Originally posted 15 Mar 2005 - Phew, I can't believe I got that much to grips with the technical discussion back when I was more 'into it'. As I've mentioned in previous posts (I recommend you read If You Think You Understand This, Then You Don't and Bell's Inequality and Bell Revisited before reading this post), I'm not so exercised now about whether the world is deterministic and local. It seems quite likely that it is at least non-local, which fits with my best intuition at this point anyway.The ManBeginning with his 1995 paper, Tim Palmer, from the European Centre for Medium-Range Weather Forecasting, questioned the binding force of Bell's Inequality and demonstrated that wholly deterministic (although non-computably chaotic) non-linear dynamical systems could produce the apparent randomness of quantum state measurement while keeping our understanding of the universe on a local and real footing. He has refined his thinking and presented it in further papers in 2004 and 2005. I think that he is onto something real and big. Through the happy chance of working with someone whose partner works with Tim at ECMWF, I got the opportunity to meet him and talk a bit about his thinking. Keep in mind that Tim's day job is in meteorological research, so his physics work is in his spare time. Although I clearly lack schooling in the range of mathematical tools necessary to follow all of the technical details, through reading his papers and talking for that hour or so, I've got a pretty good idea what he's up to. The core pointsThere are two common and related themes to his physics work: - The quantum state reduction associated with measurement via classical devices is not necessarily stochastic. It can be regarded as a deterministic non-linear dynamical system. A central element to this system is the non-computability of certain propositions within it.
- Bell's Theorem relies on an assumption of counterfactual definiteness, an assumption that is not valid in a deterministic world where counterfactual propositions are essentially non-computable and therefore lack definite truth values. Therefore, we need not accept the unavoidability of 'spooky action at a distance' in order to save deterministic dynamics.
Riddled BasinsAlthough the evolution of the state vector through time is a deterministic one, the reduction of the system to an observable state appears to be random. Conventional QM takes this indeterminacy as given. Palmer thinks that the apparent randomness hides a chaotic dynamic that is simply too messy to untangle, which makes his approach what is known as a 'hidden variables' one. Chaos theory uses the concepts of attractors and basins when speaking of how different initial conditions migrate via iterations of some non-linear operation toward some resting place. A resting place is called an attractor, and the collection of initial states that migrates to that attractor is called its basin. What I have just said is, of course, a gross over-simplification. Not all non-linear systems converge to an attractor at all. Some just explode towards infinity. Nor does an attractor necessarily constitute a single number at which the system settles forever. An attractor may be a cyclical one, whose cycle may involve simply flipping regularly between two numbers or may involve cycling through a sequence of numbers so long that it would not repeat in the history of the universe to date. Also, not all basins are defined by smooth outlines. An attractor's basin may be very messy indeed, with any point within the basin having other points arbitrarily close to it that DO NOT belong to the basin. Such basins are said to be riddled. Now imagine a system with two attractors: whose basins collectively cover the entire possible set of initial conditions; whose basins are of equal area (or volume, if the space is three dimensional) to one another; and whose basins are jointly riddled (that is to say, intertwined) as above. It is possible to construct such a system that is so riddled that (given truncation errors) it is impossible to compute algorithmically which basin a given set of initial conditions belongs to. Given the equal size of the basins, there is a 50% chance that any set of initial conditions belongs to either basin. It is also possible to construct this system in such a way that it is consistent with other aspects of the formalism of QM for the measurement of bivalent properties like spin, and Palmer shows this. There may be more work to do, but the point is that Palmer has shown that a deterministic system may exist that is consistent with QM. What about locality?But isn't such a system bounded by Bell's inequality, which is known to be violated by both QM prediction and experimental evidence? No, says Palmer, because Bell's proof makes an implicit assumption about certain counterfactual propositions having definite (yes or no) truth values. Where does this notion of counterfactual reasoning enter Bell's proof? Let's remember the experiment that tests it. Zero angular momentum electron pairs (Right and Left) are emitted from a special source. One device measures the spin of each Right electron along some axis in the plane that is orthogonal (perpendicular) to the electrons' path. Another device measures the spin of each Left electron along one of two axes, each of which constitutes a different rotation (say x for one and z for the other) from the axis of the Right device. Bell's inequality is then a relationship among the measurements taken at these three (R, Lx, Ly) orientations. Counterfactual assumption The important thing to remember, though, is that for any given pair of electrons, only TWO of these measurements can be taken (R & Lx, or R & Ly). The theorem makes the assumption that the measurements among many pairs of electrons can be lumped together and then relates correlations within the large set. So, in fact, the relationship observed for any GIVEN pair of electrons is one of two: - The relationship among R, Lx
*and what Lz would have been, had the z orientation been chosen for the Left member of this pair*, or - The relationship among R, Lz
*and what Lx would have been, had the x orientation been chosen for the Left member of this pair*.
The elements in italics are the counterfactual ones. In reality, ONLY x OR z can be chosen as the orientation for the Left member of any given pair. The assumed measure of what it would have been were the other angle chosen is taken from the statistical behaviour of the pairs whose Left element was measured at the other angle. Determinism, Free Will, and the observer as part of the systemWhat is the upshot of all of this? I want to (try to) go into a bit more of the technical detail in a minute, but it is possible to think about this initially at a philosophical level. IF the universe is deterministic in the philosophical sense, then everything that happens (everything that has ever happened and will ever happen) happens NECESSARILY. It COULD NOT have happened any other way. Palmer shows with his demonstration of a particular chaotic system that determinism is consistent with QM observations. So, in effect, we're saying that the observer only measured, say, R and Lx for a particular electron pair. And we're saying that the universe has evolved in such a way that - however free the observer felt himself to be in his choice of the L measurement orientation - he COULD NOT have chosen it to be y. So introducing a counterfactual proposition about what MIGHT have happened HAD he chosen y is meaningless. Even though it feels like a small hypothetical change in the context of a large universe, it is simply not within the set of possible states of the world. As uncomfortable as many feel with determinism, because of its implications for our pure notion of free will, this is hard to get around. Neither the electron pair nor the observer can be taken outside the universe itself. And if the evolution of that universe is deterministic (as it is if it can be modeled by a non-linear dynamical system) then not only the spin measurements but also the orientations at which they are made follow necessarily from the initial conditions of the universe and the laws that govern is evolution. Over our headsNow, Tim Palmer expresses all of this in a much more disciplined way. He gives an example of a universe defined by a famous attractor, known as the Lorenz Attractor (named after the father of non-linear dynamics, who discovered it). This attractor is defined by three differential equations on three variables. If the initial conditions of the universe sit on the attractor, and if these differential equations govern the universe's evolution, then the smallest of perturbations to one of the variables will move the system off of the attractor (given the attractor's fractal nature), thereby violating the laws of the universe. But Palmer needs to bridge a gap here. The wave function of quantum mechanics (defined by Schrodinger's equation) uses complex (i.e., using 'i', the square root of -1) linear dynamics. Palmer is talking about real (i.e. no square root of -1) NON-linear dynamics. How can his system do the work of Schrodinger's? At this point, it gets pretty hairy for us non-mathematicians. Palmer introduces a new definition of i as an operator on a sequence of real numbers. Quantum states can be defined by sets of these sequences, and Palmer shows how his i operator performs in a way analogous to the maths of the upward cascade of fluctuations in a turbulent flow (something from his meteorological world). The effect of these steps is to present a way of describing the state function in granular (like the quantum world itself) terms rather than in the continuous terms of the Hilbert space that is used in conventional QM. Applying this to the test of Bell's inequality, this means that we can't pick any angle in a continuum but are instead confined to a finite (but as large as we wish) set of angles. Palmer proves that there is no way that measurements for both the Lx and Ly angular differences from the R orientation can be simultaneously defined. All of this amounts to the more rigorous and mathematical proof of the point I made philosophically and sloppily in the section above. The bottom line is that any real physical state must be associated with a computable real number (even if the only way to compute it is to let nature 'integrate' it through a physical experiment!). RepercussionsWhere does this take us? If we re-interpret the wave function as a set of binary sequences as described above, we can think of the elements of those sequences as 'real' bits of quantum reality, which means that even in the absence of a measurement, we take the quantum state to have definite values rather than a superposition of possible values. Also, a sequence itself encodes information not just about the system it describes but also about that system's relationship to the whole. Palmer uses an analogy with the DNA in our bodies' cells. This hearkens back to the explicate and implicate order in David Bohm's interpretation of quantum theory. Look for more on Bohm in an upcoming post. I've just finished reading
The Tao of Physics by Fritjof Capra. I won't undertake a general review of the book, but I can enthusiastically recommend it.Instead, I want to concentrate on one specific point Capra discusses in the Afterward of his Second Edition. (The book was originally published in 1975, and the second edition was released seven years later.) Capra discusses the ramifications of the empirical results from tests of John Bell's inequality. As a staunch proponent of a deterministic, local, realist interpretation of quantum mechanics in an earlier day, I had come across Bell's Inequality before. I even wrote about it, which you can verify at the link above. I'm not going to recap that whole post here, so you may want to visit it before continuing. Capra helped me realise that I hadn't really got it, though. Bell set out a testable relationship that must hold if sub-atomic reality is both local and deterministic. Tests have been conducted, and the results are conclusive: quantum reality must be either non-local, non-deterministic or both. Einstein believed to his core that reality must be both local and deterministic. I paraphrase his words on each point: - There cannot be 'spooky action at a distance'.
- God does not play dice with the universe.
For reality to be local means that no force or action can act with a speed faster than the speed of light. My pushing a button while standing on the sun and immediately changing the channel on my TV would violate this, since it takes light seven minutes to traverse that distance. For reality to be deterministic means that every effect has a cause. Taken to its logical conclusion, the notion is embodied in the clockwork universe. If one knew all the initial conditions at the 'start of time' and all of the 'laws' that the universe followed as it evolved from one moment to the next, then one could know all that would happen for all time. We use probabilities in everyday life (for instance, at the roulette wheel) because either our understanding of all the (local) forces at work or the exactness with which we can measure initial conditions is insufficient to calculate outcomes exactly. Quantum mechanics raises the possibility that even with perfect understanding and measurement, we still could not accurately predict concrete sub-atomic events. I was particularly exercised by the issue of determinism, so when I read about outcomes from tests of Bell's Inequality, I focused on that element of the interpretation. I admitted, sadly, that not every effect has a cause. I need not have done so, had I paused to think sufficiently about the second condition. It could be that tests failed the inequality because the causes were non-local. I could, in theory, have held on to determinism by accepting spooky action at a distance. But in a way, admitting non-locality undermines predictability just as much as inherent non-determinism does, because an observer cannot know and therefore account for forces at great remoteness in the universe that are impacting what he sees. Even if he had appropriate sensors throughout the cosmos, they could not transmit their data to him any faster than the speed of light. Meanwhile, the spooky action at a distance will have had immediate effect. As it happens, today, I believe that reality is not determined, local or objective. Most interpretations of quantum mechanics agree, but my angle is primarily from the philosophical viewpoint rather than the scientific. A worldview consistent with eastern wisdom traditions sees reality as an undivided whole, so the confirmation of non-locality is no surprise. In a way, you can think of it as rotating causality 90 degrees in space-time. Instead of explaining a current event by appealing to causes that preceded it, you sometimes have to explain it in terms of state of everything else right now. Sometimes, the best that we can do is say that something is the way it is because everything is the way it is. Any one 'thing' is like a puzzle piece, which, in order to fit into the overall puzzle, can have one and only one shape - the shape of the 'hole' left when every other piece is in place. There are limits to reductionism, and we have touched them. At least some truths are irreducible.Of course, this philosophical sleight of hand doesn't help with predicting the future. We just have to accept that, as we push the boundaries of our understanding of the universe, sometimes the best we can do is approximate or confine our answers to a range rather than a point. There are limits to our knowledge and the control we can exercise with it. First posted 31 Oct 2003. I definitely still think there is infinite diversity out there, including many versions of 'me'. I tend now to think of it more as the existence of every possible experience from every possible perspective. See Scientific American: Parallel Universes [ COSMOLOGY ]; Not just a staple of science fiction, other universes are a direct implication of cosmological observations Buckle in, 'cause this one's a helluva ride - a real head spinner. You can read the whole article via the link above, but I'm dying to try to summarise it, to see how much of it I 'get'. The gist is that our universe is just part of a multiverse, or actually a part of four tiers of multiverses, with the result being that (based on simple probabilities) an infinite number of you's and me's are 'out there' living through every permutation of our lives. I hope only a few of the me's out there are suffering from my cold at the moment. Our Hubble SpaceThe article starts by defining our universe as our visible universe. Since light travels at 300 million metres per second, and since the Big Bang happened about 14 billion years ago, our visible universe (or Hubble space) is a spherical space with a radius of about 10^26 metres. (The article says 4x10^25). This visible universe's radius grows (by definition) by one light year (roughly 10^16 metres) each year, and the light we see emanating from the edge of our Hubble space was emitted at the beginning of time. Level 1 Multiverse = The UniverseThe first level of multiverse, then, is the collection of Hubble spaces. This is what I have always considered and shall continue to call The Universe. If we assume (as current observations suggest) that the overall universe is infinite and that matter is roughly evenly spread throughout it, then there are an infinite number of these Hubble spaces, all with the same physical laws as ours. Now, pick one of those other Hubble spaces. What is the probability that the interaction of fundamental particles and forces over the lifetime of that space just happen to produce another you? Surely unbelievably small. But is it zero? It seems irrational to assume that the probability of another you in any other given Hubble space is absolutely zero, since you have already appeared once, after all. Let's say the chance is one in a gazillion, with a gazillion being the biggest number imaginable. Then there must be another you out there, because any non-zero probability, no matter how small, when applied to an infinite number of cases, will be realised. Saying that there must be other you's living through every possible permutation of your life is just a special case. We could simply say that anything that is possible (i.e. has non-zero probability) exists. So, somewhere out there is a you with 9 fingers, a you with a squeaky voice, a you who didn't propose to your wife, a you who likes Abba songs, a you who only carries 20p pieces in his pockets. There is you who slept late on your 19th birthday, not to mention a you whose life is exactly the same as yours in this Hubble space. Now you see just how infinite infinity is! Level 2 Multiverse = The MultiverseThere are a couple of ways to think of a level 2 multiverse, which I will call just The Multiverse. At heart, The Multiverse (i.e. Level 2) is a collection of an infinite number of Universes (i.e. Level 1s), each of which can have very different physical 'constants'. We can think of these Universes as bubbles of non-stretching space within the eternally inflationary Multiverse. Alternatively, we can view The Multiverse as a cycle of continuous birth and destruction of Universes, perhaps with black holes as the agents of mutation and birth. From either angle, we could never communicate between Universes (or gain information about another one), because they are either moving apart from one another at faster than the speed of light or only 'touch' at singularities, through which no information can pass. Still, the existence of The Multiverse would explain the otherwise tricky and highly improbable fine tuning of our own Universe. If ours is just one of an infinite number, then it is no longer surprising that so many specific variables (density fluctuation, relative weights of elements, etc) have values just right for allowing life to emerge and evolve. As regards the multi-me's and multi-you's, if the infinite size of our Universe guaranteed that they were out there, then the existence of The Multiverse, containing an infinite number of Universes, really cements it! Level 3 Multiverse = Many Worlds (from quantum mechanics)A level 3 multiverse is another name for the infinite collection of worlds in the 'Many Worlds' interpretation of quantum mechanics. Each quantum event causes a split between worlds, with one proceeding along possible route 1 and the other along possible route 2. Each of those 'worlds' contains an entire Multiverse (i.e. Level 2). Since there are an infinite number of quantum events, there are an infinite number of such splits and an infinite number of worlds, one for each thread that winds its way forward through one 'choice' after another. I (as in this specific Doug in this specific level 1 and 2) only have access to, only experience one of those threads. The other me's see only their specific threads. But all threads exist. The me's in different Hubble spaces live separate but parallel lives in a different part of space-time. The different me's within the many worlds (Level 3) are not separated from me in spatial terms but in dimensional terms within the overall wave function for the Level 3 multiverse. You can think of these worlds as being perpendicular worlds, as opposed to parallel ones. Jointly, they require an infinite number of dimensions, which the 'Hilbert Space' of the wave function has. Ouch, that hurts my head. Anyway, the existence of this level depends on whether the wave function's evolution through time is unitary (no, I don't know what that means), which is as yet uncertain but is consistent with observations and wider theory. In one sense, it doesn't matter, because if physics is unitary, then Level 3 adds nothing that doesn't already exist in Levels 1 and 2. No more possibilities are generated, just additional copies of ones that already exist. Level 4 Multiverse = All possible mathematical structures (or, a bridge too far)Just a few words on a final, highest level multiverse. The wave function of quantum theory and level 3 multiverse is a mathematical structure, and most physicists today see the universe as fundamentally mathematical. Why not, then, allow for an infinite number of level 3 multiverses corresponding to any imaginable set of (mathematical) laws? Fine with me, but you'll need to check with all the other multi-me's individually. Originally posted 14 Mar 2005. I'm not aware that anything has changed on this front, but I have to admit that I've not kept a close eye on it. The big questionsIs there a reality independent of subjective observation? Is the universe deterministic in a 'clockwork' sense, or is it irreducibly random at heart? Are the world's interactions local (unable to propagate at a speed greater than that of light, per Einstein), or is there 'spooky action at a distance'? EPRAfter Einstein, Podolsky and Rosen (EPR) put forward their paper arguing that quantum theory was as yet incomplete, these questions were central to physics. Einstein believed that our world is both real (in that its states have real values independent of observation) and local. EPR attempted to use a reductio ad absurdum argument by pointing out strange non-local effects implied within Neils Bohr's interpretation of quantum theory and claiming that this proved the incompleteness of the theory. Bohr seized on some loose language in the EPR paper to issue a forceful rebuttal. Einstein and Bohr's ensuing debate never reached a resolution, but the world (and certainly the mainstream physics community) eventually adopted Bohr's view. Why? An accidental killingIn 1963, a gifted physicist named John S. Bell developed a mathematical proof of a testable inequality that must hold in a real,local and deterministic world. The predictions of existing quantum theory violated the inequality, so either quantum theory was wrong or the world was not a local deterministic one. Bell was himself in the Einstein camp and hoped that experimental evidence would settle the debate in favour of local realism. They did not. All experimental measurements have violated Bell's inequalities, vindicating Bohr's Copenhagen interpretation and seemingly proclaiming the death of locality. (Science is more willing to sacrifice locality than realism / determinism). General derivationBell's derivation of the testable inequality has been hailed as one of the greatest feats of modern physics, yet it is relatively easy to understand. First, let's do it without worrying about the actual physics. Pick three characteristics that an object might have, and call them A, B and C (although they could be something like red, round and soft). Now, imagine that you observe a large number of these objects to see which ones have which characteristics. Some objects might have all three characteristics; some might have only one; some might have combinations of two. Before going further, let's develop a shorthand notation. To indicate that an object has a characteristic, we write a '+' after the characteristic's name (like A+). To say that an object does not have a characteristic, we write a '-' after the characteristic's name (like B-). So, an object that has characteristics A and C but lacks characteristic B would be described as (A+, B-, C+). One thing that is definitely true is that in a large set of these objects, the number that are (A+, B-) plus the number that are (B+, C-) is greater than or equal to the number that are (A+, C-), or: Number (A+, B-) + Number (B+, C-) >= Number (A+, C-) There is a proof of this at the bottom of this post, but if you're willing to accept it for now, let's move on to apply it more specifically to the EPR question. Application to quantum worldThe objects we're now going to observe are electrons, and we're going to observe them in pairs, for reasons that become clearer in a minute. Electrons, like other subatomic particles, have a property called spin (which we'll measure as equalling either 1 or -1), and the A, B and C we're going to observe are the spin measurements at three different angles in the same plane. These pairs of electrons will be emitted by a special source that sends them in opposite directions to one another. The special source also ensures that their spins 'add' to zero. For example, if the right electron (R) has a spin of 1 at a given angle, then the left one (L) necessarily has a spin of -1 at that angle. The weird thing - and the thing that upset Einstein - is that according to quantum theory, between the time that the electron pair is emitted and the time at which some measurement is made, they constitute a single system that can be modelled by a single quantum state function. These electrons can travel very far from one another in this state. However, whenever one is measured, both it and its paired electron drop into a concrete state, IMMEDIATELY, not matter how distant they are from one another. And knowing the spin of the measured one allows you to know the spin of the distant one. This seems to violate the spirit of Einstein's relativity principle, which states that nothing can travel at speeds greater than that of light. This whole experiment is designed to test whether one electron does in fact impact the other in a non-local way. Next, we have to consider the measuring devices, one for R and one for L. Let's say that the right device measures each R's spin at an orientation that we'll call zero (0). The left one is a bit more fancy; it will measure each L's spin at one of two angles - one that makes an angle of size x with 0, or another that makes an angle of size z with 0. The left device can't measure any one L's spin at BOTH the x and z angles, because the first measurement will decouple the relationship that that particular L has with its R twin. Now, as long as one assumes, as Bell did, that the world is a realistic and local one, then one can substitute the following quantum state measurements into our simpler non-quantum one as follows: For A+, substitute R(1) - meaning that the right device measures the R electron of a given pair as having spin of 1. * For B-, substitute Lx(-1) - meaning that the left device measures the L electron of a given pair as having spin of -1 at angle x. * For B+, substitute Lx(1) * For C-, substitute Lz(-1) - meaning that the left device measures the L electron of a given pair as having a spin of -1 at angle z. From this, we can express Bell's Inequality as: Number [R(1), Lx(-1)] + Number [Lx(1), Lz(-1)] >= Number [R(1), Lz(-1)] Because quantum theory implies different correlations among the electron pairs at the various angles of measurement, its predictions violate this inequality. Remember that Bell's only assumptions were of realism and locality. This implies that quantum theory is incompatible with at least one of these two assumptions. Devices like those I've described do exist, and the experiment has been run many times. In every case, the experimental results have violated Bell's Inequality, thereby supporting quantum theory and driving a stake through the heart of locality (and some say realism). But have we (and more importantly generations of the world's top physicists) missed something? The final word?This remained the final word until 1995, when a meteorologist named Tim Palmer used the understanding from his physics PhD as well as his deep knowledge of non-linear dynamics from meteorology to show that, in addition to the assumptions of realism and locality, there is an implicit assumption about counterfactual definiteness embedded in Bell's proof and that that assumption may well not hold. It in effect calls into doubt the legitimacy of steps 1., 3. and 6 in the proof below. Look out for my upcoming post on Tim Palmer's work for more detail about his efforts to re-ground quantum theory in a deterministic and discrete non-linear dynamics. Proof of Bell's Theorem (using 'N' for 'Number')1. N (A+, B-) = N (A+, B-,C+) + N (A+, B-, C-); since an object must have the characteristic C or not have it. 2. So N (A+, B-) >= N (A+, B-, C-); since N (A+, B-, C+) cannot be smaller than zero. 3. N (B+, C-) = N (A+, B+, C-) + N (A-, B+, C-); similar reasoning to step 1. 4. So N (B+, C-) >= N (A+, B+, C-); similar reasoning to step 2. 5. So N (A+, B-) + N (B+, C-) >= N (A+, B-, C-) + N (A+, B+, C-); adding inequalities 2. and 4. together 6. But N (A+, B-, C-) + N (A+, B+, C-) = N (A+, C-); similar reasoning to steps 1. and 3. 7. So N (A+, B-) + N (B+, C-) >= N (A+, C-); which completes the proof First posted 26 July 2004. For a long time, I was vexed by the prevailing non-realist interpretation of quantum mechanics. I refused to accept that reality's evolution from moment to moment could have an unavoidable element of chance in it, causal effects that 'travelled' faster than light or both. You can pick up the strength of my reaction against it by my tone. I even set my own humility sufficiently to the side to accuse one of the greatest scientists of all time of a humility shortfall!I'm more comfortable with these possibilities now, and I've actually embraced an even more 'extreme' interpretation, which I'll share in a separate post. Call me a realist. I just can't help believing that there is a world out there whose existence does not rely on whether I or anyone else perceives it, measures it, imagines it or defines it. I believe this not just about the myriad objects and beings I encounter everyday in my comings and goings but also about the microscopic, quantum world of subatomic particles. This puts me in a small minority among people who bother to think about such things, squarely against the orthodox interpretation of quantum mechanics (QM). That orthodox view, espoused by influentially Bohr and Heisenberg and dubbed the Copenhagen interpretation, holds that sub-atomic particles cannot be said to have definite properties such as position or momentum until such time as those attributes are measured. In fact, in its stronger statements, this interpretation says we cannot really speak of a quantum world at all. We can only speak of the observed measurements we obtain when we interact with that world in certain ways. We should, on this account, simply celebrate the predictive success of QM's formal mathematical model, the most successful predictive model in the history of science. The slightly discomfiting corollary - that the world at its most basic levels is plagued by inescapable uncertainty - is simply something we need to accept, by throwing away our long-standing classical misconceptions about reality. Moreover, we need to accept that the theory as it stands is fundamentally impossible to improve upon. It constitutes the final word on the subject. But there is an alternative interpretation 'on the table', one first presented in 1952 by David Bohm. This interpretation, an example of a 'hidden variables' (causal-realist) theory, is wholly consistent both with the formal mathematics of Schrodinger's equations and with experimental observation. It holds, though, that the same causal relationships we observe at the macro level continue to hold at the quantum level. Given that this just sits much better with me, I plan to read much more about it and report back. In the meantime, let me address a few problems with the orthodox, or Copenhagen, view. The overall point of this post is to say not that we should reject QM but rather that we should use it for the predictive model it is while continuing to search for ways to make it more complete. We certainly shouldn't elevate the orthodox interpretation of it to the status of unassailable doctrine. Here are some reasons why: First, it falls short of what we have traditionally held to be the criteria for an adequate (let alone a complete) scientific theory. Although it has impressive predictive power, it does not subsume the classical theory that it replaces. That is to say, it does not show how, under certain 'limit' conditions, it reduces to the previous best model. This is in stark contrast to the advances that Einstein's theories of special and general relativity made on Newton's mechanics and theory of gravity. Einstein shows how, for objects that are not too massive and for velocities that are not too great, his formulae simplify to those discovered and used by Newton. QM throws out the baby with the bathwater. It discards the classical order completely, erecting a wall around the quantum world and declaring it once and for all a special kingdom where old languages shall not be spoken. A second, closely related point is that QM doesn't say where that 'wall' is. As Schrodinger showed with his reductio ad absurdum example of 'Schrodinger's cat', QM cannot delineate where the classical (macro) world stops and where the quantum (micro) world begins. Schrodinger's thought experiment uses a mechanism that connects the life-or-death fate of a feline to whether or not a particle is emitted by a nearby radioactive substance. Importantly, this set-up is contained within a closed, opaque box. Under the orthodox interpretation of QM, unless and until an experiment is carried out by a knowledgeable observer to measure the emission, the particle (or potential particle) exists in a superposed state between being emitted and not being emitted from the radioactive source. Because (in Schrodinger's thought experiment) any particle emission would trigger the release of a deadly gas within, the cat must therefore also be in a suspended state, neither alive nor dead, but rather a superposition of the two! Not until the box is opened so that the observer can inspect is the poor cat's fate real. It is difficult enough to accept that quantum particles take on concrete properties only when an observer 'collapses the wave function' - the mathematical, probabilistic function that describes a system dynamics. That such indeterminacy should encroach so glaringly into the macro-world is, to me, evidence of a shortfall in the theory (or our interpretation of it). Third, Bohr and others slip without due care between statements about what we can KNOW and statements about what actually IS THE CASE. If we take QM to be saying that, given our current best understanding, we can do no better than deal with the quantum world in a probabilistic manner because we do not understand the finer detail, then that is fine. But Bohr and his followers go on to make two much stronger statements. Clearly suffering from an appalling lack of humility, they suggest that our current best understanding cannot be improved upon. Now this would be a great break indeed from the entire history of science, which is filled with (and one might say defined by) a succession of advances whereby one 'best working model' is superseded by another. Why should it suddenly be that science (or this particular branch of it) has suddenly reached its ultimate answer? Bell's inequality and the Aspect experiments suggest that we probably have to sacrifice the principle of locality (which creates problems with Einstein's theory of general relativity). But they do NOT show that no hidden variables theory is consistent with observed evidence and theoretical formalism. Indeed, Bohm's theory is already before us as one example, and Tim Palmer has even shown how a chaotic (but wholly determinate) system with intertwined, riddles basins can satisfy Bell's inequality fits perfectly well with QM's formal mathematics. An at their most bold (and bizarre), they say that our ultimate knowledge limit - as defined by our human powers of perception and computation - actually impose limits on existence. In philosophical terms, they jump from epistemological claims to ontological ones. If, they say, we cannot verify that something exists, then it does not exist. To which I challenge: if existence is not bound by the perceptual and reasoning powers of spiders, rabbits or dogs, then why should it be constrained by our abilities? Isn't it much more reasonable to believe that a mind-independent, verification-transcendent world exists, and that the scientific advances we have seen to date constitute an ever-better understanding of that world? This seems preferable (and certainly more humble) than asserting that each scientific advance is not a discovery but an act of creation! Looking at all we are capable of verifying and then inferring to the best explanation leads me not to reject realism but to embrace it confidently. Watch this space for a bit more on both Bohm and Bell (who was himself a causal realist). First posted 21 Oct 2003. Not much to add or change now. My 'favourite' interpretation is that of Julian Barbour, which I'll share as a separate post. Is light a wave or a particle? If your answer is, 'Who cares?' you may have a point, but you probably want to read a different post or visit a different blog. It seems that our answer is that we cannot be sure, but that light behaves in some ways as if it were the first and in others as if it were the second, and this duality is just one example of the counter-intuitive, but unprecedentedly accurate, conclusions quantum mechanics helps us reach. The title of this post recalls famous physicist Richard Feynman, who said that anyone who thinks he understands quantum mechanics doesn't. Feynman admitted that he didn't really understand it. Double slitThe famous (at least among physicists) double slit experiment at its most basic shows that light behaves as a wave. Point a lamp towards a photographic plate, but on its way, have it pass through a single vertical slit in a screen. Consider the lamp plus the slitted screen to be the 'light source' - in modern times we can replace this set with a laser. Now, erect another screen between the light source and the photographic plate, and cut two parallel vertical slits in it. Some of the light shone at the screen passes through the left slit and some through the right. Like the ripples created by two pebbles dropped a few feet apart in a pond, the light coming through one slit interferes with the light coming through the other. As the light reaches the plate, at some points two 'peaks' of the ripples overlap and reinforce each other. At other points, two 'troughs' reinforce each other. In between different levels of reinforcement or canceling out occur. The visual result is a series of vertical white and black 'stripes' with varying grey bits in between. This is called an interference pattern, and it serves as great evidence that light does in fact behave as a wave. Seems simple enough. This experiment discredited Newton's 'corpuscular' theory of light in a single sweep. Photo-electric effect - Einstein lays a foundation for the quantum revolutionBut in the early 20th century, Einstein showed that when light was shone on a certain metallic surface, it knocked electrons from the surface like bullets chipping a stone wall. The brighter the light the more electrons are knocked free, but the brightness has no effect on the speed with which the electrons travel when knocked loose. Rather, the higher the frequency of the light, (moving up from red to violet) the greater the velocity (and therefore energy) of the electrons knocked loose. This all showed light to behave as a particle. Hmm, getting confusing... Moreover, when performed across a range of light frequencies, it also verified Planck's quantum hypothesis - showing that the possible sizes of the energy 'transfers' to the dislodged electrons were not continuous, but rather discrete (quantum) levels. Photons (as light particles came to be known) below a minimum frequency (and hence energy level) for a given metal will not knock any electrons free, no matter how high the intensity of the light shone. Photons and the double-slit experimentEventually, scientists were able to ‘shine’ light in smaller and smaller amounts, culminating in the ability to fire individual photons (they can do the same with electrons and get the same results). Here is where things take a very strange turn. Turning back to the double-slit experiment, when photons are fired one at a time at the photographic plate, via the slits in the screen, the result is not a distribution like one would see when bullets are fired through gaps in one wall at a target on another wall, with light 'dots' concentrated in the areas aligned with the bullets’ possible trajectories. Instead, you get just the same interference pattern as in the original double slit experiment, only now built up slowly as more and more photons are fired one after another. Whoaaaa. Wait a minute! So…the individual particles of light behave in a probabilistic, wave-like manner. Each particle seems to know what the others have done and to ‘interact’ with them, even though each is not fired until the previous one has already hit the plate. Viewed another way, each photon has a probability function, with a certain likelihood for landing in different places on the plate. But the photons do not 'pick' any one place. Each 'spreads itself out' on the plate according to that function. Another question is, how do the photons 'know' that both slits are there? Yes. This is headache material. 'Collapse' of the probability functionNow, even stranger, when you set up a contraption to measure and register when a photon passes through either the left or the right slit, the pattern on the plate is not the interference, wave-like one, but rather the bullet-type one that you might have expected based on common sense. What has happened? It seems that as long as we don’t know which slit a particle passes through, each photon fails to ‘commit’ to one or the other, instead behaving probabilistically, as described above. But by measuring which slit a photon passes through, we force it to commit to one slit or the other and thereby to a single, bullet-like point of impact with the plate. But we all know that photons don't think and that they don't 'commit'. We can't rely on such metaphors. How do we really describe what is happening? You may find the answer a bit disappointing. Although, the theory of quantum mechanics can model this behaviour mathematically and predict the behaviour of microscopic particles with unparalleled accuracy, scientists cannot agree how to explain this aspect of our world. Many refuse to even take up the challenge, defining it as within the domain of philosophy rather than science. InterpretationsVarious interpretations of this quantum mechanical outcome have been put forward, ranging from ones requiring an infinite number of dimensions in the universe to ones that question the existence of concrete properties independent of their observation by intelligent beings. The truth is that, theoretically, any number of interpretations are consistent with the mathematics and the observations with which they correspond so well. The problem, for those of us who trust common sense, is that none of them correspond with it. We shouldn't be shocked by this. Our common sense was formed by our experiences in life, none of which deal with phenomena at the microscopic level. Like Einstein's theory of relativity, which only leads to different predictions than Newton's classical physics at velocities approaching the speed of light, quantum theory deals with the world at scales completely outside our direct experience. No hidden variablesStill, many are uncomfortable with the lack of a satisfactory explanation of the unquestionable maths behind quantum theory. Einstein hoped that the theory of quantum mechanics was simply incomplete and that once we discovered other variables at play, the ‘uncertainty’ (I'll write some other time on Heisenberg's Uncertainty Principle) would disappear. Detailed experimental tests of John Bell's theorem suggest that no such variables could supplant quantum uncertainty. We may just have to celebrate quantum mechanics' great predictive powers and live, perhaps uneasily, with the uncertainty that it ascribes to the microscopic world. |
## AuthorI'm curious. I like looking beneath and behind the obvious, also looking for what is between me and the obvious, obscuring or distorting my view. ## Categories
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