Following Albert Einstein of a "Führungsfeld" or "guiding field," De Broglie interpreted the wave function of quantum mechanics as a "pilot wave" carrying a material particle along with it. De Broglie accepted Einstein's idea, made famous by Max Born as his "statistical interpretation," that the (square of the) wave function gives us the probability of finding a particle.

The de Broglie-Bohm pilot wave wave goes through both slits in the two-slit experiment, interfering with itself and accounting for the interference pattern, though the particle enters only through one slit, maintaining its discreteness. Which slit a particle passes through and its ultimate location on the detector are completely determined by its initial position and the wave function, according to Bohm.

Bohmian mechanics is also known as the "de Broglie-Bohm theory," the "pilot wave theory," and the "causal interpretation" of quantum mechanics. It is a completely deterministic theory and claims to be completely compatible with and to make exactly the same predictions as standard quantum mechanics. This is hard to believe, because quantum mechanics is indeterministic, accounting for radioactive decay and the random times and directions of atomic radiative transitions, for example.

It is called "causal" because it is a deterministic theory, with "hidden variables" suggested by Bohm as "completing" the quantum mechanics that Einstein argued was "incomplete" and "statistical." The hidden variables provide the positions of all the particles as "riding on" the waves at places where the waves have maximum intensity or amplitude.

Bohm thought that known positions would provide the determinacy and explain away the nonlocal behaviors predicted by Albert Einstein in his EPR paper. John Bell proved that if Bohm's hidden variables did exist, they would still be "nonlocal." They could not restore Einstein's locality.

Bohmian mechanics denies the "collapse of the wave function," since a collapse is associated with indeterminism. The deterministic Schrödinger equation provides no information that predicts the time, position, or direction of a collapse.

Some physicists who believe that the wave function never collapses, such as Erwin Schrödinger, decoherentists like Dieter Zeh and Wojczech Zurek, and even John Bell, even deny the existence or particles and "quantum jumps." Bohm does accept particles, while being somewhat unclear on quantum jumps.

Note that the collapse of the wave function, or "reduction of the wave packet," is one of Paul Dirac's three fundamental postulates, the others being the principle of superposition and the axiom of measurement, also known as the eigenstate-eigenvalue relation.

Bohmian mechanics also denies the role of a "conscious observer," which has been associated with the Copenhagen Interpretation of quantum mechanics and was defended by John von Neumann and Eugene Wigner.

Bohmian mechanics has a large and enthusiastic following of philosophers of science and theoretical physicists, including David Z. Albert, Jeffrey Bub (a student of Bohm), Jean Bricmont, Detlef Dürr, Sheldon Goldstein, and Tim Maudlin.

They all agree that testable predictions of Bohmian mechanics are identical to those of standard quantum mechanics, so the Bohmian view is only an interpretation of quantum mechanics.