By Kate Hogan

 Born in Wilkes-Barre, Pennsylvania 1917  Studied at Pennsylvania State College and University of California, Berkeley  Manhattan Project  Forced to leave the US to Brazil due to suspicions of Communist activity  Contributed greatly to quantum theory  Discovered Bohm diffusion  Died in London in 1992

 Formalism: equations and rules of calculation that are produce results consistent with empirical results.  Interpretation: representation of physical reality that accompanies formalism.  More than one interpretation of a physical reality may be possible given a set of equations which describe that reality.

 The formalism of quantum mechanics has been extremely successful in producing predictions that agree with observation.  It is possible to suggest alternate interpretations that produce the same predictions.  Any such theory is constrained by empirical evidence and by the math itself.

Bohmian mechanics defends a non-local hidden variable theory that provides a causal interpretation of quantum phenomenon. In this theory, quantum phenomenon can be divided into two components: a particle and a pilot-wave. The pilot-wave is described as a quantum potential that determines the behavior of the particle. The quantum effects are due to the behavior of this pilot-wave/ quantum potential.

 Bohmian mechanics and the standard Copenhagen mechanics are based on the same mathematical formalism and therefore are (largely) empirically indistinguishable.

 The particle follows one trajectory through one slit.  The quantum potential or pilot-wave displays wave-like behavior and goes through both slits.  The quantum potential “guides” the wave resulting in the observed splitting pattern.  No collapse of the wave function occurs.

 Schrodinger Equation  Bohm preformed a mathmatical transformation to rewrite the Schrodinger equation in an equivalent form.  This form produced a real and imaginary component.

 The real component could be interpreted as describing the behavior of the particle.  The imaginary component could be interpreted as describing the behavior of the quantum potential.  Bohm believed this parsing out of the Schrodinger equation hit upon a fundamental description of the situation.

 The Bohmian interpretation attempts to provide a way of understanding the physical reality of quantum phenomenon that agrees with several classical intuitions about how reality works.

 Principle of locality: no instantaneous, or faster than light, action at a distance  Bohm’s theory is non-local, which is required by Bell’s theorem  Bohm’s theory involves the transfer of information via the quantum potential that is faster than the speed of light  The quantum potential exerts an influence on the particle that is not within the constraints of the speed of light  In Bohm’s theory relativity applies only to “observational content” of the theory

 Bohm’s theory preserves determinism.  The particle follows definite trajectory that is discovered by observation. No wavefunction collapse occurs.  Quantum potential governs particle’s behavior and produces the quantum behavior observed.  The behavior of the particle is by nature able to be completely determined.  Hidden variables account for our inability to actually predict the particle’s behavior.  The fact that we are not able to determine a particles trajectory is due to our ignorance not to a fundamental indeterminacy in the system itself.

 Separateness Principle: Physical reality exists apart from observation and measurement.  Bohm’s interpretation attempts to preserve separateness by assigning a definite reality to the particle and its path.  The quantum potential, however, does not seem to have definite reality. It guides the behavior of the particle, producing the quantum effects.  The particle exists in itself and travels a specific path determined by the quantum potential.

 Bohmian mechanics assumes the existence of hidden variables that are normally distributed  Under certain conditions this distribution pattern would break down  Bohmian mechanics and Copenhagen mechanics might make distinguishable predictions under such conditions  Possible experiments preformed under such conditions could tease out hidden variables

 Does Bohmian mechanics really answer the question of separateness or just push the question into the realm of the quantum potential?

 Given that the Bohmian and Copenhagen interpretations of quantum mechanics are observationally indistinguishable, what possible criteria could be used to judge between the two?  What does it mean for an interpretation of quantum mechanics to be “understandable”?  Is quantum mechanics “required” to produce an interpretation of reality that agrees with any intuitive principles?