The Blackwell Guide to the Philosophy of Science - The Department ...

Interpreting Quantum Theories
13 Mathematical nicety demands that the quantum field be cast not (as the foregoing
suggests) as a map from space–time points to operators, but as operator-valued distributions
over space–time regions. Wald (1994) is an excellent introduction to this
and other issues discussed in this section.
14 Notoriously, it even breaks down in a subset of Minkowski space–time. Positive energy
states correspond to solutions to the Klein–Gordon equation that oscillate with purely
positive frequency. States in the standard Minkowski representation are positive frequency
with respect to time as measured by families of inertial observers. But restricting
our attention to the right Rindler wedge of two-dimensional Minkowski
space–time setting c = 1, this is the region where x is positive and |x| < t – we can
quantize the Klein-Gordon field by admitting solutions that oscillate with positive frequency
with respect to time as measured by observers whose accelerations are constant,
for Lorentz boost isometries generate a global time function for the Rindler
wedge. The Rindler representation we thereby obtain has a natural particle interpretation
– but the Rindler representation is unitarily inequivalent to the Minkowski representation!
This is sometimes, and loosely, expressed as the Unruh effect: observers
accelerating through the Minkowski vacuum “see” a thermal flux of particles (Wald,
1994, ch. 5).
References
Albert, D. (1992): Quantum Mechanics and Experience. Cambridge, Mass: Harvard.
Albert, D. and Loewer, B. (1988): “Interpreting the Many Worlds Interpretation,”
Synthese, 77, 195–213.
Albert, D. and Loewer, B. (1996): “Tails of Schrödinger’s Cat,” in R. Clifton (1996,
pp. 81–92).
Arageorgis, A., Earman, J. and Ruetsche, L. (2001): “Weyling the Time Away: The
Non-Unitary Implementability of Quantum Field Dynamics on Curved Space–time and
the Algebraic Approach to Quantum Field Theory,” Studies in History and Philosophy of
Modern Physics, forthcoming.
Bacciagaluppi, G. and Hemmo, M. (1996): “Modal Interpretations, Decoherence and
Measurements,” Studies in the History and Philosophy of Modern Physics, 27B, 239–77.
Bell, J. (1964): “On the Einstein–Podolsky–Rosen Paradox,” Physics, 1, 195–200.
Reprinted in Wheeler and Zurek (1983, pp. 403–8).
Bell, J. (1966): “On the Problem of Hidden Variables in Quantum Mechanics,” Reviews
of Modern Physics, 38, 447–52. Reprinted in Wheeler and Zurek (1983, pp. 397–402).
Bell, J. (1987): Speakable and Unspeakable in Quantum Mechanics. Cambridge: Cambridge
University Press.
Belot, G., Earman, J. and Ruetsche, L. (1999): “The Hawking Information Loss Paradox:
The Anatomy of a Controversy,” British Journal for the Philosophy of Science, 50, 189–229.
Bohm, D. (1951): Quantum Theory. Englewood Cliffs, NJ: Prentice-Hall.
Bohm, D. (1952): “A Suggested Interpretation of the Quantum Theory in Terms of
‘Hidden’ Variables, I and II,” Physical Review, 85, 166–93. Reprinted in Wheeler and
Zurek (1983, pp. 367–96).
Bohr, N. (1934): Atomic Theory and the Description of Nature. Cambridge: Cambridge
University Press.
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