It's been nearly a decade since Roger Penrose wrote "The Road to Reality." This weekend, I finally finished the book. (I had read individual chapters here and there, but I finally found the time to sit down and read the whole book.) The reason that I finally forced myself to read the whole book is that I wanted to see how many of his speculations in 2004 are still valid today. Also, Roger Penrose has some very interesting ways of describing mathematical theories, and he recognizes the ad hoc and incomplete nature of the current "Standard Model," but doesn't shy away from stating his negative opinions about supersymmetry and string theory.
The book is a breath-taking overview of fundamental physics and geometry from the perspective of a Platonist. What's refreshing about the book is the fact that it's a history of physics and mathematics from the view point of a Platonist (i.e. somebody who believes that mathematics...and perhaps beauty and morality...are eternal, unchanging, and exist eternal to the material and mental world.)
Three worlds, Three mysteries p20&1029 "The Road to Reality."
What makes the book so refreshing to read is that, in the decade since this book was published, the "physics media" (i.e. Sean Carroll, Lawrence Krauss, Brian Greene, Martin Rees. Leonard Susskind, and others) have attempted to dismantle neo-Platonism and a belief in an unchanging, external world of absolutes. Post-modernism infected most of the social sciences in the 50s-70s, but physics and mathematics were still holding strong against post-modernism and relativism until the 2000s, at which point in time, the "physics media" began hyping string theory, supersymmetry, multi-verses, universes from nothing, randomness, inflation, time symmetric laws of physics, and the quantum randomness. Luckily, as "natural" string theories and supersymmetries have faced an timely demise due to falsification by high-energy particle collider experiments, it's easier to see that the emperor has no clothes.
For those of you that don't and didn't buy into the relativism in parts of our culture (and who don't buy into the religious conformity of the rest of our culture), reading the "The Road to Reality" is like taking a deep breath after a rain storm. This doesn't mean that everything that Roger Penrose wrote in the book is correct. It just means that he is smart enough to see through the (truth, beauty, morality) relativism hidden in the theories of the so-called "science experts." So, while I share some of his negative opinions of supersymmetry and string theory, I do not agree with all of his speculations. For example, in the book, he argues that gravity is likely the cause of time asymmetry in the universe, i.e. that a non-linear form of general relativity causes the wavefunction collapse of quantum mechanics. With that having been said, I'm glad that he differentiates between the two types of quantum operators...U and R...where U is the unitary transformation of wavefunctions and R is the time-asymmetric collapse of the wavefunction.
Unlike the most physicists, Penrose is at least looking for a solution to the measurement paradox of quantum mechanics (i.e. if quantum mechanics is time-reversal-symmetric, then how is the R operator of an actual measurement time-asymmetric?) String theory and supersymmetry have nothing to say about R and the measurement paradox, and this is one of the reasons why I was never interested in studying string theory (even though, many of my friends and acquaintances studied string theory during their PhDs.) [Given the recent experimental falsification of the "minimal" or "natural" version of string theory and supersymmetry, it turns out to be a good thing that I didn't study string theory or supersymmetry.] String theory and supersymmetry don't solve the measurement paradox and they don't answer the question of why the universe appears to be time-reversal asymmetric. The so-called benefits of string theory and supersymmetry (i.e. the cancellation of some infinite terms that show up in QFT) can be obtained through a number of other methods, including various lattice-based physical theories.
In the rest of this post, I'll be quoting Roger Penrose from the book and discussing some interesting comments that he made back in 2004 that are relevant to today's hot-topics in particle physics. The first quote is from the chapter on speculative physics entitled "Supersymmetry, supra-dimensionality, and strings." In the quote below, he discusses an issues that I haven't seen supersymmetry researchers effectively answer. The question is: what is the super-partner of the Higgs boson? And is the super-partners heavier or lighter than the Higgs boson?
"It seems to be postulated [by supersymmetry] that, of the two 'partners', the one that has the smaller spin (by 1/2h_bar) is deemed to be the exceedingly more massive of the pair (except when both members are the pair are massless.) Presumably, only particles considered as 'elementary' (these apparently being the photon, the graviton, the W and Z boson, gluons, leptons, and quarks) possess superpartners. Otherwise we have trouble with 0-spin particles such as pions. If there are 0-spin elementary particles, such as the still undiscovered Higgs boson, then they would have to count as more massive than their superpartners, on this particular reckoning (since negative spin is excluded.) If this is correct, then why has the Higgs boson's superpartner not been found? Yet again, believers in both supersymmetry and inflationary cosmology must explain how the latter phenomenon's scalar particle fits into the 'superpartner' picture."
I think that this line of argument needs some defending by SUSY researchers. For example, where are the Higgsinos? i.e. where are the Fermi superpartners of the Higgs boson? According to the wiki site on Higgsinos, there is some explanation (beyond my understanding) and a prediction of a 1.1 TeV superpartner. Can somebody more knowledgeable than myself write something in the comment section about whether a 0-spin Higgs boson rules out 'natural' versions of supersymmetry and string theory?
Next topic In the following quote, Penrose discusses an interesting point that Sean Carroll doesn't seem to address on his website on the cause of the arrow of time. On that site, Carroll argues that "As far as thermodynamics is concerned, it's CPT invariance that matters, not T invariance." Because of the highly likely CPT invariance of the weak nuclear force, Carroll argues that the weak nuclear force is not the cause of the arrow of time. But, according to Penrose, there is an error in Carroll's logic. (But first it should be noted that the CPT theorem is not a theorem about thermodynamics. It's a theorem that states that all Lorentz-covariant QFTs are invariant under CPT.)
In the chapter on Quantum state reduction, Paperback pg 818, Penrose writes:
"It seems to me to be clear that the mystery of the extraordinary special nature of the Big Bang cannot be resolved within the standard framework of quantum field theory. At least this would be the case for any theory for which the word 'standard' entails the validity of the CPT theorem. Strictly speaking, that theorem is not immediately applicable to a theory that fully respects the curved-space-time basis of Einstein's general relativity. One of the premises of the CPT theorem is that the background space-time is flat Minkowski space."
What Penrose is arguing is that the CPT theorem was proven for flat curvature of space-time, and that things get much more complicated for curved space-time (i.e. when there's actually matter.) This quote is in Penrose's chapter on Gravity's role in Quantum state reduction.Unfortunately, I think that this is one of Penrose's missteps in his speculative chapters at the end of the book. (Note that the first ~29 chapters are not very speculative, but chapters 30-33 are quitre speculative, and he freely states this so that the reader is aware of what's speculation vs. what's solid theory.) It's not clear to me why Penrose would think that gravity is the cause of the wavefunction collapse. Einstein's version of gravity is non-linear, but it's still time-symemtric. I don't understand why Penrose didn't work out the details of how the weak nuclear force could be the cause of the wave function collapse. The weak nuclear force seems to be the perfect candidate for the wavefunction collapse (i.e. the R collapse of the wavefunction after a measurement) because the weak nuclear force is time asymmetric, and it actually causes particles to change (such as an up quark to change into a down quark.)
So, it may be entirely possible that the weak nuclear force can be CPT invariant, but still be the cause of the time asymmetry of the universe. It may be that, when you combine general relativity (i.e. curved space-time) with the weak nuclear force, you get the arrow of time.
While it's yet to be mathematically/experimentally proven, it's possible that the weak nuclear force is like a bit generator (i.e. a generator of new lattice points in space-time and in phase-space) that causes space-time to expand irreversibly. It's like the weak nuclear nuclear force is a discrete force that adds lattices into space-time, and can cause the overall number of particles and the overall number of lattice points to increase, such that the overall entropy of the universe increases as the particles and lattice points increases. (All the while, the total energy of the universe is constant, and hence the curvature of the 4D sphere decreases on average.) Over time, the number of particles (especially the number of neutrinos) has increased and so has the overall size of the universe. The universe likely started in a Big Bang in which there were a few particles (or large mass) and few lattice points. (Likely) due to the weak nuclear force, the number of particles and the number of lattice points has increased, which allows the entropy of the universe to increase.
In my opinion, "The Road to Reality" helps point us in the right direction of how to overcome the Standard Model of particle physics, and as Penrose states as he ends the book, "It is quite likely that the 21st century will reveal even more wonderful insights than those that we have been blessed with in the 20th. But for this to happen, we shall need powerful new ideas, which will take us in the directions significantly different from those currently being pursued. Perhaps what we mainly need is some subtle change in perspective--something that we all have missed..."