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 Maxwells electromagnetic theory, for example, the fields E and H are physical (beables, we will say) but the potentials A and are non-physical. 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 cant 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:
qi j i Beables: B Gm j (q j qi ) q j qi 3 qi (t ) i 1,..., N C
qi |qi 1 i 2m i 2 4G 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: Arent 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 (x,t) into a wave equation with finite propagation speed, etc. Something along these lines was the path to GR. So theres 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 wouldnt have been clear at all that (for example) B was superior to A.
Arguments from locality, etc., maybe suggest B Arguments from Occams 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 Im 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 21 st century. Thats 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 dBBs
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 youd do if you had version B but (for some reason) really wanted to avoid having a (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 threedimensional 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 wouldnt accept Hollands view unless I was convinced that all possible alternatives failed The DGZ view is intriguing, but somehow the wf just doesnt 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 nave 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 Summary of the virtues: Local beables allow meaningful analysis of space-time 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. Isnt that actually a case of adding lots of space-time structure compared, e.g., to the teensy little bit extra thats 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 theyve
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 wfs 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: Theres 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 its 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 dont need to reproduce all of the wfs 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 Bells argument very seriously, as he did. But we should acknowledge that we dont 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, youd 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 Bells argument (Is it not clear), we know there are particles being influenced by associated guiding waves. But its clear (from various entanglement phenomena) that we either havent got the laws right, or havent got the full ontology yet on the table. So lets 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 TELBconstruction. (For example, one of the really ugly/dubious things about my TELB is that the one-particle cwfs arent 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. Its not the *only* thing we should be doing, but its *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
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