Reply To: Why Bohmian theory?

[Robert Griffiths]

Dear Aurélien,

Let me reply to your opening paragraph by saying that the ontology of CH and of BM are very different; in fact, there is little if anything in common. In CH the ontology begins with Hilbert subspaces, whereas in BM the central idea is a collection of classical particle positions. Certainly one can find Hilbert subspaces which approximate particle positions, but the whole mathematical structure is very different. So if you wish to criticize CH for not having particle positions, my reply will be: do you criticize the cosmologists for refusing to tell you the location of the center of the universe? After all, that was well defined and located at the center of the earth during the Middle Ages. The other point of overlap between CH and BM has to do with the unitarily evolving “wavefunction of the universe”, what I call the “uniwave”. In BM this is a very important part of the theory; whether part of the ontology seems to depend on whom you talk to. In CH the uniwave is generally not necessary, but if it is used at all it is considered a pre-probability, a generator of probabilities, and therefore NOT part of the ontology.

Next, on to your discussion of beam splitters. Mach-Zehnder interferometers and Wheeler’s delayed choice. These matters are discussed extensively from the CH perspective in my book [1], chapters of which are available online if you don’t have the paper version. See in particular Chs. 12, 13, 18 (for successive measurements after a beamsplitter), and 20 (delayed choice). I think you should be able to follow the ideas, and if you work out some of the examples yourself, you will get some feeling for the CH approach to these things. There are also figures, which could aid discussion given that email is not too good for communicating figures.

One issue that you mention is retrodiction, which is easily confused with retrocausation. With reference to this you may want to take a look at the thread ‘Retrocausation vs Retrodiction’ in this workshop, under the heading of ‘Time-symmetric theories’, which I began and which contains a discussion with Wharton and Stuckey. CH is often criticized, and I think this is part of your concerns, for letting the the future ‘influence’ the past in the following way. If you are constructing a family of histories by choosing an initial state, a projective decomposition of the identity (PDI) at a later time, and another at a still later time, etc., you may find that as you add later PDIs the earlier family you constructed no longer satisfies the consistency conditions, and so the “future is influencing the past”. This overlooks the fact that families of histories are constructed by theoretical physicists in order to provide a consistent quantum description of events in a closed system (which is where consistency conditions apply), and the choices of theoretical physicists have no influence on reality. What we do is somewhat similar to historians writing historical accounts, and given the proximity of Bastille Day I refer you to a little analogy you will find towards the end of the last section of Ch. 14 of my book.

Bob Griffiths

[1] Consistent Quantum Theory (Cambridge 2002)
http://quantum.phys.cmu.edu/CQT/