Begin forwarded message:
From: Ruth Elinor Kastner <rkastner@umd.edu>
Subject: Re: [ExoticPhysics] Basil Hiley's update on current state of work in Bohm's ontological picture of quantum theory
Date: November 25, 2012 12:36:53 PM PST
To: JACK SARFATTI <sarfatti@pacbell.net>, Exotic Physics <exoticphysics@mail.softcafe.net>
Reply-To: Jack Sarfatti's Workshop in Advanced Physics <exoticphysics@mail.softcafe.net>
In this approach I still don't see a clear answer to the question 'what is a particle,' unless it is that particles are projection operators.
In PTI a 'particle' is just a completed (actualized) transaction. PTI deals with both the non-rel and relativistic realms with the same basic model, which testifies to the power of that model. It is straightforwardly realist: quantum states describe subtle (non-classical) physical entities.
It seems to me that approaches dealing with conceptual problems in terms of abstract algebras are intrinsically non-realist or even anti-realist. Physics is the study of physical reality. Algebra is purely formal. Unless one wants to say that reality is purely formal,i.e. has no genuine physical content, I don't see how appealing to an abstract algebra as the fundamental content of quantum theory can provide interpretive insight into reality.
Put more simply, a physical theory may certainly contain formal elements, but those elements need to be understood as *referring to something in the real world* in order for us
to understand what the theory is describing or saying about the physical world. That is, it is the physical world that dictates what the theory's mathematical content and
structure should be, because of the contingent features of the physical world. Saying that a theory has a certain mathematical structure or certain formal components does not specify what the theory is saying about reality. I think an interpretation of a theory should be able to provide specific physical insight into what a theory is telling us about the domain it mathematically describes.
RK
Begin forwarded message:
From: JACK SARFATTI <Sarfatti@PacBell.net>
Subject: [Starfleet Command] Basil Hiley's update on current state of work in Bohm's ontological picture of quantum theory
Date: November 25, 2012 11:58:26 AM PST
To: Exotic Physics <exoticphysics@mail.softcafe.net>
Reply-To: SarfattiScienceSeminars@yahoogroups.com
On Nov 25, 2012, at 2:55 AM, Basil Hiley <b.hiley@bbk.ac.uk> wrote:
Jack,
As I dig deeper into the mathematical structure that contains the mathematical features that the Bohm uses, Bohm energy, Bohm momentum, quantum potential etc. are essential features, as you imply, of a non-commutative phase space; strictly a symplectic structure with a non-commutative multiplication (the Moyal-star product). This product combines into two brackets, the Moyal bracket, (a*b-b*a)/hbar and the Baker bracket (a*b+b*a)/2. The beauty of these brackets is to order hbar, Moyal becomes the Poisson and Baker becomes the ordinary product ab.
Time evolution requires two equations, simply because you have to distinguish between 'left' and 'right' translations. These two equations are in fact the two Bohm equations produced from the Schrödinger equation under polar decomposition in disguised form. There is no need to appeal to classical physics at any stage. Nevertheless these two equations reduce in the limit order hbar to the classical Liouville equation and the classical Hamilton-Jacobi equation respectively. This then shows that the quantum potential becomes negligible in the classical limit as we have maintained all along. There are not two worlds, quantum and classical, there is just one world. It was by using this algebraic structure that I was able to show that the Bohm model can be extended to the Pauli and Dirac particles, each with their own quantum potential. However here not only do we have a non-commutative symplectic symmetry, but also a non-commutative orthogonal symmetry, hence my interests in symplectic and orthogonal Clifford algebras.
In this algebraic approach the wave function is not taken to be something fundamental, indeed there is no need to introduce the wave function at all!. What is fundamental are the elements of the algebra, call it what you will, the Moyal algebra or the von Neumann algebra, they are exactly the same thing. This is algebraic quantum mechanics that Haag discusses in his book "Local Quantum Physics, fields, particles and algebra". Physicists used to call it matrix mechanics, but then it was unclear how it all hung together. In the algebraic approach there is no collapse of the wave function, because you don't need the wave function. All the information contained in the wave function is encoded in the algebra itself, in its left and right ideals which are intrinsic to the algebra itself.
Where are the particles in this approach? For that we need Eddington's "The Philosophy of Science", a brilliant but neglected work. Like a point in geometry, what is a particle? Is it a hazy general brick-like entity out of which the world is constructed, or is it a quasi-local, semi-autonomous feature within the total structure-process? Notice the change, not things-in-interaction, but structure-process in which any invariant feature takes its form and properties from the structure-process that gives it subsistence. If an algebra is used to describe this structure-process, then what is the element that subsists? What is the element of existence? The idempotent E^2=E has eigenvalues 0 or 1: it exists or it doesn't exist. An entity exists in a structure-process if it continuously turns itself into itself. The Boolean logic of the classical world turns existence into a permanent order: quantum logic turns existence into a partial order of non-commutative E_i! Particles can be 'created' or 'annihilated' depending on the total overall process. Here there is an energy threshold, keep the energy low and it is the properties of the entity that are revealed through non-commutativity, these properties becoming commutativity to order hbar. The Bohm model can be used to complement the standard approach below the creation/annihilation threshold. Raise this threshold and then the field theoretic properties of the underlying algebras become apparent.
All this needs a different debate from the usual one that seems to go round and round in circles, seemingly resolving very little.
Basil.
On 24 Nov 2012, at 19:10, JACK SARFATTI wrote:
What is the ontology of "possibility"? In Bohm's picture it is a physical field whose domain is phase space (Wigner density) and whose range is Hilbert space. They are physically real, but not classical material.
The basic problem is how can a non-physical something interact with a physical something? This is a contradiction in the informal language. Only like things interact with unlike things. Otherwise, it's "then a miracle happens" and we are back to magick's "collapse". We simply replace one mystery by another in that case.
On Nov 24, 2012, at 5:59 AM, Ruth Elinor Kastner <rkastner@umd.edu> wrote:
Yes. It serves as a probability distribution because it is an ontological descriptor of possibilities.
RK
________________________________________
From: JACK SARFATTI [sarfatti@pacbell.net]
Sent: Saturday, November 24, 2012 1:56 AM
To: Jack Sarfatti's Workshop in Advanced Physics
Subject: Re: [ExoticPhysics] Asher Peres's Bohrian epistemological view of quantum theory opposes Einstein-Bohm's ontological view. Commentary #2
On Nov 23, 2012, at 9:24 PM, Paul Zielinski <iksnileiz@gmail.com<mailto:iksnileiz@gmail.com>> wrote:
Did it ever occur to anyone in this field that the quantum wave amplitude plays a dual role, first as an ontological descriptor,
and second as probability distribution?
This I think is consistent with Bohm's ideas. When there is sub-quantal thermal equilibrium (A. Valentini) the Born probability rule works, but not otherwise.
It seems reasonable to suppose that the wave interference phenomena of quantum physics reflect an underlying objective
ontology, while the probability distributions derived from such physical wave amplitudes reflect both that and also our state
of knowledge of a system.
That a classical probability distribution suddenly "collapses" when the information available to us changes is no mystery.
The appearance of collapse is explained clearly in Bohm & Hiley's Undivided Universe. See also Mike Towler's Cambridge Lectures. I will provide details later.
So the trick here I think is to disentangle the objective ontic components from the subjective state-of-knowledge-of-the-observer
components of the wave function and its associated probability density -- to "diagonalize" the conceptual matrix, so to speak.
However, other than Bohm it looks like no one in foundations of quantum physics has yet figured out a way to do that.
Yes.
My favorite example is an apple orchard at harvest, the trees having fruit with stems of randomly varying strength. Let's suppose
there is an earthquake and a seismic wave propagates along the ground. The amount of shaking of the trees at any given time
and place will be proportional to the intensity of the seismic wave, given by the square of the wave amplitude, and therefore the
smoothed density of fallen apples left on the ground after the earthquake will naturally be derivable from the square seismic wave
amplitude (since that determines the energy available for shaking the trees). However, when we see that a particular apple has fallen,
the derived probability density (initially describing *both* the intensity of the seismic wave *and* our state of knowledge about the
likelihood of any particular apple falling to the ground) suddenly "collapses", but in this example such "collapse" is purely a function
of our state of knowledge about a particular apple, and does not have any bearing on the wave amplitude from which it was
initially derived. In this example, it is quite clear that the probability distribution applying to any particular apple can "collapse" due
to an observation being made of any particular apple, even while the wave amplitude from which it was initially derived is entirely
unaffected by the observation of the state of any particular apple.
My question is, why is wave mechanics any different? Isn't this also a "Born interpretation" of the seismic wave?
On Nov 23, 2012, at 10:25 PM, "Kafatos, Menas" <kafatos@chapman.edu<mailto:kafatos@chapman.edu>> wrote:
I disagree, if one insists on just one view (realism) being the only possibility. We have to ask what do we mean by "real"? What kind of "space" does that wave function reside in? What are its units if not in Hilbert space referring to the Born interpretation?
There are numerous attempts to ontologize the wave function (see Kafatos and Nadeau, "The Conscious Universe", Springer 2000). The hidden metaphysics is to assume axiomatically that an external reality exists independent of conscious observers. This ultimately leads to an increased number of theoretical constructs without closure of anything (e.g. the multiverse).
Moreover, in the matrix mechanics the wave function is not needed. If psi were real, shouldn't it have been discovered long ago? Unless one argues that the theory of QM didn't exist until the 20th century so we couldn't have "discovered" it which case it gets us back to a description of nature dependent on observers!
It is OK to ontologize anything but in that case, please follow the hidden metaphysics that is implied. And state this metaphysics.
In a practical way to conduct science, we should remember how specific scientific constructs were developed. It didn't happen that somehow scientists like Bohr, Schroedinger, Heisenberg, Born, etc. stumbled on a physical quantity called the wave function psi. It was developed as part of wave mechanics which was complementary to Heisenberg's matrix mechanics.
The other ontology is that consciousness is real. This one naturally follows from orthodox quantum theory and leads to a pragmatic view of the cosmos. Two ontologies, take your pick for specific science to do. One leads to many worlds interpretation and ultimately to, perhaps, an infinity of universes, one of a few (or only one?) that happens to be "right" one (including having something called the wave function) to have conscious observers; the other leads to one universe that is self-driven by itself.
Can the two views/ontologies be reconciled? Yes, in a generalized complementarity framework, although one would negate the other in specific applications. What is "real" in this view is generalized principles applying at all levels and whatever science one works with. One deals with an objective view of the universe. The other with a subjective view of the universe (which relies on qualia).
I won't go any further. See also a series of articles by Chopra, Tanzi and myself in the last several months in Huffington Post and San Francisco Chronicle.
Menas Kafatos
Sent from my iPhone
On Nov 24, 2012, at 1:53 PM, "JACK SARFATTI" <sarfatti@pacbell.net<mailto:sarfatti@pacbell.net><mailto:sarfatti@pacbell.net>> wrote:
Yes, I agree with Ruth. I think Peres is fundamentally mistaken. However, there are some important insights in his papers nevertheless.
On Nov 23, 2012, at 7:22 PM, Ruth Elinor Kastner <rkastner@umd.edu<mailto:rkastner@umd.edu><mailto:rkastner@umd.edu>> wrote:
Concerning this statement by Peres and Fuchs in what is quoted below:
"Here, we must be careful: a quantum jump (also called collapse) is something that happens in our description of the system, not to the system itself. "
How do they know that? That is just an anti-realist assumption; that is, it presupposes that quantum states and processes do not refer to entities in the world but only to our knowledge (i.e. that quantum states are epistemic). This view has come under increasing criticism (e.g. via the PBR theorem which disproves some types of 'epistemic' interpretations). I present a contrary, realist view in my new book on TI, in which measurements are clearly accounted for in physical terms and quantum states do refer to entities, not just our knowledge. Quantum 'jumps' can certainly be considered real and can be understood as a kind of spontaneous symmetry breaking.
Details on that?
In my view, quantum theory is not just about knowledge or epistemic probability; it is about the real world. There is no need to give up realism re quantum theory. Prior realist interpretations simply have not been able to solve the measurement problem adequately, because they neglect the relativistic level in which absorption and emission are acknowledged as equally important physical processes.
Best
RK
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On Aug 11, 2012, at 1:41 AM, Basil Hiley <b.hiley@bbk.ac.uk> wrote:
On 27 Jul 2012, at 07:00, nick herbert wrote:
On Jul 26, 2012, at 9:50 AM, nick herbert <quanta@cruzio.com> wrote:
1. The oft-cited remark that non-relativistic Bohmian mechanics gives the same result
as conventional QM for all conceivable experiments is plain wrong. The two theories
possess radically different ontologies which lead to radically different consequences.
BH: How can it be wrong? It uses exactly the same mathematics, without the addition or subtraction of any new mathematical structure. Its predicted expectation values found in all experiments are identical to those found from the conventional rules. If you want to criticise it, why not simply say "It adds no new experimental predictions, so why bother with it?" Then you can get into arguments about which interpretation is better in your opinion. Then it is a matter of opinion not experimental science.
JS: However, Antony Valentini's extension does add new predictions consistent with my own independent investigations and also Brian Josephson's which already has observational evidence in its favor (Libet, Radin, Bierman, Puthoff-Targ, Bem)
NH: What exists in QM is a wavefunction, spread out in configuration space
(and this wavefunction is "real" according to PBR). For a given quantum state
all systems represented by that state have the same ontology.
BH: The ontology gives meaning to the notion of a "quantum state". What does it mean to say "For a given quantum state all systems represented by that state have the same ontology"?
NH: What exists in BM is an actual particle which for S-states has the remarkable property
that v=0. In BM all systems represented by the same state are different--their difference (in the
S-state case) being the differing positions of the static electron. A Bohmian S-state
consists of an ensemble of stationary electrons each in a different position whose
position pattern is given by psi squared.
It is this v=0 property of BM S-wave electrons that is used to create counterexamples to the
contention that BM and QM give the same predictions.
1. Muonic Hydrogen. Like t! he electron the muon in the BM picture is stationary. Hence the muon
lifetime in BM is the just the natural lifetime. However in QM the muon has a velocity distribution
so the lifetime is lengthened by relativity. BM and QM predict different lifetimes for the muonic atom. One may object
that I have introduced relativity into a non-rel situation. However the QM and BM states are still non-rel.
The lifetime of the muon can be seen as a measuring device probing the ontology of the muonic hydrogen.
The probe uses a relativity effect to measure a non-rel configuration.
BH: I recall having already answered this criticism some time ago. Time dilation is a relativistic phenomenon so you must use the relativistic Dirac theory in this case.
JS:: Yes, Nick's error here is obvious. He appeals to the wrong equation for the problem. It's a Red Herring.
BH: In the past there I have been entirely happy with the treatment of the Bohm model of the Dirac equation that we have given. However Bob Callaghan and myself have now obtained a new complete treatment of the Dirac equation with which I am completely happy. It uses the Clifford algebra in a fundamental way as it must to link with the known successful spinor structure. See Hiley and Callaghan: Clifford Algebras and the Dirac-Bohm Quantum Hamilton-Jacobi Equation. Foundations of Physics, 42 (2012) 192-208.
DOI: 10.1007/s10701-011-9558-z and in more detail in The Clifford Algebra Approach to Quantum Mechanics B: The Dirac Particle and its relation to the Bohm Approach, (2010) aXriv: 1011.4033.
Our work shows that the Bohm charge velocity of the electron is, in fact, given by v= Psi alpha Psi, where alpha is the Dirac 4x4 matrix, which is related to the Dirac gamma matrices. (See Bohm and Hiley The Undivided Universe, p. 272 for our original treatment which is confirmed by our latest work.) If you now look at the wave function of the ground state of the Dirac hydrogen atom which you can find in Bjorken and Drell p. 55 you will find the electron is moving in the ground state. What is interesting is that when you take this expression and go to the non-relativistic limit you find the velocity is zero, exactly the result that the Schrödinger equation gives. Remember the energy levels calculated from the Schrödinger hydrogen atom are only approximations to those calculated using the Dirac hydrogen atom.
Do you have a reference to the paper that measures the lifetime of the muon in muonic hydrogen? I can't find a good reference to a clean experiment which shows exactly how to measure the time dilation you mention. I have recently written up the details of the calculation that I have outlined above but I would like to add a better reference to the actual measurement.
2. Electron Capture decay. Certain radioactive elements (Beryllium 7, for instance) possess an excess
positive charge and do not have enough energy to decay by positron emission. Instead they capture the
S-state electron which transforms a nuclear proton into a neutron and neutrino (inverse beta decay).
Electron Capture (EC) is a very delicate probe of the ontology of the S-state electron. QM ontology
(all electrons the same) predicts a smooth exponential decay. After many half-lifes all the Be7 is gone.
BM ontology predicts a very different outcome: exponential decay for all electrons located inside the nucleus;
infinite li! fe for stationary Bohmian electrons located outside the nucleus.
BH: You must read past the simple Bohm model introduced in chapter three of our book, "The Undivided Universe". The first ten chapters contain a discussion of the non-relativistic Bohm model. There we show that if you want to apply the theory to problems where the particles interact either with other particle or with fields like the electro-magnetic field, you must introduce an appropriate interaction Hamiltonian. In section 5.3 to 5.5 we show how to deal with a very simple example of two-particle interactions. These sections were written simply to illustrate how the mathematics work and how you can explain the results using the Bohm interpretation. NB the interpretation is only applied after we have solved the Schrödinger equation containing the interaction Hamiltonian. You can't solve these equations exactly so you have to use perturbation theory. Remember the maths is the same as for the standard interpretation. It is the interpretation that is different.
What happens if the interaction Hamiltonian involves the electromagnetic potentials? To discuss interaction with the electromagnetic field you must go to a relativistic theory. This means you must use the Dirac equation. Chapter 12 of our book begins to show you how to do this. The work of Bob Callaghan and myself mentioned above takes this further. What we have done is to discuss the free Dirac electron for simplicity. We simply wanted to show how it worked without introducing more realistic interaction Hamiltonians.
Now let me try to answer your question as to how we deal with electron capture. In order to describe this capture, we have to introduce the appropriate interaction Hamiltonian. What is the appropriate interaction Hamiltonian in this case? To find this we have to go to a review article like "Orbital electron capture by the nucleus" [Rev. Mod Phys. 49 (1977) 77-221]. You will see that the interaction Hamiltonian is a weak electron current-hadron current interaction. You must now put that into the Dirac equation and calculate away. Well the calculations are all done in the Rev. Mod. Phys. paper and all we need to do is to interpret the results according to the Bohm model.
Where your analysis goes wrong is that you assume (1) the non-relativistic theory and (2) there is no interaction between the nucleus and the electron. You can do that to a first approximation to explain the principle of the Bohm model to, say, a first year undergraduate, but you must not say that's all there is. It is not a true reflection of the processes that are involved! There is an interaction between the nucleon and the electron and you must take this into account even in the Bohm model if you want to understand the physics.
If your message is simply to say that the naive Bohm model based on the Schrödinger is inadequate to deal with these problems then I totally agree with you. Bohm and I have always recognised that the '52 work was just a first step. Let me quote from his Causality and Chance book p. 118
“It must be emphasized, however, that these criticisms are in no way directed at the logical consistency of the model, or at its ability to explain the essential characteristics of the quantum domain. Rather they are based on broader criteria, which suggest that many features of the model are implausible and, more generally, that the interpretation proposed in section 4 [of the ‘52 paper] does not go deep enough.”
I thought that in our book, "The Undivided Universe", we made it clear that chapter 3 was a first step. All the remaining chapters were to show how the model was to be developed to meet many different actual situations found in nature. Finally in chapter 15, we outlined what was going to be developed in a second volume, which would probe a much deeper structure but unfortunately Bohm died just as we were finishing the first book.
NH: If these two counter-examples to the QM/BM experimental identity conjecture have been discussed in the literature,
I! am unaware of it. But they should be.
BH: You are quite right, these points should be discussed in the literature. Unfortunately I have been too involved in developing the ideas outlined in chapter 15 and that means going deeper into what I think really underlies quantum phenomena. You will find some of this work in the latest publications of mine which are accessible on the net. A good place to find a comprehensive review of my latest efforts is in my paper Process, Distinction, Groupoids and Clifford Algebras: an Alternative View of the Quantum Formalism, in New Structures for Physics, ed Coecke, B., Lecture Notes in Physics, vol. 813, pp. 705-750, Springer (2011). Unfortunately I don't think it is available on the net at present but if you are interested I can send you a copy.
Thank you for your interest in our work.
Basil.
Nick Herbert