{"id":545,"date":"2012-09-14T13:23:47","date_gmt":"2012-09-14T18:23:47","guid":{"rendered":"http:\/\/blog.richmond.edu\/physicsbunn\/?p=545"},"modified":"2012-09-15T09:05:48","modified_gmt":"2012-09-15T14:05:48","slug":"breaking-news-quantum-mechanics-works-exactly-the-way-everyone-has-known-it-did-for-75-years","status":"publish","type":"post","link":"https:\/\/blog.richmond.edu\/physicsbunn\/2012\/09\/14\/breaking-news-quantum-mechanics-works-exactly-the-way-everyone-has-known-it-did-for-75-years\/","title":{"rendered":"Breaking news: quantum mechanics works exactly the way everyone has known it did for 75 years"},"content":{"rendered":"

Different people like different literary genres. I enjoy a good mystery; you may prefer science fiction, horror, or romance.\u00a0Some people, apparently, can’t get enough of a different genre: breathless news articles claiming that some new result changes our understanding of the foundations of quantum mechanics. Just in the pages of\u00a0Nature<\/em> alone you could find enough of these to while away some long winter evenings.<\/p>\n

I’ve complained about this sort of thing a couple<\/a> of times<\/a> before, and whenever I do I quote John Baez:<\/p>\n

Newspapers tend to report the results of these fundamentals-of-QM experiments as if they were shocking and inexplicable threats to known physics. It\u2019s gotten to the point where whenever I read the introduction to one of these articles, I close my eyes and predict what the reported results will be, and I\u2019m always right. The results are always consistent with simply taking quantum mechanics at face value.<\/p><\/blockquote>\n

Here’s the latest, from\u00a0Nature<\/em><\/a>:<\/p>\n

\u00a0Heisenberg sometimes explained the uncertainty principle as a problem of making measurements. His most well-known thought experiment involved photographing an electron. To take the picture, a scientist might bounce a light particle off the electron’s surface. That would reveal its position, but it would also impart energy to the electron, causing it to move. Learning about the electron’s position would create uncertainty in its velocity; and the act of measurement would produce the uncertainty needed to satisfy the principle.<\/p>\n

Physics students are still taught this measurement-disturbance version of the uncertainty principle in introductory classes, but it turns out that it’s not always true. Aephraim Steinberg of the University of Toronto in Canada and his team have performed measurements on photons (particles of light) and showed that the act of measuring can introduce less uncertainty than is required by Heisenberg\u2019s principle1. The total uncertainty of what can be known about the photon’s properties, however, remains above Heisenberg’s limit.<\/p><\/blockquote>\n

Now there’s absolutely nothing wrong with the above. What I object to is the notion that this is (a) new, (b) surprising, or (c)\u00a0Nature<\/em>-worthy. No doubt some people who teach quantum mechanics still teach that the uncertainty principle always has to do with uncertainties induced by measurements, but I hope not many practicing physicists do so.<\/p>\n

What I really object to, though, is the last sentence of the abstract of the journal article<\/a> to which this news article refers:<\/p>\n

\u00a0[This experiment’s]\u00a0results have broad implications for the foundations of quantum mechanics and for practical issues in quantum measurement.<\/p><\/blockquote>\n

I can’t find anything in the article that substantiates this claim, and the claim itself is ridiculous on its face. It’s ridiculous because, although some people who write woo-woo popular treatments of quantum mechanics get this wrong, nobody who’s actually studied the foundations of quantum mechanics or quantum measurement theory does. The results of this experiment confirm exactly what such people would have expected all along.<\/p>\n

That’s not to say that one shouldn’t do the experiment, of course. I’m not opposed to checking whether things that everyone knows must happen really do happen! But it’s absurd to say that the results have broad implications about the foundations of the field.<\/p>\n

For those who know a bit of quantum mechanics, I’ll give an example below of a thought experiment that illustrates the idea behind the actual experiment. Just to be clear, this is a completely different physical setup, but the underlying principles and the relationship to the uncertainty principle are precisely analogous.<\/p>\n

Put a particle in a one-dimensional box (infinite square well) of length L<\/em>. Put it in the second energy level:<\/p>\n

\u03a8(x) = A<\/em> sin(2\u00a0\u03c0 x<\/em>\/L<\/em>)<\/p>\n

for some normalization constant A.<\/p>\n

As an undergraduate quantum mechanics student can tell you, the uncertainties in position and momentum of this guy are<\/p>\n

\u0394x<\/em> = 0.257 L<\/em><\/p>\n

\u0394p =\u00a0\u03c0\/L<\/em><\/p>\n

leaving out irksome h-bars. (The 0.257 is some complicated expression involving square roots and pi’s.)<\/p>\n

Now measure whether the particle is in the left half or right half of the box. After the measurement, we have<\/p>\n

\u0394x = 0.090 L<\/em><\/p>\n

\u0394p = \u03c0\/L.<\/em><\/p>\n

Each pair of uncertainties satisfies the uncertainty principle\u00a0\u0394x<\/em>\u00a0\u0394p<\/em>\u00a0\u2265\u00a0\u00bd, as we knew it would.<\/p>\n

The point of the new experiment is to show that a different version of the uncertainty principle is not satisfied. The new version is<\/p>\n

\u0394x\u00a0<\/em>\u03b7(p<\/em>) \u00a0\u2265\u00a0\u00bd<\/p>\n

Here \u03b7(p<\/em>)\u00a0\u00a0is the “disturbance”\u00a0\u00a0caused by the measurement.\u00a0According to the paper,<\/p>\n

We define the disturbance as the root mean squared (rms) difference between the value of [the expected value of the observable] on the system before and after the [measurement].<\/p><\/blockquote>\n

Here’s the thing: for the setup I’ve just described, the disturbance in the momentum is precisely zero. Both before and after the measurement, the expected value of\u00a0p<\/em> is identically zero. So no matter what happened to\u00a0\u0394x<\/em>, the disturbance version of the principle would say 0 \u00a0\u2265\u00a0\u00bd, which we know is not the case.<\/p>\n

The exact experiment I described has never been done, as far as I know. But very similar sorts of experiments have been done since the early days of quantum mechanics. I’d be very surprised if other measurements hadn’t already shown that the disturbance version of the principle wasn’t true.<\/p>\n

In any case, the behavior of quantum systems under measurements like this is extremely well-understood, which is why I say that anyone with any expertise in quantum measurement theory or foundations of quantum mechanics would know that the disturbance-based principle is a non-starter.<\/p>\n","protected":false},"excerpt":{"rendered":"

Different people like different literary genres. I enjoy a good mystery; you may prefer science fiction, horror, or romance.\u00a0Some people, apparently, can’t get enough of a different genre: breathless news articles claiming that some new result changes our understanding of the foundations of quantum mechanics. Just in the pages of\u00a0Nature alone you could find enough … Continue reading Breaking news: quantum mechanics works exactly the way everyone has known it did for 75 years<\/span><\/a><\/p>\n","protected":false},"author":12,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-545","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/posts\/545","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/users\/12"}],"replies":[{"embeddable":true,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/comments?post=545"}],"version-history":[{"count":0,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/posts\/545\/revisions"}],"wp:attachment":[{"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/media?parent=545"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/categories?post=545"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blog.richmond.edu\/physicsbunn\/wp-json\/wp\/v2\/tags?post=545"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}