An Alternative Version of Quantum Mechanics

1. An Alternative Version of Quantum Mechanics By Kate Hogan

2. David Bohm (1917-1992) • 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

3. Formalism vs. Interpretation • 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.

4. Formalism vs. Interpretation • 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.

5. Bohmian Interpretation of Quantum Mechanics •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.

6. Bohmian Interpretation of Quantum Mechanics • Bohmian mechanics and the standard Copenhagen mechanics are based on the same mathematical formalism and therefore are (largely) empirically indistinguishable.

7. Double Slit Experiment • 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.

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

9. Mathematical Basis • 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.

10. 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.

11. Locality • 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

12. Determinism • 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.

13. Separateness • 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.

14. Possible Empirical Tests • 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

15. Issues with the Bohmian Interpretation • Does Bohmian mechanics really answer the question of separateness or just push the question into the realm of the quantum potential?

16. Discussion • 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?