I will quote his response to me:
Thank you for drawing my attention to the paper by Antoine Saurez
which I had missed. I will have to read it carefully to see exactly
what assumptions are made. If everything turns out to be experimentally
sound then this is an important result in trying to understand
entanglement. It rules out one way of trying to understand entanglement
in the relativistic context. I always felt the chances that a
universal rest frame existed were very small. Bohm and I presented a
paper discussing the consequences of there being no rest frame in Bohm,
D. and Hiley, B. J., Non-locality and Locality in the Stochastic
Interpretation of Quantum Mechanics, Phys. Reports, 172 (1989)
93-122. Things are much more complicated. My preferred explanation
lies in a much deeper explanation that we were working on when Penrose
was with us at Birkbeck College, namely the notion of pre-space, or
pre-geometry. Today it is called 'non-commutative geometry’. In my
view this demands a radical new view as to what geometry actually is.
Things do not go on in space-time but space-time itself emerges from
the non-commutative algebra of process. One of my latest papers, The Algebraic way, in Beyond Peaceful Coexistence, The Emergence of Space, Time and Quantum, Ed., Licata, I., 1-25, World Scientific, 2016. [pdf link] (arXiv
1602.06071) will give you a flavour of the direction of my thinking.
Unfortunately
the Suarez paper simply concludes “Lets stick with the instantaneous
collapse of the wave function”. But what does that mean? If you merely
want a quiet life just repeat the mantra! The difficulty remains “What
is the geometric structure of the process that unites relativity and
quantum mechanics". When Dirac, Schwinger and Feynman were setting up
relativistic quantum field theory they abandoned the wave function and
replaced it with transition probabilities. Unfortunately the ideas
became a set of rules that seem only to be used in scattering theory.
Forget what they taught us and simply return the the collapse of the
wave function. What seems to have been forgotten or not recognised was
that Dirac already had the Bohm equation in his "Principles of Quantum
Mechanics” because the equations are simply a different mathematical
form of Schrödinger’s equation. What I have shown recently is that the
Bohm trajectories are the mean of an ensemble of individual Feynman
paths. Weak values are just a return to transition probabilities.
Unfortunately they are presented as “values” cf eigenvalues. See Flack, R. and Hiley, B. J., Feynman Paths and Weak Values, in Entropy, 20 (5) May 2018.
Best wishes,
Basil Hiley.
Dear Professor Hiley: Thank you very much for your thoughtful
response. I read your two papers that you referred to and I found both
to be very profound. Have you seen Alain Conne's music lecture on
noncommutative geometry? https://www.youtube.com/watch?v=bIziuv-WLMM&list=PLaxpujmz7Q04oLrfclxSKYREJyb1xYb4w&index=98
I don't do calculations much although I did take quantum
mechanics from the same professor that Lee Smolin had for his first
quantum mechanics class - Professor Herbert J. Bernstein. So when you
refer to de Broglie stating the quantum potential could be just the
change in rest mass - do you think this is due to the noncommutative
phase of light, from the relativistic mass of light as the hidden
momentum?
As we corresponded before, you replied that you
understand the noncommutative time-frequency resonance. My background is
actually music theory so that is why I find Conne's lecture so
intriguing, as he regards music theory to express the quantum sphere
with a geometric dimension of zero, precisely because music theory is
noncommutative. This was an intuitive understanding I realized while I
was in high school - so I secretly rejected commutative math early on. I
realized for example that the Pythagorean Theorem was incorrect since
it was based on the wrong music theory! Of course I kept that secret to
myself. haha. And so when I learned quantum entanglement from Professor
Bernstein - he laughed at the shocked look on my face - this was my
first year of college. Lee Smolin described a similar experience. But
Bernstein emphasized how people learn classical physics first and since
quantum physics is the foundation of science now, then people get the
wrong foundation for understanding reality. I am interested in the
entropy to ecology from the wrong symmetric math. In other words, my
master's thesis was on music theory, radical ecology and nonlocality.
But I made the error of still relying on symmetric math. So then I had
to study music theory again to realize the formal issue of the
noncommutative math. Math professor Joe Mazur then asked me to submit my
research - about the connections of continued proportions to the
geometric continuum via music theory - to the most read math journal in
the U.S. haha. Of course it was rejected without comment, and I even
brought in quantum physics near the end. But anyway I just realized
today how the alternative harmonic series that is the basis for the
natural logarithm of 2, the doubling time of growth, this alternating
harmonic series is a "conditionally convergent series" which means it is
not commutative! So by changing the order, you change the sum, and yet
the "sum of the absolute values" diverges as the harmonic series.
Anyway
thank you for clarifying how the foundation of nonlocality is not based
on probability but rather the noncommutative density matrix. Gerard 't
Hooft points out the noncommutative relation of the different
measurement settings for the double slit experiment - and so it seems
that left-brain dominant math is tied directly to right-hand dominant
technology, ever since the Pythagorean Theorem. haha. Math professor
Luigi Borzacchini calls this the "deep pre-established disharmony" that
is the "evolutive principle" of science. He is retired now, and his book
"Plato's Computer" is only in Italian, but I guess he, along with
Connes, see some kind of quantum computing AI Matrix future for the
planet. But I have been studying "abrupt" global warming - for example
the East Siberian Arctic Shelf methane "bomb" and also the Global
Dimming Effect - it is quite amazing how much "entropy" we have released
into the biosphere - and again I think this is driven by the wrong
mathematics! haha. Actually I think it's from the wrong music theory
that was the origin of the wrong math - and this is what Professor
Borzacchini points out as well - he calls it the "cognitive bias" of
geometry.
I finished my master's degree doing
intensive meditation from a Chinese spiritual healer (hence my funny
gmail name) - and so I had some very wild "esoteric" experiences. I
literally saw ghosts - and also smelled cancer - nonlocally - and also I
did healing for a while that had a lot of "power." I agree that there
is indeed a quantum non-material new causative "force" as you describe. I
know for a fact this is some kind of macroquantum relativistic energy.
There is also the assistant of the Chinese teacher - an African-American man who healed my mom long distance. He lived at our cabin for a few
months - and so he explained things to me as well. So he can leave his
body at will but he also describes changing spacetime itself. I have had
precognitive visions as well from deep meditation. So I do believe that
the quantum potential is a change in the "rest frame" or "rest mass" of
reality. haha. I do plan on just meditating as a hermit as much as
possible but I agree with you that just repeating some mantra (as the
equivalent of "instantaneous collapse of the wave function") is living a
lie. I don't think a quiet life is very easy now - with this increased
entropy. For example "acoustic ecology" studies by Bernard Krause have
shown there is no escape from industrial noise anywhere on the planet.
haha. Western civilization has killed 40% of vertebrate life in the past
40 years - and 80% of mammals in the past couple thousand years.
So
anyway who can deny the power of symmetric math? But this
non-relativistic classic limit - via the Poisson Bracket - that Dirac
discovered from studying Heisenberg - it seems that actually the
noncommutative algebra can not be denied. The entropy of depending or
converting back to the symmetric math has become too powerful. Just as
in Chaos math - the golden ratio is the slowest converging irrational or
the "most irrational" and so preferred for natural growth whereas
natural number resonance is too powerful - I think that the convergence
is a scam. The closed form of the golden ratio equation depends on
changing the order of the symmetry from A is to B as B is to (A plus B)
with the last term changed to (A minus B). So this is like the
alternating harmonic series - in the end it still diverges. haha. It is
the noncommutative phase that is the key here.
I
will share another thing - do you know the work of Eddie Oshins? He
worked with math professor Louis Kauffman at the Stanford Linear
Accelerator Center - Oshins focus was on "quantum psychology." Oshins
had worked with Karl Pribram - but Oshins said Pribram was not able to
understand the noncommutative math and so Pribram kept insisting on the
wrong understanding. Anyway Oshins also taught Wing Chun (from Bruce Lee
martial arts) and Oshins realized the secret of the martial arts "qi"
energy is from the noncommutative math! This is quite fascinating to me
and so I have studied it. For example for males - the right hand is yin,
left hand yang and upper body yang and lower body yin. So if you hold
the right hand over the upper body and the left hand over the lower body
- then this is activating the natural energy channels as a macroquantum
resonator - due to the structure of noncommutative phase! So also you
then visualize the energy from the left hand to the right foot and the
right hand to the left foot, etc.
Plato argued
that there was a unit of "two-ness" that was symmetrical and before
number and so this justified irrational magnitude and Plato's argument
was that the left and right eye are a unit of "twoness" and the same
with the left and right hand, feet, etc. But this covered up the
noncommutative phase math.
Thanks again,
drew hempel
I transcribed part of Connes talk:
What
is a parameter? The parameter is time...If you stay in the classical
world, you can not have a good set up for variables. Because variables
with a continuous range can not coexist with variables of discrete
range. When you think more, you find out there is a perfect answer. And
this answer is coming from quantum mechanics....The real variability in
the world is exactly is where are you in the spectrum [frequency] of
this variable or operator. And what is quite amazing is that in this
work that I did at the very beginning of my mathematical studies, the
amazing fact is that exactly time is emerging from the noncommutivity.
You think that these variables do not commute, first of all it is that
they don't commute so you can have the discrete variable that coexists
with the continuous variable. What you find out after awhile is that the
origin of time is probably quantum mechanical and its coming from the
fact that thanks to noncommutativity ONLY that one can write the time
evolution of a system, in temperature, in heat bath, the time evolution
is really coming from the noncommutativity of the variables....You
really are in a different world, then the world of geometry, which we
all like because we all like to draw pictures and think in a geometric
manner. So what I am going to explain is a very strange way to think
about geometry, from this point of view, which is quite different from
drawing on the blackboard...I will start by asking an extremely simple
question, which of course has a geometrical origin. I don't think there
can be a simpler question. Where are we?....The mathematical question,
what we want, to say where we are and this has two parts: What is our
universe? What is the geometric space in which we are? And in which
point in this universe we are. We can not answer the 2nd question
without answering the first question, of course....You have to be able
to tell the geometric space in an invariant manner....These invariants
are refinements of the idea of the diameter. The inverse of the diameter
of the space is related to the first Eigenoperator, capturing the
vibrations of the space; the way you can hear the music of
shapes...which would be its scale in the musical sense; this shape will
have a certain number of notes, these notes will be given by the
frequency and form the basic scale, at which the geometric object is
vibrating....The scale of a geometric shape is actually not enough....
However what emerges, if you know not only the various frequencies but
also the chords, and the point will correspond to the chords. Then you
know the complete thing....It's a rather delicate thing....There is a
very strange mathematical fact...If you take manifolds of the same
dimension, which are extremely different...the inverse space of the
spinor doesn't distinguish between two manifolds. The Dirac Operator
itself has a scale, so it's a spectrum [frequency]. And the only thing
you need to know...is the relative position of the algebra...the
Eigenfunctions of the Dirac Operator....a "universal scaling system,"
manifests itself in acoustic systems....There is something even simpler
which is what happens with a single string. If we take the most
elementary shape, which is the interval, what will happen when we make
it vibrate, of course with the end points fixed, it will vibrate in a
very extremely simple manner. Each of these will produce a sound...When
you look at the eigenfunctions of the disk, at first you don't see a
shape but when you look at very higher frequencies you see a parabola.
If you want the dimension of the shape you are looking at, it is by the
growth of these eigenvariables. When talking about a string it's a
straight line. When looking at a two dimensional object you can tell
that because the eigenspectrum is a parabola.... They are isospectral
[frequency with the same area], even though they are geometrically
different....when you take the square root of these numbers, they are
the same [frequency] spectrum but they don't have the same chords. There
are three types of notes which are different....What do I mean by
possible chords? I mean now that you have eigenfunctions, coming from
the drawing of the disk or square [triangle, etc.]. If you look at a
point and you look at the eigenfunction, you can look at the value of
the eigenfunction at this point.... The point [zero in space] makes a
chord between two notes. When the value of the two eigenfunctions [2, 3,
infinity] will be non-zero. ...The corresponding eigenfunctions only
leave you one of the two pieces; so if there is is one in the piece, it
is zero on the other piece and if it is non-zero in the piece it is zero
there...You understand the finite invariant which is behind the scenes
which is allowing you to recover the geometry from the spectrum....Our
notion of point will emerge, a correlation of different
frequencies...The space will be given by the scale. The music of the
space will be done by the various chords. It's not enough to give the
scale. You also have to give which chords are possible....The only thing
that matters when you have these sequences are the ratios, the ear is
only sensitive to the ratio, not to the additivity...multiplication by 2
of the frequency and transposition, normally the simplest way is
multiplication by 3...2 to the power of 19 is almost 3 to the power of
12....You see what we are after....it should be a shape, it's spectrum
looks like that...We can draw this spectrum...what do you get? It
doesn't look at all like a parabola! It doesn't look at all like a
parabola! It doesn't look at all like a straight line. It goes up
exponentially fast...What is the dimension of this space?...It's much
much smaller. It's zero...It's smaller than any positive.... Musical
shape has geometric dimension zero... You think you are in bad shape
because all the shapes we know ...but this is ignoring the
noncommutative work. This is ignoring quantum groups. There is a
beautiful answer to that, which is the quantum sphere... .There is a
quantum sphere with a geometric dimension of zero...I have made a
keyboard [from the quantum sphere]....This would be a musical instrument
that would never get out of tune....It's purely spectral....The
spectrum of the Dirac Operator...space is not simply a manifold but
multiplied by a noncommutative finite space......It is precisely the
irrationality of log(3)/ log(2) which is responsible for the
noncommutative [complementary opposites as yin/yang] nature of the
quotient corresponding to the three places {2, 3,∞}. The formula is in
sub-space....Geometry would no longer be dependent on coordinates, it
would be spectral...The thing which is very unpleasant in this formula
is the square root...especially for space with a meter....So there is a
solution to this problem of the square root, which was found by Paul
Dirac....It's not really Paul Dirac, it is Hamilton who found it
first...the quaternions is the Dirac Operator....Replace the geometric
space, by the algebra and the line element...for physicists this thing
has a meaning, a propagator for the Dirac Operator. So it's the inverse
of the Dirac Operator.... You don't lose anything. You can recover the
distance from two points, in a different manner....but by sending a wave
from point A to point B with a constraint on the vibration of the wave,
can not vibrate faster than 1; because what I ask is the commutator of
the Dirac Operator is less than 1...It no longer requires that the space
is connected, it works for discrete space. It no longer requires that
the space is commutative, because it works for noncommutative
space....the algebra of coordinates depends very little on the actual
structure and the line element is very important. What's really
important is there interaction [the noncommutative chord]. When you let
them interact in the same space then everything happens....You should
never think of this finite space as being a commutative space. You have
matrices which are given by a noncommutative space...To have a geometry
you need to have an inverse space and a Dirac Operator...The inverse
space of the finite space is 5 dimensional....What emerges is finite
space...it's related to mathematics and related to the fact that there
is behind the scene, when I talk about the Dirac Operator, there is a
square root, and this square root, when you take a square root there is
an ambiguity. And the ambiguity that is there is coming from the spin
structure.... We get this formula by counting the number of the
variables of the line element that are bigger than the Planck Length. We
just count and get an integer.... There is a fine structure in
spacetime, exactly as there is a fine structure in spectrals
[frequencies]....Geometry is born in quantum space; it is invariant
because it is observer dependent....Our brain is an incredible
...perceives things in momentum space of the photons we receive and
manufactures a mental picture. Which is geometric. But what I am telling
you is that I think ...that the fundamental thing is spectral
[frequency]....And somehow in order to think we have to do this enormous
Fourier Transform...not for functions but a Fourier Transform on
geometry. By talking about the "music of shapes" is really a fourier
transform of shape and the fact that we have to do it in reverse. This
is a function that the brain does amazingly well, because we think
geometrically....The quantum observables do no commute; the phase space
of a microscopic system is actually a noncommutative space and that is
what is behind the scenes all the time. They way I understand it is that
some physical laws are so robust, is that if I understand it correctly,
there is a marvelous mathematical structure that is underneath the law,
not a value of a number, but a mathematical structure....A fascinating
aspect of music...is that it allows one to develop further one's
perception of the passing of time. This needs to be understood much
better. Why is time passing? Or better: Why do we have the impression
that time is passes? Because we are immersed in the heat bath of the 3K
radiation from the Big Bang?...time emerges from
noncommutativity....What about the relation with music? One finds
quickly that music is best based on the scale (spectrum) which consists
of all positive integer powers qn for the real number q=2 to the 12th∼3
to the 19th. Due to the exponential growth of this spectrum, it cannot
correspond to a familiar shape but to an object of dimension less than
any strictly positive number. As explained in the talk, there is a
beautiful space which has the correct spectrum: the quantum sphere of
Poddles, Dabrowski, Sitarz, Brain, Landi et all. ... We experiment in
the talk with this spectrum and show how well suited it is for playing
music. The new geometry which encodes such new spaces, is then
introduced in its spectral form, it is noncommutative geometry, which is
then confronted with physics. Fields Medal math professor Alain
Connes,
1997 interview with Professor Hiley
1997 interview with Professor Hiley
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