It’s instructional to examine the "Copenhagen interpretation of quantum mechanics" with which so many reductionists and logical positivists are infatuated. Probably the one physicist who most refined the limiting aspects of this interpretation was Paul Dirac, in his book Quantum Mechanics. Accordingly, he defined first the principle of superposition which lies at the core of the Copenhagen Interpretation[1]:
A state of a system may be defined as a state of undisturbed motion that is restricted by as many conditions or data as are theoretically possible without mutual interference or contradiction
[x,
p] = -i h = -i h/ 2p (or
more generally, [x, p] ¹ 0)
where [x, p] denotes a particular
operation for a Poisson bracket[2],
e.g. such that:
[x, p] = (x · p – p · x)
And h is
the Planck constant of action.
DavidBohm-WholenessAndTheImplicateOrder.pdf (gci.org.uk)
Let's say a beam of electrons are fired from a special electron gun at a screen - bearing two holes - some distance away:
At first glance, one might reasonably
conclude that the individual electron motions follow separate, unique
paths. That is, each electron traverses
a single, predictable path, following stages 1, 2, 3 and so on, toward the
screen. This is a reasonable,
common-sense sort of expectation but alas, all wrong!
According to the Copenhagen Interpretation of quantum theory, the instant the electron leaves the gun it takes a large number of differing paths to reach the screen. Each path differs only in phase, and has the same amplitude as each of its counterparts, so there is no preference. How does the electron differ from an apple, say tossed at a wall? The electron takes all paths to the screen the baseball takes only one (at a time) to the wall at which it is tossed. And the electron exhibits phases (as a wave) while the (macroscopic scale) baseball doesn't. The electron's wave function can be expressed:
y = y(1) + y(2) + y(3) + ….y(N)
Here the total wave function for the electron is on the left hand side of the equation, while its resolved wave amplitude states (superposition of states) is on the right-hand side. If they are energy states, they would correspond to all possible electron energies from the lowest (1) to the highest or Nth state (N). There is absolutely no way of knowing which single state the electron has until it reaches the screen and an observation is made, say with one or other special detectors (D).
Prior to reaching the screen the electron exists in a superposition of states or wave packets. Is this description statistical, or individual? This depends. The wave function has a clear statistical meaning when applied to a vast number of electrons. But it can also describe a single electron as well. In the example just cited, all the energy states refer to the same electron. However, if all electrons are identical, the statistical and individual descriptions coincide.
Germane to the point made here is that in a large number of cases the approaching electrons in the beam goes through both holes in the screen, not just one. This is totally counterintuitive to one steeped in the traditions of Newtonian or classical mechanics. Of course, such electrons deviate from classical behavior precisely because of their wave nature – as demonstrated in the famous Davisson-Germer experiment that verified that particles exhibit wave properties, e.g.
This seemed too contrived and artificial to Everett. What if? He asked himself, one used instead the basis of many worlds. Not literal worlds, but rather worlds in the sense of different quantum states separated from each other. Instead of thinking of all quantum wave states co-existing in one phase space (meaning differing x-y-z coordinates assigned to each electron in one system) one could think of each phase attached to another world: a quantum world. Then all these “worlds” co-existed for the total duration of time T before an observation. At the actual observation the choice of one world became a reality. (However, in other quantum worlds those choices could still materialize in slightly different formats).
While seemingly fantastical, the Many Worlds Interpretation thereby eliminated the troublesome issue of observer disturbance of observations, so peculiar to the Copenhagen Interpretation. The core problem was best summarized in Dirac’s own words[1]:
If a system is small, we cannot observe it without producing a serious disturbance and hence we cannot expect to find any causal connections between the results of our observations.
And
Causality applies only to a system which
is left undisturbed
In other words, the observation itself disrupts causation. For if the observed state is interfered with such that the observables don’t commute, i.e. [x, p] = 0, then one cannot logically connect states in a causal sequence. Following Dirac again[2]:we know that this case [x, p] = 0 can only be for a macroscopic or classical system.
The Copenhagen Interpretation and Mysticism:
In some quarters there've been efforts to use the Copenhagen Interpretation (CI) to knock down quantum-based mysticism, for example as articulated in Fritjof Capra's The Tao Of Physics, or any of Deepak Chopra's works. But the critics fails to appreciate that it is expecting too much for CI to do this because it's been reduced to merely a kind of “cook book”.
For example at the The Philotetes Center in 2011, physicist Mark Alford attempted to rebut Deepak Chopra's claim of a "quantum mind" (i.e. one unified mind field on the basis of quantum nonlocality) by arguing no quantum mechanics (QM) is needed to parse brain function. Alford remarked (see e.g. Skeptical Inquirer, May-June, 2011 p. 8) that:
"It seems improbable that these very
delicate processes are the crucial feature in the functioning of the human
brain which is not a suitable environment for quantum subtlety".
But in fact, he is quite mistaken. For example, we
know that the scale of the synaptic cleft is on the order of 200-300 nm and
hence subject to the Heisenberg Uncertainty Principle. This is precisely a quantum scale so it makes sense that the Heisenberg
Principle would apply at this level, and one can therefore surmise all the
mutual interference effects that are attendant. Technically, the Heisenberg
Principle is the embodiment of wave-particle ambiguity at those scales <
300nm and is thus a reflection of the Principle of Complementarity in Quantum
physics. It is usually expressed via the Poisson brackets (with non-commuting
variables x= position, p = momentum, in 1D) as we saw above.
Of course, if Heisenberg's
principle didn't apply - meaning we could know both the position and momentum
to the same degree of accuracy then:
[x, p] = 0
Is this really the case? Physicist Henry Stapp (Mind, Matter and Quantum Mechanics, 1983) has shown that application of the Heisenberg
Uncertainty Principle to Ca+2 ions (involved in neural transmissions at body
temperature) discloses the associated wave packet dimension increases to many times the size of the ion itself. This means that any actual measurements made will certainly
show a non-zero result for the Poisson bracket computation. Thus we can
represent the ion uptake superposition as a separate contributing wave
function, viz.:
U (A1....An) + U (Ca+2)n
where the A1.....An designate different neuronal
complexes. (See e.g., Stapp, ibid.)
Beyond this example, we know that the vast
information capacity of the typical human brain is more readily explained by
appeal to quantum bits, "qubits" rather than ordinary bits. With
qubits, with qubits one has the superposition of a combined data element (1 +
0) which implies: U = U(1) + U(0).In general, for any given n-bit combination –
with n a whole number, a qubit register can accommodate 2 to the nth power
total combinations at one time. Thus, 16 combinations could be held in memory for
4-bits, 32 for 5-bits, and so on. This change marks an exponential (two to the
n, or 2^n) increase over any classical counterpart. Since, human brains
typically can hold the equivalent in memory of whole libraries, it seems that
qubit processing is at least worth consideration and is certainly not
"improbable".
Alford is quoted as also asserting (SI, ibid.):
"It's more likely that consciousness
arises from other, more conventional bits of science, and you don't need to
reach all the way to this, the most exotic, the most delicate, the most bizarre
bit of modern physics."
And yet, despite being "bizarre", this
"exotic bit of physics" (understatement if ever there was one) has
reshaped our entire modern scientific and technological landscape! It's given
us high powered lasers and also enables us to put solid state electronics to
practical use employing something called "quantum tunneling" -
whereby a lower energy wave can penetrate a higher energy barrier, as well as
explaining why solar fusion only occurs about once every 14 billion years in
the Sun's core. It has also enabled us to probe the inside of the atom and
atomic transition processes, including being able to associates discrete energy
levels with atomic states! Hence, it is nowhere near the abstruse,
incomprehensible theory that Alford claims.
His argument that we don't need to go that far" is also somewhat puzzling. Why not, if it
can be shown to work (see e.g. David Bohm's example in his book, Quantum Theory, pp. 168-69). His argument is analogous to
asserting we don't need to go all the way to use differential calculus to
compute rocket trajectories! That the latter is "way too exotic" and
"delicate"! Well, true! One could rely on just algebra to attend to
rocket flight(with finite differences substituted for where differentials
appear) and come away with at least some basic info. But it'd be much cruder
than what the dy/dt terms (and higher derivatives) would yield, and you might not be able to land on Mars -
even after ten years of computations!
His other remark is also rather disappointing for
a physicist:
"If you rely too much on the current
scientific paradigm, wait a hundred years- it's been replaced. So I don't think
you want to be using quantum mechanics as a foundation. You can use it as
inspiration...but I don't think you want to actually build on it.."
Here he conflates scientific paradigm with
scientific theory (e.g. Quantum theory). The two are not one and the same. The
current paradigm, if one needs to articulate it, is more accurately a form of
reductionist mechanism. That it, no emergent properties are presumed to issue
from basic material interactions or processes. In this sense, Alford and his
cohort who subscribe to it are the ones on less than firm scientific grounds,
since we know paradigms do shift. (See Thomas Kuhn's work on the 'Structure of
Scientific Revolutions') Thus, in a hundred years, the reductionist mechanical
model may be totally replaced by an emergent or "holistic" model, say
of the type proposed by the late physicist David Bohm in his Wholeness and the Implicate Order (See link to pdf above.)
Further, Alford is mistaken in how he portrays the
fate of theories. Theories, real ones which start out with solid evidence and
predictions, are seldom if ever "replaced". For a quick example, look
at Newtonian Mechanics. Did we replace it with the advent of Quantum Mechanics?
Not at all! It remains a valid theory to apply, say to launch an artificial
satellite into Earth orbit, or to put a Rover on Mars. It has not been
"replaced" and indeed, in the standard Schrodinger equation, quantum
mechanics is found to revert to Newtonian mechanics in the limit of very large
principal quantum number (n -> oo).
Another reason why quantum mechanics can't be
conflated with the current paradigm, is because it is only one of two props for
modern physics, the other being relativity (special and general theories). I
note that Alford has said nothing on those, though granted Chopra didn't
incorporate them into his "quantum mind" either. However, if one is
going to make reference to "the current scientific paradigm", one is
at least obligated to include relativity as part of it!
Now, it was physicist David Bohm who first pointed
out (op. cit., p. 169), the very precise analogy of quantum
processes to thought. In particular, the quantum "wave packet
collapse" (e.g. to a single eigenstate, from a superposition of
eigenstates) is exactly analogous to the phenomenon of trying to pinpoint what
one is thinking about at the instant he is doing such thinking. More often than
not, when one does this, as Bohm notes: "uncontrollable and unpredictable changes" are introduced into the thought process or train.
Recall as I noted from earlier blogs (See: 'A Material Model of Consciousness', Parts I-III), that Bohm also provided a putative basis for a "quantum mind" which he referred to as the Holomovement. This was done by positing a hyper (e.gt. 5-) dimensional reality in which mind was enfolded with matter as part of an implicate order. To enable a unified field within this higher dimensionality Bohm invoked hidden variables obeying the Heisenberg Uncertainty relations, e.g.
(d p)( d q)> h/ 2π
Where p, q denote two hidden variables underlying a sub-quantal scale
indeterminacy relation. From this (leaving out lots of details) he developed an
agent to assist in the nonlocal action of distal variables, and called it
the "quantum potential", defined:
VQ = {-ħ2/ 2m} [Ñ R]2 /
R
for a wave function, U = R exp(iS/ħ)
where
R,S are real.
If one then fully applies Bohm's Holomovement model to
physical reality it is possible to show the relation of explicated
individual forms to the universal aggregate (or Holomovement) -
which might be depicted:
INDIVIDUAL FORMS (EXPLICATE ORDER)
___Ç___Ç___Ç___Ç___Ç___
DIRAC ENERGY SEA (IMPLICATE
ORDER)
The relation is holographic in the sense that each of the individual forms contains the information of the whole holographic field. The Dirac Ether is equivalent to Bohm's Implicate Order, or what he calls the holomovement, and is a pure frequency domain. If one imparts to it a universal consciousness (as Bohm does) it would also be the "Universal Mind". In accord with Fritjof Capra's work, you can't get much more mystical than this!
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