## Thursday, June 11, 2020

### Quantum Superpositions Are Relative

At 4AM I had an incredible insight.

Here’s the background.  I’ve been struggling recently with the notion of gravitational decoherence of the quantum wave function, as discussed in this post.  The idea is neither new nor complicated: if the gravitational field of a mass located in Position A would have a measurably different effect on the universe (even on a single particle) than the mass located in Position B, then its state cannot be a superposition over those two locations.

Generally, we think of impacts between objects/particles as causing the decoherence of a superposition.  For instance, in the typical double-slit interference experiment, a particle’s wave state “collapses” either when the particle impacts a detector in the far field or we measure the particle in one of the slits by bouncing a photon off it.  In either case, one or more objects (such as photons), already correlated to the environment, get correlated to the particle, thus decohering its superposition.

But what if the decohering “impact” is due to the interaction of a field on another particle far away?  Given that field propagation does not exceed the speed of light, when does decoherence actually occur?  That’s of course the question of gravitational decoherence.  Let’s say that mass A is in a superposition over L and R locations (separated by a macroscopic distance), which therefore creates a superposition of gravitational fields fL and fR that acts on a distant mass B (where masses A and B are separated by distance d).  For the sake of argument, mass B is also the closest object to mass A.  Let’s say that mass B interacts with the field at time t1 and it correlates to fL.  We can obviously conclude that the state of mass A has decohered and it is now located at L... but when did that happen?  It is typically assumed in quantum mechanics that “collapse” events are instantaneous, but of course this creates a clear conflict between QM and special relativity.  (The Mari et al. paper in fact derives its minimum testing time based on the assumption of instantaneous decoherence.)

This assumption makes no sense to me.  If mass B correlates to field fL created by mass A, but the gravitational field produced by mass A travels at light speed (c), then mass A must have already been located at L before mass B correlated to field fL – specifically, mass A must have been located at L on or before time (t1 - d/c).  Thus the interaction of mass B with the gravitational field of mass A could not have caused the collapse of the wave function of mass A (unless we are OK with backward causation).

So for awhile I tossed around the idea that whenever a potential location superposition of mass A reaches the point at which different locations would be potentially detectable (such as by attracting another mass), then it would produce something (gravitons?) that would decohere the superposition.  In fact, that’s more or less the approach that Penrose takes by suggesting that decoherence happens when the difference in the gravitational self-energy between spacetime geometries in a quantum superposition exceeds what he calls the “one graviton” level.

The problem with this approach is that decoherence doesn’t happen when differences could be detected... it happens when the differences are detected and correlated to the rest of the universe.  So, in the above example, what actual interaction might cause the state of mass A to decohere if we are ruling out the production (or even scattering) of gravitons and neglecting the effect of any other object except mass B?  Then it hit me: the interaction with the gravitational field of mass B, of course!  Just as mass A is in a location superposition relative to mass B, which experiences the gravitational field produced by A, mass B is in a location superposition relative to mass A, which experiences the gravitational field produced by B.  Further, just as from the perspective of mass B at time t1, the wave state of mass A seems to have collapsed at time (t1 - d/c)... also from the perspective of mass A at time t1, the wave state of mass B seems to have collapsed at time (t1 - d/c).

In other words, the “superposition” of mass A only existed relative to mass B (and perhaps the rest of the universe, if mass B was so correlated), but from the perspective of mass A, mass B was in a superposition.  What made them appear to be in location superpositions relative to each other was that they were not adequately correlated, but eventually their gravitational fields correlated them.  When mass B claims that the wave state of mass A has “collapsed,” mass A could have made the same claim about mass B.  Nothing actually changed about mass A; instead, the interaction between mass A and mass B correlated them and produced new correlation information in the universe.

Having said all this, I have not yet taken quantum field theory, and it’s completely possible that I’ve simply jumped the gun on stuff I’ll learn at NYU anyway.  Also, as it turns out, my revelation is strongly related, and possibly identical, to Carlo Rovelli’s Relational interpretation of QM.  This wouldn’t upset me at all.  Rovelli is brilliant, and if I’ve learned and reflected enough on QM to independently derive something produced by his genius, then I’d be ecstatic.  Further, my goal in this whole process is to learn the truth about the universe, whether or not someone else learned it first.  That said, I think one thing missing from Rovelli’s interpretation is the notion of universal entanglement that gives rise to a preferred observer status.  If the entire universe is well correlated with the exception of a few pesky microscopic superpositions, can’t we just accept that there really is just one universe and corresponding set of facts?  Another problem is the interpretation’s dismissal of gravitational decoherence.  In fact, it was my consideration of distant gravitational effects on quantum decoherence, as well as implications of special relativity, that led me to this insight, so it seems odd that Rovelli seems to dismiss such effects.  Another problem is the interpretation’s acceptance of Schrodinger’s Cat (and Wigner’s Friend) states.  I think it extraordinarily likely -- and am on a quest to discover and prove -- that macroscopic superpositions large enough to encompass a conscious observer, even a cat, are physically impossible.  Nevertheless, I still don’t know much about his interpretation so it’s time to do some more reading!