On 27/04/2016 4:13 pm, Jesse Mazer wrote:
On Wed, Apr 27, 2016 at 1:40 AM, Bruce Kellett
<[email protected] <mailto:[email protected]>> wrote:
On 27/04/2016 3:22 pm, Jesse Mazer wrote:
On Wed, Apr 27, 2016 at 12:47 AM, Bruce Kellett
<[email protected] <mailto:[email protected]>> 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.
It is of no interest. You, and Rubin, advertised your work as a local
explanation of the EPR statistics. On detailed examination and pressing,
you admit that this is not the case: you simply take the quantum results
and build some Rubin Goldberg machine that will reproduce those
statistics. So what? My urn model is simpler and does the same thing.
The thing that bothers me is that I have spent so much time arguing this
when, in the final analysis, you do not have a local account of the EPR
results. All your machinery is of no use, since any account of EPR must
fit in with the rest of quantum mechanics -- it is not something you can
simply abstract away and treat in isolation. The cos^2(theta/2) comes
from applying the strict rules of quantum mechanics to this entangled
state -- it is not an arbitrary formula dreamed up simply to account for
some observed statistics. The fact that experiment followed this
distribution was a profound surprise to many -- that is why locality and
non-locality are such contentious issues.
Richard Feynman was frequently a bit "over the top" in his popular
accounts of physics. He is unkind to Newton, since the 1/r^2 form of the
law of gravitation follows simply from spherical symmetry and
conservation of flux. Coulomb's law can be derived in much the same way.
The mathematical basis is Gauss's law.
So generate whatever models you like, but it is disingenuous to claim
that you are giving a local explanation for the EPR correlations.
Bruce
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."
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