From: Henry Baker <hbaker1@pipeline.com> To: Bill Gosper <billgosper@gmail.com> Cc: math-fun@mailman.xmission.com Sent: Sat, March 26, 2011 1:26:12 PM Subject: Re: [math-fun] how do you structure causality? Some modern physicists have already started to give up on "causality", as a result of EPR experiments showing that "spooky action at a distance" does indeed happen. ________________________________ There are two assertions contained in that one sentence: an assertion about what some physicists are said to think, and an assertion about an experimental result. As for the latter, there is no experiment that demonstrates causality violation, and I invite anyone who disagrees to send me a citation to a paper in a peer-reviewed primary journal. I have seen this issue repeatedly misrepresented so many times that an explanation is called for. In an "EPR experiment", a source S emits a pair of particles, one being detected at spacetime event A, the other detected at B, with A and B having spacelike separation so that no causal signal can propagate between them, i.e. a signal traveling forward in time and no faster than the speed of light. This particle pair has been carefully crafted so that measurements at A and B exhibit correlations that (by violating Bell's inequality) cannot be explained without giving up either classical physics or causality. The individual sets of measurements are random, and these correlations can be manifested only by bringing together and comparing the two sets of measurements. It is a mathematical consequence of the principles of quantum theory that whatever kind of measurements are performed at A, or lack of measurement, and whatever the result of those measurements, is not discernible from an examination of the measurement results at B. There is no way, within quantum theory, to use this "EPR effect" to convey information between A and B. In their paper (Physical Review, v.47, p.777, 1935), Einstein, Podolsky, and Rosen tried to show that quantum theory did not provide a complete description of physics. They proposed that if the result of a measurement can be predicted with certainty, then "an element of physical reality" exists. Now then, if Mr. A and Mr. B agree in advance what kinds of measurements they will perform on their particles, then it is indeed possible (according to quantum theory) that Mr. A, upon seeing the result of his measurement on his particle, can predict with certainty the corresponding result that Mr. B will find from his measurement of the partner particle from the same pair. (Of course, if Mr. A cheats on the agreement, Mr. B won't know until the measurements are compared.) So now, EP&R conclude that the property of particle B that is about to be measured has "an element of physical reality", which presumably is supposed to mean "really exists". It would seem that the configuration and result of Mr. A's measurement has caused a "spooky action at a distance" on particle B. Now we can discuss the first assertion in the original post. A physicist who accepts the notion of "an element of physical reality", and some physicists do, as well as the experimental predictions of quantum theory, must ineluctably conclude that causality is violated. It was thus that EP&R attempted to prove that quantum theory was missing something, because if it were complete, then causality would be contradicted. This is as close as one can get (at least in 1935) in the physics world to the (P and (not P)) of mathematics. But their argument makes it clear that EP&R were three physicists who most certainly did not reject causality. In 1935, the EPR experiment was a thought experiment; today it is reality, and the experimental measurements agree with quantum theory. While this does not prove the truth of quantum theory, it does refute ((classical physics) and (causality)). Any theory that tries to cast quantum mechanics into a classical format, the so-called "hidden variable" theories, must necessarily violate causality. So while we can all agree on how to calculate the predicted experimental results (by using quantum theory), there are differing interpretations. On the one hand, accept causality fully, even at the quantum level, and adjust one's intuition to certain peculiar consequences, e.g. a particle does not possess a property until that property is actually measured. On the other hand, keep your more-or-less classical notions, but reject causality at the quantum level, yet allow that this causality violation is somehow masked from experimental observation. These interpretations themselves are not subject to observational verification, and as such they remain a matter of personal opinion. -- Gene ________________________________ So "causality" may indeed be an illusion that results from our (vastly imperfect) "memory" system. This is essentially a version of the anthropic principle: we see what our minds & memories allow us to see. http://en.wikipedia.org/wiki/Anthropic_principle Szilard/Maxwell/Bennett found that the baseball umpire's rule is true: there aren't any balls or strikes until the umpire calls them. Translation: there is a large energy cost to nailing down a memory; the cost may not show up, however, until you _clear_ the memory to zeros. http://en.wikipedia.org/wiki/Entropy_in_thermodynamics_and_information_theor... At 12:00 PM 3/26/2011, Bill Gosper wrote:
In freshman Humanities, we had to read Hume's
1. *An Enquiry Concerning Human Understanding*<http://www.infidels.org/library/historical/david_hume/human_understanding.html>
**wherein he concluded causality was essentially illusory. Or so I gathered. In his gedanken mechanics, the terminology was so muddled and in conflict with modern terminology that I boggled. --rwg