Wednesday, May 6, 2020

The Effect of Gravity in Preventing Macroscopic Quantum Superpositions

In a recent post, I posited that a quantum superposition just exists if and only if the facts of the universe are consistent with the superposition; i.e., a system described at time t by state |A> + |B> just means that there is no fact about whether the system is in state |A> or |B> at time t.  In other words, had the system been measured at time t in a basis that includes elements |A> and |B>, then either outcome A or outcome B would have been measured (with probabilities according to the Born rule), but since it was not measured, then information regarding whether the system was in state |A> or |B> did not exist at time t and no future measurement/observation/fact can contradict that fact.  The production of facts (or the happening of events) over time creates new information that reduces future possibilities.

Thinking about quantum mechanics in this way has helped me immensely in understanding and solving many of the various philosophical problems in QM.  To get feedback on it, I submitted a version of the explanation to an essay contest of the Foundational Questions Institute, entitled “Interpreting Quantum Mechanics and Predictability in Terms of Facts About the Universe,” and a preprint is also available here.

However, apparently this point of view is more revolutionary than I had originally thought.  The typical way to think about or describe a quantum superposition described by state |A> + |B> is that it “is kind of in state |A> and kind of in state |B>” or that it “is in both state |A> and state |B> simultaneously” or something like that.  But these descriptions are inaccurate, sloppy, and just plain wrong. 

For example, it is typical in QM to work with expectation values, such as the expectation of position <X>, which is found by taking a weighted average of an object’s position distribution (i.e., weighted by probability, which is the square of amplitude).  The problem arises when this is treated as something real as opposed to something simply mathematically useful for making predictions.  For instance, if a particle whose position expectation is <X> is actually measured/detected at a location X0 that is somewhere far away from <X>, then do we say there’s been a violation in conservation of energy if X0 and <X> are at different potentials?  Likewise if an object having momentum expectation <P> is measured having momentum P0, but <P>2/2m ≠ P02/2m.

The problem is that there was nothing real about the particle’s location when we calculated <X>.  If we were right that the particle was in a location superposition at time t, then there is no fact, nor will there ever be, about the particle’s location at time t, so there can’t be a violation of conservation of energy by detecting the particle at X0 at a later time if there is no fact about where the particle came from.

For instance, when Roger Penrose, whom I greatly admire, tried to analyze the effect of gravity on quantum state reduction, he postulated that the difference in gravitational self-energy (EΔ) between the spacetime geometries of a quantum superposition “in which one lump [of mass] is in two spatially displaced locations” produces an instability that results in a decay into one or the other of the spacetime eigenstates.  He even goes so far as to give a decay time T ≈ ℏ/EΔ, reminiscent of the quantum uncertainty principle.  The problem, as I see it, is that he treated the “two” lumps (in the superposition) as real, so real in fact that he requires taking into account “the gravitational interaction effects between the pair of lumps.”  What pair of lumps?!  There is only one lump!

But this (mis)understanding of QM seems to permeate the field.  So far, I have been unable to find my characterization of QM in the academic literature.  It certainly may be out there, but I feel comfortable in saying that nearly all characterizations of a quantum superposition treat it as if the terms represent something real.  For instance, in the classic Schrodinger’s Cat thought experiment (which is essentially the same as the Wigner’s Friend thought experiment), we are given a quantum state of the cat |Ψ> = |alive> + |dead>, which is a linear superposition of a state in which the cat is alive and one in which it is dead.  QM tells us that the likelihood of finding the cat in one state or another depends on the square of the amplitudes, which I’ve left out for simplicity.

So here’s the classic conundrum: before we look, is the cat dead or alive?  The answer: there is no fact about it being dead or alive until evidence exists (in the form of a correlation somewhere in the universe) that it is one or the other.  Until that information exists, there simply is no fact.  The real difficulty in this thought experiment, which almost no one points out, is the extreme difficulty (and likely impossibility) of creating state |Ψ> = |alive> + |dead> in the first place.  To do so requires that there is no evidence anywhere (beyond the cat itself, of course, which we assume is thermally isolated) of the cat’s being dead or alive.  Even a single photon bouncing off the cat – and keep in mind that the universe is inundated with radiation, such as CMB – would almost certainly provide evidence correlated to its being either dead or alive.

Getting back to Penrose’s paper, in making his argument about a superposition of spacetimes, he points out that “these two space-time geometries differ significantly from each other.”  But my question is this: how could such a superposition arise in the first place?  If I am right that a superposition exists if and only if the facts of the universe are consistent with the superposition, then what would it mean if there was a “significant difference” between two (or more) eigenstates?  If we say, “There would have been a significant difference had that difference been measured but it wasn’t actually measured,” then that does not justify Penrose’s treatment of the spacetime geometries as being actually significantly different.  But to say “There is a significant difference” is wrong because: by whose standards?  By what measure?  After all, if there is a measure (in the form of evidence anywhere in the universe) by which the spacetime geometries are different, then there could not have been a superposition!

The thing is – gravity may be weak (e.g., the electromagnetic attraction between a proton and electron in a hydrogen atom is something like 1040 greater than their gravitational attraction), but it is ubiquitous in the universe and always attractive.  So my question is this: wouldn’t gravity effectively prevent any macroscopic superposition?  To use Penrose’s example, imagine a macroscopic lump of matter near Earth that we are somehow able to perfectly isolate from the universe (already a ridiculous assumption) to allow it to enter a superposition of macroscopically distinct positions.  A lump creates a gravitational field that is tiny but – as far as we know – potentially affects everything in the universe.  If the gravitational field of the lump located at position A affects even a single particle differently than the field of the lump located at B, then the lump at one of these two positions will be correlated with the rest of the universe and a quantum superposition of the lump at position A and position B cannot exist.  Note that the speed of light is irrelevant here; if the lump’s gravity takes 20 years to affect the trajectory of a particle 20 light-years away, that correlation is enough to ensure that there could not have been a superposition at the time.  (This argument may be related to the production of gravity waves, which I know little about.)

Anyway, my point is that when Penrose discusses a superposition of spacetime geometries that “differ significantly from each other,” then wouldn’t significant differences correlate to measurable differences in effects, events, and/or interactions elsewhere (i.e., outside the isolated system)?  If so, such a superposition could never exist.  Which is to say, as soon as there is a fact in the universe that differentiates the two possibilities, they are no longer both possibilities and there is no superposition. 

I haven’t done the calculation yet, but I suspect that gravity would destroy a macroscopic superposition very quickly.  Interestingly, a group of researchers showed that relativistic time dilation at different heights on the Earth’s surface was enough to decohere a macroscopic quantum superposition pretty quickly.  They showed that an isolated gram-scale object in a superposition of locations vertically separated near Earth’s surface by 1mm would decohere in around a microsecond.  This implies that even a “perfectly isolated” Schrodinger’s Cat experiment could never even get off the ground if located anywhere near a planet; however it says little about performing such an experiment in deep space with flat spacetime curvature.  But even though the word “gravitational” appeared in its title, the article was really about time dilation.  So far, I haven’t found an article that deals with how the gravitational effects of a macroscopic object in different locations would correlate to measurable differences elsewhere in the universe, and how this would prevent macroscopic quantum superpositions.  If it were the case that an isolated system described by |dead> caused some correlated event different than an isolated system described by |alive>, then the superposition |Ψ> = |alive> + |dead> could not exist. 

Of course, the question is not really whether gravitational effects are relevant to the existence of quantum superpositions.  Of course they are.  The sun could not exist in a superposition of a state in which it is located at the center of our solar system and a state in which it is located a light-year away, as the gravitational differences between such states would be heavily correlated to measurable differences in other places in the universe.  (Obviously, other differences besides gravitational differences would decohere any potential superposition long before this point.)  The question is at what scale are gravitational effects relevant to the existence of quantum superpositions.  That may place an upper limit to the size of quantum superpositions and the applicability of QM.  (This whole notion that there is no limit, in principle, to the size of objects in interference experiments is driving me crazy, but I’ll save that rant for another time.)  If the answer happens to be such as to prevent any kind of Schrodinger’s Cat or Wigner’s Friend experiment anywhere in the universe, no matter how isolated, then we can finally stop being confused by (and hearing about) these thought experiments.

Before I spend time doing these calculations or trying to reinvent the wheel, it would be great to know if it’s already been done.  Do you know of any such calculation, article, or research? 

No comments:

Post a Comment