Wednesday, August 19, 2020

Explaining Quantum Mechanics

I’ve been on a quest to understand quantum mechanics (“QM”) and think I’ve actually made significant progress, even though Feynman claimed that no one understands it.  What I’m going to write in this post is not ready for an academic paper, so I’m not going to try to prove anything.  Instead, I’m just going to explain my understanding of QM and how it is consistent with what I’ve learned and the results of QM experiments. 

I’m not sure yet whether this explanation is: a) correct; b) original; or c) testable.  Of course, I think it is correct as so far it’s the only explanation that seems consistent with everything I’ve learned about physics and QM.  Not only do I believe it’s correct, but I also hope it’s correct since it has helped me to understand a lot more about the physical world; to discover that it is false would mean that I am fundamentally mistaken in a way that would take me back to the drawing board.  Whether or not it is original is less important to me; as I noted before in this post, even if I had naturally stumbled upon an explanation of QM that had been discovered and written about by someone else, such as Rovelli’s Relational Interpretation, I’d be fine with that because my primary quest is to understand the physical world.  As it turns out, the following explanation is not equivalent to the Relational Interpretation or, as far as I’m aware, any of the other existing interpretations of QM.  So, if I’ve come upon something original, I’d like to get it into the information ether for purposes of priority, sharing ideas, collaboration, etc.  Finally, if my explanation actually is both correct and original, I would really like it to be testable and not just another interpretation of QM.  Currently, all QM interpretations are empirically indistinguishable.  While hypothetical experiments have been proposed to distinguish one or more interpretations from others (such as Deutsch’s classic paper, which aims to show how a collapse interpretation might be distinguished from a non-collapse interpretation), not only are such experiments impossible for all practical purposes in the near future, but may actually be impossible in principle.  Of course, even if it turns out to be just another indistinguishable interpretation, it is already valuable (at least to me) from a pedagogical point of view, as it clarifies and simplifies QM in a way that I haven’t seen elsewhere.  Having said all that, here is my current understanding/explanation for QM.

Information, Facts, and Relativity of Superposition

First, let’s start with information.  If I throw a rock with my hand, then that fact – that is, the fact that the rock and my hand interacted in a particular way – gets embedded in a correlation between the rock and my hand so that they will both, in some sense, evidence the interaction/event.  The information about that fact gets carried in that correlation so that future interactions/events are consistent with that fact, which is what gives rise to predictability.  The trajectory of that rock can then be predicted and calculated relative to my hand because the information stored in the correlation between the rock and my hand guarantees that future events are consistent with that past event (and all past events).  The set of possible futures that are consistent with past events is so limited that the future trajectory of the rock can be calculated to (almost) limitless precision.  In fact, the precision to which a person could predict a rock’s trajectory is so good that it was thought until the discovery of quantum mechanics (and specifically Planck’s constant) that the physical world is perfectly deterministic.  Many (perhaps most) physicists are determinists, believing that the world evolves in a predetermined manner.  The notion of determinism is heavily related to Newtonian physics: If I know an object’s initial conditions, and I know the forces acting on it, then I can predict its future trajectory. 

This is certainly true to some degree.  However, due to chaos, the further in the future we go, the more sensitive those predictions are to the precision of the initial conditions.  So if we don’t know an object’s initial conditions to infinite precision, then it’s just a matter of time before chaos amplifies the initial uncertainty to the point of complete unpredictability.  This fascinating paper shows that that’s true even if we are looking at three massive black holes with initial conditions specified to within Planck’s constant.  Of course, QM asserts that we can’t specify initial conditions better than that, so this seems to me pretty good evidence that the universe is fundamentally indeterministic. 

The thing is... why should we ever have believed that infinite precision was possible, even in principle?  Instead, the amount of information in the universe is finite, a concept reasonably well established by the entropy concept of the Bekenstein Bound, and also well articulated by Rovelli’s explanation that the possible values of an object’s location in phase space cannot be smaller than a volume that depends on Planck’s constant.  However, even if we can all agree that information in the universe is finite, there is no agreement on whether it is constant.  Most physicists seem to think it’s constant, which is in part what gives rise to the so-called black hole information paradox.

Part of the motivation for believing that information is constant in the universe is that in quantum mechanics, solutions to the Schrodinger Equation evolve linearly and deterministically with time; that is, the amount of information contained in a quantum wave state does not change with time.  Of course, the problem with this is that a quantum wave state is a superposition of possible measurement outcomes (where those possible outcomes are called “eigenstates” of the chosen “measurement operator”)... and we never observe or measure a superposition.  So either the quantum wave state at some point “collapses” into one of the possible measurement outcomes (in which case the wave state is not always linear or universally valid), or it simply appears to collapse as the superposition entangles with (and gets amplified by) the measuring device and ultimately the observer himself, so that the observer evolves into a quantum superposition of having observed mutually exclusive measurement outcomes.  This second situation is called the Many Worlds Interpretation (“MWI”) of QM.

I regard MWI as a nonstarter and give specific reasons why it is nonsensical in the Appendix of this paper.  But there is another deeper reason why I reject MWI: it is a pseudoscientific religion that is lent credibility by many well-known scientists, among them Sean Carroll.  Essentially, neither MWI nor the concept of a Multiverse (which is mathematically equivalent to MWI, according to Leonard Susskind) is empirically testable, which already excludes them from the realm of science.  But more importantly, they both posit the concept of infinity to overcome the fine-tuning problem or Goldilocks Enigma in physics.  People like Carroll don’t like the notion that our universe (which appears “fine-tuned” for the existence of intelligent life) is extraordinarily unlikely, a fact that many (including me) suggest as evidence for the existence of a Creator.  So to overcome odds that approach zero, they simply assert (with no empirical evidence whatsoever) the existence of infinitely many worlds or universes, because 0 * ∞ = 1.  That is, infinity makes the impossible possible.  But just as anything logically follows from a contradiction, anything follows from infinity – thus, infinity is, itself, a contradiction.

Suffice it to say that I’m reasonably sure that at some point a quantum wave state stops being universal.  Call it “collapse” or “reduction” if you will, but the idea is that at some point an object goes from being in a superposition of eigenstates to one particular eigenstate.  (Later in this post, when I discuss the in-principle impossibility of Schrodinger’s Cat, it won’t actually make any difference whether wave state collapse is actual or merely apparent.)  With regard to information, some have characterized this as keeping information constant (e.g., Rovelli), as decreasing the amount of information (e.g., Aaronson), or as increasing the amount of information (e.g., Davies). 

Anyway, here’s what I think: the information in the universe is contained in correlations between entangled objects, and essentially every object is correlated directly or indirectly to every other object (i.e., universal entanglement).  That information is finite, but additional interactions/events between objects (and/or their fields) may increase the information.  (Quick note: whether or not “objects” exist at all, as opposed to just fields, doesn’t matter.  Art Hobson might say that when I throw a rock, all I experience is the electrostatic repulsion between the fields of the rock and my hand, but that doesn’t change that I can treat it as a physical object on which to make predictions about future interactions/events.)  I gave an example using classical reasoning in this post and in this paper, but the idea is very simple. 

For example, imagine a situation in which object A is located either 1cm or 2cm from object B, by which I mean that information in the universe exists (in the form of correlations with other objects in the universe) to localize object A relative to object B at a distance of either 1cm or 2cm.  (As wacky as this situation sounds, it’s conceptually identical to the classic double-slit interference experiment.)  That is, there is a fact – embedded in correlations with other objects – about objects A and B not being separated by 3cm, or 0.5cm, or 1000 light-years, etc., but there is not a fact about whether object A is separated from object B by a distance of 1cm or 2cm.  It’s got nothing to do with knowledge.  It’s not that object A is “secretly” located 1cm from object B and we just don’t know it.  Rather, there just is no fact about whether object A and B are separated by 1cm or 2cm.  (If it were simply a question of knowledge, then we wouldn’t see quantum interference.)

That’s quantum superposition.  In other words, if at some time t0 there is no fact about whether object A and B are located 1cm or 2cm apart, then they exist in a (location) superposition.   Object A would say that object B is in a superposition, just as object B would say that object A is in a superposition.  We might call this relativity of superposition.  It was in this post that I realized that a superposition of one object exists relative to another object, and both objects have the same right to say that the other object is in superposition.  Compare to Special Relativity: there is a fact about an object's speed relative to another, and each object can equally claim that the other is moving at that speed, even though it makes no sense to talk of an object's speed otherwise.  Similarly, there may be a fact about one object being in superposition relative to another, with each object correctly claiming that the other is in superposition, even though it makes no sense to talk of an object in superposition without reference to another object.

Whether or not a superposition exists is a question of fact.  If a superposition exists (because the facts of the universe are inadequate to reduce it), then the rules of quantum mechanics, which depend on interference, apply to probabilistic predictions; if a superposition does not exist, then ordinary classical probability will suffice because interference terms vanish.  If at some time t1 an event occurs that correlates objects A and B in a way that excludes the possibility of their being separated by 2cm, then that correlating event is new information in the universe about object A being located 1cm from object B.  Importantly, that information appears at time t1 and does not retroactively apply.  We cannot now say that objects A and B were in fact separated by 1cm at time t0 but we simply didn’t know.  Indeed, this is the very mistake often made in the foundations of physics that I addressed in this soon-to-be-published paper.  Said another way, if an object’s superposition is simply the lack of a relevant fact, then the measurement of that object in a manner (a “measurement basis”) that reduces the superposition is new information.  By “measurement,” I simply mean the entanglement of that object with other objects in the universe that are already well correlated to each other.

By the way, I have no idea how or why the universe produces new information when an event reduces a quantum superposition, but this is not a criticism of my explanation.  Either new information arises in the universe or it doesn’t, but since we have no scientific explanation for the existence of any information, I don’t see how the inexplicable appearance of all information at the universe’s birth is any more intellectually satisfying than the inexplicable appearance of information gradually over time.

I should also mention that when I say “superposition,” I almost always mean in the position basis.  The mathematics of QM is such that a quantum state (a unit-length ray in Hilbert space) can be projected onto any basis so that an eigenstate in one basis is actually a superposition in another basis.  However, the mathematics of QM has failed to solve many of the big problems in the foundations of physics and has arguably rendered many of them insoluble (at least if we limit ourselves to the language and math of QM).  I have far more confidence in the explanatory powers of logic and reason than the equations of QM.  So even though I fully understand that, mathematically, every pure quantum state is a superposition in some basis, when I say an object is in superposition, I nearly always mean that it is in a location or position superposition relative to something else.  There are lots of reasons for this choice.  First, I don’t really understand how a measurement can be made in anything but the position basis; other scholars have made the same point, so I’m not alone.  We typically measure velocity, for example, by measuring location at different times.  We could measure the velocity of an object by bouncing light off it and measuring its redshift, but without giving it a great deal of thought, I suspect that even measuring redshift ultimately comes down to measuring the location of some object that absorbs or scatters from the redshifted photon.  And when I say that we only measure things in the position basis, I don’t just mean in a lab... our entire experience all comes down to the localization of objects over time.  In other words, the most obvious way (and arguably the only way) to imagine a quantum superposition is in the position basis.

Second, the universe has clearly already chosen the position basis as a preferred basis.  Objects throughout the universe are already well localized relative to each other.  When an object exists in a (location) superposition, other objects and fields are constantly bathing that object to localize it and thereby reduce or decohere the superposition in the position basis.  In fact, it is the localizing effects of objects and fields throughout the universe that makes the creation of (location) superpositions of anything larger than a few atoms very difficult.  The concept of decoherence can explain why superpositions tend to get measured in the basis of their dominating environment, but does not explain why the universe chose the position basis to impose on superpositions in the first place.  Nevertheless, there is something obviously special about the position basis.

Transitivity of Correlation

Because information exists in the form of correlations between objects that evidence the occurrence of past events (and correspondingly limit future possible events), that information exists whether or not observers know it about their own subsystem, a different correlated subsystem, or even a different uncorrelated subsystem.

Consider an object A that is well correlated in location to an object B, by which I mean that relative to object A, there is a fact about the location of object B (within some tolerance, of course) and object B is not in a location superposition relative to object A.  (Conversely, relative to object B, there is a fact about the location of object A and object A is not in a location superposition relative to object B.)  Object A may be well correlated to object B whether or not object A “knows” the location of B or can perform an interference experiment on an adequate sampling of identically prepared objects to show that object B is not in a location superposition relative to object A.  The means by which objects A and B became well correlated is irrelevant, but may be due to prior interactions with each other and each other’s fields (electromagnetic, gravitational, etc.), mutual interaction with other objects and their fields, and so forth.  Now consider an object C that is well correlated in location to object B; object C must also be well correlated to object A.  That is, if object C is not in a location superposition relative to object B, then it is not in a location superposition relative to object A, whether or not object A “knows” anything about object C or can perform an interference experiment to test whether object C is in a location superposition relative to object A.

I’ll call this notion the transitivity of correlation.  It seems insanely obvious to me, but I can’t find it in the academic literature.  Consider a planet orbiting some random star located a billion light years away.  I certainly have never interacted directly with that planet, and I may have never even interacted with an object (such as a photon) that has been reflected or emitted by that planet.  Nevertheless, that planet is still well localized to me; that is, there is a fact about its location relative to me to within some very, very tiny Planck-level fuzziness.  I don’t know the facts about its location, but if I were to measure it (to within some tolerance far exceeding quantum uncertainty), classical calculations would suffice.  I would have no need of quantum mechanics because it is well correlated to me and not in a superposition relative to me.  This is true because of the transitivity of correlation: the planet is well correlated to its sun, which is well correlated to its galaxy, which is well correlated to our galaxy, which is well correlated to our sun, etc.

The thing is – everything in the universe is already really, really well correlated, thanks to a vast history of correlating events, the evidence of which is embedded in mutual entanglements.  But for the moment let’s imagine subsystem A that includes a bunch of well-correlated objects (including object 1) and subsystem B that includes its own bunch of well-correlated objects (including object 2), but the two subsystems are not themselves well correlated.  In other words, they are in a superposition relative to each other because information does not exist to correlate them.  From the perspective of an observer in A, the information that correlates the objects within B exists but is unknown, while information that would well-correlate objects 1 and 2 does not exist.  However, events/interactions between objects 1 and 2 creates new information to reduce their relative superpositions and make them well correlated.  Then, because objects in A are already well correlated to object 1, while objects in B are already well correlated to object 2, the events that correlate objects 1 and 2 correspondingly (and “instantaneously”) correlate all the objects in subsystem A to all the objects in subsystem B.

This is a paraphrasing of what Einstein called “spooky action at a distance” (and also what many scholars have argued is a form of weird or impermissible nonlocality in QM).  But explained in the manner above, I don’t find this spooky at all.  Rather, from the perspective of an observer in subsystem A, unknown facts of past events are embedded in entanglements within subsystem B, while there simply are no facts (or perhaps inadequate facts) to correlate subsystems A and B.  Once those facts are newly created (not discovered, but created) through interactions between objects 1 and 2, the preexisting facts between objects in subsystem B become (new) facts between objects in both subsystems.  Let me say it another way.  An observer OA in subsystem A is well correlated to object 1, and an observer OB in subsystem B is well correlated to object 2, but they are not well correlated to each other; i.e., they can both correctly say that the other observer is in a superposition.  When object 1 becomes well correlated to object 2, observer OA becomes well correlated to observer OB.  This correlation might appear “instantaneous” with the events that correlate objects 1 and 2, but there’s nothing spooky or special-relativity-violating about this.  Rather, observer OA was already well correlated to object 1 and observer OB was already well correlated to object 2, so they become well correlated to each other upon the correlation of object 1 to object 2.

Of course, because everything in the universe is already so well correlated, the above scenario is only possible if one or both of the subsystems are extremely small.  The universe acts like a superobserver “bully” constantly decohering quantum superpositions, and in the process creating new information, in its preferred (position) basis.  Still, if the universe represents subsystem A, then a small subsystem B can contain its own facts (i.e., embedded history of events) while being in superposition relative to A.  Imagine subsystem B containing two correlated particles P1 and P2 – e.g., they have opposite spin (or opposite momentum).  When the position of particle P1 is then correlated (e.g., by detection, measurement, or some other decoherence event) to objects in subsystem A (i.e., the rest of the universe), that position corresponds to a particular spin (or momentum).  But because particle P1 was already correlated to its entangled particle P2, the spin (or momentum) of particle P2 is opposite, a fact that preceded detection of particle P1 by the universe.  That fact will be reflected in any detection of particle P2 by the universe.  Further, facts do not depend on observer status.  An observer relative to particles P1 and P2 has as much right to say that the universe was in superposition and that the correlation event (between P1 and objects in the rest of the universe) reduced the superposition of the universe. 

This explanation seems so obviously correct that I don’t understand why, in all my reading and courses in QM, no one has ever explained it this way.  To buttress the notion that facts can exist in an uncorrelated subsystem (and that measurement of that subsystem by a different or larger system creates correlating facts to that subsystem but not within that subsystem), consider this.  As I walk around in the real world, thanks to natural quantum dispersion, I am always in quantum superposition relative to the rest of the world, whether we consider my center of mass or any other measurable quantity of my body.  Not by much, of course!  But given that the universe does not contain infinite information, there must always be some tiny superposition fuzziness between me and the universe – yet that doesn’t change the fact that my subsystem includes lots of correlating facts among its atoms.

Killing Schrodinger’s Cat

I tried to explain in this draft paper why Schrodinger’s Cat and Wigner’s Friend are impossible in principle, but the explanation still eludes the few who have read it.  The following explanation will add to the explanation I gave in that draft paper.  The idea of SC/WF is that there is some nonzero time period in which some macroscopic system (e.g., a cat) is in an interesting superposition (e.g., of states |dead> and |alive>) relative to an external observer.  It is always (ALWAYS) asserted in the academic literature that while detecting such a superposition would be difficult or even impossible in practice, it is possible in principle. 

Let’s start with some object in superposition over locations A and B, so that from the perspective of the box (containing the SC experiment) and the external observer, its state is (unnormalized) superposition state |A> + |B>.  However, from the perspective of the object, the box is in a superposition of being located in positions W and X in corresponding states |boxW> and |boxX> and the observer is in a superposition of being located in positions Y and Z in corresponding states |obsY> and |obsZ>.  But remember that the box and observer are, at the outset of the experiment, already well correlated in their positions, which means that from the object’s perspective, the system is in state |boxW>|obsY> + |boxX>|obsZ>.  When the object finally gets correlated to the box, it “instantly” and necessarily gets correlated to the observer.  It makes no difference whether the quantum wave state actually collapses/reduces or instead evolves linearly and universally.  Either way – whether the wave state remains |boxW>|obsY> + |boxX>|obsZ> or collapses into, say, |boxW>|obsY> – there is never an observer who is not yet correlated to the box and who can do an interference experiment on it to confirm the existence of a superposition.  Once the object “measures” the position of the box, it inherently measures the position of the observer, which means that there is never an observer for whom the box is in a superposition (unless the box is already in a superposition relative to the observer, which, as I pointed out in the draft paper, is impossible because of very fast decoherence of macroscopic objects).

In Eq. 1 of the draft paper, I show a simple von Neumann progression, with each arrow (à) representing a time evolution.  If it’s right, then there is a moment when the measuring system is in superposition but the observer is not.  The problem with that conclusion, as I’ve been trying to explain, is that because the observer is already well correlated to the measuring system (and the box, cat, etc.) to within a tolerance far better than the distance separating the object’s eigenstates |n>, correlation of the object’s location to that of the measuring device “instantly” correlates the observer and the rest of the universe.  Once there is a fact (and thus no superposition) about the object’s location relative to the measuring device, there is also a fact (and thus no superposition) about the object’s location relative to the observer.  There is no time at which the observer can attempt an interference experiment to confirm that the box (or cat or measuring device, etc.) are in a superposition.

Therefore, the SC and WF experiments are impossible in principle.  An MWI apologist might retort that Schrodinger’s cat is, indeed, in a superposition, along with the observer.  But since there is no time at which an interference experiment could be performed, even in principle, to confirm this, their claim is both unscientific and useless.  They may as well say that unicorns exist but are impossible to detect.

Other Thoughts and Implications

CCCH.  In this post, I heavily criticized a paper that incorrectly asserted that the consciousness-causes-collapse hypothesis (“CCCH”) has already been empirically falsified.  I did so because I despise bad logic and bad science, not because I endorse CCCH.  Indeed, if my explanation of QM is correct, then collapse (or apparent collapse) of the quantum wave function has nothing to do with consciousness but is rather the result of new information produced from correlating interactions with the environment/universe.

The Damn Cat.  What I haven’t discussed so far are “interesting” evolutions due to amplifications of quantum events.  The argument above, which is an extension of the argument in my draft paper on Schrodinger’s cat, is essentially that quantum amplification of a tiny object in superposition cannot place the macroscopic box containing SC in a superposition relative to the observer any more easily than the box itself can naturally disperse (via quantum uncertainty) relative to the observer.  And decoherence by objects and fields in the universe makes adequate dispersion of the box impossible even in principle.  But there’s more.  If I am right in my explanation of QM, then interacting subsystems will agree on the facts embedded in their correlations.  For example, if subsystem B is in a superposition of being located 1cm and 2cm from subsystem A, then when an observer in subsystem A “measures” B at a distance of, say, 1cm, then from the perspective of an observer in subsystem B, B measured A also at a distance of 1cm.

In the case of SC (and WF), I analyzed them in terms of fuzziness of objects, such as a particular carbon atom that would have been located in the live cat’s brain is instead located in the dead cat’s tail, thus requiring a quantum fuzziness to span a meter or so.  But of course SC is far more interesting: in one case there is a live cat and in another case there is a dead cat, represented by a vastly different set of correlations among its constituent atoms. 

In order for a SC superposition to actually be produced relative to the external observer (and the universe to which he is well correlated), it must be the case that a “comparable” superposition of the universe is produced relative to SC.  Then, when an event occurs that correlates the two systems – which, remember, can ultimately be traced back to the location of some tiny particle at A or B, separated by some tiny distance – observers in each of the two systems will agree on the correlations.  So let’s say we’ve somehow created a SC superposition.  We wait a few minutes, pop a bottle of champagne to celebrate the amazing feat, and then we open the box to look, at which point see a live cat – that is, we (and the rest of the universe) become correlated with |live>.  But since the correlations among the atoms in the box exist before we open the box, then the hypothetical state |dead> must be correlated with a universe that would have seen that exact set of facts as a dead cat.  How does one measure a live cat as dead?  Remember, we are not just talking about measuring a heartbeat, etc... we are talking about a universe that is constantly inundating the cat’s atoms in a way so that every observer in that universe would observe a dead cat.  That is, if it were possible to produce a cat in a superposition of |dead> and |alive> inside a box, then from the perspective of an observer inside the box, the universe would have to be in a superposition of being in a state that would measure a set of atoms as being a dead cat and another state that would measure the same set of atoms as being a live cat.  Ridiculous.

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