Archive for the ‘history’ category

Quantum Physics at the Crossroads

30th October 2006

FOLKLORE:

When I was but a young undergrad student, I read some interesting books about the history and foundations of quantum theory. In those books the Solvay conferences played a major role, particularly the 5th conference in 1927. I was informed that the official part of the proceedings was largely insignificant, and that all the action centred around the debates that took place between Bohr and Einstein, in which Einstein repeatedly tried to undermine the uncertainty principle via a series of thought experiments, but Bohr was always quick to respond with a correct analysis of the experiment that showed uncertainty to be triumphant. This always put in my mind a picture similar to da Vinci’s “Last Supper”, with Bohr playing the role of Jesus, regailaing his many disciples with the moral parable of the day over dinner.

Another piece of folklore concerns the Ph.D. thesis of one Prince Louis de Broglie. This contained the famous de Broglie relation that gives the wavelength of the waves to be associated with matter particles. The story goes that the thesis was on the verge of being rejected, but was saved by Einstein’s recommendation, who was the only person to recognize the deep significance of the relation. As the story is told, it is hardly surprising, because the contents of the rest of the thesis is never explained. One is left to imagine a document that could only have been about 10 pages long, which intrroduces the relation and then explains some of its consequences. That may seem stong enough for a very good Phys. Rev. article, but is hardly enough to warrant a Ph.D.

LIFE:

Since those distant days of my youth, I have attended many a physics conference myself. I now recognise that it is the general rule, almost without exception, that the participants regard the discussions they have outside the talks as being much more important and interesting than anything that was said in the talks themselves. This rule holds regardless of the actual inherent interest of the topics under discussion. In fact, it is quite common to find some of the older participants banging on about some Hamiltonian they wrote down in the 1970s, whereas the young guns are talking about something genuinely new and interesting, the significance of which is not understood by the older guys yet. It is also extremely unlikely to find the entire group of conference participants, however small that group may be, listening in rapt attention to the discussion of just two people over dinner (if only because there are simply some groups of people who don’t get on with each other, and others who are more interested in going to the pub), and it is equally unlikely that that conversation represents the only interesting thing going on at the conference.

Also, it goes without saying really that I don’t know of anyone who got their Ph.D. for a 10 page paper, however great the idea contained therein happens to be.
REALITY:

Currently, I am about half way through reading “Quantum Theory at the Crossroads”, the new book by Bacciagaluppi and Valentini about the 1927 Solvay conference. The second half of the book is an English translation of the proceedings, but equally interesting is the new analysis of the conference discussions from a modern point of view, contained in the first half. Here are some things I found particularly interesting.

- The only witnesses to the famous Bohr-Einstein debates were Heisenberg and Ehrenfest. The usuall account of these debates comes directly from an article written by Bohr many years after the conference took place. Heisenberg roughly confirms the account, also in recollections written many years later. The only account written shortly after the conference is a letter written by Ehrenfest, which seems to confirm that Bohr was triumphant in the debates, but gives no details.

- Bacciagaluppi and Valentini argue that it is highly unlikely that Einstein’s main target was the uncertainty relations. This is because, outside of Bohr’s account of the conference discussions, Einstein hardly mentions the uncertainty relations as a point of concern in any of his correspondence or published works. Instead, they argue, it is likely that he was trying to get at the point that the concept of separability was incompatible with quantum theory, which was later crystallized in the EPR argument. In fact, Einstein gives an argument in this direction also in the published general discsussion at the conference. It seems likely that Bohr missed this point, just as he seemed to miss the point years later in his published response to the EPR argument.

- At the time of the conference, the consolidation of quantum theory was far from complete. Three approaches were discussed in the talks: de Broglie’s pilot wave theory, Schrödinger’s wave mechanics and Heisenberg’s matrix mechanics (with additions by Born). Despite the fact that “equivalence proofs” between wave and matrix mechanics had been published at the time of the conference, they were treated as distinct theories, which could potentially make different predictions. This is because, at the time, Schrödinger did not accept Born’s statistical hypothesis for wave mechanics, which was not yet formulated for arbitrary observables in any case. Also, Heisenberg and Born did not accept the fundamental significance of the time-dependent Schrödinger equation, and still clung to a view of matrix meachanics as describing the transition probabilities for systems always to be thought of as being in definite stationary states. In fact, it seems that the only person at the conference who presented something that we would now regard as being empirically equivalent to modern quantum theory was de Broglie.
– This was not recognized at the conference, partly because de Broglie did not realize that one sometimes has to treat the apparatus as a quantum system in pilot wave theory in order to get equivalence with standard quantum theory. Also, there was as yet desciption of spin within de Broglie’s theory, but on the other hand this same objection could be levelled at wave mechanics. Finally, de Broglie himself regarded the theory as provisional, since it was not relativistic and involved waves in configuration space rather than ordinary 3d space. He placed great significance on ideas for a better theory, which were far from complete at the time of the presentation.

- Schrödinger emphasizes that de Broglie’s work was a major inspiration for his wave equation. In particular, de Broglie’s idea of unifying the variational principles of Newtonian mechanics with those of geometrical optics, was used in the derivation of the equation.

- de Broglie presented his pilot-wave theory for multiparticle systems, not just for single particles as is commonly thought.

In light of this and other arguments, Bacciagaluppi and Valentini argue that the time is ripe for a revision of the usual textbook history of quantum mechanics, and in particular of de Broglie’s contribution . Those who believe that the history of science should be written with the same objective standards that we hope to uphold for science itself, rather than simply being written by the victors, are well-advised to read this book.

Why not von Neumann?

27th September 2006

Anyone who read the comments on my last post will know that von Neumann is something of a hero of mine. Here’s a question that sometimes bothers me – why didn’t von Neumann think of quantum computing? Compare his profile with that of Feynman, who did think up quantum computing, and then ask yourself which one of them you would have bet on to come up with the idea.

  • von Neumann: Worked on a variety of different subjects thoughout his career, including interdisciplinary ones. Was well aware of the work by Turing, Church, Post and others that later became the foundation for computer science and of the role of logic in this work. Is credited with the design of the basic architechture of modern computers. Worked on the mathematical and conceptual foundations of quantum mechanics and is responsible for the separable Hilbert space formulation of quantum theory that we still use today. Finally, at some point he was convinced that the best way to understand quantum theory was as a probability theory over logical structures (lattices) that generalize some of those from classical logic.
  • Feynmann: Spent most of his career working on mainstream topics in quantum field theory and high energy physics. Only towards the end of his career did his interests significantly diversify to include the theories of computation, quantum gravity and the foundations of quantum theory. Conceived of quantum theory mainly in the “sum over paths” formalism, where one looks at quantum theory as a rule for attaching amplitudes to possible histories as opposed to the probabilities used in classical theories.

None of this is meant as a slight against Feynman – he was certainly brilliant at everything he did scientifically – but it is clear that von Neumann was better positioned to come up with the idea much earlier on. Here are some possible explanations that I can think of:

  • The idea of connecting quantum mechanics to computing just never occurred to von Neumann. They occupied disjoint portions of his brain. Ideas that seem simple in hindsight are really not so obvious, and even the greatest minds miss them all the time.
  • von Neumann did think of something like quantum computing, but it was not obvious that it was interesting, since the science of computational complexity had not been developed yet. Without the distinction between exponential and polynomial time, there is no way to identify the potential advantage that quantum computers might offer over their classical counterparts.
  • The idea of some sort of difference in computing when quantum mechanics is thrown into the mix did occur to von Neumann, but he was unable to come up with a relevant model of computing because he was working with the wrong concepts. As alluded to in a paper of mine, Birkhoff-von Neumann quantum logic is definitely the wrong logic for thinking about quantum computing because the truth of quantum logic propositions on finite Hilbert spaces may be verified on a classical computer in polynomial time. The basic observation was pointed out to me by Scott Aaronson, but one needs to set up the model quite carefully to make it rigorous. I might write this up at some point, especially if people continue to produce papers that use quantum computing as a motivation for studying concrete BvN quantum logic on Hilbert spaces. Anyway, the point is that if von Neumann thought that replacing classical logic with his notion quantum logic was the way to come up with a model of quantum computing, then he would not have arrived at anything useful.
  • As a mathematician, von Neumann was not able to think of any practical problem to do with quantum mechanics that looks hard to do on a classical computer, but could be done efficiently in the quantum world. As a physicist, Feynman was much better placed to realize that simulating quantum dynamics was a useful thing to do, and that it might require exponential resources on a classical computer.

As a von Neumann fan, I’d like to think that something other than the first explanation is true, but I am prepared to admit that he might have missed something that ought to have been obvious to him. Hopefully, someday a historian of science will take it upon themselves to trawl the von Neumann archives looking for the answer.


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