Sunday, February 04, 2018

The Copenhagen ontology

Scott Aaronson has an interesting post on his personal interpretation of quantum mechanics (he's probably a 'none-of-the-above' but with a revealed preference for the MWI).

He is, however, particularly scathing about the so-called 'Copenhagen Interpretation'.
"As for Copenhagen, I’ve described it as “shut-up and calculate except without ever shutting up about it”!  I regard Bohr’s writings on the subject as barely comprehensible, and Copenhagen as less of an interpretation than a self-conscious anti-interpretation: a studied refusal to offer any account of the actual constituents of the world, and—most of all—an insistence that if you insist on such an account, then that just proves that you cling naïvely to a classical worldview, and haven’t grasped the enormity of the quantum revolution."
This seems spot on.


'You may not be interested in ontology, but ontology is interested in you.'

What happens when a convinced adherent to the Copenhagen Interpretation is asked straight out:
"... what constitutes the "act of measurement" in a world without sentient beings? In such a world (even in a world with sentient beings) there are just physical systems with atoms and molecules all under the rule of Schrödinger's equation. So when does "collapse" occur?

When can it be decided that a measurement has been made if there are no sentient beings?

If everything is made up of particles, and the particles are under the governance of Schrödinger's equation and unitary evolution, when do "measurement" and "collapse" occur? In a world without sentient beings, what would "when the new data arrives" refer to?"
Luboš Motl answers commentator Ricky's question above (in comment 16 here):
""The conceptually right [way] to describe a world without sentient beings is that an unspecified and unknown initial wave function evolves unitarily according to Schrödinger's equation and never collapses because it's only measurements that may collapse and there are none in your theory. The complete "diffusion" of the wave function (into the linear superposition of dead and alive cats and all objects, small and big, in the most general superpositions of all conceivable states) may be said to be a problem - but another problem is that the initial state is totally unknown, too.

"It makes no sense to say that the initial wave function is a particular thing because one may only say that the wave function is a particular thing [if] something is [a] measurement - if a sentient being becomes aware of the result of some measurement. This is not happening in a universe without sentient beings. So there's no specific science to discuss in a universe without sentient beings at all. The laws may still be the same as they are in our world but they won't be applied in any particular situation because there are no particular situations or particular special wave functions in a world where no one ever measures anything.

"Einstein asked whether there is any Moon over there if no one looks. In practice, classical physics is a good enough approximation, so one may assume that the Moon is pretty much there even before observers look etc. But conceptually, if you care about similar objects for which the quantum effects are strong, the right answer is that the Moon just isn't at any particular location and has no other particular properties if no one looks. The wave function isn't a real object of any type. Its amplitudes can't be measured in a single repetition of the situation. It is only a template storing information allowing to predict probabilities of things that actually can be measured - the observables."
The arch-exponent of Copenhagenism appears to believe that the universe is really some unitary evolution in Hilbert space, presumably with space-time somehow emergent. Because ontology.


  1. Yes, the protagonists in this debate seem a little bit at cross-purposes e.g. Motl's "defence" of Copenhagen is mostly about the mathematical formalism, and then he introduces the "Observer's Knowledge (change)" as a key ingredient. Pure Bohr-Copenhagenism was as much about limits to the expressibility of classical language. Motl seems to prefer Heisenberg-Copenhagenism on these type of points, with a touch of the Bayesian QM mentioned at the beginning of the Aaronson article.

    The "no sentient being" universe is an interesting thought experiment, but one could ask about a related "Box with no sentient observers" but externally known initial wavefunction. One might say that psi diffuses everywhere for all time and no collapse occurs. The issue behind the scenes is that "Decoherence" - often associated with MWI - might be suggesting that low probability diffusions are unreal (perhaps more convincing if Prob(D) --> 0 for t --> Infinity, could be proven, for non-classical options D.)

    My own exploration at the moment is on the mathematics underlying QM. As it happens the spreading tree at the start of this Post is one place to begin that discussion. If we view the nodes as stages in the evolving quantum history tree, then we need to focus on the paths - the actual histories. These paths only exist in general courtesy of Konig's Lemma. But Konig's lemma has been introduced by the mathematics ie the observer, it is not in the physics itself. Although not immediately obvious the mathematical consequences of this simple observation can be "underneath the ZF-Radar" ie not correctly formulated within ZF(C) set theory e.g. the "Preferred Basis Problem" seems to be unproblematic in the mathematics and is seen only in the MWI. In fact there is a (perhaps) related problem to be found underneath ZF set theory when applied to Hilbert spaces.....

  2. I continue to find the MWI ontologically opaque. The contrast between the universal wavefunction and the partial wavefunctions describing a specific observer's situation doesn't seem truly fundamental (although, via decoherence, complicated).

    If space-time is somehow emergent from Hilbert space via a story on gravity, I have few intuitions as to where that leaves the MWI.

  3. There is an ultra-naive answer: Hilbert space gives an emergent 3-space via a class of representations. Thus if atom A is measured in the Energy representation we might determine E1 and E2 as the two eigenvalues with Psi1 and Psi2 as the two eigenspaces. Under collapse only Ei and Psi(i) survive to continue the evolution. This evolution might later be measured using the space representation.

    Under MWI two Worlds W1 (E1, Psi1) and W2 (E2, Psi2) have formed perhaps with two versions of the experimenter (Exp1 and Exp2). Each Experimenter is free to later use the Space representation - when Wi does this Space(i) now emerges ....

    Still I guess Quantum Gravity was never meant to be easy.

    I am reading a book/paper by Chris Isham on Physics Foundations (basically Quantum Gravity) via Topos theory - his favourite.

    1. Yep, how to get the metrical structure of space-time out of Hilbert space without secretly smuggling it in .. .

    2. I am not sure whether you mean to exclude the "Wheeler-De Witt Equation" by that comment. This equation is for Psi(gamma) where gamma is now a metric entity. This equation includes no time parameter (since that is in gamma) - and time has to be "extracted". Several "time-extraction" ideas exist, which seem to converge on the idea that "time" is a consequence of the classical IE General Relativity approximation. It has been suggested that true quantum solutions of the WdW equation exist with no time component - hence the extraction of space-time is not a quantum certainty.

  4. Sadly, past my competence grade. Lubos had a big piece on the Aaronson post at 'The Reference Frame' .. but I'm finding his level of vitriol tedious.

  5. I agree that Lubos spends far to many paragraphs in every topic criticising assorted people for not being "qualified physics" and should just stick to dealing with the point at hand. He can mention that he fundamentally disagrees with e.g. Loop Quantum Gravity every once in a while if he wants.

    The Wheeler-De Witt equation is the nearest to a direct equation in Quantum Gravity (from about 1967). It has many issues though, but it often appears in discussions of "Quantum Cosmology". But dont ask Lubos for an explanation unless you want a long list of people who are not even qualified to think about Quantum Gravity....


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