Edward Nelson's book "Quantum Fluctuations" (Princeton UP, 1985) gives an alternative way to introduce trajectories, quite different to the trajectories of de Broglie-Bohm type approaches. I've read the book in the past and university libraries generally have copies, but I've been unable to find a good open web reference

Researching this Question, I came across one of the best graphical presentations I've seen of how a 2-slit interference pattern can be generated by particles, http://www.cs.cmu.edu/~lafferty/QF/two-slit.html (in Java), with, as explanation, page images and a PDF of chapter 3 of Nelson's book.

I also found plenty of published work. WebOfScience returns 21 review articles that cite Nelson's book. "Research on hidden variable theories: A review of recent progresses", Genovese M, PHYSICS REPORTS 413(6) 319-396, JUL 2005, sent me to what at first glance looks an interesting review article "NON-LOCALITY AND LOCALITY IN THE STOCHASTIC INTERPRETATION OF QUANTUM MECHANICS", D. BOHM and B.J. HILEY, PHYSICS REPORTS 172(3) 93—122 (1989).

EDIT (modified): Does anyone know of other open access web resources? EDIT (new):If someone has a favorite subscription-only review article, that would be nice to know of as well, but my perception is that Nelson's approach is particularly unknown outside of academia; if someone is asking questions that suggest that thinking about Nelson's approach might widen their horizons, I want an easy place to tell them to look. Stanford Encyclopedia of Philosophy seems not to have a discussion of Nelson approaches, for example.

Finally, I make this request because although it's relatively little known I consider Nelson's approach something that anyone thinking about QM should know about, so I'd like something to be able to point out to people. I consider it significant partly because it demonstrates that de Broglie-Bohm approaches are not a unique way to introduce hidden variables. The way in which stochasticity is introduced is conceptually different in that the trajectories are stochastic instead of the initial conditions, which puts QM in a significantly different light than de Broglie-Bohm approaches.

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    $\begingroup$ What is your question? $\endgroup$
    – user1355
    Commented Mar 19, 2011 at 15:59
  • $\begingroup$ This looks like an "announcement" rather than question. However one could manufacture a question from it "what do people think of Nelson's approach to QM?" $\endgroup$ Commented Mar 19, 2011 at 17:10
  • $\begingroup$ Peter do you want to turn this into an actual question? It is all quite interesting so far. $\endgroup$ Commented Mar 19, 2011 at 17:14
  • $\begingroup$ @sb1 @roy Web references for Nelson's “Quantum Fluctuations”? (with a question mark is better, perhaps?) is the question I asked myself because I wanted to point out the Nelson alternative to Yayu in an Answer. I couldn't find anything, so I started to write a question. So I did a little more looking --I didn't want to ask a question for which the answer was too easy-- and found a few things, so I put them in the question, but I wasn't quite happy with them. I'll edit the fourth paragraph. More references, please! I hope someone knows of something better. I see now that it's unclear. $\endgroup$ Commented Mar 19, 2011 at 19:18
  • $\begingroup$ I looked at the interference pattern and cannot make sense of it. There is no incoming beam. Why would the particles end up interfering like that is not clear, except by hand. An experiment now, that would be impressive. $\endgroup$
    – anna v
    Commented Mar 21, 2011 at 19:21

2 Answers 2


The original web links in this response (from 2011) have become inactive, and it was not a full Answer in any case.

For now I will put down a couple of references to Nelson's work.

  1. From May 2021 the following PhD Thesis online: Nonlocality in a Stochastic Approach to Quantum Mechanics and Quantum Field Theory https://www.wm.edu/as/physics/documents/seniorstheses/class2021theses/dillard,-jackson-final_thesis.pdf

  2. Book "Stochastic Processes in Classical and Quantum Systems"(1988). Nelsons article is page 438. (May be available online)

  3. Bohm (/Hiley) Paper(s) (Non-locality and) locality in the stochastic interpretation of quantum mechanics from 1988/1989 may be available online.

Note sure if Question is asking for an uptodate review or summary of this QM Interpretation.

  • $\begingroup$ I'm pretty sure Nelson's 1985 book more-or-less gives up. He'd been working at this kind of model since his first published paper in 1966, which is often cited, but he came to a full stop. He's worked on other things since. I think I recall from the book that he proves that the 3-space dynamics for multiple systems could not be Markovian, which he regarded as killing. Part of the interest of this approach is that the "problem" with QM looks different. One could perhaps come to terms with a non-Markovian stochastic dynamics, just as people have come to terms with the nonlocal deBB dynamics. $\endgroup$ Commented Mar 21, 2011 at 22:25

I have a low opinion of Nelson's idea, even though I have a high opinion of Nelson.

I always recommend Streater's screed, http://www.mth.kcl.ac.uk/~streater/lostcauses.html

« Lost causes in Physics », where he discusses this and many other topics.

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    $\begingroup$ Please do not give Streater's insipid and vile screed more publicity than it already has. It places S-matrix theory and Sphaelerons (top notch physics) alongside Nelson's stuff (interesting flawed physics) alongside Stapp's theory of consciousness (crackpot physics). This is unbearable attempted censorship on Streater's part, and it is an unwelcome negative contribution to the science. $\endgroup$
    – Ron Maimon
    Commented Dec 30, 2011 at 13:46
  • $\begingroup$ The link to Streater's screed seems to be broken, but a snapshot is saved on the Wayback Machine. $\endgroup$
    – user337588
    Commented Jun 12, 2022 at 17:31

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