On Wed, Apr 27, 2016 at 1:40 AM, Bruce Kellett <bhkell...@optusnet.com.au> wrote:
> On 27/04/2016 3:22 pm, Jesse Mazer wrote: > > On Wed, Apr 27, 2016 at 12:47 AM, Bruce Kellett <bhkell...@optusnet.com.au > > wrote: > >> Your simulation assumes the quantum mechanical results. In other words, >> it assumes non-locality in order to calculate the statistics. Where does >> the cos^2(theta/2) come from in your analysis? >> > > The question I asked you was whether you thought you could definitively > disprove the idea that all the observable statistics of QM could be > reproduced by rules that are "local" in the specific narrow sense I had > described to you--remember all that stuff about having computers > determining what the value of local variables at each point in spacetime > should be, using only information about the value of local variables in the > past light cone of that point, plus the general rules programmed into them > (which take that information about the past light cone as input, and spit > out the value of local variables at that point as output)? This is a narrow > and mathematically well-defined question (and is based specifically on how > Bell defined 'locality'), it's completely irrelevant to the question > whether or not the *idea* for the rules that I programmed into the > computers that perform these local calculations came from looking at some > equations that are written in a 'non-local' way (i.e., the equations > generate their predictions by evolving a single 'state vector' for the > entire spatially-distributed system). Do you understand this distinction > between the narrow, well-defined definition of "local rules" (if you're > unclear on what I mean here, please ask), and broader questions about what > inspired the rules themselves? And are you claiming that even if we > restrict our attention to the narrow definition of "local rules", you can > still say with 100% certainty that no such "local rules" can accurately > reproduce all the predictions about measurement outcomes made by QM? > > > Your question, as outlined above, is completely devoid of interest to me > as a physicist. I am interested in physical models that give an insight > into how things come about. > > And yes, I am 100% certain that local rules, with local models for > deciding what statistics should be reproduced to mimic quantum results on > entangled systems, are impossible. > And are you 100% certain of that last statement even if we define "local rules" in the specific narrow sense I have described? Your comment that my question concerning this narrow definition of locality is 'devoid of interest' to you makes it unclear whether you were actually willing to stick to the narrow definition in addressing my question, as I had requested. To try to restate this "specific narrow sense" one more time, note that at the broadest level, any dynamical "law of physics" is a mathematical function that takes some boundary conditions as input, and generates a prediction about some other physical state as output--for example, for Newtonian gravity the inputs could be the positions, velocities and masses of some objects at time T1, and the output could be their positions and velocities at some later time T2. So "local" in the specific narrow sense I'm using is a condition that ONLY deals with what inputs are necessary to generate outputs, and has NOTHING to do with the function itself. If the function takes as input boundary conditions that are restricted to the past light cone of some region of spacetime R, and as output tells you the values of local physical variables in that region R, and it can do this for *any* region of spacetime R where you want to predict the local variables, then this automatically qualifies the laws of physics as "local" according to the narrow sense I am using (which again matches how Bell used it, if you have doubts about this check out his paper 'La nouvelle cuisine' which can be found in the collection 'Speakable and Unspeakable in Quantum Mechanics'). Hopefully this definition is clear, even if you find it uninteresting. > Rules that deal with non-locally produced statistical distributions can do > anything you want -- vide my urn model -- they simply have nothing to do > with physics, can teach us nothing about physics. > Your urn model does not qualify as "local" in my narrow sense above, in the sense that it only made predictions about joint results, but didn't generate predictions about the results of each experimenter's measurement in the region of spacetime where they performed the measurement, using only information about physical variables in the past light cone of that region (where the other experimenter's choice of detector settings was not part of the past light cone). Again, even if you find this narrow definition uninteresting, hopefully you agree that your urn model does not really qualify according to this definition (if not, let me know). > If your model does not explain where the cos^2(theta/2) comes from, it is > totally without interest. > > I think most professional physicists would disagree with the idea that physics is about explaining where mathematical rules "come from", as opposed to just finding the mathematical rules that generate correct predictions. To illustrate, I'll just post an extended quote from Richard Feynman from "The Character of Physical Law": "On the other hand, take Newton's law for gravitation, which has the aspects I discussed last time. I gave you the equation: F=Gmm'/r^2 just to impress you with the speed with which mathematical symbols can convey information. I said that the force was proportional to the product of the masses of two objects, and inversely as the square of the distance between them, and also that bodies react to forces by changing their speeds, or changing their motions, in the direction of the force by amounts proportional to the force and inversely proportional to their masses. Those are words all right, and I did not necessarily have to write the equation. Nevertheless it is kind of mathematical, and we wonder how this can be a fundamental law. What does the planet do? Does it look at the sun, see how far away it is, and decide to calculate on its internal adding machine the inverse of the square of the distance, which tells it how much to move? This is certainly no explanation of the machinery of gravitation! You might want to look further, and various people have tried to look further. Newton was originally asked about his theory--'But it doesn't mean anything--it doesn't tell us anything'. He said, 'It tells you how it moves. That should be enough. I have told you how it moves, not why.' But people are often unsatisfied without a mechanism, and I would like to describe one theory which has been invented, among others, of the type you migh want. This theory suggests that this effect is the result of large numbers of actions, which would explain why it is mathematical. Suppose that in the world everywhere there are a lot of particles, flying through us at very high speed. They come equally in all directions--just shooting by--and once in a while they hit us in a bombardment. We, and the sun, are practically transparent for them, practically but not completely, and some of them hit. ... If the sun were not there, particles would be bombarding the earth from all sides, giving little impuleses by the rattle, bang, bang of the few that hit. This will not shake the earth in any particular direction, because there are as many coming from one side as from the other, from top as from bottom. However, when the sun is there the particles which are coming from that direction are partially absorbed by the sun, because some of them hit the sun and do not go through. Therefore the number coming from the sun's direction towards the earth is less than the number coming from the other sides, because they meet an obstacle, the sun. It is easy to see that the farther the sun is away, of all the possible directions in which particles can come, a smaller proportion of the particles are being taken out. The sun will appear smaller--in fact inversely as the square of the distance. Therefore there will be an impulse on the earth towards the sun that varies inversely as the square of the distance. And this will be the result of a large number of very simple operations, just hits, one after the other, from all directions. Therefore the strangeness of the mathematical relation will be very much reduced, because the fundamental operation is much simpler than calculating the inverse of the square of the distance. This design, with the particles bouncing, does the calculation. The only trouble with this scheme is that it does not work, for other reasons. Every theory that you make up has to be analysed against all possible consequences, to see if it predicts anything else. And this does predict something else. If the earth is moving, more particles will hit it from in front than from behind. (If you are running in the rain, more rain hits you in the front of the face than in the back of the head, because you are running into the rain.) So, if the earth is moving it is running into the particles coming towards it and away from the ones that are chasing it from behind. So more particles will hit it from the front than from the back, and there will be a force opposing any motion. This force would slow the earth up in its orbit, and it certainly would not have lasted the three of four billion years (at least) that it has been going around the sun. So that is the end of that theory. 'Well,' you say, 'it was a good one, and I got rid of the mathematics for a while. Maybe I could invent a better one.' Maybe you can, because nobody knows the ultimate. But up to today, from the time of Newton, no one has invented another theoretical description of the mathematical machinery behind this law which does not either say the same thing over again, or make the mathematics harder, or predict some wrong phenomena. So there is no model of the theory of gravity today, other than the mathematical form. If this were the only law of this character it would be interesting and rather annoying. But what turns out to be true is that the more we investigate, the more laws we find, and the deeper we penetrate nature, the more this disease persists. Every one of our laws is a purely mathematical statement in rather complex and abstruse mathematics. ...[A] question is whether, when trying to guess new laws, we should use seat-of-the-pants feelings and philosophical principles--'I don't like the minimum principle', or 'I do like the minimum principle', 'I don't like action at a distance', or 'I do like action at a distance'. To what extent do models help? It is interesting that very often models do help, and most physics teachers try to teach how to use models and to get a good physical feel for how things are going to work out. But it always turns out that the greatest discoveries abstract away from the model and the model never does any good. Maxwell's discovery of electrodynamics was made with a lot of imaginary wheels and idlers in space. But when you get rid of all the idlers and things in space the thing is O.K. Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way." -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
