Tuesday, May 19, 2020

It is Impossible to Measure a Quantum Superposition

In a previous post, I discussed how and to what extent gravity might prevent the existence of macroscopic quantum superpositions.  There has been surprisingly little discussion of this possibility and there is still debate on whether gravity is quantized and whether gravitational fields are, themselves, capable of existing in quantum superpositions.

Today I came across a paper, "Experiments testing macroscopic quantum superpositions must be slow," by Mari et al., which proposes and analyzes a thought experiment involving a first mass mA placed in a position superposition in Alice’s lab, the mass mA producing a gravitational field that potentially affects a test mass mB in Bob’s lab (separated from Alice’s lab by a distance R), depending on whether or not Bob turns on a detector.  The article concludes that special relativity puts lower limits on the amount of time necessary to determine whether an object is in a superposition of two macroscopically distinct locations.

The paper seems to have several important problems, none of which have been pointed out in papers that cite it, notably this paper.  For example, its calculation of the entanglement time TB assumes that correlation of the location of test mass mB with the gravitational field of mass mA occurs when the change in position δx of the test mass mB exceeds its quantum uncertainty Δx, which seems like a reasonable argument – except that they failed to include the increase in quantum uncertainty due to dispersion.  (This is particularly problematic where they let Δx be the Planck length!)  Another problem is their proposed experiment in Section IV: Alice is supposed to apply a spin-dependent force on the mass mA which results in different quantum states, depending on whether or not Bob turned on the detector, but both quantum states correlate to mass mA located at L (instead of R).  The problem is that by the time she has applied the force, Bob’s test mass mB has presumably already correlated to the gravitational field produced by Alice’s mass mA located at L or R, but how could that happen before Alice applied the force that caused the mass mA to be located at L?

But the biggest problem with the paper is not in their determination of the time necessary to determine whether an object is in a superposition of two macroscopically distinct locations.  No – the bigger problem is that, as far as I understand, there is no way to determine whether an object is in a superposition at all! 

Wait, what?  Obviously quantum superpositions exist.

Yes, but a superposition is determined by doing an interference experiment on a bunch of “identically prepared” objects (or particles or masses or whatever).  The idea is that if we see an interference pattern emerge (e.g., the existence of light and dark fringes), then we can infer that the individual objects were in coherent superpositions.  However, detection of a single object never produces a pattern, so we can’t infer whether or not it was in a superposition.  Further, the outcome of every interference experiment on a superposition state, if analyzed one detection at a time, will be consistent with that object not having been in superposition.  A single trial can confirm that an object was not in a superposition (such as if we detect a blip in a dark fringe area), but no single trial can confirm that the object was in a superposition.  Moreover, even if a pattern does slowly emerge after many trials, every pattern produced by a finite number of trials – and remember that infinity does not exist in the physical world – is always a possible random outcome of measuring objects that are not in a superposition.  We can never confirm the existence of a superposition, but lots and lots of trials can certainly increase our confidence.

In other words, if I’m right, then every measurement that Alice makes (in the Mari paper) will be consistent with Bob's having turned the detector on (and decohered the field) -- thus, no information is sent!  No violation of special relativity!  No problem!

Look, I could be wrong.  I’ve been studying the foundations of quantum mechanics independently for a couple of years now, and very, very few references point out that there’s no way to determine if any particular object is in a quantum superposition, which is also why it’s taken me so long to figure it out.  So either I’m wrong about this, or there’s some major industry-wide crazy-making going on in the physics community that leads to all kinds of wacky conclusions and paradoxes... no wonder quantum mechanics is so confusing!

Is there a way to test whether a particular object is in a coherent superposition?  If so, how?  If not, then why do so few discussions of quantum superpositions mention this?

Update to this post here

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