How determined are you?

Not true, on many levels Most importantly, I simply point out that that is the nature of the universe according to GR, and is part and parcel of "Big Bang" theory (as BB is purely a prediction of GR and GR-type theories).Of course, GR is the most accurately tested theory we have (I'm fairly sure it pips QED but that may have changed), and its implications (along with SR) concerning the nature of space-time certainly suggest that simple time-evolution of a 3d space is not a viable concept. But who knows how QG/TOE is going to change this.And who said anything about 4 dimensions??? I only believe in two...

Systems do not have to be chaotic or non-chaotic. They can exhibit areas (spatially and temporally) of chaos and areas of relative stability, across all length-scales. Weather is almost certainly like this.What was the paper?

At what level? Asking questions about properties of a wave-function has a probablistic element, but evolution of any state is purely deterministic. That's not true. GR leads us to believe that it is perfectly theoretically possible. Practically possible is another matter, which certainly muddies the water. I'm not sure I understand. We have existing mental states, we have environmental states, and these are combined to produce an output. Where is the choice at this point of producing the output?This message has been edited by cavediver, 11-02-2005 06:49 AM

Sure. When we say there is a probablistic element to physics, it is constrained to measurement theory, e.g. asking where the electron is in a hydrogen atom, or where the single photon will fall in a double-slit experiement. But this probablistic nature is not related to evolving some initial conditions at time0 to some final conditions at time1. This is purely deterministic. If you know the stae at T0, you can predict the state at T1. This is what we mean when we say that physics or the universe is deterministic. The probability involved in measurement does not affect this fact. This is one of the sources of great confusion when people try to understand QM.So when I ask, at what level, I am asking if you are referring to evolution of states or just observation.For many years, Hawking was convinced that evolution was not necessarily deterministic, based upon black-hole absorption and radiation. The idea is that a black hole can absorb energy in a definite state, then re-radiate it perfectly thermally, such that all infomation contained has been lost. He held this view despite enormous objection by the rest of the community. It is only in recent years that he has changed his mind. I must say that I always hoped that he would be proved correct, becasue it would make physics that bit more exciting. Then again, theoretical physics really doesn't need any more excitement Sorry, you were talking locally of course. My mistake. Yes, this is totally true and is the basis of causality. However, globally, we could have closed timelike curves (CTCs), a fancy term for time-machines. We can use these CTCs to travel back in time with future information. This obvously has possible profound implications for determinism, free-will, etc.However, the stability of CTCs is much in question. They generally contain what we call a Cauchy Horizon (or surface of infinite blue-shift) (a "normal" event horizon is a surface of infinte red-shift). This horizon is exceptionally unstable to perturbations.In fact, nature seems to conspire to prevent CTCs, despite their theoretical possibility. This led Hawking to suggest the "Chronology Protection Conjecture" or CPC. But surely all the processes within our brains are deterministic, and thus their current state can be predicted from prior states? If the processes are not deterministic, where does the indeterminancy arise? Can we observe it?I'm not disagreeing, BTW, I'm open on all of this...

No, not at all. The uncertainty principle is purely related to measurement. It is simply a statement about the non-commutativity of conjugate-pair observables. The initial-state is not a case of specifying a position and momentum of an electron, for example. The position and the momentum are observables of the state, not the state itself. We can prepare an initial-state in a say a position eigenstate. Now it is not that we don't know the momentum, just that momentum is not a well-defined concept for that state. It is not something that exists to know. The state is completely defined without any concept of momentum. Hmmm, sounds like you may be a victim of popular science gobbledegook. There's nothing like New-Scientist to completely confuse a very straight-forward concept There's nothing odd about tunneling. Believe me, unitary (deterministic) evolution of states is at the heart of all QM. To suggest otherwise (as Hawking did) is to really rock the boat, and is a very big issue. Not at all. Hidden variables are not required. All you need is the state vector, unitary evolution via the Schro Eqn, and obsevables as operators and associated eigenvalues of the state vector.

Which is why we don't use the term "collapse of the wave-function"! This "collapse" is simply making an observation of the state. If the state is not in an eigenstate of the observable you are measuring, then you will get a probablistic observation. But in a sense that is because you are asking the wrong question.

Can you firm this up at all? It's a little too easy to sound like some new-ager talking about vibrations and energy and other such stuff...Not trying to be (too ) picky, but what are "bundles" and "energy", and do these exist in space(time) or is space itself made up of these?At what scale are we talking, and in fact, how do they give rise to scale? If it is bulk statistical behaviour, then given the accuracy to which QED appears to operate across the universe, you are almost certainly talking about behaviour far below the Planck scale to generate such a level of conformity.BTW, what is statistics in this context and why does it operate if these "bundles" are not subject to laws per se? For instance, is there any notion of a "number" of these things? Why should this number be conserved? And what is "number" if countability has been relaxed?This message has been edited by cavediver, 11-02-2005 11:07 AM

Sorry, I'm using state as shorthand for state-vector which I admit can be damn confusing. The wave-function is not supposed to be predicting which state you will observe. If the wave-function is not in an eigenstate of the observable you are measuring, you will get a probablistic outcome. Having a superposition just means you are going to get confused if you try to naively work out the probabilities. BUT, this is still restricting the probability to the measurement process.

Well, I used to help teach advanced QM at a place they do a lot of punting, if that helps Yes, absolutely. Don't think that I'm trying to push the UP into that stupid world of "oh, well when you try to measure something, you will disturb it with the photons you are using" crap!The UP is in the absolute fundemental mathematics of QM. Take position and momentum... they are properties of the wave-function, but we have to project them out to observe them. But you can't hold the wave-function in the same orientation to project both at the same time. You have to measure one, then turn the WF around to measure the other, by which time it will have evolved and thus changed. Not my best analogy, but a better will have to wait as I'm dashing for the post now!

Sometimes it better to say nothing at all...

At this level, I think it is misleading to refer to the particle AND its state vector as if they are two entities. The "particle" is an observation of some property of the state vector. And the state vector is not fixed, but evolves. A property is "fixed" if we observe it the same after repeated observation. For example, take spin. The total spin of an electron remains the same, even though the components of spin evolve in a way that makes observations of the components probablistic.

I think we are rapidly running out of "things". We have reduced all matter to a small bunch of fields, where there is no "thing" to which we apply a mathematical description. There is only the mathematics. The "things" that we deal with within physics seem to emerge at a higher level. At this level we have lost the concept of even an individual particle. Thus the concept of wave-function is more fundemental than the concept of thing or particle. This is what QFT appears to be showing us. Well, you have to be careful, because those properties cannot exist at the same time, they are mutually exclusive. So I've been a little confusing in using the term property. They are properties of the classical observation, but really they are projections of the wave-function. They are as much properties of the observation as they are of the wave-function. It's not that they are there, but we can't measure them (this is essentially hidden variables). So given what I said above, no, this is not the case. Yes, but position and momentum have nothing to do with evolution of the wavefunction. They are not required to have deterministic (unitary) evolution. This is obviously very different to the classical picture.

Couldn't put it better myself

Well, "evolution" of the wavefunction is purely deterministic. At least theory says it is, and evidence backs it up to a very deep level of accuracy.Hawking was hoping that non-unitary evolution would show up at some scale not yet reached as evidence of the purely thermal emmision of black holes. The idea was that planck scale virtual black hole pairs would create observable non-unitary scattering. No one believes this now. Schrodinger is only the non-relativistic approximation, so no, it is not accurate. As soon as you try to make it accurate (relativistic), you are pretty much forced to leave QM behind and embrace QFT (quantum field theory). QM still has the concept of a single entity (single electron, single photon), and this is not a consistent picture of the real world. You cannot have single electrons and you cannot have a useful theory of just photons.This message has been edited by cavediver, 11-05-2005 01:12 PM