rutgers, october 2007.giancarlo ghirardi1. rutgers, october 2007.giancarlo ghirardi2 the...

Rutgers, october 2007. GianCarlo Ghirardi 1


The Interpretation of The Interpretation of Q.M.: where do we Q.M.: where do we

stand?stand?

GianCarlo GhirardiGianCarlo GhirardiDepartment of Theoretical Physics,

Trieste University The Abdus Salam I.C.T.P., Trieste,

The INFN, Sezione di Trieste,


This simple talk has been prepared as a contribution to the meeting honoring Shelly Goldstein on the occasion of his 60th birthday.

I cannot express adequately I sorry I am of not beeing able to be here, at Rutgers, to honour this dear friend, this exceptional scientist who has taught so many things to me and who has honored me with his precious friendship.

I am really indebted to him for his lesson of full dedication to the scientific enterprise, for the coherence of his actions, for the passionate interest that we share on foundational problems.

I cannot do better that thanking him from the deep of my heart and whishing him still many more years of important scientific achievements and of a life full of joy and satisfaction.


1. THE MACRO-1. THE MACRO-OBJECTIFICATION PROBLEMOBJECTIFICATION PROBLEMA quite general argument without any assumption of ideality.A.Bassi and G.C. Ghirardi: A general argument against the universal validity of the superposition principle, Phy.Lett.A275,373 (2000).

The scheme is highly idealized and somebody (e.g.- H. Primas) has considered this fact as responsible of the problems it gives rise to. We agree that we cannot control all degrees of freedom of the “apparatus”, to avoid its interactions with the environment, to guarantee that its final states are orthogonal etc. etc. Accordingly, we consider the microsystem and an ensemble of apparata . The first label specifies that the pointer “points at AR” and distinguishes the various members of the ensemble. In terms of the weights we define a measure according to:

The macro-objectification (or measurement) problem, is usually discussed within the framework of the von Neumann chain. One is interested in “measuring” an observable of a microsystem and uses it to trigger a macroscopic change in a macro-object (e.g. a pointer). Then one has: ??


In general, when we write expressions like and we make reference to two sets of states and for which it is legitimate to claim: the pointer points at A, at B, respectively. We will not require orthogonality of such states but, obviously, we have to impose that they are to a large extent “distinguishable”, a fact we will characterize mathematically by imposingAssumptions:

1.The microsystem can be prepared in two states and as well as in the state

3. We define some physically meaningful sets

2. The system-apparatus interaction and combined evolution, when the triggering state is one of the first two, is:

4. We make a natural reliability assumption concerning the apparatus:

which implies:


See also: B. d’Espagnat: GianCarlo Ghirardi and the Interpretation of Quantum Physics, Special Issue: The Quantum Universe, JPA. 2007.

Conclusion: The macro-objectification problem has nothing to do with the assumptions of ideality made by J. von Neumann.

It is then trivial to show that, for i.e., for the large majority of the (initial states of the) apparata, if one triggers them with the state and assumes the unrestricted validity of the superposition principle, the final state cannot belong to the set or, analogously, to the set , or to any other one for which the pointer “points at a definite position”.


See, e.g.: S. Adler: Why decoherence has not solved the Measurement Problem: A Response to P.W. Anderson, Studies in History and Philosophy of Modern Physics, 34 135-142 (2003).

2. 2. DECOHEREDECOHERENCENCE

so that the reduced statistical operator obtained by partial tracing on the environmental degrees of freedom actually leads to a situation which is (FAPP) equivalent to the one implied by WPR.

Why is it so? Because of the unavoidable and uncontrollable coupling with the environment. Actually one should read the first expression as:

Q.M.: WPR in the statevector and statistical operator languages (A,B, two macroscopically different states).

|


The flaw in the argumentThe flaw in the argument: we have already seen that actually, if one pretends to have a reliable way of ascertaining microproperties and assumes the unlimited validity of Q.M., linear superpositions of macroscopically different states occur. But there is another weak point in the argument. In fact it goes like this:

Here one ignores completely that, within Q.M. the correspondence

[Statistical Ensembles] [Statistical operators]

is infinitely many to one.On which basis one disregards the fact that the same statistical operator describes the ensemble:

??


In fact even some of the most convinced supporters of the decoherence way out of the difficulties of the formalism have been compelled to recognize this basic fact:The local description “is assumed” and the specific choice of a basis can perhaps be justified by a fundamental inderivable assumption about the local nature of the observer ... no unitary treatment of the time dependence can explain why only one of these dynamically independent components is experienced.

E. Joos and H.D. Zeh, Z. Phys. B 59, 223 (1985).


A final remark.A final remark.The most recent investigations aiming to implement new and innovative technological devices based on quantum mechanics (Quantum Cryptography, Quantum teleportation and Quantum computation) deal, obviously, with individual physical systems and make a systematic use of the wave packet reduction process at the individual levelat the individual level as an important resource.If, following the measurement of Bell’s states by Alice, reduction of the wave packet would not actually take place, the whole protocol for implementing teleportation or secure transmission of information would collapse …

(unless one adopts a many universes or many minds interpretation of the theory).


3. DIGRESSION: The 3. DIGRESSION: The Primitive OntologyPrimitive OntologyMany scientists believe that the purely technical and formal aspects of a theory represent all there is to say about it. I share with J.S. Bell and many others the opinion that further requirements must be imposed to a theory to be taken seriously as a fundamental description of natural processes.

In what follow we will limit our considerations to two approaches to solve the macro-objectification problem which, at the nonrelativistic level, seem to be fully consistent: Bohmian Mechanics and the so called GRW-theory.

This fact has been stressed with great lucidity in recent papers, pointing out the necessity of making precise the Primitive Ontology (PO) of the theory. The PO is the specification of “what the theory is fundamentally about”.

V. Allori, S. Goldstein, R. Tumulka and N. Zanghì: On the common structure of Bohmian Mechanics and the GRW-Theory, quant-ph/0603027,

T. Maudlin, Completeness, supervenience and ontology, in: The Quantum Universe, IOP.

They correspond to the two alternatives indicated by Bell: either the wave function, as given by the Schrödinger equation, is not everything, or it is not right.


4. BOHMIAN MECHANICS4. BOHMIAN MECHANICSFormal aspects:Formal aspects:States:Wavefunction+Positions

Initial conditions:

Evolution:

Equivariance:

as an immediate consequence of the quantum continuity equation

Primitive Primitive OntologyOntologyAll particles of the universe have, at all times, precisely definite positions. They move along trajectories in such a way to reproduce the position density distribution of standard Q.M.

The famous two-slit experiments looks like this:

Note: the theory is (purposedly) predictively equivalent to Standard Note: the theory is (purposedly) predictively equivalent to Standard Quantum Mechanics but overcomes its problems.Quantum Mechanics but overcomes its problems.


5. THE GRW-THEORY5. THE GRW-THEORYFormal Formal aspects:aspects:•One addsadds to Schrödinger’s equation

nonlinear and stochastic terms describing universal localization processes affecting all particles of the universe:

•The statistical operator obeys an equation of the Quantum Dynamical Semigroup type.

Some Physically Some Physically interesting featuresinteresting features

•The trigger mechanism: the localization frequency is amplified with the number of particles (actually of the nucleons, since is made proportional to the mass).

•One proton suffers a localization every 108 years, the c.o.m of a macrosystem every 10-

8 sec.!•The universal dynamics leaves (practically) all quantum predictions for micro-systems unaltered, it accounts for WPR and for the classical behaviour of macrosystems.

•The phenomenological theory is, in principle, testable against Q.M.S. Adler, A. Bassi and E. Ippoliti: Towards Quantum superpositions of a mirror I,II; Phys. Rev,

Lett. 94, 030401 (2005); J. Phys. A 38, 2715 (2005).

•The collapses occur at randomly distributed times with a mean frequency •The center of the collapse x is chosen randomly with probability distribution


Localization of a microsystemLocalization of a microsystem

|>

The trigger mechanismThe trigger mechanism


Further mathematical Further mathematical refinements:refinements:The Continuous version of the model. P.Pearle,Phys. Rev., A39,

2277(1989).Ito stochastic differential equation

W(i)t(x) a set of real Wiener processes such

that

The above (Raw) equation is linear but it does not preserve the norm. Prescription: determine and then normalize it (it does not matter when). The physically relevant equation (Cooked) is obtained by the replacement:

The dynamics induces individual reductions. At the ensemble level it is accouted for by the following equation of the QDS type:

Primitive Primitive Ontology:Ontology:

I have considered both the discrete and continuous versions of the model (physically equivalent) in order to be able to discuss two possible primitive ontologies which have been proposed for it.

The “Mass density” ontologyThe “Mass density” ontology (Ghirardi,Grassi, Benatti ): what the theory is about, what is real “out there” is the mass density in the 3-dim Euclidean space:

The “Flashes” ontologyThe “Flashes” ontology (J.S. Bell): what the theory is about are the localizations which take place at definite times and at definite points of ordinary space. “A macrobody is a Galaxy of such beables”


6. Some positions about the two 6. Some positions about the two previous approaches.previous approaches.Bohmian Mechanics: being empirically indistinguishable from standard NRQM, it is often criticized as ‘bad science’ or as ‘a degenerate research program’ (Lakatos) . An illuminating example:At the regular weekly luncheon meeting today, I asked my collegues what they think of B.M. The answers were pretty uniform and much what I would have said myself. First, as we understand it, Bohm’s quantum mechanics uses the same formalism as ordinary quantum mechanics, including a wave function that satisfies Schrödinger equation, but adds an extra element, the particle trajectory. The prediction of the theory are the same as for ordinary quantum mechanics, so there seems little point in the extra complication, except to satisfy some a priori ideas about what a physical theory should be like . Letter by S. Weinberg to S. Goldstein 1996.

Two remarks: the sentence ignores completely that the theory describes consistently WPR and the classical behaviour of macro-objects, which is not a trivial fact.

Moreover, not all proposed solutions to the macro-objectification problem are empirically indistinguishable from NRQM.


GRW: The ‘new ortodoxy’ (Bub) claims that superpositions are there but we do not see them due to environmental induced decoherence. We have already analyzed this point.

Moreover: many of these people claim that HVThs are ‘ad hoc’ and ‘bad science’. But ignoring that the macro-objectification problem admits an empirical solution they tolerate the same ad hocness with respect to Q.M. Thus, either they must renounce to criticize HVThs, or they have to recognize that they also are holding on to a degenerate research program.Their attitude is illustrated by another formal aspect to which they make often reference: the so called ancilla argument. It is well known that any quantum evolution equation of the QDS-type for the statistical operator is physically equivalent to a quantum mechanical theory with a unitary and linear dynamics of the quantum state defined on a larger Hilbert space.


Question: what is the purpose of this position, besides the will to protect the standard theory come what may? The ancilla field has, by construction, no observable effect and it amounts precisely to introducing hidden variables whose only role is to save the formal structure of Q.M.

In view of the fact that dynamical reduction theories qualify themselves as rival theories of the standard theory, would it not be more serious, scientifically, to try, as Penrose, Adler and many others do, to see whether some crucial test can be performed?


7. The real problem: relativistic 7. The real problem: relativistic generalizations.generalizations.J.S. Bell concluded his Touschek lecture, in which he had

considered Bohmian Mechanics and GRW in detail with the following sentence: The real problem now is which one of these two exact theories admits a relativistic generalization.

I want to quickly mention some attempts to get this. Bohmian mechanics admits relativistic generalizations of various kinds, from the original attempts by Bohm and Hiley dealing with a relativistic theory of the scalar field, to the recent investigations by Goldstein, Duerr, Zanghi’ and their collaborators, resorting to a preferred space-like slicing. What really matters are not the details of such approaches but a general fact which characterizes them all: they turn out to be not ‘genuinely invariant’ in the sense that they admit a (hidden) preferred reference frame.

This is a consequence of the fact that any theory which violates the locality condition by violating parameter dependence does not admit a ‘genuine’ relativistic generalization.

G.C. Ghirardi and R. Grassi, Bohm’s theory versus dynamical reduction in: Bohmian Mechanics and Quantum theory, an Appraisal, Kluwer 1996


There have been also many attempts to generalize the dynamical reduction models.

The first is due to P. Pearle, and has been discussed in detail and proven to formally be perfectly Lorentz invariant. A Fermion field is coupled to a meson field and a reduction process is assumed to forbid superpositions of different mesonic clouds.

However a new problem immediately arises: the appearence of untractable divergencies. They are mainly due to the need of introducing stochastic processes in a relativistic context.

In this way one induces a localization of nucleons.


Other attempts should be mentioned, like, e.g. those of Dove and Squires and of Dowker and Henson, formulated on a discrete space-time.

Up to very recent times no real step forward has been done. In 2004 R. Tumulka presented a relativistic generalization of GRW for N noninteracting distinguishable particles based on the consideration of a multi-time Dirac equation. It sticks strictly to what we have called the flashes ontology. The mass ontology has to be enriched before one can resort to it for relativistic generalizationsIt is particularly interesting to mention Tumulka’s conclusions :


A somewhat surprising feature of the present situation is that we seem to arrive at the following alternative: Bohmian mechanics shows that one can explain quantum mechanics, exactly and completely, if one is willing to pay with using a preferred slicing of space-time; our model suggests that one should be able to avoid a preferred slicing if one is willing to pay with a certain deviation from quantum mechanics.I will not embarque myself in discussing the newest newest ortodoxyortodoxy characterizing the position of eminent scientists involved in quantum computation. It would require a too long and subtle analysis. I will simply state that I do not share their claim that science is only and exclusively about information. In spite of the great interest with which I look to this extremely interesting and promising field of research I think that on foundational issues it has lead back to complacent and ambiguous positions.

rutgers, october 2007.giancarlo ghirardi1. rutgers, october 2007.giancarlo ghirardi2 the...

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