Paul P. Mealing

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Sunday, 20 May 2018

Quantum mechanics and the arrow of time

Before I get started I need to make an important point. Every now and then I hear or read about someone who puts my life into perspective. Recently, I read an article on Lisa Harvey-Smith, a 39 year old, educated in England who is ‘Group Leader’ of astronomy at Australia’s CSIRO. She appeared on an ABC programme called Stargazing Live (last year) with Brian Cox and Julia Zemiro. She won the 2016 Eureka Science Prize for ‘promoting science research in Australia’. She also runs ultra-marathons (up to 24hs) and is an activist for LGBTI people. The point I’m making is that she’s a real scientist, and by comparison, I’m a pretender.

And I make this point because many people who know more about this subject than me will tell you that much of what I have to say is wrong. So why should you even listen to me? Because I have a philosophical point of view on a subject with many philosophical points of view, some of which border on science fiction. For example: interacting parallel universes; and physical reality only becoming manifest when perceived by a conscious observer. I’ve written about both of these philosophical perspectives on other posts, but they indicate how much we don’t know and how difficult it is to reconcile quantum mechanics (QM) with what we actually perceive in our everyday interaction with the world.

I recently read a very good book on this subject by Philip Ball titled Beyond Weird. He gives a history lesson whilst simultaneously discussing the philosophical nuances inherent in QM in the context of experimental evidence. Ball, more than any other author I’ve read in recent times, challenges my perspective, which makes him all the worth while to read. But in so doing, I’m able to delineate with more confidence between the lesser and greater contentious aspects of my viewpoint. In fact, there is one point which I now realise is the most contentious of all, and it is related to time.

Regarding the title of this post, they seem like separate topics, but I’m aware others have made this connection; in particular Richard A Muller in NOW; The Physics of Time, though he didn’t really elaborate. He did, however, elaborate on why entropy does not provide the arrow of time, which is an oft made misconception. And it is one I’ve made myself in the past, but I now fully realise that the cause and effect is the other way round. Entropy increases with time due to probabilities. There is a much higher probability for disorder than order providing the system is in equilibrium. If there is an energy source (like the sun) that keeps a system out of equilibrium then you can have self-organising complexity occurring (such as life).

I’m unsure if QM provides an ‘arrow of time’, as people like to express it, but I do believe it provides an asymmetry, which is best expounded by Roger Penrose’s 3 phases of U, R and C. U is the evolution of the wave function as expressed by Schrodinger’s equation, R is the measurement or observation process (also called decoherence of the wave function) and C is the classical physics world which we generally call reality. These always occur in that sequence, hence the logical temporal connection.

I say ‘always’ yet Ball gives an example whereby physicists in Canada in 2015 ‘reversed the entanglement of photons’ in a crystal, which Ball calls 'recoherence'. But he also describes it as ‘.. the kind of exception that, in the proper sense, proves the rule.’ The ‘rule’, according to Ball, is that decoherence is the loss of quantum information to the environment. This is a specific interpretation by Ball, which has merit and is analogous to entropy (though he doesn’t make that connection) therefore time-directional in the same way that entropy is.

Towards the end of his book, Ball effectively argues that an ‘information’ approach to QM is the most logical approach to take and talks about a ‘reconstruction’ of QM based on principles like the ‘no cloning’ rule (quantum particles can’t be copied so teleportation destroys the original), the 'no-signalling' rule (you can’t transmit information faster than light) and there is ‘no unconditional secure bit commitment’ (which limits quantum encryption). These 3 were called ‘no-go principles’ by Rob Clifton, Jeffrey Bub and Hans Halvorson. To quote Bub from the University of Maryland: ‘[QM] is fundamentally about the representation and manipulation of information, not a theory about the mechanics of nonclassical waves or particles’. In other words, we scrap wave functions and start again with information. Basically, Ball is arguing that QM should be based on a set of principles and not mathematical formulations, especially ones that describe things we can't perceive directly (we only see interference patterns, not waves per se).

Of course, we’ve known right from its original formulation, that we don’t need Schrodinger’s equation or his wave function to perform calculations in QM (I’ll talk about QED later). Heisenberg’s matrices preceded Schrodinger’s equation and gave the same results without a wave function in sight. So how can they be reconciled philosophically, if they are mathematically equivalent but conceptually at odds?

From my limited perspective, it seems to me that Heisenberg’s and Schrodinger’s respective mathematical approaches reflect their philosophical approaches. In fact, I would argue that they approached the subject from 2 different sides, even opposite sides, and came up with the same answer, which, if I’m correct, says a lot.

Basically, Schrodinger approached it from the quantum side or U phase (to use Penrose’s nomenclature) and Heisenberg approached it from the measurement side or R phase. I’m reading another book on the same subject, What is Real? by Adam Becker, which I acquired at the same time as Ball’s book, and they are complementary, in that Becker’s approach is more historical yet also examines the philosophical aspects. Heisenberg was disappointed (pissed off may be more accurate) at Schrodinger’s success, even though Heisenberg’s matrix approach preceded Schrodinger’s wave function.

But it was Heisenberg’s specific interest in the ‘measurement problem' that led him to his famous Uncertainty Principle and a Nobel Prize. Schrodinger’s wave function, using a Fourier transform, also gives the Uncertainty Principle, so mathematically they are still equivalent in their outcomes. But the point is that Schrodinger’s wave function effectively disappears as soon as a measurement is made, and Heisenberg’s matrices with their eigenvalues don’t tell us anything about the evolution of any wave function because they don’t express it mathematically.

Ball makes the point that Schrodinger’s and Heisenberg’s approaches reflect an ontological and epistemological consideration respectively, which he delineates using the shorthand, ‘ontic’ and ‘epistemic’. In this sense, the wave function is an ontic theory (this is what exists) and Heisenberg and Bohr’s interpretation is purely epistemic (this is what we know).

I’m getting off the track but it’s all relevant. About a month ago, I wrote a letter to New Scientist on 'time'. This is an extract:

There is an obvious difference between time in physics - be it governed by relativity, entropy or quantum mechanics - and time experienced psychologically by us. Erwin Schrodinger in his seminal tome, What is Life? made the observation that consciousness exists in a constant present, and I would contend that it's the only thing that does; everything else we perceive has already happened, except quantum mechanics, which prior to a 'measurement' or 'observation', exists in the future as probabilities. An idea alluded to by Sir William Lawrence Bragg, albeit using different imagery: the future are waves and the past are particles – "The advancing sieve of time coagulates waves into particles at the moment ‘now’". So it's not surprising that the concepts of past, present and future are only meaningful to something with consciousness, because only the continuous ‘now’ of consciousness provides a reference.

Those of you who regularly read my blog will notice that this is consistent with a post I wrote earlier.

The letter was never published and New Scientist inform you in advance that they refer letters to ‘experts’ and that they don’t provide explanations if they don’t publish, which is all very fair and reasonable. I expect in this case the expert (possibly Philip Ball, as I referenced his review of Carlo Rovelli’s book) probably said that this is so wrong-headed that it shouldn’t be published. On the other hand, their expert (whoever it was) may have said this insight is so obvious it’s not worth mentioning (but I doubt it).

I expect that both my citing of Erwin Schrodinger and of Sir William Lawrence Bragg would have been considered, if not contentious, then out of date, and that my views are far too simplistic.

So let me address these issues individually. One reads a lot of words (both in science and philosophical essays) on the so-called ‘flow of time’, and whether it’s an illusion or whether it’s only in the mind or whether it’s the wrong metaphor altogether; as if time is a river and we stand in it and watch it go by.

But staying with that metaphor, the place where we are standing remains ‘now’ for ever and always, whilst we watch the future become the past in a series of endless instants. In fact, we never see the future at all, which is why I say that ‘everything we perceive has already happened’. But the idea that this constant now that we all experience is a consequence of consciousness is contentious in itself. We don’t see ourselves as privileged in that sense; we assume that it only seems a privileged position because we witness it. We assume that everything in the Universe rides this wave of now. But, for everything else, the now becomes frozen, especially if ‘now’ represents the decoherence of a quantum wave function into a classical particle. Without consciousness, ‘now’ becomes relative, an objective point in time between a future event and a past event that quickly only becomes perceived as a past event.

Let’s look at light, because it’s the most ubiquitous quantum phenomena that we all witness all the time (when we are awake). The other thing about light is that we can examine it on a cosmic scale. The Magellanic Clouds (galaxies) are approximately 200,000 light years from here and we can see them with the naked eye in Australia, if you can get away from townships on a clear night. So we can literally look 200,000 years into the past. (That is roughly when homo sapiens evolved in Africa, according to one reference I looked up.)

Now, in my previous post I argued that light is effectively in the future until it interacts with matter, so how is that possible if it took the entire history of humanity to arrive at my retina? Well, from the star’s perspective (in the Magellanic Cloud) it’s in the future because it’s going away from it into the future, quite literally. And no one can perceive the light ray until it interacts with something, so it’s always in the future of whatever it interacts with. For the photon itself, it travels in zero time. Light turns time into distance, which is why there is really only spacetime, and if light didn’t do that (because it has a constant velocity) then everything would happen at once. So, as soon as it hits my retina and not before, I can see 200,000 years into the past. That's a quantum event.

Early in his book, Adam Becker (What is Real?) provides a very good metaphor. A traveller arrives at a fork in a path and we don’t know which one he takes until he arrives at his destination. According to QM he took both at once until someone actually meets him and then we learn he only took one. The 2 paths he can take are in the future and the one he actually took is in the past. But wait, you say, in QM a photon or particle can literally take 2 paths at once and create an interference pattern. Actually, the interference pattern is created by the probabilistic outcomes of individual photons or particles, so there is still only one path for each one.

Superposition is a much misunderstood concept. As Ball explains in a foonote: “…superposition is not really ‘two states at once’, but a circumstance in which either state is a possible measurement outcome.”

He gives a very good description of the Schrodinger wave function and its role in QM:

The Schrodinger equation defines and embraces all possible observable states of a quantum system. Before the wave function collapses (whatever that means) there is no reason to attribute any greater degree of reality to any of these possible states than to any other. For remember that quantum mechanics does not imply that the quantum system is actually in one or other of these states but we don’t know which. We can confidently say that it is not in any one of these states, but is properly described by the wavefunction itself, which in some sense ‘permits’ them all as observational outcomes. Where then do they all go, bar one, when the wavefunction collapses? (emphasis in the original)

He was making this point in the context of explaining why the parallel universe or ‘Many World Interpretation’ (which he calls MWI) is so popular and seductive, because in the MWI they do all exist. Ball, by the way, is not a fan of MWI and gives extensive and persuasive arguments against it.

This leads logically to Feynman’s integral path method or his version of QED (quantum electrodynamics) where all paths are allowed, but the phase interaction of the superposed wave functions cancel most of them out. Only a wave function version of QM with its time dependent phases can provide this interaction. Brian Cox gives a very good, succinct exposition of Feynman’s version of QM on Youtube and Freeman Dyson, who worked with Feynman and who originally showed that the independent work of Schwinger, Feynman and Tomonaga were equivalent, which got them all the Nobel Prize (except Dyson), explains that Feynman’s integral method predicts 'future probabilities from a sum over histories'. The point is, as Ball says himself, none of these histories actually happen. I argue that they never happen because they’re all in the future. Certainly, we never see them or measure them, but one of the probability outcomes will be realised when it becomes the past.

Because a specific path is only known once an observation is made, it appears that we are determining the path backwards-in-time, which has been demonstrated experimentally. I feel this is the key to the whole enigma, like the photon coming from the Magellanic Clouds – the path is revealed in retrospect. Until it’s revealed, it’s effectively in our future. Also this is consistent with the asymmetry in time we all experience. The future is many paths (as per QED) but the past is only one.

Ball argues consistently that there is a transition from ‘quantumness’ to classical physics (as per Penrose, though he doesn’t reference Penrose) but he argues that classical physics is a special case of QM (which is the orthodoxy).

His best argument is that decoherence is the loss of quantum information to the environment, which can happen over time, so not necessarily in an instance. He uses the same idea to explain why large objects decohere virtually instantaneously, because they are exposed to such a massive expanse of the environment.

There is much about QM I don’t discuss, like spin states that distinguish bosons from fermions and the role of symmetry and Emmy Noether’s famous theorem that relates symmetry to conservation laws (not only in QM but relativity theory).

I’m trying to understand QM and how it relates to time. Why is it, as Ball himself asks, are there many possibilities that become one? My contention is that this is exactly what distinguishes the future from the past as we experience it. The enigma with QM, as when we look backwards in time through the entire cosmos, is that those many paths only become one when the quantum object (photon or particle) interacts with something, forcing a wave function collapse or decoherence. Is there a backwards-in-time cosmic scale loop as proposed by John Wheeler? Maybe there is. Maybe the arrow of time goes both ways.


Footnote: This video gives a good summary of QM as discussed above; in particular, the presenter discusses the fundamental enigma of the many possibilities becoming one, and the many paths becoming one, only when an observation or measurement is made. He specifically discusses the so-called Copenhagen interpretation, but in effect describes QED.

Addendum 1: Sometimes I can't stop thinking about what I've written. I'm aware that there is a paradox with a light ray from the past intersecting with our future, so I've shown it in a very crude spacetime diagram, with time on the vertical axis and space on the horizontal axis. The Magellanic Clouds and Earth are 200,000 light years apart (closer to 190,000, so some artistic licence) and there is a light cone which goes at 45 degrees from the source to the Earth 200,000 years into the future.

It's assuming that the distance between the Magellanic Clouds and Earth doesn't change (for simplicity) which is almost certainly not true. It allows the Earth to be a vertical line on the spacetime diagram with light being at 45 degrees, so they intersect 200,000 light years in the future.

It also suggests that the photon exists in a constant 'now' (until it interacts with something). As I said before, light is unique in that it has zero time, which explains that particular effect. Consciousness is unique in that it provides a reference for ‘now’ all the time. Light is always in the future of whatever it interacts with, when it becomes ‘now’, then becomes frozen in the past, possibly as an image or a dot on a screen. Consciousness never becomes frozen, but it does become blank sometimes.

Addendum 2: This is a Youtube lecture by Carlo Rovelli, who would tell you that everything I've said above is wrong.


2 comments:

Anonymous said...

In both Schrodinger’s wave function and Heisenberg’s matrices, something seems to be lost or “reduced”. According to Ball, decoherence is the loss of quantum information to the environment.
Why should it be a loss? When you get the measure of something in the sense of assessing or evaluating something, you pay attention to this something, you gain something from your "meditation". (in Spanish "meditar" = to meditate and "medir" = to measure)

Paul P. Mealing said...

Thanks Anonymous for your comment. I think the 'environment' is the 'reality' we all see and interact with. In other words, when decoherence happens the quantum wave function becomes part of the environment and the information becomes more explicit, be it spin or position or whatever.

Regards, Paul.