On 27 Apr 2016, at 08:35, Bruce Kellett wrote:
On 27/04/2016 4:13 pm, Jesse Mazer wrote:
On Wed, Apr 27, 2016 at 1:40 AM, Bruce Kellett <[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]
> 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.
The cos^2(theta/2) works also for 1/sqrt(2)ABI+>I-> - 1/sqrt(2)ABI->I+>
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.
It is not local, because the end situation is not local, but the
infinitely many Alice and Bob do recover the right statistics in each
of their branches, just by the correlation made locally when they
prepare their state. Action at a distance is not needed, *because* the
state 1/sqrt(2)ABI+>I-> - 1/sqrt(2)ABI->I+> describes an infinity of
relative states. Bell concludes to action at a distance because he
discards the superposition after the measurement.
Bruno
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."
--
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 [email protected].
To post to this group, send email to everything-
[email protected].
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
--
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 [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
http://iridia.ulb.ac.be/~marchal/
--
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 [email protected].
To post to this group, send email to [email protected].
Visit this group at https://groups.google.com/group/everything-list.
For more options, visit https://groups.google.com/d/optout.
