Re: Basil Hiley's update on current state of work in Bohm's ontological picture of quantum theory
- Begin forwarded message:From: Ruth Elinor Kastner <rkastner@...>Subject: Re: [ExoticPhysics] Basil Hiley's update on current state of work in Bohm's ontological picture of quantum theoryDate: November 25, 2012 12:36:53 PM PSTReply-To: Jack Sarfatti's Workshop in Advanced Physics <exoticphysics@...>
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.
RKOn Nov 25, 2012, at 11:58 AM, JACK SARFATTI <sarfatti@...> wrote:On Nov 25, 2012, at 2:55 AM, Basil Hiley <b.hiley@...> wrote:
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.
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@...> wrote:
Yes. It serves as a probability distribution because it is an ontological descriptor of possibilities.
From: JACK SARFATTI [sarfatti@...]
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@...<mailto:iksnileiz@...>> 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.
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@...<mailto:kafatos@...>> 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.
Sent from my iPhone
On Nov 24, 2012, at 1:53 PM, "JACK SARFATTI" <sarfatti@...<mailto:sarfatti@...><mailto:sarfatti@...>> 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@...<mailto:rkastner@...><mailto:rkastner@...>> 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.
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