Editing De Broglie–Bohm theory (section)

=== Heisenberg's uncertainty principle ===
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The Heisenberg's uncertainty principle states that when two complementary measurements are made, there is a limit to the product of their accuracy. As an example, if one measures the position with an accuracy of <math>\Delta x</math> and the momentum with an accuracy of <math>\Delta p</math>, then <math>\Delta x \Delta p \gtrsim h.</math>

In de Broglie–Bohm theory, there is always a matter of fact about the position and momentum of a particle. Each particle has a well-defined trajectory, as well as a wavefunction. Observers have limited knowledge as to what this trajectory is (and thus of the position and momentum). It is the lack of knowledge of the particle's trajectory that accounts for the uncertainty relation. What one can know about a particle at any given time is described by the wavefunction. Since the uncertainty relation can be derived from the wavefunction in other interpretations of quantum mechanics, it can be likewise derived (in the [[Epistemology|epistemic]] sense mentioned above) on the de Broglie–Bohm theory.

To put the statement differently, the particles' positions are only known statistically. As in [[classical mechanics]], successive observations of the particles' positions refine the experimenter's knowledge of the particles' [[initial conditions]]. Thus, with succeeding observations, the initial conditions become more and more restricted. This formalism is consistent with the normal use of the Schrödinger equation.

For the derivation of the uncertainty relation, see [[Heisenberg uncertainty principle]], noting that this article describes the principle from the viewpoint of the [[Copenhagen interpretation]].