Erratum, I should have written "(quark disappears) (weak interaction happens) (antiquark appears)". My point is that the algebraic reversal of that expression is different from the time reversal of it, so those two parts of the Hamiltonian do actually say different things about the amplitude gradients in configuration space, even when you think about it "timelessly".

I don't buy this abolition of time at all, but this question of how CP violation appears in Barbour's scheme seems like a good test of one's understanding.

The abolition of a time coordinate in quantum gravity is not Barbour's invention. The usual Schrodinger equation is HĎˆ = -i/hbar dĎˆ/dt, where the H operator represents total energy (typically, sum of a potential and a kinetic term). But in general relativity, the total energy persistently shows up as zero (gravitational potential energy cancelling out against mass-energy, I believe; I confess I'm just relating this secondhand). So H=0, and there's no time evolution, just the stipulation that Ďˆ has an H-eigenvalue of zero. Barbour's contribution is to offer an interpretation of configuration space as a set of "time capsules", static configurations containing static observers experiencing an illusion of time due to their memories. (I don't know what meaning Barbour ascribed to the amplitudes, and perhaps he has problems comparable to those suffered by the usual, timeful many worlds interpretation.) So that's it: H=0 gives you a standing wave in configuration space, and Barbour proposes a timeless variant on many worlds, with variables internal to the cosmic configuration, like cosmological radius, acting as clock variables, proxies for time.

Back to this CP violation problem. It is a theorem that quantum field theories have CPT symmetry, and it is an experimental result that CP symmetry is violated, i.e. that T symmetry is violated, in kaon-antikaon transitions. We actually have a quantum field theory implementing T-violation, the Standard Model, where it's implemented in the quark mass matrix. The numbers in that matrix would be coefficients of interaction terms in the potential-energy part of H, connecting quark fields and weak-boson fields, I think. It is something like postulating that the amplitude for (quark disappears) (weak interaction happens) (antiquark disappears) is different from the amplitude for (antiquark disappears) (weak interaction happens) (quark appears). In a sense it is quite unmysterious, since there is no mathematical barrier to postulating such an asymmetry, though one would like to know a deeper reason for it; the CPT theorem only says that if you transform those two processes by CPT, the amplitudes for the corresponding processes had better have the same relation.

Now formally it is a straightforward thing to take a quantum field theory and couple it to general relativity. For example, you can just take the QFT's old H, add a term for scalar curvature, and multiply the whole thing by "sqrt(determinant(metric))". Set the new H equal to zero, and you now have what should be the equation for a Standard Model universe with Einstein gravity thrown in; and though you probably can't solve that equation, you can still go ahead and follow Barbour's procedure in the resulting configuration space.

It seems obvious(?) that the expression of CP violation in the timeless picture will have something to do with those quark/antiquark fields in the CP-violating terms, and I would point out that although my informal description of those terms might seem to make one the time reverse of the other, actually there is an algebraic difference. Algebraically, "X appears" means that you use a "creation operator", while "X disappears" involves an "annihilation operator". So understanding the implications of those operators for amplitude gradients in the timeless picture may be the key to figuring this out. Also, since other physical variables act as clocks in the time capsules - proxies for an actual time - kaons and antikaons ought to somehow have a different relationship to the clock variables. If I was seriously trying to figure this out, I'd be thinking at the intersection of those two approaches. (And I'd be doing it using the simplest T-violating QFT I could find, rather than with the full Standard Model.) This is an excellent question to think about, for anyone trying to understand Barbour's interpretation in detail.

Caledonian, perhaps I should have written "objectivity-negating subjectivity" and "subjectivity-negating objectivity". The first would deny that reality has any intrinsic qualities (qualities independent of observation, basically), while the latter ends up denying the qualities of experience itself ("not even mind is moving").

frelkins, taking a stance in opposition to Nagarjuna is difficult because he's so neither-nor, but maybe just saying that something, somewhere, has an intrinsic nature is enough to do it. :-) You shouldn't read too much more into my remarks than that. I am agnostic on many points, and I am skeptical that anyone has ever yet known the truth about metaphysics. I have my preferred hypotheses, and I'm prepared to reject certain others, and that's about it.

frelkins: There's a story (which you may know) that Tibet held a debate between Indian Buddhists, who insisted that enlightenment can only be reached after many stages of analysis, and Chinese Buddhists, who said you could get there in one step. The Indians are said to have won the debate, but I was writing with the Chinese side in mind; I was trying to describe the path to nonduality in the most abbreviated way I could. I am aware of Nagarjuna and "codependent origination", and it may be that it was misleading of me to pass over that aspect. I welcome discussion and correction, though here may not be the place. (There is an unofficial Overcoming Bias forum here. Also, I'll mail you privately.) But, speaking mostly metaphorically, I favor Shankara over Nagarjuna. I believe in substances, essences, and a self. I think Buddhism is at the opposite extreme of error from the error of eliminative materialism - an all-negating subjectivity, rather than an all-negating objectivity - yet somehow complementary to it, as I suggested.

This love affair of modern rationalist materialists for Buddhism's metaphysical negations is peculiar in that the superficial similarities derive from completely different trains of thought. In a nutshell, as I understand it, the Buddhist argument (or a very prominent version) reduces all things to mind, by noticing the subjective element in all experience, and then reduces mind itself to ineffable formlessness by turning the argument on itself. By contrast, modern materialism in effect proceeds by substituting mathematics for subjectivity at every turn, until it reaches the point of saying that there is no subjectivity, only number (or whatever abstract category forms the basis of the preferred formalism).

I suppose the two approaches genuinely are potentially complementary, in that a Buddhist procedure could serve to make the scientific ontology subjectively plausible. But two wrongs don't make a right. We don't just think that time moves or that we are conscious; they are both quite real. At most it may be the case that the former is internal to the latter. But that is metaphysical idealism, not materialism or Buddhist relativism.

Color isn't out there; but how can it be "in here", if the brain also just consists of particles in space? And color is either somewhere, or it's nowhere. Dennett takes the "nowhere" option, as part of his general denial of a "Cartesian theater", a place where appearances happen.

Except for those who think mental states can supervene directly on processes extending far outside the physical body, I think most scientifically minded people suppose that the world of appearance is somehow identical with something inside the brain: that (in one sense) what you see is in your visual cortex, even if (in another sense) what you see is far away. (Though they may prefer to say that it's the seeing that is in the cortex, rather than what is seen.) As I have just argued, this does not resolve the problem of locating perceived color (etc) in the physical world, it merely localizes the problem. We still await the identification of some physical thing or property in the brain which can plausibly be identified with an actual instance of color. And I think that's hopeless so long as you restrict yourself to states built up from fuzzy mesoscopic properties like membrane polarizations. The ghost of a homogeneous shade of color has to somehow hover over something which in actual fact consists of large numbers of ions on either side of a big macromolecule.

So I look for the true Cartesian theater to be found at a level where physically, even a 'particle' is just an approximation, such as in a decomposition of a global quantum state into what formally just appear to be algebraic structures lacking even a spatial interpretation. Quantum theory actually permits such an abstract perspective, if you step away from the use of a particular basis, such as configuration. I think that here, and only here, out of all the physics we know and half-know, is there something removed enough from spatializing presuppositions that it might be identifiable directly with a state of consciousness. This has the empirical consequence that there had better be a distributed quantum condensate (or other locus of entanglement) somewhere in the brain, causally situated so as to function as a Cartesian theater and locus of consciousness. All I'm doing is displacing the hard problem onto the properties and structures of that hypothesized quantum object, but it had to be done because the problem appears to be unsolvable out in the world of disentangled 'individual particles'.

Are you color-blind, Caledonian? Do you ever use color words? Do you think they refer to nothing more than "neurological associations"? Or is it that they do refer to something of which you are directly aware, but which you have a way of talking around?

When I look out the window right now, I see a blue patch of sky. Am I seeing neurological associations? Am I seeing a mathematical description of neurological associations?

You are free to deny that 'blueness is there', but if that is your only counterargument, I have to think my original argument must have been quite strong.

Caledonian: What evidence do you offer us that mathematical descriptions cannot produce the properties of which you speak?

First of all, let's be clear regarding what we have to work with. Things are complicated a little by the variety of specific theories and formalisms used in physics, but let's take multi-particle quantum mechanics in the configuration basis as illustrative. The configurations are all of the form 'A particle of species a1 at location x1, and a particle of species a2 at location at x2,...', and so forth. The quantum states consist of associations of complex numbers with such configurations. There is the basic dynamical fact that a quantum state ψ evolves into another state ψ + dψ according to the Schrödinger equation, and (if you're not taking the many-worlds path) Born's postulate that the probability of there actually being particles a1, a2,... at locations x1, x2,... is |ψ|^2.

Then there are various entities and facts that can be obtained from these through abstraction, deduction, and comparison, e.g. 'the number of particles in configuration c' or 'the average number of expected particles in quantum state ψ, as calculated via the Born probabilities' or 'the Hilbert-space inner product of states ψ1 and ψ2'. We could, if necessary, describe a formal combinatorial grammar describing all and only those entities and facts implied by the theory-defining postulates in my first paragraph. It would amount to saying: the entities and relationships directly postulated by the theory exist, and so do those which can be logically or mathematically inferred from those postulates. But speaking informally, all we have to work with are featureless spatial configurations of point particles, superpositions thereof, dynamics of superpositions, and empirical probabilities derived from superpositions.

And what sort of entity or property are we trying to extract from the theory, if we are trying to derive consciousness from physics? It's tiresome to resort repeatedly to the same example, but nonetheless, let's consider color: the variety of hues and shades which we lump together into the natural language categories of red, blue, and so forth. (I put it that way because I do not want to turn this into a discussion of whether those natural language categories are "natural kinds". Focus instead on the numerous instances of color which populate visual experience and which unquestionably exist, regardless of how they get categorized.) On one side we have "quantity and causality", as I put it above - and I'll even throw in spatial geometry and dispositional behavior; on the other side, the colors. How might we go about making the latter out of the former?

There are some things we can do. We can quantify certain things about subjective color; and we can describe certain physical realities which are somehow correlated with color. Thus 450-nm wavelength light "is" a type of blue light. But I submit that it makes no sense to say that when you see a particular shade of blue, you are "seeing a length"; or that blue itself "is a length". That might do as a poetic description of the physics behind the perception, but as an ontological statement, it simply substitutes the correlated geometric property for the sensory property we are trying to explain.

Another approach is the cognitive one: things are blue because your nervous system classified them that way. But although the correlated purely-physical property is a lot more complicated here, it's the same story. Put informally, to use this as an explanation of blueness is to say that our perceptions turn blue because we call them blue or think they are blue.

I think Dennett would understand my point, but as usual he bites the bullet and denies that color is there. He calls it "figment" - figmentary pigment - because according to physics, there is nothing actually blue, inside or outside one's head. But blueness is there, therefore that ontology is wrong.

"Emergence" is a popular dodge: colors and other subjective properties, though not being identical with any elementary physical property, somehow "emerge" when a brain enters the picture. Apart from being vague, that's just dualism: if the emergent properties are not identical with one of the purely physical properties in that combinatorial grammar I mentioned, then it is different from all of them, no matter how correlated it is.

As I said, my answer is to turn it around, and to say that the existence of blueness (etc) is axiomatic, and so it must be one of the things that a true and complete theory of reality would be about. It is as if one were to look at electromagnetism and say, my God, those things we thought were lengths, they're actually colors! - rather than vice versa. But it's also my thesis that when you look at doing this in detail, some of the obvious candidates for this ontological inversion, such as "computational states of neurons", present too many specific difficulties to work (in that case, because a computational state of a meso-scale system like a neuron is a vague property, microphysically speaking). Thus I find myself pursuing quantum ontological exotica.

Eliezer: From all the books that created me, I was never once warned that Science is not strict enough.

I am trying to figure out exactly what your better methodology is. Is it

(1) Science + Occam's razor, with the razor used to choose between experimentally indistinguishable theories?

(2) Bayes's Law, with Science somehow merely being an application of the law?

(3) Science, Bayes, and an assortment of introspective methods meant to prevent wasting one's time on a-priori extravagant hypotheses?

I do not think anyone will argue with the advice that if a theory contains entities which are predictively irrelevant, you should try doing without them. Whether "Science" is merely an instance of "Bayes" will be a little more contentious; to employ probability theory requires structure - a space of possibilities, a prior on that space - which may not be available. The utility of the psychological tips is even more open to question, though it's surely useful to at least know about this perspective.

Some of the examples you use I have to disagree with. I do not think many worlds can be shown to be the clear favorite among quantum interpretations, either by the simple argument that it's orthodoxy minus collapse and therefore simpler than orthodoxy, nor by some more complicated argument that also tries to incorporate qualitative principles like adherence to the spirit of relativity. You are also getting Penrose wrong, as I wrote above. People adopt quantum mind theories for a variety of reasons. For example, I do it because I do not believe in the reducibility of consciousness to a collective or swarm phenomenon, and some of the quantum ontologies permit options that don't exist in classical atomism. But Penrose did it because it gave him a means of physically implementing neural hypercomputation, which in turn he deemed to be necessary because of the incompleteness theorems. He was not trying to explain qualia, so the fact that his hypothesis introduces no insight on that front is irrelevant.

The most profound criticism I can make of science as it is presently conducted is that it assumes a type of ontology which is necessarily wrong; and this really only applies to sciences which touch on something ontologically fundamental. The ontology assumed might be called objectified mathematical materialism; it is necessarily wrong because conscious experience manifestly contains properties which cannot be obtained by any combination of the entities which that ontology says are all that exists; but this is irrelevant to, say, a biologist, unless their work really does touch upon consciousness. A biologist can utilize the everyday subjective ontology, and the quantitative world-image of the natural sciences founded upon physics, and not have them clash in an impossible way.

Your younger self sensed, correctly, that something more is needed. If he made an error, I would say it was in supposing that more of the same could make a difference: that extra mathematical physics can solve the hard problem. Even if it's there, and causally relevant, it's just more physics. What's needed is new ontology. Realist fundamental physics is ontology, so a change there does mean new ontology, but if it's just mathematics, it's not enough. We have to remember that subjectively speaking, the mathematical image of the world was created by deliberately excluding from consideration certain aspects of experience as "secondary", and that the hard problem of consciousness arises from this unfinished business. I've given my prescription in comments elsewhere: transcendental idealism, transcendental phenomenology, and a quantum monadology in which the qualities revealed in appearance are taken to be the ontological content behind the mathematical formalism used to describe the physical correlates of consciousness.

Even though they are based on the impoverished ontology of mathematical physics, according to which quantity and causality are everything, I do think some of your qualitative methodological principles are still relevant to these deeper investigations. But they would have to be applied in a frame of mind which no longer tries to ground everything in mathematics as we know it, and remains open to aspects of being which fall radically outside anything we know how to formalize at present.

A belated meta-response to Caledonian: this is your earlier remark to which I referred. We may have no more than a terminological difference. As I said above, I would (hope to) never say "A exists relative to B", only that A was detectable, rationally inferable, etc., relative to B. It's too confusing to use "existence" as if it only means "epistemically assertible existence".