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Epistemological Letters
Hidden Variables and Quantum Uncertainty
Between 1973 and 1984, thirty-six issues of a privately published newsletter were circulated to about 180 of the most prominent physicists in the world. It contained contributions on the foundations of physics inspired by the work of John Bell, which in turn had been inspired by David Bohm's revival of Louis de Broglie's "pilot wave theory."
The Epistemological Letters were digitized and cataloged at Notre Dame's Hesburgh Libraries under the supervision of philosopher of science Don Howard and his graduate student Sebastián Margueitio Ramírez.
Here is a rough translation of the "Elementary Introduction" in the first issue, De quoi s'agit-il? It set the stage and opened the discussion.
In the nineteenth century, Fresnel proves, by experiments considered as irrefutable, the wave character of light. 1905 Einstein suggests explaining the photoelectric effect by a corpuscular theory of light, using the quanta recently discovered by Planck. 1924 To explain whole numbers (quantum numbers) which appeared in the quantum theory and based on Hamilton-Jacobi mechanics, de Broglie conversely proposes to associate a wave with material corpuscles such as the electron. One therefore has, in these two fields, coexistence of a wave theory and a corpuscular theory. The problem arises of reconciling them. 1926 Born interprets the amplitude of the wave (or rather the square of its modulus) as a probability density of the presence of a particle, an interpretation universally accepted today. Bohr and Heisenberg introduce the notion of complementarity: according to the experiment one proposes to do, physical reality sometimes appears under the corpuscular aspect, sometimes under the wave aspect. Experiments show one or the other mutually exclusive aspect. There is never experimental contradiction. But our conception of physical reality must be a synthesis of these two aspects contradictory and yet complementary. 1927 At the Solvay congress, a big discussion between the great theoretical physicists. Einstein disputes the interpretation of Bohr and Heisenberg (Copenhagen School). De Broglie offers a so-called pilot wave theory or he admits that the trajectory of the corpuscle is determined by the wave as it is where it is (theory of the pilot wave ), Because it must be said that the Born statistical interpretation does not resolve every problems. Take for example Young's experience: We drill two holes in a screen A and we examine what happens on screen B when sending light through the holes
Epistemological Letters Index
Hidden Variables and Quantum Uncertainty
Issue 1, February 1973
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On screen B we observe interference fringes which can be explained very well by a wave theory.
On the other hand, in a corpuscular theory, we
have great difficulties. Because the interference figure that we get on screen B is not
simply the superimposition of what we would get with each hole separately. To some
places, there is less light when the
two holes are open than when only one
is open. It’s also experiences of this
guy who had allowed Fresnel to lay down his
wave theory.
Suppose now that we send a light
very weak, so that it doesn’t fall on
The device that has a grain of light (photon)
sometimes. This photon will either pass through
one hole or through the other.
The trajectory of the photon which passes through a hole
must therefore be modified by the fact that the second hole is open or not, even if it no photon passes through this second hole.
Now what can pass through this second hole?
We have a ready answer: the wave associated
with the corpuscle.
But if this wave only represents a probability of presence, how can we understand that it physically influences the trajectory of the corpuscle? Because a probability, on an individual event represents nothing real: either a photon is in a certain area or else it is not
there. Probability only took meaning
statistically, over a large number of events
of the same type. As Ashby says, the
notion of probability makes it possible to artificially attribute to an individual event a property which belongs only to a set of events of the same type. How are we to understand how this
set of events, which are not concretely present at the time of the passage of the photon,
can influence its movement?
We therefore understand that L. de Broglie was led to formulate a so-called double theory
solution, which assumes that the equation of
Schrödinger admits two solutions: one being
the Ψ wave, giving the probability of presence,
the other being a physical wave u which could
influence the trajectory of the corpuscle of such
so that statistically the probability of
presence of the corpuscle restores that predicted by
the Ψ wave. (More precisely, the wave u would be
a nonlinear solution comprising singularities which would represent the corpuscles :)
But, faced with the mathematical difficulties encountered, he fell back on the theory of the more
simple pilot wave.
The discussion started at the Solvay congress did not
never completely die. The majority of physicists are rallying around the Copenhagen interpretation, which refuses to ask questions about an individual event in
space-time and is only interested in
what we can actually measure..
But some physicists, not least
(Einstein, Schrödinger, De Broglie, Bohm), all
admitting the experimental successes of quantum mechanics, remained of the opinion that
we should obtain a description having the true character of reality, that is to say,
not dependent on what the observer arbitrarily decided to measure.
An example may help to understand better:
in thermodynamics, we can describe a macroscopic system using global quantities::
temperature, pressure etc. and enact laws
for the evolution of these quantities.
Boltzmann and Gibbs succeeded, starting from a
model of molecules obeying the laws of mechanics
to find these macroscopic magnitudes and the laws which govern them.
From the point of view of macroscopic thermodynamics, the positions and velocities of individual molecules may be hidden variables?
not predictable. But we can make reasonable assumptions about these hidden variables and recover thermodynamics, its magnitudes and
its laws.
In this sense, macroscopic (or "phenomenological") thermodynamics
is not a complete description; it only processes molecules
by statistical, global quantities,
averages; it does not take into account movements
and individual deviations and proves unable to
predict phenomena such as fluctuations.
Likewise, according to Einstein and others, the same.
quantum quantum would not be a complete description. We will have to invent a theory making certain assumptions about hidden variables, inaccessible to experience, (such
as velocity, position, and trajectory of the corpuscles), the theory which underlies quantum mechanics like statistical mechanics underpins phenomenological thermodynamics. And
it's our ignorance of the value of some
parameters that would force us to fall back
on a statistical description. Indeterminism
it will not be in the things themselves, it would come from our ignorance.
The developments are as follows:
Bell was able to show in 1965 that, using certain reasonable assumptions, theories of
hidden variables had to satisfy a certain inequality, an inequality which would allow them
to differentiate their predictions from those of quantum mechanics.
An experiment was proposed by Shimony, Horne,
Holt and Clauser, then carried out by Freedman and
Clauser. It gave a result clearly supporting quantum mechanics and excluding
at least some type of hidden variable theories.
The discussion is open to evaluate the scope of the
exact results and the consequences
we must draw from it.
