Transcript Quanta and Consciousness

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Let’s recall. There was:
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Robbie, in the TV series (guess the answer)
HAL 9000, in ……………
Mr. Data, in …………..
Marvin the Paranoid Android, in ……………….
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Some here will think of many more. Can machines be
taught to really think? Perhaps more importantly, are we
merely very complex computers? Or is “mind” more than a
collection of neurons?
Quanta and Consciousness
An overview of two significant and
surprising developments in 20th-century
science, one in physics and the other in
mathematics. Both of these have
implications regarding the nature of
perception and consciousness.
First, some background . . .
The development of quantum ideas
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James Clerk Maxwell
Max Planck
Niels Bohr
Louie de Broglie
Erwin Schrodinger
“If we are going to stick to
this damned quantumjumping, then I regret that I
ever had anything to do with
quantum theory”
Werner Heisenberg
Albert Einstein
The Bohr-Einstein debate
Bohr and Einstein: a study in contrasts.
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These are the conditions under which Einstein wrote he
would agree to continue to live with Mileva in Berlin:
A. You will see to it that: 1. My clothes and laundry are
kept in good order; 2. I will be served three meals
regularly in my room; 3. My bedroom and study are kept
tidy, and especially that my desk is left for my use only.
B. You will relinquish all personal relations with me
insofar as they are not completely necessary for social
reasons. Particularly, you will forgo my: 1. Staying at
home with you; 2. Going out and traveling with you. C.
You will obey the following points in your relations with
me: 1. You will not expect any tenderness from me, nor
will you offer any suggestions to me; 2. You will stop
talking to me about something if I request it; 3. You will
leave my bedroom or study without any back talk if I
request it. D. You will undertake not to belittle me in front
of our children, either through words or behavior.
Mileva Maric left Berlin with the children shortly after this.
Bohr and his sons
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Einstein generally worked alone. In addressing a
government agency after WW2, concerning what could
be done with out-of-work scientists, he said in all
seriousness that jobs such as “lighthouse keeper” would
be ideal for many scientists.
Bohr was a gregarious Dane who founded and built up
an institute in Copenhagen. There are still physicists
from all over the world who can say “I worked with Bohr”
or at least their doctoral advisors did.
The “Copenhagen interpretation”
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Quantum theory is probabilistic in nature. One can
calculate exactly what an outcome will be --- one can
only calculate the probability of obtaining one outcome or
another.
These probabilities are contained in the “wavefunction”
of the system. Before we do the observation, the
wavefunction may contain many possible, overlapping
outcomes. During the measurement, one of these
outcomes is “selected.”
Example: the position of an electron in an atom: the
original “Bohr model” vs the “electron cloud.”
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Another example: decay of a nucleus. In a uranium
atom, one can picture an alpha particle (two protons/two
neutrons) bouncing back an forth against a potential
barrier. Every time it hits, there is a probability that it will
escape --- to tunnel through the barrier. In a certain
time, we cannot predict whether the particle will escape
or not, but we can predict the probability that it will
escape in that time. (This would be like rolling a ball up
a hill. Instead of stopping an rolling back down, there is
a probability that it would disappear and reappear on the
other side of the hill.)
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(More on this later)
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A central part of quantum theory is the Heisenberg
Uncertainty Principle, which puts certain limits on our
possible knowledge of the state of a quantum system. In
a nutshell, it states that we cannot know two “conjugate
variables” to arbitrary precision at the same time. For
example, we cannot know the position and the velocity of
a particle at the same time; there must be an uncertainty
in our measurement. To wit,
(Delta)x times (Delta)v >= Planck’s constant
Einstein’s take on all this
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(From a letter to Max
Born, 1926): “Quantum
mechanics is very
impressive. But an inner
voice tells me that it is not
yet the real thing. The
theory produces a good
deal but hardly brings us
closer to the secret of the
Old One. I am at all
events convinced that He
does not play dice.”
The “EPR” paradox
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To illustrate deficiencies in the quantum theory, Einstein
came up with many “gedanken experiments.” Bohr
always came up with resolutions to Einstein’s proposed
contradictions, but Einstein doggedly kept at it. In 1934,
in one of his rarely co-authored papers, Einstein issued
one last challenge. This was the famous Einstein,
Podolsky, and Rosen (EPR) paper. It caused quite a stir.
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Excerpt from a letter by
Wolfgang Pauli to
Heisenberg: “Einstein has
once again expressed
himself publicly on quantum
mechanics. . . .(together
with Podolsky and Rosen --no good company, by the
way). As is well known,
every time that happens it is
a catastrophe.”
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The original EPR paper dealt with the linear momentum
(mass times velocity) of two particles which interact but
are then separated. A fundamental tenet of the paper is
that after the particles separate, there is a “local reality”
associated with each. The idea that one particle could
affect the other, say, when on opposite sides of the solar
system seems preposterous. In this way, EPR seemed
to “get around” the limitations of Heisenberg uncertainty.
This time, Bohr did not have an iron-clad comeback. He
eventually said that “the trend of their argumentation. . .
does not seem to me to meet the actual situation with
which we are faced in atomic physics.” As lame as this
was, most physicists seemed to buy his arguments, gave
a sigh of relief, and went back to “real” work.
Bohr talked of his
arguments with Einstein
until the day of his death
in 1962. He had
countered every attack on
the theory as if it had
been a personal one.
The issue then lay more
or less dormant for many
years.
Entanglement
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In 1952, David Bohm changed the setting of the EPR paper in a
way that made the issues more clear and concise. He reduced
the problem to two particles and only one variable for each: the
spin or polarization. He also championed the notion of “hidden
variables” which provide a complete picture of quantum reality.
John Bell was a researcher at CERN (a high-energy facility in
Geneva), and in his “spare time” worked on the deeper issues of
quantum theory. In the mid sixties, he published two groundbreaking papers. Bell’s Theorem, as it was called, provided a
means for real experiments to test alternatives to quantum ideas.
John Bell and his wife Mary,
also a physicist.
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David Bohm
Bell’s Theorem
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John Bell knew that Einstein and colleagues were partly correct:
the “EPR paradox” was no paradox at all. What was wrong was
their insistence on “local reality” --- that the total, “mixed” wave
function could not extend across large regions of space.
Thus, Bell viewed two alternatives: (1) Quantum theory is right,
or (2) local realistic models are right. But both cannot be right.
Bell produced a mathematical theorem containing certain
inequalities. He suggested that if his inequalities could be
violated by experimental tests, it would provide evidence in favor
of orthodox (Copenhagen) quantum theory.
Tests of Bell’s Theorem
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With apologies I am
leaving out the work of
Shimony, Clauser, Horne,
Aravind, Zeilinger, and
others.
The most convincing
tests of Bell’s inequalities
has been done by Alain
Aspect (in France).
Aspect’s experiments
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We conclude that “hidden variables” or other forms of local
reality are NOT correct. “Spooky action at a distance” (to use
Einstein’s description) correctly describes quantum systems.
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By the way, the notion of entanglement is absolutely fundamental to
the development of quantum computing, a hot topic these days.
Now, back to some “old” stuff……
The role of the “Observer”
Schrodinger’s cat.
The Von Neumann-London-Bauer argument
The probabilities that are computed in quantum
mechanics are probabilities of outcomes of
measurements.
The observer is outside the system. He intervenes in the
system by making a measurement. The observer’s
intervention takes one out of the realm of the
hypothetical and into the realm of the actual.
One might think we could give a complete mathematical
description of not only the experimental devices but of
the observer herself, at least in principle.
But this cannot be done!
If we could describe by the mathematics of quantum
theory everything that happened in a measurement,
even up to the point where a definite outcome was
obtained by an observer, then the math would have to
tell us what the outcome was. But this cannot happen,
for in quantum theory the math will yield only
probabilities.
In short, the mathematical descriptions of the physical
world given to us by quantum theory presuppose the
existence of observers who lie outside those
mathematical descriptions. And the theory works.
What about the line between the “system” and the
“observer”?
Godel’s theorem
§ Kurt Godel was an
Austrian logician and a
good friend of Einstein.
§ (In the movie “IQ”,
Walter Matthau played
Einstein and Lou
Jacobi played Godel.
Meg Ryan played
Einstein’s niece.)
The theorem - 1931
§ Godel proved that in any consistent formal
mathematical system (in which one can at least do
arithmetic and simple logic), there are arithmetical
statements which can neither be proved nor disproved
using the rules of that system but which are
nevertheless true statements.
§ These are called “formally undecidable propositions” of
that system.
§ Moreover, Godel showed how to find, in any particular
consistent formal system, how to actually find one of its
formally undecidable-but-true propositions.
§ If F is any consistent formal system that
contains logic and arithmetic, Godel showed
how to find a statement in arithmetic, which we
may call G(F), that is neither provable nor
disprovable using the rules of F. He further
showed that G(F) is nevertheless a TRUE
arithmetical statement.
§ This can be applied to computer programs. For
a computer program P that is known to be
consistent, one can find a statement in
arithmetic, G(P), that cannot be proven nor
disproven by that program. And one can show
that G(P) is a true statement.
The Lucas-Penrose argument.
§ In 1961, John R. Lucas, a philosopher at Oxford U., set
forth an argument based on Godel’s Theorem, to the
effect that the human mind cannot be a computer
program.
§ Roger Penrose, the widely-known mathematician and
physicist, revived Lucas’ argument in the late 80’s. His
book The Emperor’s New Mind was published in 1989.
In answer to the large amount of criticism it provoked,
Penrose published a second book, Shadows of the
Mind.
While no one has succeeded in refuting the LucasPenrose argument, it has not changed many minds.
The argument
§ Suppose someone shows me a computer program, P,
that has the ability to do simple arithmetic and logic. I
know this program to be consistent, and I know all the
rules by which it operates. Then as Godel proved, I
can find a statement in arithmetic (call it G(P)) that the
program P cannot prove (or disprove.) But following
Godel’s reasoning, I can show G(P) to be a true
statement of arithmetic.
§ So far, no big deal. The programmer could modify the
program so that it can also prove G(P). But I know all
the new rules, too, so I can find a new statement which
is true but which cannot be proven or disproven by the
new program. Again the programmer could improve
the program, and we can keep playing this game, with
me always “outwitting” the new programs. However….
§ Suppose I myself AM a computer program: call me H
(for human). When I prove things, it is just by some
computer program running in my brain. And now
suppose I am shown that program, learning in complete
detail how H works. Then assuming I know H to be a
consistent program, I can construct a statement in
arithmetic, call it G(H), that cannot be proven or
disproven by H, but which I, using Godel’s reasoning,
can show to be true.
§ Contradiction: it is impossible for H to be unable to
prove a result that I am able to prove, because H is me!
§ (Thanks to Stephen Barr for this concise description of
the Lucas-Penrose argument.)
Our assumptions were:
§ (a) I am a computer program.
§ (b) I know that the program is consistent.
§ (c) I can learn the structure of the program in complete
detail.
§ (d) I have the ability to go through Godel’s “steps.”
A materialist has “escape routes” by denying (b),
(c), or (d) instead of (a).
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In conclusion
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Herrmann Weyl, one of the great
mathematicians and physicists of the
twentieth century, wrote in 1931:
“We may say that there exists a world,
causally closed and determined by precise
laws, but . . . the new insight which modern
[quantum] physics affords opens several
ways of reconciling personal freedom with
natural law. It would be premature, however,
to propose a definite and complete solution
of this problem. One of the great differences
between the scientist and the impatient
philosopher is that the scientist bides his
time. We must await the further
development of science, perhaps for
centuries, perhaps for thousands of years,
before we can design a true and detailed
picture of the interwoven texture of Matter,
Postscript
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The answer is NOT “42”.
(With apologies to Douglas Adams, who wrote
The Hitchhikers Guide to the Galaxy.)