## September 27, 2007

### A quantum measurement paradox: the reallocation by measurement problem

I spend lots of time thinking about puzzling foundational issues in quantum mechanics (search for "quantum measurement paradox" and I often show in the top five), and do I have a deal for anyone else like me. I have been thinking of this problem for awhile, and the post on Uncertain Principles stimulated me to post a version of it. If you want something really strange and "after the fact" about measurement, please consider my following proposal: In a Mach-Zehnder interferometer, insert a gray filter G into leg L2. Given a traditional stream of light, that alters the amplitudes delivered to the beam-splitter/recombiner R. With a 25% transmitting filter, the L2 amplitude is 0.5 of that in L1 (which itself is sqrt (0.5) of the original pre-split input.) Hence, with symmetrical R, we get an output mix rather than all A channel output. We can adjust R to a compensatory split so that output is again all A channel. Using individual photons, the statistics should be the same. FEL optical physicist Michelle Shinn of J-Lab agreed with me that's so, despite the weirdness of the photon's wave function in L2 being attenuated by the chance that it could have been absorbed, even if it wasn't (well, superposition of absorption and not-absorption in the dye molecules in the filter, etc, right?) Also, as G gets darker, this has to be the limiting factor approaching the results of an opaque stop in L2. But what happens if we can find out whether a photon has been absorbed in the filter?

Consider an opaque stop: the stop clearly "reallocates" the WF all into L1, in a manner akin to the Renninger negative result problem, even though no actual "measurement" is takeną„¤ But there, a photon will just never get through. However, G may or may not absorb a photon, something we can in principle check on (There are semi-transparent optical detectors, no? Just consider film for example.) Now, while G is still "deciding" (in a state of superposition) whether it will absorb or not, it makes sense to consider the L2 wave to be attenuated relative to L1. Maybe that's the normal time scale to allow interference in R before that happens. But, after a certain time, if we check G carefully to look for evidence of absorption, it should be settled: absorption or not. If it did, there's no paradox. But if we find "no absorption," why in the world should the L2 wave continue attenuated? The measurement result was "no" for G, so there is no longer "a chance" that the photon might end up there. The filter might as well have been clear glass, right? If so, then the interference at R would be different (it would follow normal equal-balance rules instead.)

The really weird thing is, that reallocation should take place as soon as the absorption/detection issue is settled. If so, we could manipulate the pattern of hits (with sequential photon shots) at the output by looking for evidence of absorption in the filter, which would start rearranging the WF as per Renninger etc. In principle, there's nothing to stop this from being a true FTL signal, since manipulating G (or perhaps the distance to R) causes noticeable effects (not distant signal correlations) at R. Sure, that's problematical, but you can't just blow off the supposed effect on the WF of the negative measurement in G, can you? Have fun.
(I also just put this up on sci.optics, sci.physics, etc.)

Carl said...

Neil, This does not work. You cannot readjust R to compensate for G in L2.
That requires some wavefunction amplification in R that is forbidden in QM. You can only adjust for phase in R and that will not do the trick.

Carl

31/10/07 20:23
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23/12/07 21:29
CarlBrannen said...

Neil, your comment "Yes, that sounds weird, but: if you imagine (whatever that means) that the first BS splits the beam into two waves, and just deal with "waves" until there's an actual "collapse" at the detector, it makes sense." is exactly dead on correct, and it points out an interpretation of measurement.

If you define "event" as something defined by 4 coordinates such as (x,y,z,t), then you end up having a problem assigning coordinates to the events in this problem. The QM guys might tell you that it doesn't make sense to break apart a QM problem (and Feynman implied it will make you insane, LOL).

The problem in assigning events this way is that the wave description of QM and the particle description are descriptions of the same events. So to split them, and separate the wave function description of the experiment from the particle description, you need to add another coordinate to your events.

Call the new coordinate T and let it mean the age of the universe. So the 5 coordinates are (x,y,z,t,T). Little t gives the time position of the event relative to the creation of the universe. So if the experiment is run on January 3rd, then t is January 3rd.

T, on the other hand, gives the age of the universe and is either greater or less than t depending on whether the experiment is in the observer's past (t < T) or in the future (t > T).

Then measurement is something that happens as the universe gets older. As T increases and passes t, the wave functions become more sharply peaked until finally a consistent history is picked out.

Then the probability assumption of QM becomes a statement about what happens as the process of time ages a wave function.

Of course we can't measure how fast the universe ages because the only tools we have measure the difference between the "t" of events. So our speeds are always things like dx/dt and cannot be things like dx/dT.

All this adds extra complication to QM without any extra improvement in how to calculate things. So I really see no reason to push it. However, it does allow one to understand a relationship between waves and probabilities that is compatible with our personal feeling of the passage of time.

And it eliminates the quantum paradoxes with photons. The energy of the photon gets stuck into any of the possible choices as its wave function gets sharpened into a delta function peaked on the result.

By the way, I'm not the "Carl" who wrote the (wrong) comment above.

31/12/07 23:17
Neil' said...

Carl, thanks for the input. The main point of my post, however, is not the overall issue of measurement, but the following: the gray filter supposedly attenuates the amplitude of the photon wave function even though it didn't actually absorb the photon: it "could have", meaning the photon had a chance of being absorbed in that gray filter. That attenuated amplitude is shown in the recombination statistics.

To me, that's weird (even in the context of the "weirdness" of wave-particle duality already being accepted as a given) because it seems like, if the photon doesn't get absorbed by the gray filter that filter "might as well not have been there in the first place." What might have happened to the photon at one place becomes an actual effect somewhere else (pls. note that the statistics for intermittent complete blocking in that channel are not the same as for a gray filter transmitting the same fraction.)

On top of that, there's an entanglement-type issue: what if we study the gray filter so we know the photon isn't absorbed there even before the photon is found in a detector elsewhere? Does that make a difference?

1/1/08 21:38
D said...

OK, so I have to admit that we're getting beyond my ken here. I was able to understand the article you linked, but without a picture of your own thing, I think I'm going to be helpless here (I haven't done physics in years).

As for the other article, the most sense I can make of the experiment is that it confirms the observer effect in a particularly strong sense without clearly saying which interpretation is correct. We've still got the possibility of hidden variables (as always), or there could be many worlds, or just the one with some genuine randomness which we're somehow "breaking" with the second splitter.

Optics is weird. QM is weird. OK, maybe a single photon breaks up into a wave, and then you get no interference the one way because the "half-photon" tunnels through at the second splitter? But... argh, I don't know. Even if that wild speculation is right, I can't justify believing in it.

12/10/09 23:21
Anonymous said...