Download Hogan: An Alternative Version of Quantum Mechanics

By Kate Hogan
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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
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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.
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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.
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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.
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Schrodinger Equation
Bohm preformed a mathmatical
transformation to rewrite the Schrodinger
equation in an equivalent form.
This form produced a real and imaginary
component.
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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.
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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.
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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
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Bohm’s theory preserves determinism.
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The particle follows definite trajectory that is discovered by
observation. No wavefunction collapse occurs.
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Quantum potential governs particle’s behavior and produces
the quantum behavior observed.
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The behavior of the particle is by nature able to be completely
determined.
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Hidden variables account for our inability to actually predict
the particle’s behavior.
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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.
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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.
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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
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Does Bohmian mechanics really answer the
question of separateness or just push the
question into the realm of the quantum
potential?
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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?