Transcript Rutgers, october 2007. GianCarlo Ghirardi 1

Rutgers, october 2007.
GianCarlo Ghirardi
1
The Interpretation of Q.M.:
where do we stand?
GianCarlo Ghirardi
Department of Theoretical Physics, Trieste
University
The Abdus Salam I.C.T.P., Trieste,
The INFN, Sezione di Trieste,
Rutgers, october 2007.
GianCarlo Ghirardi
2
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
Rutgers, october 2007.
GianCarlo Ghirardi
3
1. THE MACROA
quite general argument without
any
OBJECTIFICATION
PROBLEM
assumption
ideality.
A.Bassi and G.C. Ghirardi: Aof
general
argument against the universal validity of the superposition principle,
Phy.Lett.A275,373 (2000).
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:
?
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:
Rutgers, october 2007.
GianCarlo Ghirardi
4
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 imposing
Assumptions:
1.The microsystem can be prepared in two states
and
as well as in
the state
2. The system-apparatus interaction and combined evolution, when the triggering
state is one of the first two, is:
3. We define some physically meaningful sets
4. We make a natural reliability assumption concerning the apparatus:
which implies:
Rutgers, october 2007.
GianCarlo Ghirardi
5
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”.
Conclusion: The macro-objectification problem has nothing to
do with the assumptions of ideality made by J. von Neumann.
See also: B. d’Espagnat: GianCarlo Ghirardi and the Interpretation of Quantum Physics, Special Issue:
The Quantum Universe, JPA. 2007.
Rutgers, october 2007.
GianCarlo Ghirardi
6
2.
DECOHERE
Q.M.: WPR in the statevector and statistical operator languages (A,B, two
macroscopically different states).
NCE
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).
|
Why is it so? Because of the unavoidable and uncontrollable coupling with the
environment. Actually one should read the first expression as:
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.
Rutgers, october 2007.
GianCarlo Ghirardi
7
The 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:
?
Rutgers, october 2007.
GianCarlo Ghirardi
8
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).
Rutgers, october 2007.
GianCarlo Ghirardi
9
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 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).
Rutgers, october 2007.
GianCarlo Ghirardi
10
3. DIGRESSION: The
Primitive
Ontology
Many 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.
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”.
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 GRWtheory.
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.
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.
Rutgers, october 2007.
GianCarlo Ghirardi
11
4. BOHMIAN MECHANICS
Formal aspects:
States:Wavefunction+Positio
ns
Initial conditions:
Evolution:
Primitive
Ontology
All particles of the universe
have, at all times, precisely
definite positions. They
move along trajectories in
such a way to reproduce
the
position
density
The
famous
two-slit
distribution
of standard
experiments
looks like this:
Q.M.
Equivariance:
as an immediate consequence of
the quantum continuity equation
Note: the theory is (purposedly) predictively equivalent to Standard Quantum
Rutgers, october 2007.
GianCarlo Ghirardi
12
Some
Physically
5. THE GRW-THEORY
interesting features
Formal
•One
adds to
aspects:
Schrödinger’s equation
nonlinear and stochastic terms describing
universal localization processes affecting
all particles of the universe:
•The collapses occur at randomly
distributed times with a mean frequency
•The center of the collapse x is chosen
randomly with probability distribution
•The trigger mechanism:
the localization frequency
is amplified with the
number
of
particles
(actually of the nucleons,
since
l
is
made
•One proton suffers a
proportional to the mass). 8
localization every 10
years, the c.o.m of a
macrosystem every 10-8
•The
sec.! universal dynamics
leaves (practically) all
quantum predictions for
micro-systems unaltered,
it accounts for WPR and
for
the classical
behaviour
•The
phenomenological
of
macrosystems.
theory
is, in principle,
testable against Q.M.
•The statistical operator obeys an
equation of the Quantum Dynamical
Semigroup
type.
S. Adler, A. Bassi
and E. Ippoliti: Towards Quantum superpositions of a mirror I,II; Phys. Rev, Lett. 94,
030401
Rutgers, (2005);
october 2007.J. Phys. A 38, 2715 (2005).GianCarlo Ghirardi
13
Localization of a microsystem
|Y>
The trigger mechanism
Rutgers, october 2007.
GianCarlo Ghirardi
14
Further mathematical
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:
Rutgers, october 2007.
GianCarlo Ghirardi
Primitive
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 “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”
The
“Mass
density”
(Ghirardi,Grassi, Benatti ):
theory is about, what is
there” is the mass density
dim Euclidean space:
ontology
what the
real “out
in the 3-
15
6. Some positions about the two
Bohmian
Mechanics:
being empirically indistinguishable from
previous
approaches.
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
Two remarks: the sentence ignores completely that the
satisfy some a priori ideas about what a physical theory
theory describes consistently WPR and the classical
should be like . Letter by S. Weinberg to S. Goldstein 1996.
behaviour of macro-objects, which is not a trivial fact.
Moreover, not all proposed solutions to the macroRutgers, october 2007.
GianCarlo Ghirardi
16
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 QDStype 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.
Rutgers, october 2007.
GianCarlo Ghirardi
17
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?
Rutgers, october 2007.
GianCarlo Ghirardi
18
7. The real problem: relativistic
J.S.
Bell concluded his Touschek lecture, in which he
generalizations.
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
admit
‘genuine’
relativistic
G.C. Ghirardi and R. Grassi,
Bohm’s not
theory versus
dynamicalareduction
in: Bohmian Mechanics
and
Quantum theory, an Appraisal, Kluwer 1996
generalization.
Rutgers, october 2007.
GianCarlo Ghirardi
19
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.
In this way
induces
localization
nucleons.
one
a
of
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.
Rutgers, october 2007.
GianCarlo Ghirardi
20
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 generalizations
It is particularly
conclusions :
Rutgers, october 2007.
interesting
GianCarlo Ghirardi
to
mention
Tumulka’s
21
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
ortodoxy 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 Ghirardi
22
Rutgers, october 2007.
GianCarlo Ghirardi
23
Rutgers, october 2007.
GianCarlo Ghirardi
24