2nd draft
On Sep 9, 2010, at 6:10 PM, JACK SARFATTI wrote:
Or, The Emperor Really Has No Clothes
Here is an interesting talk with some good points I think clearly. ;-) In any case I agree with his argument because I thought the same myself.
MAKING BOHMIAN MECHANICS
COMPATIBLE WITH RELATIVITY
AND QUANTUM FIELD THEORY
Hrvoje Nikoli´c
Rudjer Bo?skovi´c Institute, Zagreb, Croatia
Vallico Sotto, Italy, 28th August - 4th September 2010
It is frequently argued that:
1. Bohmian mechanics (BM) contradicts the theory of relativity
(because BM is nonlocal)
2. BM based on particle trajectories is not consistent with
particle creation/destruction in QFT
(because particle trajectories are continuous in BM)
The purpose of this talk is to show that BM can be formulated
such that:
- BM is nonlocal but relativistic covariant
- BM with continuous particle trajectories describes
particle creation/destruction in QFT ...
1.1 Relativistic Bohmian interpretation
- Nonlocality in BM requires superluminal (faster than light)
communication between particles.
- The most frequent argument that it is not compatible with relativity:
Superluminal communication
⇒ there is a Lorentz frame in which communication is instantaneous
⇒ there is a preferred Lorentz frame
⇒ the principle of relativity is violated.
- However, this is not a valid argument, because
this is like using the following argument on subluminal communication:
Subluminal communication
⇒ there is a Lorentz frame in which particle is at rest
⇒ there is a preferred Lorentz frame
⇒ the principle of relativity is violated.
The argument on subluminal communication is wrong:
- It is the general law of motion that must have the same form
in any Lorentz frame.
- A particular solution (a particle at rest with respect to some particular
Lorentz frame) does not need to have the same form
in all Lorentz frames.
But the argument on superluminal communication is
completely analogous.
⇒ It is wrong for exactly the same reason:
- A particular solution (communication instantaneous with respect to
some particular Lorentz frame) does not need to have the same form
in all Lorentz frames.
BRAVO! Another analogous case is spontaneous broken symmetry in the (off-shell) virtual particle vacuum/many-real (on-shell) particle ground state in which Goldstone phase rigid macro-quantum coherence emerges (P.W. Anderson's "More is different.") e.g. Penrose-Onsager ODLRO in the reduced density matrices with macroscopic eigenvalues.
CONCLUSIONS
- The usual formulation of BM is not relativistic covariant because
it is based on standard QM which is also not relativistic covariant.
- To make BM covariant ⇒ first reformulate standard QM
in a covariant way!
⇒ Treat time on an equal footing with space:
1. space probability density → spacetime probability density
2. single-time wave function → many-time wave function
- To make particle BM compatible with QFT and particle/destruction:
1. Represent QFT states with wave functions
(depending on an infinite number of coordinates).
2. Use quantum theory of measurements ⇒
effective collapse into states of definite number of particles.
On Sep 9, 2010, at 2:52 PM, nick herbert wrote: Jack, I consider it silly for you to be making a fuss about who thought first about future influencing the present. It is a very old idea, at least as old as Aristotle (333 BC) and St Thomas Aquinas (1270 AD) who used the term "final cause" to refer to any cause that lies in the future.
Of course. Look who's talking about "silly"! Takes one to know one I guess. At least I am not on "all fours." Kidding aside, there is a serious priority issue here for the history of physics on how the idea of final causation is now creeping back into mainstream physics in a highly technical way (weak measurements, time machines, super oscillations). Hopefully David Kaiser and other serious historians of physics will set the record straight. ?
The notion of a future cause is included in the scope of "teleology"--See "teleology", "Aristotle" and "Aquinas" in Wikipedia. Aharonov came much much later than these fine dudes. If you can prove that Sarfatti came up with the notion of final cause before Aristotle that would be worth putting in the history books.
Like I came back from the future in a flying saucer and became Aristotle? Kidding aside once more, I never made any such claim of course. I am quite familiar with the history having minored in philosophy at Cornell with Max Black et-al. Indeed I got an A in Mario Einaudi's course in Aquinas. I would have made a good Jesuit like Jerry Brown.
Neither Feynman nor Aharonov have priority in proposing the notion of "final cause."
No one is making that claim either of course.
Aharonov's priority is in actually proposing an experiment to test whether "final causes" exist in nature. Whether his experiment actually accomplishes this end is a matter of some dispute.??
It's obvious to me that final cause is the only way to really understand uncontrollable quantum randomness in the present and passion at a distance in the entanglement of space-time separated subsystems. Aharonov et-al are 100% correct on that score. But that's only my opinion and unreasonable physicists who think they are thinking clearly but aren't, have the right not to agree with me! ??Of course, the important issue beyond that is signal nonlocality's strong violation of quantum physics as normally understood. I think that is necessary for life to exist in a non-equilibrium state (at the level of the not-so-hidden variables).