking denying the known basic fact that the initial conditions are defined in the past and what evolves out of them is the future - never the other way around.

Loop quantum cosmology

In Sean's mishmash or random ideas, he seems to put loop quantum cosmology on equal footing with the Hartle-Hawking wavefunction. I don't know whether it was meant as a joke but if it was not, I think that it is an insane approach to these questions.

The work of Hartle and Hawking is an essential and robust proposal explaining the only known natural way how the initial conditions of the Universe may be derived dynamically, from the known path integral or an equivalent definition of dynamics. The existing calculations of the wavefunction of the Universe are arguably primitive but in a more complete theory, it is conceivable that someone just takes their ideas and repeats the calculation in a more rigorous and controllable way that will lead to much more familiar and encouraging results.

The Hartle-Hawking proposal also trivially explains why the entropy of a young Universe is tiny: it's because the Hartle-Hawking wavefunction is really a pure state whose entropy is zero and this value can be trusted as long as the Universe is microscopic.

Loop quantum cosmology is, on the other hand, a silly oversimplification of loop quantum gravity whose purpose is to present childish kindergarten games as a work on quantum gravity although these games have clearly nothing to do with physics of gravity. Loop quantum cosmology doesn't even follow from loop quantum gravity. Loop quantum cosmology is obtained by similar dumb "quantization" procedures directly from the special FRW classical cosmological Ansatz as the procedures that lead from classical 4D general relativity to loop quantum gravity.

Given the fact that even the full loop quantum gravity is demonstrably inconsistent and silly and the procedures themselves are clearly flawed, making further oversimplifications makes the situation really disastrous. Loop quantum cosmology doesn't satisfy any elementary consistency criteria we expect from a theory of quantum cosmology - such as unitarity or the existence of space and particles with spins and familiar interactions - and it will clearly never say anything interesting about physics.

This whole enterprise is just a tool for some people to convince themselves that a game shallower than LEGO can be marketed as quantum gravity. All details are wrong and all questions it offers are completely disconnected from real questions needed in physics. And because there are many stupid people around, be sure that it can be marketed in this way.

Sean's collection of random, mostly flawed ideas is an example how physics would look like if the lowest possible standards were accepted. It would become a conglomerate of myths, religious and anti-religious dogmas, confusion about things that are not confusing at all, and contrived, arbitrary, and mathematically shallow constructions that don't explain anything.

And that's the memo.

3 comments:

  1. These days, aside from home-brewed hooch, I associate the word "moonshine" mostly with "Monstrous Moonshine". See http://en.wikipedia.org/wiki/Monstrous_moonshine ], which includes:

    "It turns out that lying behind monstrous moonshine is a certain string theory having the Monster group as symmetries; the conjectures made by Conway and Norton were proven by Richard Ewen Borcherds in 1992 using the no-ghost theorem from string theory"

    Why should a large symmetry group relate to string theory? you ask. Easy - because both relate to lattices, or hypersphere packings. See for example [ http://en.wikipedia.org/wiki/Leech_lattice ], in which we read:

    "The vertex algebra of the conformal field theory describing bosonic string theory, compactified on the 24-dimensional quotient torus R24/Λ and orbifolded by a two-element reflection group, provides an explicit construction of the Griess algebra that has the monster group as its automorphism group. This monster vertex algebra was also used to prove the monstrous moonshine conjectures."

    I think that before long strings and branes will come to be seen not as fundamental structures in themselves but derived artifacts or dislocations in a fairly uniform distribution of point-like objects at smaller scales.
    Here's a quote from "Gauge Fields in Condensed Matter" by Prof H M Kleinert [ http://www.physik.fu-berlin.de/~kleinert/ ]

    "It is obvious that for each point defect there is a whole neighborhood where the crystalline order is disturbed. Therefore it becomes easier to create a second point defect close to it. Continuing this procedure, it is possible to imagine that an entire section of an atomic layer can disappear by interstitial migration. It is easy to see that such a missing layer is energetically favoured over an equal number of disjoint defects. The reason is that the crystal is capable of repairing the defect over most of the layer. Only at the circumference is such a repair impossible. [..] What has been obtained is a line-like defect called a dislocation line.

    The energy of a straight dislocation line is proportional to the length of the line while the sum of energies of defects from which it was created would be proportional to the number of removed atoms, i.e. to the surface of the layer. As a consequence, larger numbers of point defects always prefer to combine and form line-like defects."

    I think these point-like objects are none other than miniature black holes which evolve according to metrics, including time and temperature, at their intrinsic scale. Although the latter of course is not observable at our familiar scale, in principle it can be said that they behave like a vastly scaled-down and speeded up equivalent of familiar scales and consequently are equivalent at their scale to the familiar scale as it will appear in the very distant future - a bleak and very cold place comprising essentially only vastly separated black holes all of the same mass.

    My basic point is that to explain the very small one must study and understand the very large, namely the ultimate symmetric endpoint (barring subsequent external influences - see below) of the Universe's evolution. The faintest whisps of assymetry in the latter evolve over countless eons and unimaginable distances in exactly the same way as an assembly of sub-Planck scale black holes, which by an identical evolution flip states in an instant (at our scale) too short to be measured!

    Assuming average local temperature at the sub-Planck scale is equal by dissipation, one can identify this mass of a terminally-evolved miniature black hole with none other than the Planck unit of mass-energy at our scale.

    So how do these Planck black holes evolve and interact? If it is safe to assume they rotate, I suggest that in isolation and at a sufficiently low ambient temperature, the effects of relativistic frame dragging build up so that the hole effectively wraps itself in what I call a Lens-Thirring scroll.

    Perhaps this offers an ontological explanation of compacted "curled up" dimensions and at the same time explains the embarrasing "vacuum energy" problem, whereby the vacuum energy is 120 orders of magnitude less than what it should be - The missing energy quanta are there alright but each tucked up inside (or outside?) its own compact dimension scroll like a grub in a pupa!

    As to how these Planck holes interact, if an increase in ambient temperature or background radiation reaches a threshold then the Lens-Thirring scroll unwraps, possibly adiabatically to some extent which reduces the ambient temperature sufficiently for the hole to shrink and vanish by Hawking radiation (which a hole below the ambient temperature will not do).

    So then we have our "gap in the lattice" to which the Kleinert quote above referred, and the radiation will raise the ambient temperature of surrounding holes and perhaps cause them to evaporate in turn ..

    In this situation, if the Planck hole separation is below a certain threshold, one can imagine a chain reaction where every hole is converted in an expanding shell. This it seems to me is reminiscent of a Big Bang (and I feel justifies the presence of this schpiel as a fast comment here ;-) )

    However, black holes do not absorb all incoming matter. According to the article "Black Hole Blowback" [Scientific American, 2007-03], a rapidly spinning black hole expels about 25% of this matter in two narrow beams that issue from its poles.

    (Could the 75% that is absorbed correspond to dark energy? The value sounds about right, and if we assume that most Planck black holes readily return to their scrolled or "dormant" state, then this mass-energy is effectively temporarily removed from the picture, from the standpoint of familiar scales, and could therefore be construed as "negative energy".)

    The above should be sufficient to give a preliminary picture of how I think physicists should picture reality at sub-Planck scales. Although a big fan of string theory (to the extent I understand it, which isn't much admittedly), in my opinion insisting that strings and branes are the absolute rock bottom level of reality will ultimately condemn string theorists to do no more than "look through a glass darkly".

    I could waffle on about all this for ages, but will mercifully end here with a couple of parting thoughts.

    Firstly, everything discovered by scientists the past few centuries indicates that our place in the universe is nothing out of the ordinary. For example the laws of physics, and the properties of spacetime, don't vary across the observable Universe as far as any measurements can discern. So why should familiar scales, of space and time and temperature, be any different?

    Theology aside, it seems a small step then to assume that the reality we perceive is but one scale in an infinite heirarchy, above and below. Furthermore, Occam's razor seems to dictate that all have the same physical laws (although that is more debatable).

    However it would be very naive to think that scales are directly linked by "compatible" metrics. The evidence suggests that they are separate arenas, bordered by singular loci, where the metrics of one somehow collectively generate in different combinations those of the next.

    Secondly (and lastly, you may be relieved to hear), physics has been very successful by working with simple symmetries. Some people spout a lot of mystical nonsense about God loving symmetry and suchlike. But surely a more down to earth explanation is that atomic scale phenomena, and macroscopic phenomena such as gravity that ultimately depend on it, are symmetrical because their components have had all the assymetry knocked out of them by long evolution from their standpoint. Like pebbles on a beach - it's not so much that God delights in the symmetry of round pebbles, but over time all the corners get knocked away.


    Cheers

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