Philosophy of the Sciences, 1997
Meeting 13: Quantum Theory I
Summary
1. Last time, we considered
the famous `Young's Slit Experiment'. In his Lectures on Physics,
Richard Feynman stresses the importance of this experiment, because here
we have `a phenomenon which is impossible, absolutely impossible,
to explain in any classical way, and which has in it the heart of quantum
mechanics. In reality, it contains the only mystery ... the
basic peculiarities of all quantum mechanics'.
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2. Consider what happens experimentally when S is emitting, and
both quantum slits 1 and 2 are open. What we get on the screen is
an interference pattern characteristic of waves. If Slit 1
were closed and Slit 2 open we should get a particular pattern on the screen.
If Slit 2 were closed and Slit 1 open we should get a similar (symmetrical)
pattern. The result of superimposing these two patterns is known
as the additive pattern and this is quite dissimilar to the interference
pattern. Even if we decrease the intensity of S until there is just
one electron at a time being emitted, we get the same result. With
one slit closed, the behaviour of that electron will contribute to a diffraction
pattern; with both slits open, it will contribute to an interference pattern.
It is as if, just before entering a slit, the electron `knows' whether
the other slit is open or closed -- another causal anomaly.
3. However, if, in this set-up,
we observe the path of the electron, by recording when an electron
is passing through a slit, then we find that any given electron only passes
through only one slit (this is consistent with its being a particle) but
now, with both slits open, we get the additive pattern! As
John Gribbin says, in his In Search of Schrödinger's Cat, p.171,
`there is no clearer example of the Sf interaction of the observer with
the experiment'.
4. Now this situation does not present a worry for
the Copenhagen Interpretation. Because that interpretation adopts
the principle of the indeterminateness of state descriptions it would simply
say that some of the statements we have been making about the paths and
locations of electrons (e.g. `a particular electron is about to pass through
Slit 1') are meaningless so that the alleged causal anomalies (which,
remember, are statements) cannot be derived. So, for the Copenhagen
Interpretation, the alleged difficulties presented by the 2-slit experiment
vanish. J.J.C. Smart summarizes the position with characteristic
verve: `These difficulties do not trouble an adherent of the Copenhagen
interpretation, since he regards the theory as merely a convenient instrument
with which to make predictions. He is therefore perfectly happy to
use a wave picture on Mondays, Wednesdays and Fridays (when predicting
interference patterns) and a particle picture on Tuesdays, Thursdays and
Saturdays (when predicting individual scintillations). Even though
the two pictures are incompatible with one another, the use of both of
them (at different times) enables the correct predictions to be made'.
(J.J.C. Smart, Between Science and Philosophy, p.159).
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5. Dissatisfaction with the Bohr-Heisenberg
interpretation led Einstein, in collaboration with Podolsky and Rosen,
to devise a thought experiment aiming to prove that nature is not constitutionally
uncertain. The set-up in EPR is that we imagine a single particle exploding
into two equal parts which separate in opposite directions at the same
speed. In other words, we have a symmetry about the origin.
Since we can measure the position of one and the momentum of the other,
we can infer that each particle does have definite position and
momentum. The Heisenberg principle tells us that accurately measuring
the momentum of one of the particles will preclude our being able to state
its position, but, if the two particles are far apart, measuring one should
not affect the other, so for that particle we should be able
to infer its momentum and to measure its position. Thus, so it seems,
we can say of that particle, where it really is, and what momentum it really
has. Thus, EPR argues, realism is restored. In the EPR, there
is no relevant difference between each member of the particle pair, ergo
the momentum of one will be equal to the momentum of the other ... (For
interesting discussion of the EPR, see Arthur Fine, The Shaky Game.)
Bohr, however, rejected the argument, saying that we must consider the
system as a whole (rather than each particle in isolation), so that measuring
one particle does constrain what we can say about the other, even though
there is no force that the one can exert on the other. Einstein said
that this response brought in `spooky action at a distance'. His
own position is not that quantum theory is wrong, only that it is incomplete.
I.e., he wished to preserve the idea of energy quanta, while denying that
laws of nature must be probabilistic. God does not play dice.
We should be able to give a completely determinate account of the trajectory
of particles once we have found the parameters that must be taken into
account but which, at present, are hidden from us.
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6. A local realist theory is one that embraces
realism (that there are things and properties which exist independent of
any observer) and is local in the sense that it denies that a measurement
made with one instrument can affect a measurement made by another if the
measurements are performed at roughly the same time (i.e. no influences
propagating at > speed of light). Bernard d'Espagnat, `The Quantum
Theory and Reality' (an excellent article dealing with the issues
we are discussing) has a useful analogy to explain the notion of an independently
existing property (pp.130-1).
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7. Bell's inequality n[A+B+]
<= n[A+C+] + n[B+C+] (for
a derivation of it, see e.g. d'Espagnat) concerns correlated definite properties
(whereas Quantum mechanics allows only probabilistic values). If
local realism is true, the Bell inequality will be respected, whereas according
to QM it will sometimes be violated.
go to summary
8. Experiments such as Alain Aspect's have
vindicated QM. In the correlation experiments, such as Aspect's,
a photon either passes or fails to pass through a filter. So whichever
it does can be construed as an asymmetry, and we can ask `Why did it do
that ?' (e.g., when its predecessor did different). Moreover, it
does exactly the same as its `twin' that has gone off in the opposite direction,
although there is no way known to physics whereby any `message' could be
transmitted from one photon to its `twin'.
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