Waking Up to Witten

Do you like driving? I hate it. Driving fast and dangerous in a computer game is ok, but a quick and ephemeral thrill. But for real driving, to and from work, I have a long commute, and no amount of podcasts or music relieves the tiresomeness. Driving around here I need to be on constant alert, there are so many cockroaches (motor scooters) to look out for, and here in Thailand over half the scooter drivers do no t wear helmets, and I cannot drive 50 metres before seeing a young child driven around on a scooter without a helmet. Neither parent nor child will have a helmet. Mothers even cradle infants while hanging on at rear on a scooter. It might not be so bad if the speeds were slow, but they are not. That’s partly why I find driving exhausting. It is stressful to be so worried about so many other people.

Last evening I got home and collapsed and slept for 6 hours. Then woke up and could not get back to sleep, it was midnight. So naturally I got up made a cup of tea, heated up some lasagna and turned on a video of Edward Witten speaking at Strings 2015, What Every Physicist Should Know About String Theory.


True to the title it was illuminating. Watching Witten’s popular lectures is always good value. Mostly I find everything he presents I have heard or read about elsewhere, but never in so much seemingly understandable depth and insight. It is really lovely to hear Witten talk about the φ3 quantum field theory as a natural result of quantising gravity in 1-dimension. He describes this as one of nature’s rhymes: patterns at one scale or domain get repeated in others.

Then he describes how the obstacle to a quantum gravity theory in spacetime via a quantum field theory is the fact that in quantum mechanics states do not correspond to operators. He draws this as a Feynman diagram where a deformation of spacetime is indicated by a kink in a Feynman graph line. That’s an operator. Whereas states in quantum mechanics do not have such deformations, since they are points.


An operator describing a perturbation, like a deformation in the spacetime metric, appears as an internal line in a Feynman diagram, not an external line.

So that’s really nice isn’t it?

I had never heard the flaw of point particle quantum field theory given in such a simple and eloquent way. (The ultraviolet divergences are mentioned later by Witten.)

Then Witten does a similar thing for my understanding of how 2D conformal field theory relates to string theory and quantised gravity. In 2-dimensions there is a correspondence between operators and states in the quantum theory, and it is illustrated schematically by the conformal mapping that takes a point in a 2-manifold to a tube sticking out of the manifold.


The point being (excuse the pun) the states are the slices through this conformal geometry, and so deformations of the states are now equivalent to deformations of operators, and we have the correspondence needed for a quantum theory of gravity.

This is all very nice, but 3/4 of the way through his talk it still leaves some mystery to me.

  • I still do not quite grok how this makes string theory background-free. The string world sheet is quantize-able and you get from this either a conformal field theory or quantum gravity, but how is this background-independent quantum gravity?

I find I have to rewind and watch Witten’s talk a number of times to put all the threads together, and I am still missing something. Since I do not have any physicist buddies at my disposal to bug and chat to about this I either have to try physicsforums or stackexchange or something to get some more insight.

So I rewound a few times and I am pretty certain Witten starts out using a Riemannian metric on a string, and then on a worldsheet. Both are already embedded in a spacetime. So he is not really describing quantum gravity in spacetime. He is describing a state-operator correspondence in a quantum gravity performed on string world sheets. Maybe in the end this comes out in the wash as equivalent to quantising general relativity? I cannot tell. In any case, everyone knows string theory yields a graviton. So in some sense you can say, “case closed up to phenomenology”, haha! Still, a lovely talk and a nice pre-bedtime diversion. But I persisted through to the end of the lecture — delayed sleep experiment.

My gut reaction was that Witten is using some slight of hand. The Conformal Field Theory maybe is background-free, since it is derived from quantum mechanics of the string world sheets. But the stringy gravity theory still has the string worldsheet fluffing around in a background spacetime. Does it not? Witten is not clear on this, though I’m sure in his mind he knows what he is talking about. Then, like he read my mind, Witten does give a partial answer to this.

What Witten gets around to saying is that if you go back earlier in his presentation where he starts with a quantum field theory on a 1D line, then on a 2d-manifold, the spacetime he uses, he claims, was arbitrary. So this partially answers my objections. He is using a background spacetime to kick-start the string/CFT theory, which he admits. But then he does the slight-of-hand and says

“what is more fundamental is the 2d conformal field theory that might be described in terms of a spacetime but not necessarily.”

So my take on this is that what Witten is saying is (currently) most fundamental in string theory is the kick-starter 2d conformal field theory. Or the 2d manifold that starts out as the thing you quantise deformations on to get a phenomenological field theory including quantised gravity. But this might not even be the most fundamental structure. You start to get the idea that string/M-theory is going to moprh into a completely abstract model. The strings and membranes will end up not being fundamental. Which is perhaps not too bad.

I am not sure what else you need to start with a conformal field theory. But surely some kind of proto-primordial topological space is needed. Maybe it will eventually connect back to spin foams or spin networks or twistors. Haha! Wouldn’t that be a kick in the guts for string theorists, to find their theory is really built on top of twistor theory! I think twistors give you quite a bit more than a 2d conformal field, but maybe a “bit more” is what is needed to cure a few of the other ills that plague string theory phenomenology.

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For what it’s worth, I actually think there is a need in fundamental physics to explain even more fundamental constructs, such as why do we need to start with a Lagrangian and then sum it’s action over all paths (or topologies if you are doing a conformal field theory)? This entire formalism, in my mind, needs some kind of more primitive justification.

Moreover, I think there is a big problem in field theory per se. My view is that spacetime is more fundamental than the fields. Field theory is what should “emerge” from a fundamental theory of spacetime physics, not the other way around. Yet “the other way round”, — i.e., fields first, then spacetime — seems to be what a lot of particle or string theorists seem to be suggesting. I realize this is thoroughly counter to the main stream of thought in modern physics, but I cannot help it, I’m really a bit of a classicist at heart. I do not try to actively swim against the stream, it’s just in this case that’s where I find my compass heading. Nevertheless, Witten’s ideas and the way he elaborates them are pretty insightful. Maybe I am unfair. I have heard Weinberg mention the fields are perhaps not fundamental.

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OK, that’s all for now. I have to go and try to tackle Juan Maldacena’s talk now. He is not as easy to listen to though, but since this will be a talk for a general audience it might be comprehensible. Witten might be delightfully nerdy, but Maldacena is thoroughly cerebral and hard to comprehend. Hoping he takes it easy on his audience.

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Eternal Rediscovery

I have a post prepared to upload in a bit that will announce a possible hiatus from this WordPress blog. The reason is just that I found a cool book I want to try to absorb, The Princeton Companion to Mathematics by Gowers, Barrow-Green and Leader. Doubtless I will not be able to absorb it all in one go, so I will likely return to blogging periodically. But there is also teaching and research to conduct, so this book will slow me down. The rest of this post is a light weight brain-dump of some things that have been floating around in my head.

Recently, while watching a lecture on topology I was reminded that a huge percentage of the writings of Archimedes were lost in the siege of Alexandria. The Archimedean solids were rediscovered by Johannes Kepler, and we all know what he was capable of! Inspiring Isaac Newton is not a bad epitaph to have for one’s life.

The general point about rediscovery is a beautiful thing. Mathematics, more than other sciences, has this quality whereby a young student can take time to investigate previously established mathematics but then take breaks from it to rediscover theorems for themselves. How many children have rediscovered Pythagoras’ theorem, or the Golden Ratio, or Euler’s Formula, or any number of other simple theorems in mathematics?

Most textbooks rely on this quality. It is also why most “Exercises” in science books are largely theoretical. Even in biology and sociology. They are basically all mathematical, because you cannot expect a child to go out and purchase a laboratory set-up to rediscover experimental results. So much textbook teaching is mathematical for this reason.

I am going to digress momentarily, but will get back to the education theme later in this article.

The entire cosmos itself has sometimes been likened to an eternal rediscovery. The theory of Eternal Inflation postulates that our universe is just one bubble in a near endless ocean of baby and grandparent and all manner of other universes. Although, recently, Alexander Vilenkin and Audrey Mithani found that a wide class of inflationary cosmological models are unstable, meaning that could not have arisen from a pre-existing seed. There had to be a concept of an initial seed. This kind of destroys the “eternal” in eternal inflation. Here’s a Discover magazine account: What Came Before the Big Bang? — Cosmologist Alexander Vilenkin believes the Big Bang wasn’t a one-off event”. Or you can click this link to hear Vilenkin explain his ideas himself: FQXi: Did the Universe Have a Beginning? Vilenkin seems to be having a rather golden period of originality over the past decade or so, I regularly come across his work.

If you like the idea of inflationary cosmology you do not have to worry too much though. You still get the result that infinitely many worlds could bubble out of an initial inflationary seed.

Below is my cartoon rendition of eternal inflation in the realm of human thought:

Oh to be a bubble thoughtoverse of the Wittenesque variety.

Quantum Fluctuations — Nothing Cannot Fluctuate

One thing I really get a bee in my bonnet about are the endless recountings in the popular literature about the beginning of the universe is the naïve idea that no one needs to explain the origin of the Big Bang and inflatons because “vacuum quantum fluctuations can produce a universe out of nothing”. This sort of pseudo-scientific argument is so annoying. It is a cancerous argument that plagues modern cosmology. And even a smart person like Vilenkin suffers from this disease. Here I quote him from a quote in another article on the PBS NOVA website::

Vilenkin has no problem with the universe having a beginning. “I think it’s possible for the universe to spontaneously appear from nothing in a natural way,” he said. The key there lies again in quantum physics—even nothingness fluctuates, a fact seen with so-called virtual particles that scientists have seen pop in and out of existence, and the birth of the universe may have occurred in a similar manner.
Source: http://www.pbs.org/wgbh/nova/blogs/physics/2012/06/in-the-beginning/

At least you have to credit Vilenkin with the brains to have said it is only “possible”. But even that caveat is fairly weaselly. My contention is that out of nothing you cannot get anything, not even a quantum fluctuation. People seem to forget quantum field theory is a background-dependent theory, it requires a pre-existing spacetime. There is no “natural way” to get a quantum fluctuation out of nothing. I just wish people would stop insisting on this sort of non-explanation for the Big Bang. If you start with not even spacetime then you really cannot get anything, especially not something as loaded with stuff as an inflaton field. So one day in the future I hope we will live in a universe where such stupid arguments are nonexistent nothingness, or maybe only vacuum fluctuations inside the mouths of idiots.

There are other types of fundamental theories, background-free theories, where spacetime is an emergent phenomenon. And proponents of those theories can get kind of proud about having a model inside their theories for a type of eternal inflation. Since their spacetimes are not necessarily pre-existing, they can say they can get quantum fluctuations in the pre-spacetime stuff, which can seed a Big Bang. That would fit with Vilenkin’s ideas, but without the silly illogical need to postulate a fluctuation out of nothingness. But this sort of pseudo-science is even more insidious. Just because they do not start with a presumption of a spacetime does not mean they can posit quantum fluctuations in the structure they start with. I mean they can posit this, but it is still not an explanation for the origins of the universe. They still are using some kind of structure to get things started.

Probably still worse are folks who go around flippantly saying that the laws of physics (the correct ones, when or if we discover them) “will be so compelling they will assert their own existence”. This is basically an argument saying, “This thing here is so beautiful it would be a crime if it did not exist, in fact it must exist since it is so beautiful, if no one had created it then it would have created itself.” There really is nothing different about those two statements. It is so unscientific it makes me sick when I hear such statements touted as scientific philosophy. These ideas go beyond thought mutation and into a realm of lunacy.

I think the cause of these thought cancers is the immature fight in society between science and religion. These are tensions in society that need not exist, yet we all understand why they exist. Because people are idiots. People are idiots where their own beliefs are concerned, by in large, even myself. But you can train yourself to be less of an idiot by studying both sciences and religions and appreciating what each mode of human thought can bring to the benefit of society. These are not competing belief systems. They are compatible. But so many believers in religion are falsely following corrupted teachings, they veer into the domain of science blindly, thinking their beliefs are the trump cards. That is such a wrong and foolish view, because everyone with a fair and balanced mind knows the essence of spirituality is a subjective view-point about the world, one deals with one’s inner consciousness. And so there is no room in such a belief system for imposing one’s own beliefs onto others, and especially not imposing them on an entire domain of objective investigation like science. And, on the other hand, many scientists are irrationally anti-religious and go out of their way to try and show a “God” idea is not needed in philosophy. But in doing so they are also stepping outside their domain of expertise. If there is some kind of omnipotent creator of all things, It certainly could not be comprehended by finite minds. It is also probably not going to be amenable to empirical measurement and analysis. I do not know why so many scientists are so virulently anti-religious. Sure, I can understand why they oppose current religious institutions, we all should, they are mostly thoroughly corrupt. But the pure abstract idea of religion and ethics and spirituality is totally 100% compatible with a scientific worldview. Anyone who thinks otherwise is wrong! (Joke!)

Also, I do not favour inflationary theory for other reasons. There is no good theoretical justification for the inflaton field other than the theory of inflation prediction of the homogeneity and isotropy of the CMB. You’d like a good theory to have more than one trick! You know. Like how gravity explains both the orbits of planets and the way an apple falls to the Earth from a tree. With inflatons you have this quantum field that is theorised to exist for one and only one reason, to explain homogeneity and isotropy in the Big Bang. And don’t forget, the theory of inflation does not explain the reason the Big Bang happened, it does not explain its own existence. If the inflaton had observable consequences in other areas of physics I would be a lot more predisposed to taking it seriously. And to be fair, maybe the inflaton will show up in future experiments. Most fundamental particles and theoretical constructs began life as a one-trick sort of necessity. Most develop to be a touch more universal and will eventually arise in many aspects of physics. So I hope, for the sake of the fans of cosmic inflation, that the inflaton field does have other testable consequences in physics.

In case you think that is an unreasonable criticism, there are precedents for fundamental theories having a kind of mathematically built-in explanation. String theorists, for instance, often appeal to the internal consistency of string theory as a rationale for its claim as a fundamental theory of physics. I do not know if this really flies with mathematicians, but the string physicists seem convinced. In any case, to my knowledge the inflation does not have this sort of quality, it is not a necessary ingredient for explaining observed phenomena in our universe. It does have a massive head start on being a candidate sole explanation for the isotropy and homogeneity of the CMB, but so far that race has not yet been completely run. (Or if it has then I am writing out of ignorance, but … you know … you can forgive me for that.)

Anyway, back to mathematics and education.

You have to love the eternal rediscovery built-in to mathematics. It is what makes mathematics eternally interesting to each generation of students. But as a teacher you have to train the nerdy children to not bother reading everything. Apart from the fact there is too much to read, they should be given the opportunity to read a little then investigate a lot, and try to deduce old results for themselves as if they were fresh seeds and buds on a plant. Giving students a chance to catch old water as if it were fresh dewdrops of rain is a beautiful thing. The mind that sees a problem afresh is blessed, even if the problem has been solved centuries ago. The new mind encountering the ancient problem is potentially rediscovering grains of truth in the cosmos, and is connecting spiritually to past and future intellectual civilisations. And for students of science, the theoretical studies offer exactly the same eternal rediscovery opportunities. Do not deny them a chance to rediscover theory in your science classes. Do not teach them theory. Teach them some theoretical underpinnings, but then let them explore before giving the game away.
With so much emphasis these days on educational accountability and standardised tests there is a danger of not giving children these opportunities to learn and discover things for themselves. I recently heard an Intelligence2 “Intelligence Squared” debate on academic testing. One crazy women from the UK government was arguing that testing, testing, and more testing — “relentless testing” were her words — was vital and necessary and provably increased student achievement.

Yes, practising tests will improve test scores, but it is not the only way to improve test scores. And relentless testing will improve student gains in all manner of mindless jobs out there is society that are drill-like and amount to going through routine work, like tests. But there is less evidence that relentless testing improves imagination and creativity.

Let’s face it though. Some jobs and areas of life require mindlessly repetitive tasks. Even computer programming has modes where for hours the normally creative programmer will be doing repetitive but possibly intellectually demanding chores. So we should not agitate and jump up and down wildly proclaiming tests and exams are evil. (I have done that in the past.)

Yet I am far more inclined towards the educational philosophy of the likes of Sir Ken Robinson, Neil Postman, and Alfie Kohn.

My current attitude towards tests and exams is the following:

  1. Tests are incredibly useful for me with large class sizes (120+ students), because I get a good overview of how effective the course is for most students, as well as a good look at the tails. Here I am using the fact test scores (for well designed tests) do correlate well with student academic aptitudes.
  2. My use of tests is mostly formative, not summative. Tests give me a valuable way of improving the course resources and learning styles.
  3. Tests and exams suck as tools for assessing students because they do not assess everything there is to know about a student’s learning. Tests and exams correlate well with academic aptitudes, but not well with other soft skills.
  4. Grading in general is a bad practise. Students know when they have done well or not. They do not need to be told. At schools if parents want to know they should learn to ask their children how school is going, and students should be trained to be honest, since life tends to work out better that way.
  5. Relentless testing is deleterious to the less academically gifted students. There is a long tail in academic aptitude, and the students in this tail will often benefit from a kinder and more caring mode of learning. You do not have to be soft and woolly about this, it is a hard core educational psychology result: if you want the best for all students you need to treat them all as individuals. For some tests are great, terrific! For others tests and exams are positively harmful. You want to try and figure out who is who, at least if you are lucky to have small class sizes.
  6. For large class sizes, like at a university, do still treat all students individually. You can easily do this by offering a buffet of learning resources and modes. Do not, whatever you do, provide a single-mode style of lecture+homework+exam course. That is ancient technology, medieval. You have the Internet, use it! Gather vast numbers of resources of all different manners of approach to your subject you are teaching, then do not teach it! Let your students find their own way through all the material. This will slow down a lot of students — the ones who have been indoctrinated and trained to do only what they are told — but if you persist and insist they navigate your course themselves then they should learn deeper as a result.

Solving the “do what I am told” problem is in fact the very first job of an educator in my opinion. (For a long time I suffered from lack of a good teacher in this regard myself. I wanted to please, so I did what I was told, it seemed simple enough. But … Oh crap, … the day I found out this was holding me back, I was furious. I was about 18 at the time. Still hopelessly naïve and ill-informed about real learning.) If you achieve nothing else with a student, transitioning them from being an unquestioning sponge (or oily duck — take your pick) to being self-motivated and self-directed in their learning is the most valuable lesson you can ever give them. So give them it.

So I use a lot of tests. But not for grading. For grading I rely more on student journal portfolios. All the weekly homework sets are quizzes though, so you could criticise the fact I still use these for grading. As a percentage though, the Journals are more heavily weighted (usually 40% of the course grade). There are some downsides to all this.

  • It is fairly well established in research that grading using journals or subjective criteria is prone to bias. So unless you anonymise student work, you have a bias you need to deal with somehow before handing out final grades.
  • Grading weekly journals, even anonymously, takes a lot of time, about 15 to 20 times the hours that grading summative exams takes. So that’s a huge time commitment. So you have to use it wisely by giving very good quality early feedback to students on their journals.
  • I still haven’t found out how to test the methods easily. I would like to know quantitatively how much more effective journal portfolios are compared to exam based assessments. I am not a specialist education researcher, and I research and write a about a lot of other things, so this is taking me time to get around to answering.

I have not solved the grading problem, for now it is required by the university, so legally I have to assign grades. One subversive thing I am following up on is to refuse to submit singular grades. As a person with a physicists world-view I believe strongly in the role of sound measurement practice, and we all know a single letter grade is not a fair reflection on a student’s attainment. At a minimum a spread of grades should be given to each student, or better, a three-point summary, LQ, Median, UQ. Numerical scaled grades can then be converted into a fairer letter grade range. And GPA scores can also be given as a central measure and a spread measure.

I can imagine many students will have a large to moderate assessment spread, and so it is important to give them this measure, one in a few hundred students might statistically get very low grades by pure chance, when their potential is a lot higher. I am currently looking into research on this.

OK, so in summary: even though institutions require a lot of tests you can go around the tests and still given students a fair grade while not sacrificing the true learning opportunities that come from the principle of eternal rediscovery. Eternal rediscovery is such an important idea that I want to write an academic paper about it and present at a few conferences to get people thinking about the idea. No one will disagree with it. Some may want to refine and adjust the ideas. Some may want concrete realizations and examples. The real question is, will they go away and truly inculcate it into their teaching practices?


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Coupling to the Universe — or “You Are You Because You Are You”

Carlo Rovelli can sure talk up a blizzard (I’m reviewing his conference talk: (The preferred time direction in the dynamics of the full universe). For an Italian native he can really weave a blinding spell in English.

He has my confused when he tries to explain the apparent low entropy Big Bang cosmology. He uses his own brand of relational quantum mechanics I think, but it comes out sounding a bit circular or anthropomorphic. Yet earlier in his lectures he often takes pains to deny anthropomorphic views.

So it is quite perplexing when he tries to explain our perception of an arrow of time by claiming that, “it is what makes us us.” Let me quote him, so you can see for yourself. He starts out by claiming the universe starts in a low entropy state only form our relative point of view. Entropy is an observer dependent concept. It depends on how you coarse grain your physics. OK, I buy that. We couple to the physical external fields in a particular way, and this is what determines how we perceive or coarse grain our slices of the universe. So how we couple to the universe supposedly explains way wee see the apparent entropy we perceive. If by some miracle we coupled more like antiparticles effectively travelling in the reverse time direction then we’d see entropy quite differently, one imagines. So anyway, Rovelli then summarizes:

[On slides: Entropy increase (passage of time) depend on the coarse graining, hence the subsystem, not the microstate of the world.] … “Those depend on the way we couple to the rest of the universe. Why do we couple to the rest of the universe in this way? Because if we didn’t couple to the rest of the universe this way we wouldn’t be us. Us as things, as biological entities that very much live in time coupled in a manner such that the past moves towards the future in a precise sense … which sense? … the one described by the Second Law of Thermodynamics.”

You see what I mean?

Maybe I am unfairly pulling this out of a rushed conference presentation, and to be more balanced and fair I should read his paper instead. If I have time I will. But I think a good idea deserves a clear presentation, not a rush job with a lot of vague wishy-washy babble, or obscuring in a blizzard of words and jargon.

OK, so here’s an abstract from an arxiv paper where Rovelli states things in written English:

” Phenomenological arrows of time can be traced to a past low-entropy state. Does this imply the universe was in an improbable state in the past? I suggest a different possibility: past low-entropy depends on the coarse-graining implicit in our definition of entropy. This, in turn depends on our physical coupling to the rest of the world. I conjecture that any generic motion of a sufficiently rich system satisfies the second law of thermodynamics, in either direction of time, for some choice of macroscopic observables. The low entropy of the past could then be due to the way we couple to the universe (a way needed for us doing what we do), hence to our natural macroscopic variables, rather than to a strange past microstate of the world at large.”

That’s a little more precise, but still no clearer on import. He is still really just giving an anthropocentric argument.

I’ve always thought science was at it’s best when removing the human from the picture. The problem for our universe should not be framed as one of “why do we see an arrow of time?” because, as Rovelli points out, for complex biological systems like ourselves there really is no other alternative. If we did not perceive an arrow of time we would be defined out of existence!

The problem for our universe should be simply, “why did our universe begin (from any arbitrary sentient observer’s point of view) with such low entropy?”

But even that version has the whiff of observer about it. Also, you just define the “beginning” as the end that has the low entropy, then you are done, no debate. So I think there is a more crystalline version of what cosmology should be seeking an explanation for, which is simply, “how can any universe ever get started (from either end of a singularity) in a low entropy state?”

But even there you have a notion of time, which we should remove, since “start” is not a proper concept unless one already is talking about a universe. So the barest question of all perhaps, (at least the barest that I can summon) is, “how do physics universes come to exist?”

This does not even explicitly mention thermodynamics or an arrow of time. But within the question those concepts are embedded. One needs to carefully define “physics” and “physics universes”. But once that is done then you have a slightly better philosophy of physics project.

More hard core physicists however will never stoop to tackle such a question. They will tend to drift towards something where a universe is already posited to exist and has had a Big Bang, and then they will fret and worry about how it could have a low entropy singularity.

It is then tempting to take the cosmic Darwinist route. But although I love the idea, it is another one of those insidious memes that is so alluring but in the cold dead hours of night, when the vampires of popular physics come to devour your life blood seeking converts, seems totally unsatisfying and anaemic. The Many Worlds Interpretation has it’s fangs sunk into a similar vein, which I’ve written about before.


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Going back to Rovelli’s project, I have this problem for him to ponder. What if there is no way for any life, not even in principle, to couple to the universe other than via the way we humans do, through interaction with strings (or whatever they are) via Hamiltonians and mass-energy? If this is true, and I suspect it is, then is not Rovelli’s “solution” to the low entropy Big Bang a bit meaningless?

I have a pithy way of summarising my critique of Rovelli. I would just point out:

The low entropy past is not caused by us. We are the consequence.

So I think it is a little weak for Rovelli to conjecture that the low entropy past is “due to the way we couple to the universe.” It’s like saying, “I conjecture that before death one has to be born.” Well, … duuuuhhh!

The reason my photo is no longer on Facebook is due to the way I coupled to my camera.

I am an X-gener due to the way my parents coupled to the universe.

You see what I’m getting at? I might be over-reaching into excessive sarcasm, but my point is just that none of this is good science. They are not explanations. It is just story-telling. Still, Rovelli does give an entertaining story if you are a physics geek.

So I had a read of Rovelli’s paper and saw the more precise statement of his conjecture:

Rovelli’s Conjecture: “Any generic microscopic motion of a sufficiently rich system satisfies the second law (in either time direction) for a suitable choice of macroscopic observables.

That’s the sort of conjecture that says nothing. The problem is the “sufficiently rich” clause together with the “suitable choice” clause. You can generate screeds of conjectures with such a pair of clauses. The conjecture only has “teeth” if you define what you mean by “sufficiently rich” and if a “suitable choice” can be identified or motivated as plausible. Because otherwise you are not saying anything useful. For example, “Any sufficiently large molecule will be heavier than a suitably chosen bowling ball.”

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Rovelli does provide a toy example to illustrate his notions in classical mechanics. He has yellow balls and red balls. The yellow balls have an attractor which gives them a natural second law of thermodynamic arrow of time. The same box also has red balls with a different attractor which gives them the opposite arrow of time according to the second law. (Watching the conference video for this is better than reading the arxiv paper.) But “so what?”

Rovelli has constructed a toy universe that has entities that would experience opposite time directions if they were conscious. But there are so many things wrong with this example it cannot be seriously considered as a bulwark for Rovelli’s grander project. For starters, what is the nature of his Red and Yellow attractors? If they are going to act complicated enough to imbue the toy universe with anything resembling conscious life then the question of how the arrow of time arises is not answered, it just gets pushed back to the properties of these mysterious Yellow and Red attractors.

And if you have only such a toy universe without any noticeable observers then what is the point of discussing an arrow of time? It is only a concept that a mind external to that world can contemplate. So I do not see the relevance of Rovelli’s toy model for our much more complicated universe which has internal minds that perceive time.

You could say, in principle the toy model tells us there could be conscious observers in our universe who are experiencing life but in the reverse time direction to ourselves, they remember our future but not our past, we remember their future but not their past. Such dual time life forms would find it incredibly hard to communicate, due to this opposite wiring of memory.

But I would argue that Rovelli’s model does not motivate such a possibility, for the same reason as before. Constructing explicit models of different categories of billiard balls each obeying a second law of thermodynamics in opposite time directions in the same system is one thing, but not much can be inferred from this unless you add in a whole lot of further assumptions about what Life is, metabolism, self-replication, and all that. But if you do this the toy model becomes a lot less toy-like and in fact terribly hard to explicitly construct. Maybe Stephen Wolfram’s cellular automata can do the trick? But I doubt it.

I should stop harping on this. Let me just record my profound dissatisfaction with Rovelli’s attempt to demystify the arrow of time.

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If you ask me, we are not at a sufficiently mature enough juncture in the history of cosmology and physics to be able to provide a suitable explanation for the arrow of time.

So I have Smith’s Conjecture:

At any sufficiently advanced enough juncture in the history of science, enough knowledge will have accumulated to enable physicists to provide a suitable explanation for the arrow of time.

Facetiousness aside, I really do think that trying to explain the low entropy big bang is a bit premature. It would be much better to be patient and wait for more information about our universe before attempting to launch into the arrow of time project. The reason I believe so is because I think the ultimate answers about such cosmological questions are external to our observable universe.

But even whether they are external or internal there is a wider problem to do with the nature of time and our universe. We do not know if our universe actually had a beginning, a true genesis, or whether it has always existed.

If the universe had a beginning then the arrow of time problem is the usually low entropy puzzle problem. But if the universe had no beginning then the arrow of time problem becomes a totally different question. There is even a kind of intermediate problem that occurs if our universe had a start but within some sort of wider meta-cosmos. Then the problem is much harder, that of figuring out the laws of this putative metaverse. Imagine the hair-pulling of cosmologists who discover this latter possibility as a fact about their universe (but I would envy them the shear ability to discover the fact, it’d be amazing).

So until we know such a fundamental question I do not see a lot of fruitfulness in pursuing the arrow of time puzzle. It’s a counting your chickens before they hatch situation. Or should I say, counting your microstates before they batch.

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