Quantum Physics Without Quantum Philosophy
Detlef Dürr, Sheldon Goldstein, Nino Zanghì
Language: English
Pages: 304
ISBN: 3642433774
Format: PDF / Kindle (mobi) / ePub
It has often been claimed that without drastic conceptual innovations a genuine explanation of quantum interference effects and quantum randomness is impossible. This book concerns Bohmian mechanics, a simple particle theory that is a counterexample to such claims. The gentle introduction and other contributions collected here show how the phenomena of non-relativistic quantum mechanics, from Heisenberg's uncertainty principle to non-commuting observables, emerge from the Bohmian motion of particles, the natural particle motion associated with Schrödinger's equation. This book will be of value to all students and researchers in physics with an interest in the meaning of quantum theory as well as to philosophers of science.
Fundamentals of Physics (9th Edition)
Einstein's Miraculous Year: Five Papers That Changed the Face of Physics
The Emerging Quantum: The Physics Behind Quantum Mechanics
Introduction To Superconductivity (2nd Edition)
Essential Mathematical Methods for Physicists (5th Edition)
Quantum Mechanics and Experience
constant c = 0. ψ In order to arrive at a form for vk we shall use symmetry as our main guide. Consider first a single free particle of mass m, whose wave function ψ(q) satisfies the free Schrödinger equation i h¯ ∂ψ h¯ 2 =− ψ. ∂t 2m (2.4) We wish to choose vψ in such a way that the system of equations given by (2.4) and dQ = vψ (Q) dt (2.5) is Galilean and time-reversal invariant. (Note that a first-order (Aristotelian) Galilean invariant theory of particle motion may appear to be an
removed from the basic ingredients of Bohmian mechanics. However from the perspective of Bohmian phenomenology positive-operatorvalued measures form an extremely natural class of objects—indeed more natural than projection-valued measures. To see how this comes about observe that (3.18) defines a family of bounded linear operators Rα by P[ α] [U (ψ ⊗ Φ0 )] = (Rα ψ) ⊗ α, (3.58) in terms of which we may rewrite the probability (3.20) of obtaining the result λα (distinct) in a generic discrete
two changes must be made in (3.98) to reflect this information: |ψ ψ| must be replaced by (Rα |ψ ψ|Rα∗ )/ Rα ψ 2 , and p(dψ) must be replaced by p(dψ|α), the conditional distribution of the initial wave function given that the outcome is α. For the latter we have p(dψ|α) = Rα ψ 2 p(dψ) tr (Rα W Rα∗ ) ( Rα ψ 2 p(dψ) is the joint distribution of ψ and α and the denominator is the probability of obtaining the outcome α.) Therefore W undergoes the transformation W = p(dψ) |ψ ψ| → Rα |ψ ψ|Rα∗ Rα
almost on nothing, in effect just on the linearity of the evolution of the wave function. However, one should not overlook the crucial role of quantum equilibrium. We observe that the nonmeasurability of the wave function is related to the impossibility of copying the wave function. (This question arises sometimes in the form, “Can one clone the wave function?" [55, 56, 57]). Copying would be accomplished, for example, by an interaction leading, for all ψ, from ψ ⊗ φ0 ⊗ Φ0 to ψ ⊗ ψ ⊗ Φ, but this
each A, one of the experiments, call it E A , with which A is associated, and define ZA to be ZE A . Then the map so defined can’t be good, because of the impossibility theorems; moreover there is no reason to have expected the map to be good. Suppose, for example, that [A, B] = 0. Should we expect that the joint distribution of ZA and ZB will agree with the joint quantum mechanical distribution of A and B? Only if the experiments E A and E B used to define ZA and ZB both involved a common
