“It Hurts my Brain” — Wrong! Thinking is Not Hard, Thinking is Beautiful

Can we all please get beyond the myth that “thinking is hard”! This guy from Veritasium means well, but regurgitates the myth: How Should We Teach Science? (2veritasium, March 2017) Thinking is not hard because of the brain energy it takes. That is utter crap. What is likely more realistic psychologically is that people do not take time and quiet space to reflect and meditate. Deep thinking is more like meditation, and it is energizing and relaxing. So this old myth needs replacing I think. Thinking deeply while distracting yourself with trivia is really hard, because of the cognitive load on working memory. It seems hard because when your working memory gets overloaded you cannot retain ideas, and it appears like you get stupid and this leads to frustration and anxiety, and that does have physiological effects that mimic a type of mental pain.

But humans have invented ways to get around this. One is called WRITING. You sit down meditate, allow thoughts to flood your working memory, and when you get an insight or an overload you write them down, then later review, organize and structure your thoughts. In this way deep thinking is easy and enjoyable. Making thinking hard so that it seems to hurt your brain is a choice. You have chosen to buy into the myth when you try to concentrate on deep thinking while allowing yourself to be distracted by life’s trivia and absurdities. Unfortunately, few schools teach the proper art of thinking.

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Greater Thoughts that Cannot Be Imageoned

Most scientists do not enter their chosen fields because the work is easy. They do their science mainly because it is challenging and rewarding when triumphant. Yet few scientists will ever taste the sweet dew drops of triumph — real world-changing success — in their lifetimes. So it is remarkable perhaps that the small delights in science are sustaining enough for the human soul to warrant persistence and hard endeavour in the face of mostly mediocre results and relatively few cutting edge break-throughs.

Still, I like to think that most scientists get a real kick out of re-discovering results that others before them have already uncovered. I do not think there is any diminution for a true scientist in having been late to a discovery and not having publication priority. In fact I believe this to be universally true for people who are drawn into science for aesthetic reasons, people who just want to get good at science for the fun of it and to better appreciate the beauty in this world. If you are of this kind you likely know exactly what I mean. You could tomorrow stumble upon some theorem proven hundreds of years ego by Gauss or Euler or Brahmagupta and still revel in the sweet taste of insight and understanding.

Going even further, I think such moments of true insight are essential in the flowering of scientific aesthetic sensibilities and the instilling of a love for science in young children, or young at heart adults. “So what?” that you make this discovery a few hundred years later than someone else? They had a birth head start on you! The victory is truly still yours. And “so what?” that you have a few extra giants’ shoulders to stand upon? You also saw through the haze and fog of much more information overload and Internet noise and thought-pollution, so you can savour the moment like the genius you are.

Such moments of private discovery go unrecorded and must surely occur many millions of times more frequently than genuinely new discoveries and break-throughs. Nevertheless, every such transient to invisible moment in human history must also be a little boost to the general happiness and welfare of all of humanity. Although only that one person may feel vibrant from their private moment of insight, their radiance surely influences the microcosm of people around them.

I cannot count how many such moments I have had. They are more than I will probably admit, since I cannot easily admit to any! But I think they occur quite a lot, in very small ways. However, back in the mid 1990’s I had, what I thought, was a truly significant glimpse into the infinite. Sadly it had absolutely nothing to do with my PhD research, so I could only write hurriedly rough notes on recycled printout paper during small hours of the morning when sleep eluded my body. To this day I am still dreaming about the ideas I had back then, and still trying to piece something together to publish. But it is not easy. So I will be trying to leak out a bit of what is in my mind in some of these WordPress pages. Likely what will get written will be very sketchy and denuded of technical detail. But I figure if I put the thoughts out into the Web maybe, somehow, some bright young person will catch them via Internet osmosis of a sort, and take them to a higher level.

geons_vs_superstrings_1

There are a lot of threads to knit together, and I hardly know where to start. I have already started writing perhaps half a dozen manuscripts, none finished, most very sketchy. And this current writing is yet another forum I have begun.

The latest bit of reading I was doing gave me a little shove to start this topic anew. It happens from time to time that I return to studying Clifford Geometric Algebra (“GA” for short). The round-about way this happened last week was this:

  • Weary from reading a Complex Analysis book that promised a lot but started to get tedious: so for a light break YouTube search for a physics talk, and find Twistors and Spinors talks by Sir Roger Penrose. (Twistor Theory is heavily based on Complex Analysis so it was a natural search to do after finishing a few chapters of the mathematics book).
  • Find out the Twistor Diagram efforts of Andrew Hodges have influenced Nima Arkani-Hamed and even Ed Witten to obtain new cool results crossing over twistor theory with superstring theory and scattering amplitude calculations (the “Amplituhedron” methods).
  • That stuff is ok to dip into, but it does not really advance my pet project of exploring topological geon theory. So I look for some more light reading and rediscover papers from the Cambridge Geometric Algebra Research Group (Lasenby, Doran, Gull). And start re-reading Gull’s paper on electron paths and tunnelling and the Dirac theory inspired by David Hestene’s work
  • The Gull paper mentions criticisms of the Dirac theory that I had forgotten. In the geometric algebra it is clear that solving the Dirac equation gives not positively charge anti-electrons, but unphysical negative frequency solutions with negative charge and negative mass. So they are not positrons. It’s provoking that the authors claim this problem is not fully resolved by second quantisation, but rather perhaps just gets glossed over? I’m not sure what to think of this. (If the negative frequencies get banished by second quantisation why not just conclude first quantisation is not nature’s real process?)
  • Still, whatever the flaws in Dirac theory, the electron paths paper has tantalising similarities with the Bohm pilot wave theory electron trajectories. And there is also a reference to the Statistical Interpretation of Quantum Mechanics (SIQM) due to Ballentine (and attributed also as Einstein’s preferred interpretation of QM).
  • It gets me thinking again of how GA might be helpful in my problems with topological geons. But I shelve this thought for a bit.
  • Reading Ballentine’s paper is pretty darn interesting. It dates from 1970, but it is super clear and easy to read. I love that in a paper. The gist of it is that an absolute minimalist interpretation of quantum mechanics would drop Copenhagen ideas and view the wave function as more like a description of what could happen in nature, tat is, the wave functions are descriptions of statistical ensembles of identically prepared experiments or systems in nature. (Sure, no two systems are ever prepared in the exact same initial state, but that hardly matters when you are only doing statistics rather than precise deterministic modelling.)
  • So Ballentine was suggesting the wave functions are;
    1. not a complete description of an individual particle, but rather
    2. better thought of as a description of an ensemble of identically prepared states.

This is where I ended up, opening my editor to draft a OneOverEpsilon post.

So here’s the thing I like about the ensemble interpretation and how the geometric algebra reworking of Dirac theory adds to a glimmer of clarity about what might be happening with the deep physics of our universe. For a start the ensemble interpretation is transparently not a complete theoretical framework, since it is a statistical theory it does not pretend to be a theory of reality. Whatever is responsible for the statistical behaviour of quantum systems is still an open question in SIQM. The Bohm-like trajectories that the geometric algebra solutions to the Dirac theory are able to compute as streamline plots are illuminating in this respect, since they seem to clearly show that what the Dirac wave equation is modelling is almost certainly not the behaviour a single particle. (One could guess this from Schrödinger theory as well, but I guess physicists were already lured into believing in the literal wave-particle duality meme well before Bohm was able to influence anyone’s thinking.)

Also, it is possible (I do not really know for sure) that the negative frequency solutions in Dirac theory can be viewed as merely an artifact of the statistical ensemble framework. No single particle acts truly in accordance with the Dirac wave equation. So there is no real reason to get ones pants in a twist about the awful appearance of negative frequencies.

(For those in-the-know: the Dirac theory negative frequency solutions turn out to have particle currents in the reverse spatial direction to their momenta, so that’s not a backwards time propagating anti-particle, it is a forwards in time propagating negative mass particle. That’s a particle that’d fall upwards in a gravitational field if the principle of equivalence holds universally. As an aside note: it is a bit funky that this cannot be tested experimentally since no one can yet clump enough anti-matter together to test which way it accelerates in a gravitational field. But I presume the sign of particle inertial mass can be checked in the lab, and, so far, all massive particles known to science at least are known to have positive inertial mass.)

And as a model of reality the Dirac equation has therefore, certain limitations and flaws. It can get some of the statistics correct for particular experiments, but a statistical model always has limits of applicability. This is neither a defense or a critique of Dirac theory.  My view is that it would be a bit naïve to regard Dirac theory as the theory of electrons, and naïve to think it should have no flaws.  At best such wave-function models are merely a window frame for a particular narrow view out into our universe.  Maybe I am guilty of a bit of sophistry or rhetoric here, but that’s ok for a WordPress blog I think … just puttin’ some ideas “out there”.

Then another interesting confluence is that one of Penrose’s big projects in Twistor theory was to do away with the negative frequency solutions in 2-Spinor theory. And I think, from recall, he succeeded in this some time ago with the extension of twistor space to include the two off-null halves. Now I do not know how this translates into real-valued geometric algebra, but in the papers of Doran, Lasenby and Gull you can find direct translations of twistor objects into geometric algebra over real numbers. So there has to be in there somewhere a translation of Penrose’s development in eliminating the negative frequencies.

So do you feel a new research paper on Dirac theory in the wind just there? Absolutely you should! Please go and write it for me will you? I have my students and daughters’ educations to deal with and do not have the free time to research off-topic too much. So I hope someone picks up on this stuff. Anyway, this is where maybe the GA reworking of Dirac theory can borrow from twistor theory to add a little bit more insight.

There’s another possible confluence with the main unsolved problem in twistor theory. The Twistor theory programme is held back (stalled?) a tad (for 40 years) by the “googly problem” as Penrose whimsically refers to it. The issue is one of trying to find self-dual solutions of Einstein’s vacuum equations (as far as I can tell, I find it hard to fathom twistor theory so I’m not completely sure what the issue is). The “googly problem” stood for 40 years, and in essence is the problem of “finding right-handed interacting massless fields (positive helicity) using the same twistor conventions that give rise to left-handed fields (negative helicity)”. Penrose maybe has a solution dubbed Palatial Twistor Theory which you might be able to read about here: “On the geometry of palatial twistor theory” by Roger Penrose, and also lighter reading here: “Michael Atiya’s Imaginative Mind” by Siobhan Roberts in Quanta Magazine.

If you do not want to read those articles then the synopsis, I think, is that twistor theory has some problematic issues in gravitation theory when it comes to chirality (handedness), which is indeed a problem since obtaining a closer connection between relativity and quantum theory was a prime motive behind the development of twistor theory. So if twistor theory cannot fully handle left and right-handed solutions to Einstein’s equations it might be said to have failed to fulfill one it’s main animating purposes.

So ok, to my mind there might be something the geometric algebra translation of twistor theory can bring to bear on this problem, because general relativity is solved in fairly standard fashion with geometric algebra (that’s because GA is a mathematical framework for doing real space geometry, and handles Lorentzian metrics as simply as Euclidean, not artificially imposed complex analytic structure is required). So if the issues with twistor theory are reworked in geometric algebra then some bright spark should be able to do the job twistor theory was designed do do.

By the way, the great beauty and advantage Penrose sees in twistor theory is the grounding of twistor theory in complex numbers. The Geometric Algebra Research Group have pointed out that this is largely a delusion. It turns out that complex analysis and holomorphic functions are just a sector of full spacetime algebra. Spacetime algebra, and in fact higher dimensional GA, have a concept of monogenic functions which entirely subsume the holomorphic (analytic) functions of 2D complex analysis. Complex numbers are also completely recast for the better as encodings of even sub-algebras of the full Clifford–Geometric Algebra of real space. In other words, by switching languages to geometric algebra the difficulties that arise in twistor theory should (I think) be overcome, or at least clarified.

If you look at the Geometric Algebra Research Group papers you will see how doing quantum mechanics or twistor theory with complex numbers is really a very obscure way to do physics. Using complex analysis and matrix algebra tends to make everything a lot harder to interpret and more obscure. This is because matrix algebra is a type of encoding of geometric algebra, but it is not a favourable encoding, it hides the clear geometric meanings in the expressions of the theory.

*      *       *

So far all I have described is a breezy re-awakening of some old ideas floating around in my head. I rarely get time these days to sit down and hack these ideas into a reasonable shape. But there are more ideas I will try to write down later that are part of a patch-work that I think is worth exploring. It is perhaps sad that over the years I had lost the nerve to work on topological geon theory. Using spacetime topology to account for most of the strange features of quantum mechanics is however still my number one long term goal in life. Whether it will meet with success is hard to discern, perhaps that is telling: if I had more confidence I would simply abandon my current job and dive recklessly head-first into geon theory.

Before I finish up this post I want to thus outline very, very breezily and incompletely, the basic idea I had for topological geon theory. It is fairly simplistic in many ways. There is however new impetus from the past couple of years developments in the Black Hole firewall paradox debates: the key idea from this literature has been the “ER=EPR” correspondence hypothesis, which is that quantum entanglement (EPR) might be almost entirely explained in terms of spacetime wormholes (ER: Einstein-Rosen bridges). This ignited my interest because back in 1995/96 I had the idea that Planck scale wormholes in spacetime can allow all sorts of strange and gnarly advance causation effects on the quantum (Planckian) space and time scales. It seemed clear to me that such “acausal” dynamics could account for a lot of the weird correlations and superpositions seen in quantum physics, and yet fairly simply so by using pure geometry and topology. It was also clear that if advanced causation (backwards time travel or closed timelike curves) are admitted into physics, even if only at the Planck scale, then you cannot have a complete theory of predictive physics. Yet physics would be deterministic and basically like general relativity in the 4D block universe picture, but with particle physics phenomenology accounted for in topological properties of localised regions of spacetime (topological 4-geons). The idea, roughly speaking, is that fundamental particles are non-trivial topological regions of spacetime.  The idea is that geons are not 3D slices of space, but are (hypothetically) fully 4-dimensional creatures of raw spacetime topology.   Particles are not apart from spacetime. Particles are not “fields that live in spacetime”, no! Particles are part of spacetime.  At least that was the initial idea of Geon Theory.

Wave mechanics, or even quantum field theory, are often perceived to be mysterious because they either have to be interpreted as non-deterministic (when one deals with “wave function collapse”) or as semi-deterministic but incomplete and statistical descriptions of fundamental processes.   When physicists trace back where the source of all this mystery lies they are often led to some version of non-locality. And if you take non-locality at face value it does seem rather mysterious given that all the models of fundamental physical processes involve discrete localised particle exchanges (Feynman diagrams or their stringy counterparts).   One is forced to use tricks like sums over histories to obtain numerical calculations that agree with experiments.  But no one understand why such calculational tricks are needed, and it leads to a plethora of strange interpretations, like Many Worlds Theory, Pilot Waves, and so on.   A lot of these mysteries I think dissolve away when the ultimate source of non-locality is found to be deep non-trivial topology in spacetime which admits closed time-like curves (advanced causation, time travel).  To most physicists such ideas appear nonsensical and outrageous.  With good reason of course, it is very hard to make sense of a model of the world which allows time travel, as decades of scifi movies testify!  But geon theory doe snot propose unconstrained advanced causation (information from the future influences events in the past).   On the contrary, geon theory is fundamentally limited in outrageousness by the assumption the closed time-like curves are restricted to something like the Planck scale.   I should add that this is a wide open field of research.  No one has worked out much at all on the limits and applicability of geon theory.    For any brilliant young physicists or mathematicians this is a fantastic open playground to explore.

The only active researcher I know in this field is Mark Hadley. It seemed amazing to me that after publishing his thesis (also around 1994/95 independently of my own musings) no one seemed to take up his ideas and run with them.  Not even Chris Isham who refereed Hadley’s thesis.  The write-up of Hadley’s thesis in NewScientist seemed to barely cause a micro-ripple in the theoretical physics literature.    I am sure sociologists of science could explain why, but to me, at the time, having already discovered the same ideas, I was perplexed.

To date no one has explicitly spelt out how all of quantum mechanics can be derived from geon theory. Although Hadley I surmise, completed 90% of this project!  The final 10% is incredibly difficult though — it would necessitate deriving something like the Standard Model of particle physics from pure 4D spacetime topology — no easy feat when you consider high dimensional string theory has not really managed the same job despite hundreds of geniuses working on it for over 35 years. My thinking has been that string theory involves a whole lot of ad hockery and “code bloat” to borrow a term from computer science! If string theory was recast in terms of topological geons living as part of spacetime, rather than as separate to spacetime, then I suspect great advances could be made. I really hope someone will see these hints and connections and do something momentous with them.  Maybe some maverick like that surfer dude Garett Lisi might be able to weigh in and provide some fire power?

In the mean time  geometric algebra has so not been applied to geon theory, but GA blends in with these ideas since it seems, to me, to be the natural language for geometric physics. If particle phenomenology boils down to spacetime topology, then the spacetime algebra techniques should find exciting applications.  The obstacle is that so far spacetime algebra has only been developed for physics in spaces with trivial topology.

Another connection is with “combinatorial spacetime” models — the collection of ideas for “building up spacetime” from discrete combinatorial structures (spin foams, or causal networks, causal triangulations, and all that stuff). My thinking is that all these methods are unnecessary, but hint at interesting directions where geometry meets particle physics because (I suspect) such combinatorial structure approaches to quantum gravity are really only gross approximations to the spacetime picture of topological geon theory. It is in the algebra which arises from non-trivial spacetime topology and it’s associated homology that (I suspect) combinatorial spacetime pictures derive their use.

Naturally I think the combinatorial structure approaches are not fundamental. I think topology of spacetime is what is fundamental.

*      *       *

That probably covers enough of what I wanted to get off my chest for now. There is a lot more to write, but I need time to investigate these things so that I do not get too speculative and vague and vacuously philosophical.

What haunts me most nights when I try to dream up some new ideas to explore for geon theory (and desperately try to find some puzzles I can actually tackle) is not that someone will arrive at the right ideas before me, but simply that I never will get to understand them before I die. I do not want to be first. I just want to get there myself without knowing how anyone else has got to the new revolutionary insights into spacetime physics. I had the thrill of discovering geon theory by myself, independently of Mark Hadley, but now there has been this long hiatus and I am worried no one will forge the bridges from geon theory to particle physics while I am still alive.

I have this plan for what I will do when/if I do hear such news. It is the same method my brother Greg is using with Game of Thrones. He is on a GoT television and social media blackout until the books come out. He’s a G.R.R. Martin purest you see. But he still wants to watch the TV adaptation later on for amusement (the books are waaayyy better! So he says.) It is surprisingly easy to enforce such a blackout. Sports fans will know how. Any follower of All Black Rugby who misses an AB test match knows the skill of doing a media blackout until they get to watch their recording or replay. It’s impossible to watch an AB game if you know the result ahead of time. Rugby is darned exciting, but a 15-aside game has too many stops and starts to warrant sitting through it all when you already know the result. But when you do not know the result the build-up and tension are terrific. I think US Americans have something similar in their version of Football, since American Football has even more stop/start, it would be excruciatingly boring to sit through it all if you knew the result. But strangely intense when you do not know!

So knowing the result of a sports contest ahead of time is more catastrophic than a movie or book plot spoiler. It would be like that if there is a revolution in fundamental physics involving geon theory ideas. But I know I can do a physics news blackout fairly easily now that I am not lecturing in a physics department. And I am easily enough of an extreme introvert to be able to isolate my mind from the main ideas, all I need is a sniff, and I will then be able to work it all out for myself. It’s not like any ordinary friend of mine is going to be able to explain it to me!

If geon theory turns out to have any basis in reality I think the ideas that crack it all open to the light of truth will be among the few great ideas of my generation (the post Superstring generation) that could be imagined. If there are greater ideas I would be happy to know them in time, but with the bonus of not needing a physics news blackout! If it’s a result I could never have imagined then it’d be worth just savouring the triumph of others.


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Bohm and Beability

I write this being of sound mind and judgement … etc., etc., …

At this stage of life a dude like me can enter a debate about the foundations of quantum mechanics with little trepidation. There is a chance someone will put forward proposals that are just too technically difficult to understand, but there is a higher chance of getting either something useful out of the debate or obtaining some amusement and hilarity. The trick is to be a little detached and open-minded while retaining a decent dose of scepticism.

Inescapable Non-locality

Recently I was watching a lecture by Sheldon Goldstein (a venerable statesman of physics) who was speaking about John Stewart Bell’s contributions to the foundations of quantum mechanics. Bell was, like Einstein, sceptical of the conventional interpretations that gave either too big a role for “observers” and the “measurement process” or swept such issues aside by appealing to Many Worlds or some other fanciful untestable hypotheses.

What Bell ended up showing was a theory for a class of experiments that would prove the physics of our universe is fundamental non-local. Bell was actually after experimental verification that we cannot have local hidden variable theories. Hidden variables being things in physics that we cannot observe. Bell hated the idea of unobservable physics (and Einstein would have agreed, (me too, but that’s irrelevant)). The famous “Bell’s Inequalities” are a set of relations referring to experimental results that will give clear different numbers for outcomes of experiments if our universe’s physics is inherently non-local, or classical-with-hidden-variables.  The hidden variables are used to model the weirdness of quantum mechanics.

Hidden variable theories attempt to use classical physics, and possibly strict locality (no signals going faster than light, and even no propagation of information faster than light) to explain fundamental physical processes. David Bohm came up with the most complete ideas for hidden variables theories, but his, and all subsequent attempts, had some very strange features that seemed to be always needed in order to explain the results of the particular types of experiments that John Bell had devised. In Bohm’s theories he uses a feature called a Pilot Wave, which is an information carrying wave that physicists can only indirectly observe via it’s influence on experimental outcomes. We only get to see the statistics and probabilities induced by Bohm’s pilot waves. They spread out everywhere and they thus link space-like separated regions of the universe between which no signals faster than light could ever travel between. This has the character of non-locality but without requiring relativity violating information signalling faster than light, so the hope was one could use pilot waves to get a local hidden variables theory that would agree with experiments.

Goldstein tells us that Bell set out to show it was impossible to have a local hidden variables theory, but he ended up showing you could not have any local theory — at all! — all theories have to have some non-locality. Or rather, what the Bell Inequalities ended up proving (via numerous repeated experiments which measured conformance to the Bell inequalities) was that the physics in our universe could never be local, whatever theory one devises to model reality it has to be non-local. So it has to have some way for information to get from one region to another faster than light.

That is what quantum mechanics assumes, but without giving us any mechanism to explain it. A lot of physicists would just say, “It’s just the way our world is”, or they might use some exotic fanciful physics, like Many Worlds, to try to explain non-locality.

History records that Bell’s theorems were tested in numerous types of experiments, some with photons, some with electrons, some with entire atoms, and all such experiments have confirmed quantum mechanics and non-locality and have dis-proven hidden variables and locality. For the record, one may still believe in hidden variables, but the point is that if even your hidden variables theory has to be non-local then you lose all the motivation for believing in hidden variables. Hidden variables were designed to try to avoid non-locality. That was almost the only reason for postulating hidden variables. Why would you want to build-in to the foundations of a theory something unobservable? Hidden variables were a desperation in this sense, a crazy idea designed to do mainly just one thing — remove non-locality. So Bell and the experiments showed this project has failed.

ER.EPR_JohnStewartBell_CERN_1982

I like this photo of Bell from CERN in 1982 because it shows him at a blackboard that has a Bell Inequality calculation for an EPR type set-up. (Courtesy of : Christine Sutten, CERN https://home.cern/about/updates/2014/11/fifty-years-bells-theorem)

Now would you agree so far?  I hope not.  Hidden variables are not too much more crazy then any of the “standard interpretations” of quantum mechanics, of which there are a few dozen varieties, all fairly epistemologically bizarre.  Most other interpretations have postulates that are considerably more radical than hidden variables postulates. Indeed, one of the favourable things about a non-local hidden variables theory is that it would give the same predications as quantum mechanics but without a terribly bizarre epistemology.  Nevertheless, HV theories have fallen out of favour because people do not like nature to have hidden things that cannot be observed.  This is perhaps an historical prejudice we have inherited from the school of logical positivism, and maybe for that reason we should be more willing to give it up!  But the prejudice is quite persistent.

Quantum Theory without Observers

Goldstein raises some really interesting points when he starts to talk about the role of measurement and the role of observers. He points out that physicists are mistaken when they appeal to observers and some mysterious “measurement process” in their attempts to rectify the interpretations of quantum mechanics. It’s a great point that I have not heard mentioned very often before. According to Goldstein, a good theory of physics should not mention macroscopic entities like observers or measurement apparatus, because such things should be entirely dependent upon—and explained by—fundamental elementary processes.

This demand seems highly agreeable to me. It is a nice general Copernican principle to remove ourselves from the physics needed to explain our universe. And it is only a slightly stronger step to also remove the very vague and indiscreet notion of “measurement”.

The trouble is that in basic quantum mechanics one deals with wave functions or quantum fields (more generally) that fundamentally cannot account for the appearance of our world of experience. The reason is that these tools only give us probabilities for all the various ways things can happen over time, we get probabilities and nothing else from quantum theory. What actually happens in time is not accounted for by just giving the probabilities. This is often a called the “Measurement Problem” of quantum mechanics. It is not truly a problem. It is a fundamental incompleteness. The problem is that standard quantum theory has absolutely no mechanism for explaining the appearance of classical reality that we observe.

So this helps explain why a lot of quantum interpretation philosophy injects the notions of “observer” and “measurement” into the foundations of physics. It seems to be necessary for proving an account of the real semi-classical appearance of our world. We are not all held in ghostly superpositions because we all observe and “measure” each other, constantly. Or maybe our body cells are enough, they are “observing each other” for us? Or maybe a large molecule has “observational power” and is sufficient? Goldstein, correctly IMHO, argues this is all bad philosophy. Our scientific effort should be spent on trying to complete quantum theory or find a better more complete theory or framework for fundamental physics.

Here’s Goldstein encapsulating this:

It’s not that you don’t want observers in physics. Observers are in the real world and physics better account for the fact that there are observers. But observers, and measurement, and vague notions like that, and, not just vague, even macroscopic notions, they just seem not to belong in the very formulation of what could be regarded as a fundamental physical theory.

There should be no axioms about “measurement”. Here is one passage that John Bell wrote about this:

The concept of measurement becomes so fuzzy on reflection that it is quite surprising to have it appearing in physical theory at the most fundamental level. … Does not any analysis of measurement require concepts more fundamental than measurement? And should not the fundamental theory be about these more fundamental concepts?

Rise of the Wormholes

I need to explain one more set of ideas before making the note for this post.

There is so much to write about ER=EPR, and I’ve written a few posts about ER=EPR so far, but not enough. The gist of it, recall, is that the fuss in recent decades over the “Black Hole Information Paradox” or the “Black Hole Firewall” have been incredibly useful in leading a group of theoreticians towards a basic dim inchoate understanding that the non-locality in quantum mechanics is somehow related to wormhole bridges in spacetime.  Juan Maldacena and Leonard Susskind have pioneered this approach to understanding quantum information.

A lot of the weirdness on quantum mechanics turns out to be just geometry and topology of spacetime.

The “EPR”=”Einstein-Podolsky-Rosen-Bohm thought experiments”, precisely the genesis of the ideas that John Bell devised his Bell Inequalities for testing quantum theory, and which prove that physics involves fundamentally non-local interactions.

The “ER=”Einstein-Rosen wormhole bridges”. Wormholes are a science fiction device for time travel or fast interstellar travel. The idea is that you might imagine creating a spacetime wormhole by pinching off a thread of spacetime like the beginnings of a black hole, but then reconnecting the pinched end somewhere else in space, maybe a long time or distance separation away, and keep the pinched end open at this reconnection region.  So you can make this wormhole bridge a space length or time interval short-cut between two perhaps vastly separated regions of spacetime.

It seems that if you have an extremal version of a wormhole that is essentially shrunk down to zero radius, so it cannot be traversed by any mass, then this minimalistic wormhole still acts as a conduit of information. These provide the non-local connections between spacelike separated points in spacetime. Basically the ends of the ER=EPR wormholes are like particles, and they are connected by a wormhole that cannot be traversed by any actual particle.

Entanglement and You

So now we come to the little note I wanted to make.

I agree with Goldstein that we aught not artificially inject the concept of an observer or a “measurement process” into the heart of quantum mechanics. We should avoid such desperations, and instead seek to expand our theory to encompass better explanations of classical appearances in our world.

The interesting thing is that when we imagine how ER=EPR wormholes could influence our universe, by connecting past and future, we might end up with something much more profound than “observers” and “measurements”. We might end up with an understanding of how human consciousness and our psychological sense of the flow of time emerges from fundamental physics. All without needing to inject such transcendent notions into the physics. Leave the physics alone, let it be pristine, but get it correct and then maybe amazing things can emerge.

I do not have such a theory worked out. But I can give you the main idea. After all, I would like someone to be working on this, and I do not have the time or technical ability yet, so I do not want the world of science to wait for me to get my act together.

First: it would not surprise me if, in future, a heck of a lot of quantum theory “weirdness” was explained by ER=EPR like principles. If you abstract a little and step back from any particular instance of “quantum weirdness”, (like wave-particle duality or superposition or entanglement in any particular experiment) then what we really see is that most of the weirdness is due to non-locality. Now, this might take various guises, but if there is one mechanism for non-locality then it is a good bet something like this mechanism is at work behind most instances of non-locality that arise in quantum mechanics.

Secondly: the main way in which ER=EPR wormholes account for non-local effects is via pure information connecting regions of spacetime via the extremal wormholes. And what is interesting about this is that this makes a primitive form of time travel possible. Only information can “time travel” via these wormholes, but that might be enough to explain a lot of quantum mechanics.

Thirdly: although it is unlikely time travel effects can ever propagate up to macroscopic physics, because we just cannot engineer large enough wormholes, the statistical effects of the minimalistic ER+EPR wormholes might be enough to account for enough correlation between past and future that we might be able to eventually prove, in principle, that information gets to us from our future, at least at the level of fundamental quantum processes.

Now here’s the more speculative part: I think what might emerge from such considerations is a renewed description of the old Block Universe concept from Einstein’s general relativity (GR). Recall, in GR, time is more or less placed on an equal theoretical footing to space. This means past and future are all connected and exist whether we know it or not. Our future is “out there in time” and we just have not yet travelled into it. And we cannot travel back to our past because the bridges are not possible, the only wormhole bridges connecting past to future over macroscopic times are those minimal extremal ER=EPR wormholes that provide the universe with quantum entanglement phenomena and non-locality.

So I do not know what the consequences of such developments will be. But I can imagine some possibilities. One is that although we cannot access our future, or travel back to our past, the information from such regions in the Block Universe are tenuously connected to us nonetheless. Such connections are virtually impossible for us to exploit usefully because we could never confirm what we are dealing with until the macroscopic future “arrives” so to speak.  So although we know it is not complete, we will still have to end up using quantum mechanics probability amplitude mathematics to make predictions about physics.  In other words, quantum mechanics models our situation with respect to the world, not the actual state of the world from an atemporal Block Universe perspective.  It’s the same problem with the time travel experiment conducted in 1994 in the laboratory under the supervision of Günter Nimtz, whose lab sent analogue signals encoding Mozart’s 40th Symphony into the future (by a few milliseconds).

For that experiment there are standard explanations using Maxwell’s theory of electromagnetism that show no particles travel faster than light into the future. Nevertheless, Nimtz’s laboratory got a macroscopic recording of bits of information from Mozart’s 40th Symphony out of one back-end of a tunnelling apparatus before it was sent into the front-end of the apparatus. The interesting thing to me is not about violation of special relativity or causality.  (You might think the physicists could violate causality because one of them could wait at the back-end and when they hear Mozart come out they could tell their colleague to send Beethoven instead, thus creating a paradox.  But they could not do this because they could not send a communication fast enough in real time to warn their colleague to send Beethoven’s Fifth instead of Mozart.)  Sadly that aspect of the experiment was the most controversial, but it was not the most interesting thing. Many commentators argued about the claimed violations of SR, and there are some good arguments about photon “group velocity” being able to transmit a signal faster than light without any particular individual photon needing to go faster than light.

(Actually many of Nimtz’s experiments used electron tunnelling, not photon tunnelling, but the general principles are the same.)

All the “wave packet” and “group velocity” explanations of Nimtz’s time travel experiments are, if you ask me, merely attempts to reconcile the observations with special relativity. They all, however, use collective phenomena, either waves, or group packets. But we all know photons are not waves, they are particles (many still debate this, but just bear out my argument). The wave behaviour of fundamental particles is in fact a manifestation of quantum mechanics. Maxwell’s theory is, thus, only phenomenological. It describes electromagnetic waves, and photons get interpreted (unfortunately) as modes of such waves. But this is mistaken. Photons collectively can behave as Maxwell’s waves, but Maxwell’s theory is describing a fictional reality. Maxwell’s theory only approximates what photons actually do. They do not, in Maxwell’s theory, impinge on photon detectors like discrete quanta. And yet we all know this is what light actually does! It violates Maxwell’s theory every day!

So what, I think, is truly interesting about Nimtz’s experiments is that they were sensitive enough to give us a window into wormhole traversal. Quantum tunnelling is nothing more than information traversal though ER=EPR type wormholes. At least that’s my hypothesis. It is a non-classical effect, and Maxwell’s theory only accounts for it via the fiction that photons are waves. A wrong explanation can often fully explain the facts of course!

Letting Things Be

What Goldstein, and Bohm, and later John Stewart Bell wanted to do is explain the world. They knew quantum field theory does not explain the world. It does not tell us why things come to be what they are. Why a measurement pointer ends up pointing in particular direction rather than any one of the other superposed states of pointer orientation the quantum theory tells us it aught to be in.  Such outcomes or predictions are what David Bohm referred to as “local Beables”.  Goldstein explains more in his seminar: John Bell and the Foundations of Quantum Mechanics” Sesto, Italy 2014, (https://www.youtube.com/watch?v=RGbpvKahbSY).

My favourite idea, one I have been entertaining for over twenty years, in fact ever since 1995 when I read Kip Thorne’s book about classical general relativity and wormholes, is that the wormholes (or technically “closed timelike curves”) are where all the ingredients are for explaining quantum mechanics from a classical point of view. Standard twentieth century quantum theory does not admit wormholes. But if you ignore quantum theory and start again from classical dynamics, but allow ER=EPR wormholes to exist, then I think most of quantum mechanics can be recovered without the need for un-explained axiomatic superpositions and wave-function collapse (the conventional explanation for “measurements” and classical appearances). In other words, quantum theory, like Maxwell’s EM theory, is only a convenient fictional model of our physics. You see, when you naturally have information going backwards and forwards in time you cannot avoid superpositions of state. But when a stable time-slice emerges or “crystallizes” out of this mess of acausal dynamics, then it should look like a measurement has occurred. But no such miracle happens, it simply emerges or crystallizes naturally from the atemporal dynamics. (I use the term “crystallize” advisedly here, it is not a literal crystallization, but something abstractly similar, and George Ellis uses it in a slightly different take on the Block Universe concept, so I figure it is a fair term to use).

Also, is it possible that atemporal dynamics will tend to statistically “crystallize” something like Bohm’s pilot wave guide potential.  If you know a little about Bohmian mechanics you know the pilot wave is postulated as a real potential, something that just exists in our universe’s physics.  Yet is has no other model alike, it is not a quantum field, it is not a classical filed, it is what it is.  But what if there is no need for such a postulate?  How could it be avoided?  My idea is that maybe the combined statistical effects of influences propagating forward and backward in time give rise to an effective potential much like the Bohm pilot wave or Schrödinger wave function.  Either way, both constructs in conventional or Bohmian quantum mechanics might be just necessary fictions we need to describe, in one way or another, the proper complete Block Universe atemporal spacetime dynamics induced by the existence of spacetime wormholes.  I could throw around other ideas, but the main one is that wormholes endow spacetime with a really gnarly stringy sort of topology that has, so far, not been explored enough by physicists.

Classically you get non-locality when you allow wormholes. That’s the quickest summary I can give you. So I will end here.

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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.

cosmo_OnceUponATimeInRovellisUniverse

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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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Primacks’ Premium Simulations

After spending a week debating with myself about various Many Worlds philosophy issues  and other quantum cosmology questions, today I saw Joel Primack’s presentation at the Philosophy of Cosmology International Conference, on the topic of Cosmological Structure Formation. And so for a change I was speechless.

Thus I doubt I can write much that illumines Primack’s talk better than if I tell you just to go and watch it.

He, and colleagues, have run supercomputer simulations of gravitating dark matter in our universe. From their public website Bolshoi Cosmological Simulations they note: “The simulations took 6 million cpu hours to run on the Pleiades supercomputer — recently ranked as seventh fastest of the world’s top 500 supercomputers — at NASA Ames Research Center.”

To get straight to all the videos from the Bolshoi simulation go here (hipacc.ucsc.edu/Bolshoi/Movies.html).

cosmos_BolshoiSim_MD_cluster01_gas_sn320

MD4 Gas density distribution of the most massive galaxy cluster (cluster 001) in a high resolution resimulation, x-y-projection. (Kristin Riebe, from the Bolshoi Cosmological Simulations.)

The filamentous structure formation is awesome to behold. At times they look like living cellular structures in the movies that Primack has produced. Only the time steps in his simulations are probably about 1 million year steps. for example, on simulation is called the Bolshio-Planck Cosmological Simulation — Merger Tree of a Large Halo. If I am reading this page correctly these simulations visualize 10 billion Sun sized halos.  The unit they say they resolve is “1010 Msun halos”. Astronomers will often use a symbol M to represent a unit of one solar mass (equal to our Sun’s mass). But I have never seen that unit “M halo” used before, so I’m just guessing it means the finest structure resolvable in their movie still images would be maybe a Sun-sized object, or a solar system sized bunch of stuff. This is dark matter they are visualizing, so the stars and planets we can see just get completely obscured in these simulations (since the star-like matter is less than a few percent of the mass).

True to my word, that’s all I will write for now about this piece of beauty. I need to get my speech back.

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Oh, but I do just want to hasten to say the image above I pasted in there is NOTHING compared to the movies of the simulations. You gotta watch the Bolshoi Cosmology movies to see the beauty!

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Rovelli’s Roll

In a highly watchable talk in the Oxford University lecture mini-series on Cosmology and quantum Foundations Carlo Rovelli gives a lot of persuasive arguments about why the Many Worlds Interpretation is suspect. But he goes fast and furious sometimes. Sometimes constructing strawman arguments (I do not think anyone seriously thinks just literally interpreting mathematics in a given model of physics leads to necessarily great ontological truths, apart from the likes of characters like Tegmark perhaps) but I think generally even these points are well made and interesting to ponder. Rovelli describes his own current opinion as “Everettian” — which means not a traditional Many Worlds interpretation but rather Relative State interpretation.

relativestateQM_screenshot_Rovelli_lecture_twoobservers

One observer observing another, screenshot from Carlo Rovelli’s lecture.

There are many key slides in his presentation that I thought worthy of mentioning and which inspired this current post of mine.

In another slide Rovelli puts up a couple of threads, one is,

    • “Why don’t we see superpositions?” — what a silly question! Because in textbook QM we do not see the state, we see eigenvalues. We see where is the position o the electron or it’s momentum, never it’s wavefunction.
    • These (facts) are described by the position in phase space in classical physics; and by points in the spectra of elements of the observable algebra in quantum physics.

Which is cool, but then he riles the zen masters by writing:

  • They can be taken as primary elements, and the quantum formalism built up from them.

First, I should point out this is not erroneous. You can build up a theory from elements that are such primitives as “points in the spectra of elements of the observable algebra”.

But I think this is misleading for purists and philosophers of physics. Just because one approach to calculating expectation values works does not make it’s mathematical elements isomorphic in some sense to elements of physical reality. So I think Rovelli un-does some of his good arguments with such statements. (I’m not the expert Rovelli is, I’m just sayin’ ya know …)

You might counter: “Well, if you are not willing to take your theoretical elements of reality direct from the best mathematical model’s primitives, then where are you going to define your ontology (granting you are wishing to construct a realist interpretation)?”

I would concede, “ok, for now, you can have a favoured realist interpretation based on the primitives of your observables algebra.” But I think you are always going to have to admit this will be temporary, only an “effective interpretation” that is current to our present understandings.

My point is that while this makes for great contemporary physics it does not make for good philosophy (love of both knowledge and truth). The reason is blatant. If all you have is a model for computing amplitudes then there is really only a small probability for hoping this is a dead accurate and “True” picture of the real ontology in our universal physics. You can certainly freely pin your hopes on this chance and see where it leads.

I, for one, think that such an abstraction as an “observable algebra” although nice and concrete and clean, is just too abstract to be wisely taken literally as the basis for a realist interpretation. Again, I’m “just sayin’…”.

There are many more good discussion points in Rovelli’s lecture.

The Wavefunction is a Computational Tool

This meme has always gelled with me. You can map a wavefunction over time, for example, you can visualize an atomic electron’s orbital. But at no single moment in time is the electron ever seen to be smeared out over it’s orbital. To me, as a realist, this means the electron is probably not a wave. But it’s temporal behaviour manifests aspects of wave-like properties. Or to be bold: over time the (non-relativistic) constant energy electron’s state is completely coded as a wave. I will admit in future we might find hard evidence that electron’s truly are waves of some weird spacetime foamy medium, not waves in an abstract mathematical space, but I do not think we are there yet, and I think we will not find this to be so. My guess would be electrons are extended topological geons, perhaps a little more gnarly than superstrings, but less “super”. I think more like solitons of spacetime than embedded strings.

The keyword there for philosophy is “coded”. The wave picture, or if you prefer, the Heisenberg state matrix representation, (either the Schrödinger or Heisenberg mathematical tool will do) is a code for the time evolution of the electron. But in no realist sense can it be identified as the electron.  Moreover, if you are willing to accept the Schrödinger and Heisenberg pictures are equivalent then you have a doubled-up ontology.  To me that’s nonsense if you are also a realist.

Believe it or not though, I’ve read books where this is flatly denied and authors have claimed the electron is the wavefunction. I really cannot subscribe to this. It violates the principle of separation of ontology from theory (let me coin that principle if no one has before!). A model is not the thing being modelled, is another way to put it.

On a related aside note: John Wheeler was being very cheeky or highly provocative in suggesting the “It from Bit” meme. It sounds like a great explanatory concept, but it seems (to me) to lack some unknown extra structure needed to motivate sound belief. Wheeler also talked about “equations written on paper cannot bring themselves into existence” (or something to that effect). But I think “It from Bit” is not very far removed from equations writing themselves into a universe.

EPR is Entanglement with the Future?

That’s not quite an accurate way to encapsulate Rovelli’s take on EPR, but I think it captures the flavour. Rovelli is saying that in a Relational QM interpretation you do not worry about non-locality, because from each observers (the proverbial Alice and Bob at each end of an EPR experiment, or non-human apparatus if you prefer to drop the anthropomorphisms) point of view there is a simple measurement, nothing more. The realisation entanglement was happening only occurs later in the future when the two observers get back together and compare data.

I’m not quite with Rovelli fully on this. And I guess this makes me a non-Everettian. There might be something I’m missing about all this, but I think there is something to explain about the two observers from a “Gods eye” view of the universe at the time each makes their measurements. (Whether God exists is irrelevant, this is pure gedankenexperiment.)  If you are God then you witness effects of entanglement in the measurement outcomes of Alice and Bob.

The recent research surrounding the ER=EPR meme seem to give a fairly sound geometric or geometrodynamic interpretation of EPR as a wormhole connection. So I think Rovelli does not need to invoke anything fancy to explain away EPR entanglment. ER=EPR has, I believe, put the matter of the realist interpretation mechanism of entanglement to rest.

No matter how many professors shout out, “do not attempt to make mental mechanical models of QM, they will fail!” I think ER=EPR defies them at least on it’s own ground. (Ironically, Susskind says just such things in his popular Theoretical Minimum lectures, and yet he was one of the original ER=EPR co-authors!)

What About Superposition: Is Superposition=ER?

I am now going beyond what Rovelli was entertaining.

If you can explain entanglement using wormholes, how about superposition?

ERequalsEPR_NingBao_etal_PenroseCompressed

ER=EPR depiction from a  nice article by “Splitting Spacetime” Bao, Pollack, and Remmen (2015) http://inspirehep.net/record/1380145

 

I have not read any good papers about this yet. But I predict someone will put something on the arxiv soon (probably have already since I just haven’t gotten around to searching.) In a hand-waving manner, superpositions are bit like self-entanglement. A slightly harder interpretation might be that at the ends of a wormhole you could get particle duplication or mirror-effects of a sort.

One might even get quite literal and play with the idea that when an electron slips down a minimal wormhole it’s properties get mirrored at each end. Although, “mirror” is not the correct symmetry. I think perhaps just “copied at each end” is better. Cloned at each end? Whatever.

Maybe the electron continually oscillates back and forth between the mouths in some way? Who knows. It does require some kind of traversable ER bridge, or maybe just that when the bridge evaporates in a finite time the electron’s information snaps but to one end, but not both ends. Susskind and Hawking both concur now that there is no black hole information loss right? So surely a little ol’ electron’s information is not going to get lost if it wanders into a minimal ER bridge.

Then measurement or “wave function collapse” is likely a process of collapse of the wormhole. But in snapping the ER bridge the particle property can (somehow) only get restored at one end. Voila! You solve Schrodinger’s Cat’s dilemma.

Oh man! Would I not love t0 write a detailed technical mathematical exposition of all this. Sigh! Someone will probably beat me to it. Meehhh … what do I care, I’m not doing physics for fame or fortune.

Someone will have to eventually worry about stability of minimal ER bridges and the like. Then there are Lorentzian wormholes and closed time-like curves to consider. That Bao, Pollack, Remmen (2015) paper I cited above talks about “no-go” theorems arising from admitting ER bridges, no-go for causality violation and no-go for topology change.  I think what theoretical physics needs is an injecting of going past such no-go theorems.  They have to be “goes”.  Especially topology change.  If topology change implies violation of causality then all the better.  It only needs to have direct consequences at the Planck scale, then it’s not so scary to admit into theory, whatever the mess it might cause for modelling.  The upshot is that at the macroscopic scale I think allowing the “go” for these theorems rather than the “no-go” will reveal a lot of explanatory power, maybe even most of the explanation for the core phenomenon of quantum mechanics.  They mention concerns about violation of causality All of which I think is brilliant. I can see this sort of deep space structure explaining a lot of the current mystery about quantum mechanics, and in a realist interpretation. Awesome! And that I am not “just sayin” — it truly would be justifiably awesome.

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Hmmm … had a lot more to say about Rovelli’s talk. Maybe another day.

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Pressing the Origins

If I were pressed to write less than 700 words on the current state of cosmology and tie it in with infinite number theory and the deplorable state of scientific media communication, then I might write something like this following email to my friend Syko.

Let me first get you “in” on this conversation:

Syko made a comment in an earlier email to the effect that he could agree the origin of the universe can be taken seriously, but … (in his words):

I … rather support the notion of the origin. I struggle with the idea that the universe is infinite. Doesn’t make sense to me. Don’t buy it.

Then I wrote back saying something like:

Things do not need to make sense for them to be real.  There are some wonderful and bizarre levels of “infinite”, in fact far more infinitely many layers of infinity than most ordinary people realise, but since you Syko are not an ordinary person I can reveal some of the panorama for you.  And in any case, you do not get to buy in to Nature, Nature has bought you, and you have no say in this deal!   If it is an infinite universe then it’s infinite and you’ll have to suck that up, if it is finite then it’s finite and we have to live within that.    As Feynman said, “The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you accept Nature as She is — absurd.”

One thing about the potentially infinite expanse is that it is darn hard to kill off our universe.  How can you destroy it?  In 1998 those crazy astronomers measured the expansion was accelerating.  So gravity will not seem to be crushing us out of existence in a few trillion trillion years, so it’ll just keep expanding forever from what current measurements can predict.

But within that infinite expansion there are amazing things that could happen.

One is a cyclical time cosmology.  You can Google that along with “Penrose” since any discussion of cyclic time without Roger Penrose is probably New Age clap-trap. Penrose is however the real deal.  I WARN YOU, it is pretty awesome stuff!   So Google at your own peril!  hahahaha!
cosmology_conformal_cyclic_cosmology
Then Syko replied:

Haha. Nature is not for me to buy, but the theories of mere men are, until proven. The infinite thing is a little to abstract. I get that there was a beginning. That the universe could be expanding. But the idea that it has no end or frontier and that it never ends. Well , I don’t think that’s right. It seems lazy to say it’s infinite.

And that led to my longer email about cosmology, the infinite, and science communication.  Here it is …

         *          *          *

Hey Syko,

I’m curious why you think it is lazy to theorise the universe could have infinite extent in time?  (Note that this does not imply infinite extent in space unless the expansion does not slow down to an asymptotic limit.)

Surely the idea of an infinite time is not really lazy, none more so than theorising time will be finite.  However, stating a theory which begins with such an assumption, either way, finite or infinite, is a lazy approach in a sense (and perhaps that’s what you mean?)  because it is simply assuming a fact that should be provable or falsifiable by other means, either by a less presumptive theory or by observational evidence.

But in any case, the best evidence available to date tells us the universe will expand forever.  This is not a theory.  It is a fact about the dark energy component of the universe together with the theory of general relativity.  It could be wrong, but it’s the best answer we have at present.

These physical “potential infinities” are one thing.  But the really exciting stuff, I think, is in pure mathematics where the transfinite numbers are considered.  It takes some mental effort to wrap your head around the concepts, but there are amazing possibilities involving transfinite number theory being applied to solve hitherto impossible problems in analysis (calculus) including maybe tackling problems that arise in quantum mechanics and general relativity when calculations arrive at irreducibly infinite numerical answers.  The idea before was that the theories had to be wrong or incomplete because they gave infinite numerical answers to fairly basic questions.   But modern mathematic suggests the idea that the infinite number answers might be totally sensible if interpreted according to transfinite arithmetic.  However, this is not all worked out and there is a communication gap between the physicists and the mathematicians.

Ordinal number spiral

When you have time… I am also curious about people who cannot conceive of anything existing prior to the “Big Bang”.   People are fond of saying that the Big Bang arose out of nothingness as a quantum fluctuation.  But this is sheer madness, since quantum fluctuations cannot fluctuate without a pre-existing spacetime in which to fluctuate.  And no one has ever shown how spacetime can fluctuate itself into existence from nothing.   In fact, there is not even a primitive philosophy about how to do it, so the physics has absolutely no hope of actually explaining the existence and origin of the universe.

So I really lose patience and can get quite irate with scientists in the media who get into the public airways and start saying things like how physics has explained the origin f the universe.  It is utter nonsense and gives physics a bad reputation in my opinion.   To give you some idea of the scale of this lunacy, at least in my opinion, I would describe it as analogous to a reputable biologist speaking to the media in all calmness and coolness and seriousness telling them that not only all known diseases, but in fact all future possible diseases from all possible vectors whether they be based either on DNA-based pathogens or non-DNA based life, have all been cured in theory by recent discoveries in the field of quantum medicine.

What physics can do is explain how things evolved after the period of cosmic hyper-inflation which happened after the universe became more than a singularity.  The actual history prior to this is completely mysterious to physics.  We do not even know if there ever was an initial singularity.   People who argue science says otherwise are completely deluded and are impossible to debate and argue rationally with.

That’s my opinion.  I wish people would take my opinion more seriously and read them, and take them to heart, before issuing any public relations announcements on behalf of science.  Of course if people did so and qualified all their claims and speculations correctly no science press conference could possibly last for less than about 30 minutes I imagine.  Hahahaha!

         *          *          *

You know what, I actually prefer Sir Roger’s hand-drawn diagrams:

Penrose CCC diagram

If you are interested in business strategy and economics and marketing, there is a dude Ben Thompson writing a great blog on such matter.  I mention him because he also uses hand-drawn diagrams to amazing effect.  It’s only data viz art, but funky cool.  Check him out here: https://stratechery.com/,  and there is his podcast here: http://exponent.fm/.

 

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Small and Large Prime Lecture Times

Is this why blogs were invented? So people could just let off steam.

TerryTao_on_gaps_between_primes_the_glance_at_the_watch_moment

The glance at the wrist watch.

Whatever the case, I have some steam about academic seminars which needs something to heat. Preferably a department HOD or resident seminar organizer, or the lecture hours manager.

In my lunch hours I get time to hold a mathematics seminar in my office. The audience size is 1, and the guest speaker is not present.

Well I don’t have the privilege of working in a great mathematics or physics department at the moment. So I need to YouTube for all my seminars. This gives up control. So if something annoys me all I have is a blog and a few friends who occasionally do not mind a small buzzing noise in their ears emanating from my general direction.

The origin of my current plume of steam is Terry Tao, Ph.D. Small and Large Gaps Between the Primes (www.youtube.com/watch?v=pp06oGD4m00).

Here I am enjoying my lunch with coffee listening to Professor Tao explain the sieves, the loglogloglog theorems, the probabilistic number theoretic models and other tricks for deducing the bounds on gaps between primes. Then about 43 minutes into the video he glances at his wrist-watch and clearly wonders if he has enough time to explain the ideas in some detail. He says,

“Zhang’s big breakthrough was that he found a new theorem about primes in arithmetic progressions that was not available before.

[glances at his watch]

Ummm, arrr, or, ok, maybe I, I won’t say exactly what it is … “

Well, damn! That kinda’ spoils the whole movie doesn’t it!

So it’s understandable isn’t it. You have 55 minutes for a seminar and should really stick to it, since lecturers have students waiting for classes and so forth. But then I thought, why?

It’s bullshit. Students can attend the darned seminar. They could learn something. Or at worst catch some useful zzz’s. Classes can be put on hold, or even canceled, did that ever hurt a single student? Then you just go and let a guy like Terrance Tao talk for as long as he damn well pleases without a single clock in sight to distract him.

That’s how to run seminars people!

Not so’s people are all like this …

Tyranny_of_time_white_rabbit_2

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Clock Time, Cosmic Time, and Free Time

This is about time and transformation and what changes and what never changes.  It began with reading a novel.

Caterpillar_to_Butterfly_001

Courtesy: Lisa D. Anness Butterfly Garden.

Recently I had some rare free time to read fiction. While reading Joyce Carol Oates’ novel Black Girl, White Girl which I had found in a stack of withdrawn library books, I came across the following quotation recited by one of the characters in the novel, Minette Swift,

“That which hath been is now; and that which is to be hath already been;”
— from Ecclesiastes, 3:15.

Here is a bit of the context. The narrator is the main character, the “white girl”, Genna Meade. Minette is her roommate at University.

*        *        *

JoyceOates_BlackGirlWhiteGirl_01

But no, Minette couldn’t be reasoned with. Minette knew that things were “meant to be” and some things were a “test” of how you could take them.

There was weakness, and there was strength. Oh, in the smallest thing!

“Do you believe that everyday is a `test,’ Minette?”

Minette sniffed, fixing me a look confident as Reverend Virgil Swift’s at the pulpit. “Every day? Every minute.  Why’d you think, we are here on earth in clock time?

I asked Minette how else we could be here, except clock-time, and Minette said briskly, ” `That which hath been is now; and that which is to be hath already been.’ ” This was a reply I could not challenge for I had no idea what it meant.
— from Black Girl/White Girl, Joyce Carol Oates, page 50–51.

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There are other cool biblical excerpts concerning time. I won’t list them all. I do not do bible studies a’ight!

Ecclesiastes 3:14. “I know that everything God does will remain forever; there is nothing to add to it and there is nothing to take from it, for God has so worked that men should fear Him.

3:15 “That which is has been already and that which will be has already been, for God seeks what has passed by.”

Ecclesiastes 1:9. “What has been will be again, what has been done will be done again; there is nothing new under the sun.”

Ecclesiastes 6:10. “Whatever exists has already been named, and what humanity is has been known; no one can contend with someone who is stronger.”

King James Bible: “That which has been is now; and that which is to be has already been; and God requires that which is past.”

*        *        *

OK, so what’s that all about? Is if some kind of pre-modern scifi? haha!

Well, I often think of some of the great prophetic books of ancient times, like the Torah, the Bhagavad Gita, the Tripitakas, the Zend Avesta, the Bible and the Q’urân, as works of science fiction in disguise. I think the reason is that all those scriptures were written in allegorical language. You simply cannot read them literally or you will fall into the pit of fanaticism.

Countless in number are the people who read the Bible literally and then use it as an excuse to do crazy murderous things, or just plain crazy things. Likewise with the Q’urân. It’s not that these books are evil. Quite the contrary if you read them with spiritual metaphorical eyes. But if you take their meanings literally then you will be led into all sorts of paradoxes, confusions, delusions and ultimately madness, only you won’t think you are mad, you will think you are doing the work of God“, which is the most tragic irony because you will probably be doing the exact opposite!

One thing for sure I know, in my heart, is that the bible and the Q’urân teach tolerance and kindness as quintessential attributes people should strive for as default behaviours and inner states of mind. Yet time and again Biblical literalists (people who preach the gospel’s of the great scriptures directly as if every sentence had a direct literal meaning) turn in to people who are intolerant, didactic, unsympathetic and cruel. Witness that they will often insist their word is law, or their God offers the only truth, and their truth is the word of God. It’s all madness, yet they see it not as such. Fanatics like this are easy to recognise. They seem so proud of their ”faith“ that they hold on to it in the face of all contradictory evidence, and they twist facts to fit their warped view of religion, and will insist all other views of religion are the warped ones. It is so pathetic, I truly feel sorry for such souls.

And that is one reason why I think treating these Holy books as science fiction is a profitable venture. It may not be what the authors or inspirer’s for those scriptures intended, but it is healthier and, I think, more helpful to think of them in terms of science fiction than to read them literally.

Well, what else can you do with allusions like, The Moon will turn blood red and the stars will fall from heaven?  There is no other rational option other than scifi, right? Or at lest you can treat such passages as allegorical poetry, full of hidden allusions, and interpreted in terms of spiritual reality rather than the literal physical reality in the bare words.

Thus, one scifi reading of “the stars shall fall from heaven” can be assumed as follows: the stars of religion are the clergy and priests of former dispensations. When they “fall” this means they become egotistical and threatened by a new dispensation of religion, a new prophet, and they seek to murder the new religion, kill it off (either literally or figuratively I suppose! It has happened, the attempt at least, to quell a new revelation, in fact it seems to happen regularly in history whenever a new prophet arises). The “stars falling” is thus the debasement in spiritual station of the revered elders and clergy of previous religious establishments. That’s the scifi reading.

And the “Moon turning to blood” might refer metaphorically to the sacrifices a prophets’ followers may make in the formative years of a new revelation, their blood (meaning their energy and spirit) is spent in the effort to teach and establish a renewal of religious laws and teachings and guidance. There may be other good interpretations equally valid. You just need to figure out what “blood” symbolises in religious canons, and what the Moon symbolises. I’m not an expert on these matters, but I’m sure someone can full in a decent scifi interpretation of such biblical passages. A lot of the weirder stuff appears in Revelations, so I’m sure someone has studied this in the correct non-literalist light.

But my purpose in this essay is to look at the quotation about past and future and “now”. It’s good stuff because it is not all scifi. There is some interesting science fact in it as well.

How the Future Has Already Been

So far this is just a warm-up to the quote about past present and future. This took my fancy because I used to work in a Time Standards laboratory with atomic clocks. And although that job did not involve time travel or other cool scifi, it was a cool job for me because I’ve always been fascinated by time and general relativity and cosmology. In time and frequency standards you do not get to explore cosmology, and general relativity is sort-of hidden behind all the software and atomic clock internals.

Time and frequency standards plays a very important role in modern technology, especially in GPS and stock market trading and airline scheduling and navigation. This is all fine and good, but the truly interesting physics only happens at the research frontier, which unfortunately was not in my job brief (my research was supposed to be on microwave measurement standards, but I never got hooked on it).

Cosmology, the large scale features of the universe, is intimately connected to time. And no one really understands time. It is perhaps the most common concept in physics, but also one of the least understood. Einstein’s theory of general relativity, for example, tells us that the future has already happened, and we are merely creatures with past-only memory cells in our brains which makes us think we are experiencing a flow of time, when in fact we are merely observers, watching our completed life as if through a movie reel, one frame at a time.

This is why we can say the future has already been. From the proverbial “god’s eye” view into our universe, all future events are connected to the past by the geometry of spacetime. In Einstein’s theory space cannot be separated from time, in fact, they are merged together in a deep way. Experiments confirm Einstein’s insights. One of which is the observation that an object travelling close to the speed of light measurably ages slower, but it’s spacetime velocity (4-velocity) never changes. In fact every object, even objects at rest, have a constant 4-velocity which is always equal to the speed of light (300 million metres per second).

Einstein explained this by postulating that our universe is not just an isolated sequence of “nows”, but is rather a continuum of all times over all space, and our entire universe must be regarded as a complete four-dimensional geometry. When we move we simply shift from maximum velocity through time (called “ageing” rather than “moving”) to part movement through time and part movement through space. At the extreme and object might move only through space and not at all through time, and such things do exist, they are called photons (or particles of light). Since photons move entirely through space and not through time they never age.

To visualise this, think of an object as having a 4-velocity vector (an arrow pointing in it’s direction of motion). The four directions are three of space and one of time. So you might try to imagine four perpendicular axes, but if that’s too hard, imagine space is squeezed down to just 2D or 1D, and then you can draw time as an axis on a sheet of graph paper. An objects’s 4-velocity is a vector (arrow) measuring the objects direction of motion in all four directions.

When at rest this 4-vector is pointed only into time. Then as it starts moving, say after being pushed by a motor, it’s 4-velocity doesn’t change in length, it just rotates so that now it points a little bit into space and still mostly into the time direction. Then as the object picks up speed and gets faster and faster it’s 4-velocity still never changes but rotates further into space and less into the time direction.

So in general relativity, the theory of our cosmos as a whole, time and space are inseparable. And aging is just another word for motion that is motion through time.

So the Future is Out There

The future is just events in space time ahead of the events in spacetime you are currently experiencing. But what does “currently experiencing” mean? It means there is a local notion of “now” which is the time on a clock travelling through life with you. This could be any clock. Your biological clock is a good one. You can measure the age of a person by examining their DNA damage or their bone cross section structure and/or other indicators, a bit like a tree’s age can be measured by examining core’s of it’s trunk which reveal growth rings.

But “now” for you is not “now” for me as I write this essay. Your “now” is in my future since you cannot be reading this until after I finish typing and posting this.

Which is why “now” has no objective meaning. It’s a purely subjective and relative notion. And such concepts, while accessible to science, are not part of fundamental physics theory. Physics deals with only objective reality.

The objective reality is that space and time are a single connected continuum we should call spacetime. And so all of your subjective “past” is connected to your “future” and so the future exists already and is in an anthropomorphic sense waiting for you to experience it. It’s dangerous to use anthropomorphisms in scientific explanations, but I think there is little danger here. Most people understand what this means. The “future” is not a thinking entity which can “wait for you”. But it is a bit like film frames on a movie reel that are waiting to be run through the projector when you will then see them on screen in your subjective “now”.

So “future” is entirely relative to your “now”, and what you consider to be “now” is purely an invention of your brain and it’s senses. It’s changing all the time, right?!

Your conception of future is thus largely an objective fiction, although subjectively it is very real and perfectly natural. Part of your nature. But not part of the nature of the cosmos as a whole.

What is objectively true is that the cosmos encodes your future for you. It all unfolds in your timeline, and your brain’s memory gives you it’s conscious perception of an unfolding universe through time. This is a subjective fact for you, but an objective fiction for the cosmos.

Or rather, to be more precise, it is not an objective fiction. Imagine yourself to be a “god of our universe”. You can look at all of spacetime as a completed structure. You can slice space along some direction, and then all perpendicular coordinates become a relative past or future to the slice that you’ve created or picked out. So future and past can be generated by simply choosing some spacetimes coordinates for a “now”.

Thus, for theological scifi we can get quite close to scifact by using general relativity. The future already exists, and you are just watching and otherwise sensing it flow into your life and memory.

Foreknowledge and Free Will

There is an apparent conflict between general relativity cosmology and quantum mechanics. Quantum mechanics is an undeniably established feature of physical reality. It tells us that the future cannot be predicted with pure certainty. Experiments confirm this. Quantum mechanics dictates that we can only ever have statistical knowlegde of the future. The universe evolves in time only probabilistically. The amazing thing about quantum mechanics is that it can be experimentally confirmed with certainty that the universe and the future unfold non-deterministically.

The future is totally uncertain, but odds and likelihoods about the future can be computed precisely. So the future is not all chaotic and chancy. Certain weird thing could happen, but with exceedingly small odds. The laws of quantum mechanics mathematically tell us what all the odds are, the odds the Sun will still rise in the East tomorrow, for instance. (That’s one event with near 100% probability, but it is not absolutely exactly 100%, would you believe! No kidding. And I’m not talking about human government officials overnight deciding to redefine the direction of “East”.)

This is great for those who wish to believe in free will. Since it means the future could be partly determined by decisions made by conscious creatures, which is what we normally refer to as “free will”.

But it seems to conflict with general relativity which, as I’ve mentioned above, implies the future already exists. How is this paradox resolved?

The interesting thing is that physicists do not have an agreed resolution. General relativity and Quantum Mechanics have not been fully unified. Physicists still seek a unified theory of all reality. It is a great unsolved problem in physics.

Also, the future is locked-away from our knowledge because the way our brain memory works is limited. It can only store information about the past. Some other type of entity might have two-way memory, of past and future. But not our biological brains. So we cannot access the future even if it does already exist. Of course, we actually do access the future all the time, but it is very poor access, it is serial sequential access. That’s another way of saying that psychologically time seems to “flow in one direction”, towards the future.

There are some fascinating issues about the psychologically perceived “flow of time” which relate to statistical mechanics and the Second law of Thermodynamics. But I do not want to expand them here. I will probably leave them for future articles!

One point I should make is that there is no logical puzzle in the fact that the future is unpredictable and yet maybe pre-existent. So logically quantum mechanics and general relativity could be in complete harmony. The reason is that quantum mechanics does not dictate the future universe is non-existent. It merely tells us that we cannot predict the future with any certainty, only with prescribed probability.

But you see, if a thing can be subject to accurate and empirically confirmed probability estimates, then it is a reality which will happen, and who can say it has not already happened? Like making bets on a horse race in a movie that has already been filmed. Provided none of the audience has access to the film reel, they can have a fair betting game. This is basically what our universe does to us scientists! Why? Because our physics seems to forbid time-travellers. If time-travelling were allowed then it would completely mess up the foundations of quantum mechanics, and general relativity would win the theoretical battle. That’s because time-travel would in principle allow perfect prediction of the future, whereas quantum mechanics says (in it’s core mathematical development based on many good experiments) that no measurements can ever be used to determine the future exactly. But as I’ve hinted, there is no logical reason why the two theories cannot be fully compatible.

It is perfectly logically reasonable for the future to be entirely unknown to present measurements, and yet entirely pre-determined. One way to see how is to imagine tachyons — influences on our past or present which have arrived from the future. Since we do not have memory or measurements of the future, because we cannot observe tachyons, we cannot use them to construct precise predictions of the future. And yet the future can be “out there”, pre-existent. It would just be inaccessible to our measurement instruments. This could be the big key to understanding quantum mechanics. But is is not established accepted physics yet. The trouble is most tachyons are indistinguishable from anti-matter.

Ironically, if such a reconciliation between relativity and quantum mechanics could be established it would probably mean we’d be able to detect tachyons, i.e, confirm they carry future information and are not merely anti-matter particles. And if we could confirm they were in fact tachyonic (carrying information backwards in time) then would we not thus have access to future information and thus enable predictions of the future, and thus overturn the principles of quantum mechanics? These are interesting philosophical questions. But no one can foresee the answers!

So our future is already determined, but we cannot know it because our memory works only in one direction through time. It cannot encode tachyonic information. And in a deeper way the laws of quantum mechanics forbid our knowledge of the future because of the way information from future states of the cosmos are locked-away in structures which our present measurements can only ever, even in principle, detect using probability.

For theology one can say that although God may see all future and past as one completed whole, just as Einstein theory of general relativity would allow, we sentient thinking conscious creatures nevertheless have a sense of free-will because our future cannot be foretold within spacetime.

Caterpillar to Butterfly Metamorphosis

Purely by accident, while I was writing this article i was listening to an episode of RadioLab called “Black Boxes” (radiolab podcast 2014-01-17). It was an entire podcast devoted to various black-box phenomena. These could be anything at all for which something known goes “in” and something knowable comes “out” but for which what happens in between going in and but is mysterious = a black box.

There was a cool one about a pair of Aussie radio broadcasters back in the 1950’s who did a telepathy trick which no one has ever discovered the secret for.

But the black box which interested me a lot more was the podcast about the metamorphosis of a caterpillar into a butterfly. This is still a largely mysterious biological process. If you slice the pupa of a caterpillar mid-transformation, you see just a lot of yellow-white goo, like snot. But within this goo are bits of the caterpillar’s brains and nerves, which can survive the liquification process and impart some residual memory for the butterfly. What butterfly’s do with this memory is fairly primitive, but adaptively useful. For example, a caterpillar can be trained to respond to avoid certain smells, e.g., by behavioural association of a certain previous neutral smell with some kind of nasty induced shock, like an electric shock or simultaneous exposure to a bitter chemical.

This was pretty cool science, the fact that a humble caterpillar can actually be behaviourally conditioned. Normally only higher conscious animals can be behaviourally conditioned. But now I learn insects can be conditioned crudely.

But what was really interesting turned out to be that some dude back a century go sliced a caterpillar length-wise along it’s body and showed that inside the caterpillar, were embryonic butterfly wing and antennae structures — near transparent fine structures close to the caterpillar’s skin. And when slicing a young pupa open similarly length-wise you can see the wing and antennae and other butterfly parts are initially squeezed up against the inside of the outer shell of the pupa.

That’s so cool. Especially since while listening to this podcast I was writing about transformations of past to present and to future.

So a caterpillar already contains within itself the image and form of it’s future adult butterfly.

But when you think about it, so do we all. Within our cells is hidden an almost complete image of what we will look like in old age, provided we survive so long, and neglecting injuries and such-like.

How the Past is Now

The other half of the biblical quote is also true. And is a little easier to understand.

Most of your immediate past is still with you, in the form of memory patterns stored in your brain’s cells and neurological structure. Actually, nerve cells in the brain do not store memory, it is the connections between brain cells which constitute memory. Yeah, but memory is not perfect, and so your brain does not record the past history of the entire universe.

There is a deeper scifact way in which the “past is now”. Do you know what it is?

Now is a Boundary on the Past

The basic idea is classical physics. The laws of physics dictate how one state of the universe transforms into a future state. But you can run this script in reverse, and so use current state of the universe to “predict” or may “postdict”, what had to have been the immediate prior state, say one second ago, or a millisecond ago, or whatever resolution in time you desire.

No one can reconstruct the past like this perfectly, which is why history is largely a humanities topic, not a scientific or physics topic, other than the stuff studied in geology and astrophysics and archeaology.  But the physics idea is that the present is a boundary on the past, and from this boundary one can in principle reconstruct all of the past.  All the past universe gets encoded in information on it’s boundary.  In a slightly different guise, in modern physics this concept of information for an entire volume being encoded in it’s boundary is known as the Holographic Principle, and it has been extended well beyond the classical physics paradigm in order to complement Superstring Theory and add to our understanding of Black Holes.  But that is another topic for another time.

Memory has been mentioned already, and this is another illustration of how the past is always “with us” in some sense. All events in the past contributed to our present conditions, and if anything had been different in the past then by the laws of physics the present would not be the same as it is. So, in principle, even though not even remotely in practice, one can conceive of reconstructing the past from only the knowledge of the present.

Scientists cannot do this for the universe as a whole, not even for a glass of water, but an imaginary all-seeing God could do such a trick if they knew the precise laws of physics and the precise arrangement of all molecules in the universe at just the present time. So it’s science baby, not scifi!

The Encoded Past and the Decoding Future

In information theoretical terms, our past is present with us, but trapped within all the results of history mingled together, unravelling it is a decoding process. Running the outcome of the laws of physics in reverse. Curiously, in our known universe, those reversed laws of physics are precisely the same as the forward laws of physics. Amazing huh? Not kidding you. But to explain this — to explain why it is surprising — would be another excursion into statistical mechanics, which I will not take.

Likewise, our future is already determined, but we cannot know it because our memory works only in one direction through time. Yet from our present, given the laws of physics, these laws are constantly decoding the information about the past and somehow (no one really knows the how of it, how does it happen, are we inside a computer simulation, a Matrix, or something more bizarre?) these laws, or whatever it Is that rules them, is ceaselessly and relentlessly generating the reality of our present and near future. At least this is how we psychologically perceive the universe unfolding. The reality is more likely that the future already exists and we are merely walking into it with perennially uncertain knowledge of it.

And in a deeper way the laws of quantum mechanics forbid our knowledge of the future because of the way information from future states of the cosmos are locked-away in structures which our present measurements can only ever, even in principle, detect using probability. We cannot access hypothetical tachyonic information from the future.

Aside: This thing about an inherently probabilistic universe raises an interesting didactic point I feel like remonstrating about for a paragraph: a universe ruled by quantum mechanics is deeply an fundamentally a universe of probability mechanics, in fact this is probably a better description, why people say “quantum mechanics” is an accident of history, arrived at because the first clues that our universe is ruled by probability mechanics came from experiments revealing atomic spectra — which are due to light emitted from atoms from transitions between quantized energy levels of electrons orbiting atoms. (When an electron drops in energy level it emits a photon.) There were also experiments on electron magnetic properties which revealed that electrons have a type of spacetime symmetry property called “spin” which is also quantised (electron spin is discrete, in fact it is either +1/2 or −1/2). These experiments are why the newly emerging quantum mechanics. Yet there are plenty of things with energy or with symmetry in nature which are not quantized like this, and yet everything in nature obeys the probability principles which are the true foundation of quantum physics. Hence the theory should properly be called probability mechanics. Or since Isaac Newton’s name is often associated with classical (pre-quantum) mechanics, perhaps another famous physicist could lend their name to the modern theoretical structure, although it is hard to think of a name which resonates — Heisenberg, Bohr, Dirac, Schrödinger, de Broglie, Pauli, maybe Feynman? Feynman was not one of the first inventors of quantum mechanics, but his name sounds the nicest to my ears, the others are too harsh or exotic. The dudes who actually discovered the mathematical mechanics of quantum mechanics were Heisenberg and Schrödinger, and their respective formulations are often used, they are “matrix mechanics” and “wave mechanics”. In Heisenberg’s formulation the probabilities are represented by matrices (specific types of arrays of numbers). In Schrödinger’s formulation the probabilities are represented in wave amplitudes. OK, that’s all for this aside. I guess we are stuck with “quantum”.

In summary, I guess I just want to emphasise that biblical quotations should be treated a little more like scifi than as literal fact. But I’m being mischievous here. What is more serious is to read the great works and scriptures of theology with an open mind and an open heart and try to extract spiritual meaning from them before any literal meaning. I’m fairly certain there is nothing truly literal intended in the holy scriptures. The original authors (or inspirer’s) surely were writing (or inspiring) from the vantage of a far highly plane of reality than the mere physical. So their “Moon” and “stars” and “Sun” and “heaven” and “blood” are almost surely nothing to do with the (physical) cosmological stars and galaxies and creatures. I think our future civilisation will prove me right, but I can only place a probability on it.

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Like the caterpillar, we all carry our future with us, and from our present cells we can in principle decode our entire past, in more detail and with superior fidelity than our memory.

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