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Quantum Errors and Disturbances: Response to Busch, Lahti and Werner
Busch, Lahti and Werner (BLW) have recently criticized the operator approach
to the description of quantum errors and disturbances. Their criticisms are
justified to the extent that the physical meaning of the operator definitions
has not hitherto been adequately explained. We rectify that omission. We then
examine BLW's criticisms in the light of our analysis. We argue that, although
the approach BLW favour (based on the Wasserstein 2-deviation) has its uses,
there are important physical situations where an operator approach is
preferable. We also discuss the reason why the error-disturbance relation is
still giving rise to controversies almost a century after Heisenberg first
stated his microscope argument. We argue that the source of the difficulties is
the problem of interpretation, which is not so wholly disconnected from
experimental practicalities as is sometimes supposed.Comment: AMS latex, 29 page
Concerning Dice and Divinity
Einstein initially objected to the probabilistic aspect of quantum mechanics
- the idea that God is playing at dice. Later he changed his ground, and
focussed instead on the point that the Copenhagen Interpretation leads to what
Einstein saw as the abandonment of physical realism. We argue here that
Einstein's initial intuition was perfectly sound, and that it is precisely the
fact that quantum mechanics is a fundamentally probabilistic theory which is at
the root of all the controversies regarding its interpretation. Probability is
an intrinsically logical concept. This means that the quantum state has an
essentially logical significance. It is extremely difficult to reconcile that
fact with Einstein's belief, that it is the task of physics to give us a vision
of the world apprehended sub specie aeternitatis. Quantum mechanics thus
presents us with a simple choice: either to follow Einstein in looking for a
theory which is not probabilistic at the fundamental level, or else to accept
that physics does not in fact put us in the position of God looking down on
things from above. There is a widespread fear that the latter alternative must
inevitably lead to a greatly impoverished, positivistic view of physical
theory. It appears to us, however, that the truth is just the opposite. The
Einsteinian vision is much less attractive than it seems at first sight. In
particular, it is closely connected with philosophical reductionism.Comment: Contribution to proceedings of Foundations of Probability and
Physics, Vaxjo, 200
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