Out of this World Ontology
Non-Local Beables and 21st century directions for dBB
Travis Norsen
Marlboro College
Vermont, USA
Outline:
1.
2.
3.
4.
5.
Beables, local and non
Non-local beables in dBB: possible reactions
Virtues of local beables
Theories of Exclusively Local Beables (TELBs)
dBB as the (most likely) path to TELB
Part 1: “Beables”
• Bell: “The word ‘beable’ will [carry the distinction] familiar already in
classical theory between ‘physical’ and ‘non-physical’ quantities. In
Maxwell’s electromagnetic theory, for example, the fields E and H are
‘physical’ (beables, we will say) but the potentials A and φ are ‘nonphysical’. Because of gauge invariance the same physical situation can be
described by very different potentials. It does not matter that in Coulomb
gauge the scalar potential propagates with infinite velocity. It is not really
supposed to be there. It is just a mathematical convenience.” (1976)
• Bell: “The beables of the theory are those entities in it which are, at least
tentatively, to be taken seriously, as corresponding to something real.”
(1990)
• “Local beables are those which are definitely associated with particular
space-time regions. The electric and magnetic fields of classical
electromagnetism, E(t,x) and B(t,x) are again examples…” (1990)
How to decide what gets “beable status”?
• Proposal: If you can’t formulate your theory without X, then X is a beable.
 Note this allows a lot of flexibility!
• Example: Three “versions” of Newtonian gravitational theory:
A
Version:
Laws:
Beables:
qi  
j i
B
Gm j (q j  qi )
q j  qi
3
qi (t ) i  1,..., N
C
qi   |qi
1
i 2m
i
 2  4G
qi 
2
 Gmi m j S
 S 

  

0
t
 qi  i  j qi  q j
1 S
mi qi
qi (t ) i  1,..., N
qi (t ) i  1,..., N
 ( x, t )
S (q1 ,..., q N , t )
So… which version is true?
• But wait: Aren’t they in fact all equivalent?
– Yes: they produce the same particle trajectories
– But no: in terms of the beables they posit and the kinds of research programs
they suggest.
• For example, “version B” – as contrasted to “version A” – resonates with
the successes of electromagnetic theory, invites extending the law
(Poisson equation) for φ(x,t) into a wave equation with finite propagation
speed, etc.
• Something along these lines was the path to GR.
• So there’s some sense in which – with the benefit of hindsight – we should
say that “version B” is the “right” way to think about the earlier, purely
classical gravitational theory.
• Note that “hindsight” is crucial here: 300 years ago, it wouldn’t have been
clear at all that (for example) B was superior to A.
– Arguments from locality, etc., maybe suggest B…
– Arguments from Occam’s razor, etc., maybe suggest A (but maybe not)…
– Both should have been regarded as reasonable candidates for the title of
“right” way to think about it…
What about “version C”?
• Though still mathematically equivalent, this is radically different from “A”
and “B”, because it involves a non-local beable: S(q1, q2, …, qN, t)
• Simply put, that makes “C” really really weird. It would just be very very
hard to take it seriously in the way I’m suggesting one should take “B”
seriously.
– If, contrary to actual history, “C” had somehow been written down first as an
account of (say) the motions of planets, people would immediately assume
that there was some mathematically-related TELB – like “A” or “B” – that
should be found and then taken seriously.
• Why? “C” involves OUT OF THIS WORLD ONTOLOGY! To take it
seriously, you really have to posit not just some relatively-unexpected new
“stuff” in the world, but a whole parallel (and very very unusual) world
with its own stuff in it, which somehow causally interacts with the stuff
(local beables) in this world. Really really weird!
Analogy to us, today, with dBB
• dBB (and basically all other extant candidate quantum theories) include a
non-local beable: the wave function.
• So we are in fact in something like this sort of hypothetical situation.
• Perhaps we should be responding in the way that I said the hypothetical
people would have responded…
• That, I think, should be an active direction of research for dBB in the 21st
century.
• That’s basically all I want to say. But we can shed a little more light on this
by coming at it again from a couple different angles.
Part 2: other possible attitudes to
dBB’s nonlocal beable
1. Holland: “a complete and accurate account of the motions of particles moving in
accordance with the laws of quantum mechanics must be directly connected with
multidimensional waves dynamically evolving in configuration space.” (emph.
added, p. 321)
 Need to bite the bullet and learn to live with this OOTWO
2. DGZ: “We propose that the wave function belongs to an altogether different
category of existence than that of substantive physical entities [--] that the wave
function is a component of physical law rather than of the reality described by the
law.”
 Do what you’d do if you had “version B” but (for some reason) really wanted to avoid
having a φ(x,t) field in the picture: shuffle it into the law for q as in “version A”
3. Heisenberg: “For [de Broglie and] Bohm, the particles are ‘objectively real’
structures, like the point masses of classical mechanics. The waves in
configuration space also are objective real fields, like electric fields…” “Here we
meet a first difficulty: what does it mean to call waves in configuration space
‘real’? This space is a very abstract space. The word ‘real’ goes back to the Latin
word ‘res,’ which means ‘thing’; but things are in the ordinary three-dimensional
space, not in an abstract configuration space.”
 Need to dismiss the whole thing as misguided (retreat back to Copenhagen)
Summary so far:
•
Non-local beables are really really weird. We should admit this more openly, not
obfuscate it by:
– introducing lots of (otherwise basically pointless) other local beables (energy densities,
quantum potentials, etc.) which still require the wf to define their dynamics
– using the word “beable” to mean “hidden variables” so that the question of the beable status
of the wf is never raised.
– understating or evading how bizarre it is to take nonlocal beables seriously.
•
Three ways of responding to the non-local beable in dBB were mentioned.
– I wouldn’t accept Holland’s view unless I was convinced that all possible alternatives failed
– The DGZ view is intriguing, but somehow the wf just doesn’t smell like a law to me.
– Heisenberg? Please.
•
I want to propagandize for Theories of Exclusively Local Beables – TELBs – as an
alternative research program.
– Einstein, de Broglie, and others tried to construct such theories.
– Then this research program was just abandoned.
– But now we know a lot more about what will be required to make it work (e.g. non-locality,
entanglement)
– My toy example TELB
Part 3: Virtues of
Theories with Local Beables
• J.S. Bell: “It is in terms of local beables that we can hope to
formulate some notion of local causality.” (1976)
• AGTZ: “Under a space-time symmetry the [local beables]
must be transformed in accord with its intrinsic geometrical
nature, while wave functions (and other [nonlocal]
ontology, if any) should be transformed in a manner
dictated by their relationship to the [local beables].” (2008)
• Tim Maudlin: “the principles of translation [between what
a theory predicts and the kinds of experiences we take as
evidence for (or against) the theory] are extremely easy
and straightforward when the connection is made via the
local beables of the theory.” (2007)
…and corresponding vices of theories
without local beables (e.g., MWI)
•
Any claim of consistency with “relativistic local causality” is misleading and
vacuous: the theory posits no physical objects in ordinary space-time!
•
Same for “lorentz invariance”: there is no reasonable a priori expectation about
how the universal wf should transform under lorentz boosts, hence no reason that
any particular such transformations should be accepted as demonstrating its
Lorentz invariance.
•
“Empirical adequacy” for dBB consists in its providing an account of the motion of
stuff (parsed as collections of particles) that is consistent with how we actually
observe the stuff to move; accounts of alleged “emprical adequacy” for MWI
involve some element of delusion and some kind of “direct” interaction between
the wf and “a mind” which interaction somehow gives rise to the appropriate
delusions. (no psycho-physical parallelism)
•
Note that these issues are all tightly coupled for MWI: its proponents rely on
some tacit assumption like “naïve realism about operators” which underwrites an
in-fact-unjustified assumption that certain familiar configurations of stuff are
realized; arguments about locality or lorentz invariance or empirical adequacy are
then parasitic on these “ill gotten” notions.
Summary of the virtues:
• Local beables allow meaningful analysis of spacetime symmetries and locality.
• Local beables allow meaningful claims of
empirical adequacy.
• But…
Is just having local beables enough?
• For example: can a theory with both local and nonlocal beables really be
consistent with relativity?
– Relativity as roughly: “formulatable without using any spacetime structure
other than the relativistic 4-metric”.
– But a theory w/ non-local beables by definition requires this whole parallel
world, with its own structured space-time, etc.
– Isn’t that actually a case of adding lots of “space-time structure” – compared,
e.g., to the teensy little bit extra that’s added with say a preferred foliation of
(3+1) space-time?
• Can there really be any convincing, direct empirical evidence for nonlocal
beables?
– Abductive, not H-D
Perhaps the answer to both questions is “yes”. I doubt it, but perhaps. The
point here is just that they require more – and more careful – attention
than they’ve been given.
Part 4: TELBs
• A (plausible, empirically adequate) Theory of Exclusively Local Beables – a
theory with no Out of This World Ontology – would be nice.
• My toy example:
– Taylor expand the wf around the (actual, moving) dBB particle configuration
– Individual particles guided by associated pilot waves (conditional wf’s that can
be taken to propagate in physical 3-space)
– But: an infinite number of auxiliary fields (corresponding to higher-order
derivatives of the config space wf) are also posited as local beables
– Reproduces dBB particle trajectories (under simplified conditions: no spin,
analytic wave functions, etc.) but too ugly and contrived to take really
seriously as a theory.
• The basic problem: There’s a lot of structure in the wave function, and a
TELB somehow has to reproduce this.
– e.g., lots of structured fields in 3-space equivalent to one structured field in
3N-space
Part 5: TELB and dBB
• Claim: dBB is a privileged jumping-off point for constructing a TELB. Why?
• Most of the structure in the (big, universal) wave function is irrelevant to
the motion of the particles, and it’s in terms of the particles that empirical
adequacy is achieved.
– Branching structure familiar from MWI
– Decoherence
• So dBB strongly suggests that one could have a pilot-wave type TELB with
much less structure than my toy example. You just don’t need to
reproduce all of the wf’s structure
– Note that eliminating some of the structure will at least tweak the empirical
predictions, rendering candidate TELBs empirically distinguishable from QM
• So this just seems like a really promising research program.
In addition:
•
The pilot-wave (particle + guiding wave) ontology is really strongly suggested by
paradigmatic quantum experiments:
•
Bell: “Is it not clear from the smallness of the scintillation on the screen that we
have to do with a particle? And is it not clear, from the diffraction and
interference patterns, that the motion of the particle is directed by a wave? De
Broglie showed in detail how the motion of a particle, passing through just one of
two holes in a screen, could be influenced by waves propagating through both
holes. …. This idea seems to me so natural and simple…”
Conclusion:
• We should take Bell’s argument very seriously, as he did.
• But we should acknowledge that we don’t yet actually have a
theory that matches his qualitative description of the 2-slit
experiment..
• …and start working to produce one
Works cited:
•
Valia Allori, Shelly Goldstein, Roderich Tumulka, Nino Zanghi (AGTZ), “On the
Common Structure of Bohmian Mechanics and [GRW]”, quant-ph/0603027
•
J.S. Bell, “The theory of local beables”, 1976
•
J.S. Bell, “La Nouvelle Cuisine”, 1990
•
Detlef Durr, Shelly Goldstein, Nino Zanghi (DGZ), “Bohmian Mechanics and the
Meaning of the [WF]”, quant-ph/9512031
•
Werner Heisenberg, “The Development of the Interpretation of the Quantum
Theory” in Niels Bohr and the Development of Physics, W. Pauli, ed., 1955; also
chapter VIII of “Physics and Philosophy”
•
Peter Holland, The Quantum Theory of Motion, 1993
•
Tim Maudlin, “Completeness, Supervenience, and Ontology”, 2007
I think about it this way:
• If you somehow elminated the ridiculous, anti-realist philosophy of
Bohr and Heisenberg, the whole Copenhagen movement and the
associated “orthodox” approach to QM, you’d never for a second
take anything but the basic pilot-wave ontology seriously.
– MWI, GRW, etc. as reactions to a “measurement problem” that never
should have existed in the first place!
• So the question is: Starting from Bell’s argument (“Is it not
clear…”), we know there are particles being influenced by
associated guiding waves. But it’s clear (from various entanglement
phenomena) that we either haven’t got the laws right, or haven’t
got the full ontology yet on the table.
• So let’s work on it.
Top-down vs. bottom-up
• I see two mutually-supportive avenues of potential
progress:
– Top down, i.e., starting with existing formulations of dBB
with a nonlocal beable wf, and using (among other things,
but perhaps primarily) symmetry considerations to guide
one in TELB-construction. (For example, one of the really
ugly/dubious things about my TELB is that the one-particle
cwf’s aren’t scalar fields under galilean transformations.
This already strongly suggests finding some different
candidate local beable pilot wave object.)
– Bottom up, i.e., starting with the empirical evidence that
led originally to ordinary QM, but trying to see where one
would instead be led if one insisted on tolerating only local
beables.
Conclusion
• Currently, with dBB, we have a theory that is analogous
to “version C” of classical gravity – it works but is
indigestible.
• In that case, we know there are closely-related
mathematical reformulations (which for example
replace the nonlocal beable S with a local beable g)
that “get the ontology right” as evidenced by their
historical successes.
• We should be looking for the analog of this with dBB.
It’s not the *only* thing we should be doing, but it’s
*one* of the things we should be doing.
Einstein:
• “If one asks what, irrespective of quantum mechanics,
is characteristic of the world of ideas in physics, one is
first of all struck by the following: the concepts of
physics relate to a real outside world, that is, ideas are
established relating to things such as bodies, fields,
etc., which claim ‘real existence’ that is independent of
the perceiving subject – ideas which, on the other
hand, have been brought into as secure a relationship
as possible with the sense data. It is further
characteristic of these physical objets that they are
thought of as arranged in a space-time continuum.”
(Einstein, from BEL, page 170)
Heisenberg:
• “Bohm considers the particles as ‘objectively real’ structures, like the point
masses in Newtonian mechanics. The waves in configuration space are in
his interpretation ‘objectively real’ too, like electric fields. Configuration
space is a space of many dimensions referring to the different co-ordinates
of all the particles belonging to the system. Here we meet a first difficulty:
what does it mean to call waves in configuration space ‘real’? This space is
a very abstract space. The word ‘real’ goes back to the Latin word ‘res,’
which means ‘thing’; but things are in the ordinary three-dimensional
space, not in an abstract configuration space. One may call the waves in
configuration space ‘objective’ when one wants to say that these waves do
not depend on any observer; but one can scarcely call them ‘real’ unless
one is willing to change the meaning of the word.”
• From “Criticism and Counterproposals to the Copenhagen Interpretation
of Quantum Theory, chapter VIII of “Physics and Philosophy”