Thursday, December 20, 2007

David Bohm born 90 years ago

David Joseph Bohm (12/20/1917 - 10/27/1992) was born in Pennsylvania into a Jewish family of immigrants from Eastern Europe, 43 days after the Great October Socialist Revolution. As you can expect, this paragraph is probably going to be the most flattering one. That's why I also choose the first paragraph to mention that Bohm's most valuable contributions to physics is the Aharonov-Bohm effect - that showed that the Wilson line is a physical observable in a quantum theory even if the magnetic field strength vanishes - and the Bohm diffusion (of plasma in a magnetic field). He also wrote a decent book on quantum mechanics but this book already had some bias related to his unorthodox interpretation of quantum mechanics. See Chapter 23 where he writes that quantum mechanics cannot exist without a classical theory etc. - things that we surely consider wrong today.

Politics

In May 1949, as soon as McCarthy's policies were implemented, he was asked to testify about his (former?) colleagues from the communist movement. He refused to testify and was arrested and fired. I don't dispute that these events look unfortunate and suspicious. And I am not able to say whether Bohm actually had the right not to testify at the time. Nevertheless, I am completely sure that Bohm's involvement with the dangerous organizations is being generally underestimated.

Some people even want to dispute that he was a radical communist. Already in the late 1930s, he became active in the Young Communist League, the Campus Committee to Fight Conscription, and the Committee for Peace Mobilization. All three organizations were classified as communist organizations by the FBI long before McCarthy's era.




I find it understandable that in the late 1940s, when the tension between the capitalist and communist worlds increased, these two worlds were protecting themselves from the other world's spies and their fifth columns that undoubtedly existed.

While there might have been qualitative similarities between the events in both portions of the world, it is just unacceptable for me to say that "the same things" were taking place in both regions. While Stalin and his comrades in the Soviet bloc were routinely killing millions of inconvenient people, only a few thousands of people were investigated and/or arrested during the era of McCarthyism in the U.S.

Sorry but it is not the same thing. The communist threat was real and many countries that were less lucky than America after the World War II became victims of this totalitarian system for almost half a century. My country was among them. Please feel free to call me a McCarthy apologist but I am convinced that a comparable care was needed, after all. David Bohm was among the most active communist activists so it is natural that he was investigated and it is equally natural that his refusal to testify wasn't viewed as helpful by the folks responsible for the security of America.

We may ask: in the ideal democratic world, does a person have the right to believe in communist ideals? Well, he almost certainly does. But at some moment, we must carefully distinguish beliefs from real acts. The processes that were taking place in the late 1940s were not about Platonic beliefs. They were about the establishment of criminal regimes in whole countries and subcontinents.

The fuss wasn't about dreams and values: it was about actual plans to change the society and about the ability of freedom and democracy to protect themselves. Much like other people who have had problems with democratic laws, David Bohm was able to escape to Latin America.

Bohmian mechanics

Bohmian mechanics is profoundly wrong but what also irritates me is that it wasn't really invented by David Bohm. I will talk about its being incorrect for a long time but let me start with the comment that the interpretation was published as the "pilot wave theory" by Louis de Broglie in 1927. In 1952, Bohm wrote down a very straightforward multi-particle generalization of de Broglie's equations and added a very controversial version of "measurement theory". Is it a substantial improvement you expect from 25 years of progress?

The basic idea of the pilot wave theory is simple and superficially natural. The wave function is a real wave but besides this wave function, there also exists an actual particle that has a well-defined position and velocity, after all. The role of the wave function is to "push" the particle away from the interference minima. One can rewrite and reinterpret the Schrödinger equation in such a way that the probability distribution to find the real particle at a given point mimicks the prediction from the wave function if it did so at the beginning.

Louis de Broglie wrote these equations for the position of one particle, David Bohm generalized them to N particles.

I think that in analogous cases, we wouldn't be using the name of the "updater" for the final discovery. For example, we use the term "Schrödinger equation" even for the multi-particle case although Schrödinger didn't really discover - or understand - the role of his equation in more general setups.

But that's a detail. What is much more important is that Bohm's interpretation is profoundly incorrect.

Determinism vs unnecessary superconstructions

Einstein wanted to preserve determinism or at least "realism": he wanted physics to imply that a particle or another physical system has well-defined values of certain quantities already before they are measured. When I was a high school kid, I remember that I had the very same sentiments. But the general conceptual problem was a simple one. So I decided to construct/understand a working "realist" version of quantum mechanics in three months and because I inevitably failed, I simply started to believe orthodox quantum mechanics.

"Realism" in the technical sense has been a part of physics for centuries and something may be philosophically attractive about it, at least for the people who have spent some time with classical physics. However, is it a sufficient justification for the pilot wave theory?

Einstein's answer, much like mine, was a resounding No. He called the picture an unnecessary superconstruction. One can perhaps create classical mechanistic models that mimic the internal workings of quantum mechanics in many situations. For example, one can write a computer simulation. But you can't say that the details of such a program or Bohmian picture is justified as soon as you confirm the predictions of conventional quantum mechanics.

The mechanistic models add a new layer of quantities, concepts, and assumptions. They are not unique and they are not inevitable. The similarity with the luminiferous aether seems manifest. If they only reproduce the statistical predictions of quantum mechanics, you could never know which mechanistic model is the right one: it could be a computer simulation written by Oracle for Windows Vista, after all. Moreover, the mechanistic models brutally violate certain symmetries and other properties (Lorentz symmetry and locality) as well as the democracy between different observables and the emergent character of the classical limit. Let me discuss these problems one by one.

Locality and Lorentz invariance

Multi-particle Bohmian mechanics requires one to introduce the wave function of many positions and treat it as a real wave. This object is manifestly non-local and has the ability to propagate signals faster than light, at least in principle.

Although the theory is constructed to be as similar to proper quantum mechanics as possible, this feature makes its essence dramatically different. In proper quantum mechanics, locality holds. If one considers a Hamiltonian that respects the Lorentz symmetry - such as a Hamiltonian of a relativistic quantum field theory - the Lorentz symmetry is simply exact and it guarantees that signals never propagate faster than light.

In proper quantum mechanics, one can define the operators that generate the Poincaré group and rigorously derive their expected commutators. Also, it is exactly true that operators in space-like-separated regions exactly commute with each other. This fact is sufficient to show that the outcome of a measurement in spacetime point B is never correlated with a decision made at a space-like-separated spacetime point A.

These facts allow us to say that quantum field theory respects relativity and locality. The actual measurements can never reveal a correlation that would contradict these principles. And it is the actual measurements that decide whether a statement in physics is true or not. Bohmian mechanics is different because these principles are directly violated. You may try to construct your mechanistic model in such a way that it will approximately look like a local relativistic theory but it won't be one. Consequently, you won't be able to use these principles to constrain the possible form of your theory. Moreover, tension with tests of Lorentz invariance may arise at some moment.

Many people often say that normal quantum field theory is non-local. This is partly because of a wrong terminology, partly because of a misunderstanding of the probabilistic interpretation of quantum mechanics. Quantum field theories such as QED are perfectly local and we call them local. The Lorentz symmetry perfectly holds and one can show that the measurements are perfectly uncorrelated to space-like-separated decisions: whether something is uncorrelated may only be found by a repeated experiment, of course. The statement about a vanishing correlation is true both experimentally as well as theoretically, assuming a probabilistic interpretation of quantum mechanics.

The wave function may look like a non-local object but the statement that it makes quantum mechanics non-local is a misconception. As long as it is interpreted probabilistically, the question about locality depends on the actual observables and their commutators outside their light cones. Because these commutators vanish in QED, the theory is perfectly local and every experiment will confirm that it is impossible to send superluminal signals. There is no experimental hint of non-locality and if you abandon strange philosophical prejudices, there is no theoretical evidence of non-locality either.

Problems with spin

Bohmian mechanics remembers the positions of particles. What does it do with their spin? You can easily see that there is no solution that would agree with experiments and that would also treat different observables in the same way.

If de Broglie and Bohm claim that a particle should also have a well-defined position and velocity, it should naturally have a well-defined z-projection of spin, too. But once you adopt such an assumption, you clearly break the rotational symmetry. Particles would only have classical projections of spin with respect to the z axis so the z axis is preferred and you can measure its direction, at least in principle, uncovering anisotropy of space. The rotational symmetry of a theory including spinors heavily depends on the probabilistic nature of quantum mechanics.

If you give up the equal treatment of position and spin and decide to treat spin differently and give an electron well-defined binary-valued projections of spin with respect to all axes, you will also encounter problems. Bell's inequality will show you very sharply that the required dynamics is completely non-local but you will also have problems with the Lorentz invariance and the precise rules for the evolution of the discrete function of the direction.

The probabilistic meaning of the spinorial wave functions is completely essential for us to be able to translate a physical arrangement to any convention, including an arbitrary choice of the z-axis.

There are no preferred observables

All these problems are related to one general problem of Bohmian mechanics and this whole line of reasoning. Because experiments eventually measure some well-defined quantities, the likes of Bohm think that there must exist preferred observables - and operators - that also exist classically. They are classical to start with, they think. Positions of objects are an important example.

But the quantum mechanical founding fathers have known from the very beginning that this was a misconception. All Hermitean operators acting on a Hilbert space may be identified with some real classical observables and none of them is preferred. Moreover, the question which of them will emerge as natural quantities in a classical limit cannot be answered a priori. Which observables like to behave classically? Well, it is those whose eigenstates decohere from each other.

But the details of decoherence depend on the Hamiltonian of our physical system. The emergent classical eigenstates therefore cannot be "assumed" from the beginning - which is what the pilot wave theory is doing. Instead, they must be dynamically calculated. At least a qualitative calculation is needed to show that the "dead cat" and "alive cat" are good classical eigenstates that you may obtain as a result of a measurement but their generic complex superpositions are not. These facts are all about decoherence and decoherence depends on the Hamiltonian.

In the past, people could have used phenomenological rules that said which preferred directions in the Hilbert space behaved as "classical eigenstates" ("dead cat" vs. "alive cat", for example). But those phenomenological rules didn't quite explain why the states were what they were and they didn't allow one to calculate the time scale where the classical limit becomes a good replacement of quantum mechanics. Decoherence can do both - it is clearly a superior modern component of measurement theory that supersedes its phenomenological predecessors.

If I summarize, the pilot wave theory was known to be misguided 80 years ago but it has become even more incompatible with proper physics in the second half of the 20th century. Mechanistic models of state-of-the-art quantum theories are not available: it is partly because it's not really possible and it's not natural but it is also partly because the champions of Bohmian mechanics are simply not good enough physicists to be able to study state-of-the-art quantum theories. They're typically people with philosophical preconceptions who simply believe that the world has to respect their rules of "realism" or even "determinism".

But science is not about beliefs and the world doesn't respect these principles. It has been established that the right description of the world is probabilistic. 80 years ago, the only reason to believe so was that a hidden-variable theory couldn't tell us any new useful predictions of experiments and it looked unnatural and contrived. Today, we have some more concrete reasons to know that the hidden-variable theories are misguided. Via Bell's theorem, hidden-variable theories would have to be dramatically non-local and the apparent occurrence of nearly exact locality and Lorentz invariance in the world we observe would have to be explained as an infinite collection of shocking coincidences.

I just don't think that this is a rationally sustainable belief. It's just another repetition of the old story of the luminiferous aether.

Bohm vs Pauli and Bohm vs Feynman

David Bohm was almost certainly the person whom Wolfgang Pauli addressed the famous sentence "it is not even wrong" and the theories that Bohm was offering Pauli were probably related to some non-orthodox models of quantum mechanics discussed above.

The readers of Feynman's books may remember that when Feynman decided to investigate supernatural phenomena, he was told that Uri Geller has convinced "a professor David Bohm" of his supernatural powers. As an old man, Bohm started to believe all kinds of nonsensical supernatural theories. This fact sounds even more crazy when you realize that Marxism is supposed to build on common sense and atheism. But it is not such a paradox, after all. These extremes - a mechanical model of quantum mechanics on one side and Uri Geller's magic on the other side - share a certain feature, namely their large distance from reality and an elevated role of philosophical and religious preconceptions.

To summarize, my portrait of David Bohm wasn't the most flattering one but it is how it sometimes works out. Nevertheless, he was an interesting character.

3 comments:

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    ReplyDelete
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  3. http://pcillu101.blogspot.com

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    ReplyDelete