{"id":4914,"date":"2010-08-02T11:37:06","date_gmt":"2010-08-02T11:37:06","guid":{"rendered":"http:\/\/scienceblogs.com\/principles\/2010\/08\/02\/quantum-measurement-lotto\/"},"modified":"2010-08-02T11:37:06","modified_gmt":"2010-08-02T11:37:06","slug":"quantum-measurement-lotto","status":"publish","type":"post","link":"http:\/\/chadorzel.com\/principles\/2010\/08\/02\/quantum-measurement-lotto\/","title":{"rendered":"Quantum Measurement Lotto"},"content":{"rendered":"

Thoreau at Unqualified Offerings gets credit for inspiring two posts today with his proposed Murphy’s Law experiment<\/a> and this one, about an unrelated issue in quantum measurement. This is an analogy suggested by a colleague a couple of years ago, comparing the projection of a quantum wavefunction in the measurement process to the lottery.<\/p>\n

The classic example of this problem is something like the double slit experiment with single particles<\/a>. You have some position-sensitive detector that we can imagine as being made up of a large number of pixels, each having some probability of detecting a particle in the next little interval of time. When one of these detectors registers a particle, the probability of detection at any of the other detectors instantly drops to zero (either because there’s been some real collapse of the wavefunction, or because decoherence has separated all the branches corresponding to detections by the various pixels into their own “universes”– it doesn’t really matter which). This strikes a lot of people as being problematic when they first hear it. After all, if you have enough detectors, this would seem to run afoul of relativity– if the particle is detected in one corner, the probability of finding it in the opposite corner goes to zero faster than a light-speed signal could travel from one corner to the other. This seems to involve some “spooky action at a distance” (to slightly misappropriate a great phrase from Einstein).<\/p>\n

My colleague, Jon Marr, suggests the lottery as an example of a classical analogue to this situation.<\/p>\n

<\/p>\n

In the analogy, the role of the individual pixels is played by the many lottery tickets in circulation. Prior to the drawing of the number, each ticket has an equal probability of winning, but at the instant the drawing is completed, one ticket is selected as the winner, and all the rest are instantaneously projected into the “loser” state. This projection happens immediately, even though it may be some time before the holders of the tickets find out what happened.<\/p>\n

This fits best with an information-oriented approach to quantum mechanics, I think. The “instantaneous” change, as in the pixel case, is a change in something you don’t measure directly, and you don’t end up with complete information about the situation until some time has passed– if you imagine individual observers monitoring each pixel, they may know that their own pixel has not recorded a particle instantaneously (assuming they know the expected arrival time of the particle well enough), but they won’t know which pixel did<\/em> detect the particle until enough time has passed to get a message from the “winning” pixel. This is one of the factors that keeps you from being able to violate causality using quantum measurement.<\/p>\n

When Jon first suggested this, I thought there was some problem with the analogy, beyond the fact that I didn’t think of it first. I didn’t use it in the book<\/a> because dogs don’t buy lottery tickets, but I can no longer remember what my other problem with it was. In keeping with Furr’s Law, though, posting it here will generate a nearly instantaneous complaint in comments that will remind me what the problem was, or point out some other flaw. Pending that, though, I kind of like this.<\/p>\n","protected":false},"excerpt":{"rendered":"

Thoreau at Unqualified Offerings gets credit for inspiring two posts today with his proposed Murphy’s Law experiment and this one, about an unrelated issue in quantum measurement. This is an analogy suggested by a colleague a couple of years ago, comparing the projection of a quantum wavefunction in the measurement process to the lottery. The… Continue reading Quantum Measurement Lotto<\/span><\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"1","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[13,7,23,11],"tags":[425,426,92,93,427,88],"class_list":["post-4914","post","type-post","status-publish","format-standard","hentry","category-education","category-physics","category-quantum_optics","category-science","tag-analogy","tag-lottery","tag-physics-2","tag-quantum","tag-quantum-measurement","tag-science-2","entry"],"_links":{"self":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/4914","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/comments?post=4914"}],"version-history":[{"count":0,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/posts\/4914\/revisions"}],"wp:attachment":[{"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/media?parent=4914"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/categories?post=4914"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/chadorzel.com\/principles\/wp-json\/wp\/v2\/tags?post=4914"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}