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 f

_{L}and f_{R}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 t_{1}and it correlates to f_{L}. 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 f

_{L}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 f_{L}– specifically, mass A must have been located at L on or before time (t_{1}- 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 t_{1}, the wave state of mass A seems to have collapsed at time (t_{1}- d/c)... also from the perspective of mass A at time t_{1}, the wave state of mass B seems to have collapsed at time (t_{1}- 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!

I think you're making this more complicated than it need to be by assuming Local Realism, which the 2022 Nobel prize pretty much threw out the window if I understand it correctly.

ReplyDeleteYou're assuming that if we see f-sub-L acted on B when the superposition decoheres, it must have always been in location L is assuming Realism and misunderstanding that when an object is in a superposition it doesn't actually exist as a real object, but as a probability.

I'm by no means an expert here (amateur hobbyist at most), I think reading more about the 2022 Nobel prize for physics and Local Realism may help solve your problem here.

Good read, thanks!

-AR

Thanks for the note. As for realism, I assert that for an object in superposition, there is no fact as to its position. Regarding relativity of superpositions, the extent to which there is a fact about an object (such as its position) is relative to another object (such as a measuring device) to which it is compared.

ReplyDeleteThis seems like it would have to do with quantum gravity, which doesn't have an established theory as far as I know.

ReplyDeleteBut even though this is dealing with quantum gravity, I don’t see how this is any different that any other force or field an object in superposition would exert on another object. What's the difference?