- Slides: 16
An Alternative Version of Quantum Mechanics By Kate Hogan
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
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.
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.
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.
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.
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.
Mathematical Basis � Schrodinger � Bohm Equation preformed a mathmatical transformation to rewrite the Schrodinger equation in an equivalent form. � This form produced a real and imaginary component.
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.
� 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.
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 theory
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.
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.
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
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?
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?