Download A New Ontological View of the Quantum Measurement Problem

A New Ontological View of the
Quantum Measurement Problem
Xiaolei Zhang
US Naval Research Laboratory
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“... Einstein told me again that he had very little confidence
in the indeterminist interpretation, and that he was worried
about the exaggerated turn toward formalism which
quantum mechanics was taking. Then, possibly going
farther than he might normally have liked to go, he told me
that all physical theories, their mathematical expression
apart, ought to lend themselves to so simply a description
‘that even a child could understand them.’ And what could
be less simple than the purely statistical interpretation
of wave mechanics!
“ … I, too, adopted the almost unanimous view of quantum
physicists in 1928, … Einstein, however, stuck to his guns
and continued to insist that purely statistical interpretation
of wave mechanics could not possibly be complete.”
- Louis de Broglie “My Meeting with
Einstein at the Solvay Conference”
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Objectives of this Work

To recover a realist attitude and to better
connect with our intuition. To use empirical
facts to constrain our intellectual endeavor.

To obtain an effectively classical ontology
for quantum phenomena, to rid the
probabilistic element from the foundations
of quantum mechanics.

To learn from the examples of classical and
quantum collective phenomena and nonequilibrium phase transitions, in order to
gain better understanding of the hierarchies
of laws and structures in the natural world.
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Time Evolution of a Physical State S(t)
According to Quantum Mechanics

The unitary time evolution |S(t)> = U(t) |S(0)>. Covariant and
energy conserving.

Quantum measuremnt: reduction of |s(t)> into an eigenstate
of an observable. P |s(t)>, where P is the projection operator.
This is the so-called “collapse of wavefunction”. Apparent
non-energy conserving.

Example: 1d position and momentum measurements:
SP0 ( r, t ) = 1/sqrt(2 p ħ) exp (i/ ħp0 r) exp (-i/ħ EP t)
Sr0 ( r, t ) = δ(r – r0) exp (-i ħ Er t)
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Existing Theories for the
Quantum Measurement Problem
The Orthodox Copenhagen Interpretation


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Probability interpretation of the wave function relating to our
subjective expectations of the measurement outcome. Linear
superposition of states before measurement (Born 1926)
Uncertainty relations (Heisenberg 1927)
Complementarity principle, wave-particle duality, microscopic and
macroscopic division (Bohr 1928)

Many-World hypothesis (Everett III, 1957; De Witt 1970): all
branches of wavefunction realized, no collapse: yet collapse is real
(atom interferometry, VLBI). Also what basis to use for branching.

Decoherence theories (von Neumann 1927, 1932; Wigner 1963;
Zurek 2002 and the references therein): two-step process, needs
conscious observer for the second step.
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Schrödinger’s Cat Paradox
Question: When did the wavefunction collapse happen exactly?
Was the Cat in a superposition state before the observer stared at it?
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Non-Equilibrium Phase Transitions
and Dissipative Structures
Classical dissipative structures (Prigogine et al.) examples:
- Chemical clock
- Benard’s Instability (atmosphere convection)
- Spiral structures of galaxies
Conditions for formation: open system, far from equilibrium
Modal Characteristics: nonlinear, dissipative/irreversible,
dynamical equilibrium, property determined by basic state
Zhang, X. 1996, ApJ, 457, 125
Zhang, X.1998, ApJ, 499, 93
Zhang, X. 1999, ApJ, 518, 613
Zhang, X., Lee, Y., Bolatto, A.,
& Stark, A.A. 2001, ApJ, 553, 274
Lucentini, J. 2002, Sky & Telescope
(September)
Zhang, 2002, Ap&SS, 281, 281
Zhang, 2003, JKAS, 223, 239
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The New Ontological View of the
Quantum Measurement Problem

The quantized nature of fundamental processes is the result of
their being resonance phenomena in a giant resonant cavity
encompassing the entire universe.

Quantum measurement process or “wave function collapse” is a
spontaneous non-equilibrium phase transition in the universe
resonant cavity, under the proper boundary condition set by the
object being measured, the measuring instrument, and the rest
of the universe. No intervention of conscious observer needed.

Quantum mechanical wavefunction has substantial meaning.
Probability element is not intrinsic to the foundations of
quantum processes. Uncertainty relation is derived from the
exact commutation relation of quantum conjugate variables.

Quantum vacuum fluctuations are the “left-over” fluctuations
after forming the whole number of quantum modes.
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Schrödinger 1926: “The Continuous
Transition from Micro- to Macro-Mechanics”
Substantiality of the quantum mechanical wavefunction: amplitude represents
the relative density of the matter wave, phase reflects the wave nature of the
quantum modes, while also responds to different types if force fields. The quantum
mode for a particle (as obtained in non-interacting quantum field theory) naturally
spreads out (akin to a momentum eigenstate) until the moment of detection.
This explains wave-particle duality. Probability element due to the sensitivity to
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boundary condition of phase transitions in a many DOF system.
Empirical Support

Hilbert-space representation of quantum wave function and the
non-local, probabilistic nature of quantum measurement
processes.

The “give and take” with the rest of the universe during a quantum
measurement explains the apparent violation of energy
conservation in certain quantum measurement processes
(position-momentum, virtual particles, tunneling: appear on
“borrowed energy”).

Physical laws observe the least action type of variational principle,
which is a reflection of their sampling all the possible paths in the
entire space allowed.

Hierarchies of natural orders indicating their origin in successive
phase transitions. No single universal quantum wavefunction.

Universality of fundamental constants. Constancy of the elemetary
particle properties during different physical processes (particles
are only generated at the moment of phase transition, not before).

Quantum stationary state as a dynamical equilibrium. Constant
exchange with vacuum.
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Connections with Practices
in Quantum Field Theories

S-Matrix theory (only the input-output plane wave states are
clearly defined. The poles in the analytical functions used
in S-matrix approach correspond to modal solutions).

Renormalization and Feynmann’s diagrammatic approach
(QFT is a local theory, the interacting version is not selfconsistent. The need for renormalization reflect the global
influence of the environment. Feynmann diagrams
incorporated the modal nature of fundamental processes
and are linked to the S-matrix approach).

Gauge field theories, spontaneous symmetry breaking, and
effective field theories (nature is ordered in hierarchies due
to successive phase transitions. Dynamical laws are also
results of these phase transitions).
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Connections with Classical Mechanics

Generalized Mach’s principle (originally for inertial only). Matter
distribution played a role in forming laws. All fundamental
constants and universal laws are results of their being resonantly
selected out of the universe cavity, thus all physical laws obey
variational (action) type principles.

Noether’s theorem reveals that the form of laws as we have,
connects the symmetry/invariance of matter distribution in
space/time to the invariance of laws in time. True for both
classical and quantum mechanics.

Classical mechanics and classical trajectories as the emergent
phenomena of quantum mechanism when S is large compared to
ħ.
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Approximate Symmetry and
Spontaneous Symmetry Breaking

Parity non-conservation in weak interactions: Shows the impact
of global asymmetry in matter distribution on local processes at
the quantum level (weak interaction is the shortest in range, thus
less sensitive to immediate env environment). The “helical”
nature of parity violation is consistent with the universe having a
beginning (i.e., the Big Bang). Approximate symmetry in laws
related to approximate symmetry in matter distribution. CPT
conservation → T violation, shows phase transition nature of
microscopic processes as well.

Speed of light itself could be an emergent quantity (similar to
mass generated through Higg’s mechanism during spontaneous
symmetry breaking). Feynmann path-integral formulation allows
faster-than-c propagation on the non-classical paths. At the
highest levels of the hierarchy, i.e., during the formation of laws
and fundamental constants, and during quantum measurement
phase transition, the speed-of-light limit is violated.
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Quantum Vacuum
Everything that so far has been attributed the quantum
vacuum can be regarded as due the influence of the rest
of the matter distribution in the universe. These include:
- Renormalization/scale dependence
- Casimir force
- Virtual particles and lifetime of levels
- Spontaneous emission/spontaneous decoherence
- Quark confinement
Possibility for energy non-conservation due to time variance of
constants and laws. Accelerated expansion of the universe and dark
energy.
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Conclusions

By adopting the new ontological view of the quantum
measurement problem, a diverse range of quantum and
classical phenomena acquire natural and coherent
explanation.

Quantum measurement is regarded as a non-equilibrium
phase transition in the Universe cavity, the probability element
is removed from the foundations of quantum mechanics.

Classical physics and the speed-of-light limit are both
emergent phenomena, not universally applicable.

Natural processes appear to be organized by hierarchies.
Physical laws, physical processes, as well as fundamental
constants could all be the result of a resonant selection
process regulated by the global matter distribution.

As a working hypothesis, the new ontology may allow us to
unveil new physics and achieve greater synthesis.
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