Talk:Negative probability

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This isn't mathematics

Well, I guess Pr{A} < 0 sort of rules out Lebesgue measure theory, eh? Let's see – if Pr{A} = 0 means that the event A cannot possibly occur, then Pr{A} < 0 must mean that it will unhappen with some regularity. So time can flow backwards, and entropy need not increase. Wonderful!

I don't know how this one got a Math tag stuck on it, so I'm sending it to Physics. DavidCBryant 01:22, 17 February 2007 (UTC)[reply]

Where's the beef?

No where in the article is there an attempt to define what a negative probability means. There is a reference to its application in finance (where there is no reference to negative probability). This article is cleverly written but I cannot help but wonder if it is a hoax without seeing a definition. Yes, I understand negative number (and even complex numbers) and could imagine that someone defined a negative probability and that such a definition is useful. However, why keep it a secret? It cannot be that complicated to understand. Wikinewbie123 (talk) 03:38, 10 September 2009 (UTC)[reply]

I don't know the finance angle, but in physics, a negative probability has no physical interpretation. No measurable event can ever have negative probabilities; it's only intermediate contributing steps ("ghost states") that can. It's harder to explain this in more detail without going into phase space (and picking an interpretation of quantum physics), but once you consider that the amplitudes of quantum wave functions are complex numbers with no physical interpretation (it's the square of the absolute value of the amplitude that describes the probability, but squaring a complex number loses information), this is really no worse.

These ghost states effectively contribute negative kinetic energy to the system, but there's really no more of a physical explanation for that than for the negative probability we started with.

Here's something that might help: Imagine two independent events. The probability of the first one occurring is 1/4, but the probability of both occurring is 1/2. This means the probability of the second event must be 2. And therefore, the probability of the second event _not_ occurring is 1 - 2 = -1. Some people might argue that what is really happening here is that the two events aren't really independent; there's some kind of connection between them that isn't being taken into account. Given that the second event can't be observed and doesn't describe an actual physical state, there's really no way to disprove that. But using the probability of 2 (or -1) makes the math a lot simpler. --99.35.135.150 (talk) 15:37, 16 September 2009 (UTC)[reply]

I would applaud the explanation. Refs 2 and 4 go into lots of detail, but this is only a stub, and should not have to go into such, especially given the counter-intuitive nature of the techniques. Typically, in phase space, a small region of negative probability in a distribution deducts from an expectation value of an observable a certain amount. The uncertainty principle ensures that no region of purely negative values in the distributions can be measured directly to yield a paradoxical negative number, and thus these negative regions are shielded and unknowable; but, still, these negative probabilities are at the heart of quantum mechanical interference. A motion of particles in a negative probability area in one direction physically amounts to a counterflow of real particles in the opposite direction. I doubt any technical detail would illuminate the general reader who does not wish to go into the primary references, though. Cuzkatzimhut (talk) 17:12, 16 September 2009 (UTC)[reply]

This isn't Mathematical Finance either

The work by Espen Haug is more or less a clever joke, there is no application of "negative probabilities" in Finance as far as I know. It impresses only those who don't understand the subject, IMHO. 67.243.54.129 (talk) 18:27, 2 February 2011 (UTC)[reply]

Vandalism?

Both edits of 58.152.201.165 today appear to virtually obliterate the entire page. Likely Vandalism. Cuzkatzimhut (talk) 20:39, 30 April 2011 (UTC)[reply]

Negative probability as means of falsification of hidden variables in Aspect's Experiment

I'm not a Wikipedian so I'm not sure if this application of negative would be appropriate. There are references at the bottom but I can't say if the work is published: Negative probability interpretation of Bell's Theorem George Dishman (talk) 19:54, 18 February 2014 (UTC)[reply]

Possible Error

I have checked the work of Gábor J. Székely about "half coins" ("Half of a Coin: Negative Probabilities"). The original article says that if X is a signed probability distribution, we can find oridinary random variables with X + Y = Z (in distribution). But Székey says that in this decomposition X and Y are independent, otherwise the the article in wikipedia says that Y and Z are independent. I'm not sure if the two conditions are equivalent, and maybe, the wikipedia article contains a misinterpretation of the original work of Székely. Maybe it is necessary to check it --Davius (talk) 01:58, 10 January 2016 (UTC)[reply]