Dear Jonathan, Andrei, and colleagues,
May I offer a few remarks regarding quantum interference?
Its neccessary, I believe, to be very careful when we try to identify
quantum interference, since not all the observable properties of
physical objects exhibit interference. Interference implies that a
single physical object possesses more than one value of some property at
an instant in time. This phenomenon is of great interest to philosophers
of science since its traditional to define a single physical object (or
single quantum system ) by single-valued, definitive characteristics.
For instance, one elementary particle , the electron, has the singular
properties of a specific charge, a total spin of one-half, and a
particular rest mass. As long as the thing is an electron, it has these
single-valued, definitive properties. And, those characteristic values,
significantly, are identical when viewed by every observer, even if
observers are moving relative to each other.
But the phenomenon of interference is, as we know, real. The canonical
example is interference of light. A single photon of light can pass
through two separated slits in an opaque screen at the same instant, and
the light pattern thats detected beyond the slits cannot be caused by
the photon passing through just one of the slits. Nor can that pattern
by caused by many photons, each one of which passed through just one of
the two slits. (I hope colleagues who are entirely familiar with these
things will forgive me. I suspect some of us, some who are not
scientists, perhaps, are not so well-acquainted with physics.) So, the
interference pattern is caused by the physical extension in space of
every photon particle. Each photon has a spread of position values, not
just one, at each time. Just like an apple, say, or an elephant, the
photon is located at more than one point. But unlike the elephant or
apple, the photon can pass through both slits simultaneously. Still the
photon is always characterized by a definitive, single value of spin,
charge, rest mass, etc.
Another example of quantum interference is Bragg scattering of electrons
from the periodic atomic structure of a crystal (like nickel). The
scattered pattern detected must be due to a single electron hitting more
than one atom simultaneously. And, the EPR experiment performed by Alain
Aspect, for those of us familiar with it, shows that the S-state of two
correlated photons possesses more than one direction of spin
simultaneously. Not the total spin of the system, which is always zero,
but spin direction, which points along multiple directions simultaneously.
Many of us know that the quantum wavevector (or wavefunction) somehow
represents the physical object (quantum system). And, in general, that
the wavevector is composed of a sum (superposition) of vector components
(eigenvectors or eigenfunctions) at each instant in time. Each
eigenvector has a complex numerical value at each time. Associated with
each independent eigenvector is a unique value of some property of the
physical object, its position, or momentum, or energy, etc. Multiplying
the complex value of the eigenvector times its complex conjugate value
gives the real value of the probability that that particular property
will characterize the physical object at the next measurement.
So we note, very, very carefully that the wavevector, or wavefunction,
does not, in general, specify any actual property of a physical object
at any time, but rather specifies the probabilities of measuring each
value for that property if such a measurement were performed. Even
though its common to misname the wavefunction a state function or
state vector .
And we know that these probabilities for quantum objects are calculated
from the complex value of each eigenvector (the probability amplitude)
but not, as is done classically, by determining the real-valued
probabilities associated with, for example, each roll of a die. (Again,
I hope colleagues who know these things much better than I do, will
forgive me for going into the details that may help our other, less
technically knowledgable, participants.)
Id emphasize, now, that theres no empirical evidence for any quantum
interference of total spin, or energy, or any other property of a
physical object that is observer independent. (Any property that
actually defines the object.) So, we cannot assume that the
superposition of eigenvectors characterizing the energy of the object,
or those characterizing its total spin, etc., means that the object
possesses, at an instant, more than one value of energy, or total spin..
Again, in general, the superposition of eigenvectors in the wavevector
means there is a probability for each of several values of that property
if it were measured at some time, not that the object acually does have
more than one value for that property. (An electron can only have a
single, unique value of rest energy, charge, etc.) This is so, even
though we know that where quantum interference is observed, for position
or spin direction, for instance, the superposition of position
eigenvectors, or spin direction eigenvectors, does imply simultaneous
possession of more than one value of that type of property by the object.
Cordially,
Michael Devereux
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Received on Mon May 22 08:05:06 2006
