1 A New Ontological View of the Quantum Measurement Problem Xiaolei Zhang US Naval Research Laboratory.

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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 couldbe less simple than the purely statistical interpretationof 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 non-equilibrium 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 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 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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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, 274Lucentini, J. 2002, Sky & Telescope (September)Zhang, 2002, Ap&SS, 281, 281 Zhang, 2003, JKAS, 223, 239

Non-Equilibrium Phase Transitions and Dissipative Structures

Classical dissipative structures (Prigogine et al.) examples:- Chemical clock- Benard’s Instability (atmosphere convection)- Spiral structures of galaxiesConditions for formation: open system, far from equilibriumModal Characteristics: nonlinear, dissipative/irreversible, dynamical equilibrium, property determined by basic state

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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 quantummode 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 toboundary condition of phase transitions in a many DOF system.

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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 self-consistent. 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.