Heisenberg misunderstood the Uncertainty Principle
Probabilities are the precondition of the
Uncertainty Principle and not its effect.
We devised and analyzed both real and thought experiments that bypass the
uncertainty relation, in effect, to "trick" the quantum objects under study.
Nevertheless, the results always reveal that..complementarity remains intact
even when the uncertainty relation takes no role.
Englert, Scully, and Walther / 1994, p56
The true world--we have abolished. What world has remained? The apparent one
perhaps? But no! With the true world we have also abolished the apparent one.
Friedrich Nietzsche / Twilight of the Idols
I cannot now see any problem in the dualism of waves and particles and never could.
Light penetrates a double-slit and projects an interference pattern on a
photo-screen. If one of the slits is closed, then no interference pattern is
formed but there exists a certain probability of the light
penetrating the open slit and a certain probability for the fact
that the light strikes the covering behind the second slit.
One sees that here the light corresponds to a certain probability distribution
to cause local density dots, a dynamic probability distribution which
possesses the character of waves and is capable of interference. This
is the simple stating of the empiric factual matter, thus of the
phenomenon.
We cannot a priori expect from light behaviour like that of small billiard
balls with a precisely defined place and known speed at every moment, just as
little as we would attempt to describe snow flakes as billiard
balls. We must first take the phenomenon for that which it depicts.
In doing so, it turns out that light constitutes a probability
distribution. Thus we accept it as such! Hypotheses non fingo.
On the other hand, I see a problem in the Copenhagen interpretation of quantum
theory. That view does not take light for what it constitutes - a probability
distribution.
The Uncertainty Principle
The principle of complementarity is certainly more fundamental than is the
uncertainty relation."
(Englert, Scully, and Walther / 1994, p60 ).
Heisenberg’s argumentation contains a classical case of circular reasoning,
confusion between cause and effect, since the probability distribution (statistic
interference pattern) is the prerequisite for establishing the Uncertainty Principle.
Before going into Bohr's analysis of the uncertainty principle, two points should
be made clear. First, the mathematical formalism expressing relationships encompassed
by the "uncertainty principle" are straight forward deductive consequences of the
quantum postulate. All too often, discussions of the principle begin with a series
of thought experiments intended to demonstrate that observations which determine
the value of one observable within a certain range require physical conditions
which preclude determining its canonically conjugate observable within a range
that would contradict the uncertainty principle.
It is then easy to get the mistaken impression that the principle expresses
an empirical generalization derived from analyzing physical situations and
that such a presumed empirical discovery is then injected as a postulate into
the theoretical formalism. However, this is not the case. Heisenberg first
developed his formalism for theoretical representation of the atomic system
processes, and then showed that the consequence of his formalism was that the
system could not be characterized by a state which was defined in terms of
precise values for both canonically conjugate parameters.
Dan Glover (
mirror /
WWW)
In the succinct statement of the law of causality, “If we know the
present precisely, we can calculate the future,” it is not the
final clause which is false but the presupposition.
Since one is not able to measure with absolute precision the initial values
of impulse and location, one can only calculate probabilities for location and
impulse of the particle at any future moment.
According to Heisenberg, only from measurement or interference does the statistical
divergence of the particle orbit follow.
Heisenberg writes:
Only when we proceed from the Schrödinger function to the physical
behaviour of the system, and thus disturb the system from the
outside in order to be able to observe it, then the result of the
experiments can only be predicted statistically. One can always
consider the interference to be the cause of the indeterminateness
which the measuring equipment provokes in the system.
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Heisenberg argues as
follows:
1. The shorter the
waves of light with which the location of electrons is measured, the
more precisely can the location be measured, but the stronger will
the impulse be disturbed.
2. The longer the waves of
the light with which the location of electrons is measured, the more
precisely can the electron impulse be measured, since long-waved
light contains less energy than short-waved light and the impulse is
less disturbed.
But with long-waved light
the location cannot be precisely measured since it diverges
statistically.
3. Impulse/location
uncertainty follows from this. From that in turn there follows the
statistical divergence of particle orbits. If one were actually able
to conduct a precise simultaneous measurement of location or
impulse, then it would be possible to exactly predetermine the
particle orbit deterministically and thus to exclude statistical
divergence.
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Heisenberg is totally right!
With long-waved light, the exact location of a particle cannot be
determined because it only appears on a photo-screen with a widely
dispersed statistical pattern. The probability wave of light prevents
exact measurement.
It would be otherwise if squaring the amplitude of the wave would not signify
the location probability of the photon, but if light had a completely even
energy distribution, such as for instance a wave of water. For then it
would indeed be possible to exactly determine the location of
an electron with long-waved light as well without unduly
disturbing its impulse through such measurement.
Such a wave would generate a completely evenly smeared pattern of interference
on a photo-screen (and not merely individual, statistically distributed
density dots). Such an even interference pattern would provide such
a plenty of data (namely for each individual dot of the
photo-screen a completely specific energy value), since the latter
could be deduced exactly from that one
measurement of the electron’s location.
One thus sees: Heisenberg’s argumentation presupposes that the light wave
corresponds to a probability distribution. But this is what he wanted to
derive!!!
The objection, that what has been presupposed for proof is what was
supposed to be proven, is the strongest objection which can be raised
against an hypothesis altogether.
Formal neatness is more important than anything else. This critical point
cannot be underestimated.
The statistical nature of waves prevents simultaneous precise location
and impulse measure in the first place and is thus the prerequisite for
establishing the Uncertainty Principle. Thus it cannot be derived
from it.
The basic phenomenon is the basic probability and the Uncertainty Principle
is one of its aspects.
Though it forms no part of complementarity, the disturbance principle was
frequently defended as part of the Copenhagen Interpretation and often
identified with Bohr's view in the years following Heisenberg's discovery.
From the perspective of Heisenberg, it appeared that the basis of the disturbance
principle lay in the fact that the instruments doing the observing "disturbed"
the observed system such that its state after observation is no longer what was
determined in the measurement.
However, the disturbance interpretation plays havoc with the facts behind the
genesis of the uncertainty principle and its status within the mathematical
formalism of quantum mechanics. The principle is a straight forward deductive
consequence of the quantum theoretical formalism which provides a highly confirmed
means of predicting the outcome of interaction between radiation and matter.
There is no mention of disturbance in the derivation of the principle itself,
nor of how to go about determining the relevant parameters.
The design of experiments is relevant only to interpreting the physical
significance of the principle.
Dan Glover (
mirror /
WWW)
