Reimagining Physics — Part 5
The Reality of Time and Change — Part 1
Physics’ Timeless Universe — Part 2
A Thermocontextual Perspective — Part 3
What is Time? — Part 4
Wavefunction Collapse and Symmetry-Breaking— Part 5
Entanglement and Nonlocality — Part 6
The Arrow of Functional Complexity — Part 7
Wavefunction Collapse and Symmetry-Breaking
The symmetry of mathematics predicts equal amounts of matter and antimatter, but the universe has an overwhelming preponderance of matter. This is one of the great mysteries of the universe’s origin. Observations commonly reveal symmetry breaking associated with wavefunction collapse. For example, the symmetry of Schrödinger’s live-dead cat in Figure 1 is found to be broken upon observation. But the physical signficance of wavefunction collapse, and whether it actually happens, is debated. Wavefunction collapse and symmetry breaking are closely associated with measurement, so we will start by describing the measurement process.
The Thermocontextual interpretation [1] (TCI) defines perfect measurement as a reversible transition of a metastable system to its ground state (Figure 5–2). A metastable system has positive exergy and generally positive ambient heat and entropy. As described in Part 3, these are thermocontextual properties of state, defined with respect to the system’s ambient ground state in equilibrium with its ambient surroundings. A system’s exergy is defined by its potential for work on its ambient surroundings, and ambient heat is energy thermalized at the ambient temperature of its surroundings. Ambient heat’s energy is thoroughly randomized, and it has zero work potential. Entropy is the ratio of ambient heat and the positive temperature of its thermalization.
Perfect measurement involves reversible transfers of the system’s exergy and ambient heat to the surroundings, but reversibility means that there is no dissipation of exergy or production of entropy. In the case of an actual measurement, the exergy transferred to the surroundings does work of actualizing a measurement result on an external observer or measurement device.
Perfect measurement is reversible, but measurement of a superposed quantum system involves an intrinsically random process of wavefunction collapse (Figure 5–1). To understand random reversible measurements, and random wavefunction collapse more generally, we need to separate the transition process into two separate subprocesses — instantiation and actualization. These are defined by:
Instantiation is the reversible transition of a superposed and positive-entropy state to a definite zero-entropy state. Instantiation transfers the system’s ambient heat and entropy to the surroundings, while preserving its mass and exergy.
Actualization involves the reversible transition of a definite (zero-entropy) state to the system’s zero-exergy ground state. The transition transfers exergy from the system to the surroundings, where it can actualize work on an external system (e.g., a measurement device).
Instantiation involves the transfer of ambient heat and entropy to the surroundings, and actualization involves transfer of exergy to the surroundings. To describe the instantiation and actualization processes, we first need a deeper understanding of entropy.
TCI Entropy
The TCI defines entropy by Q/Tₐ, where Q is ambient heat and Tₐ is the ambient temperature. The TCI entropy and ambient heat are thermocontextual properties, defined with respect to the system’s ground-state reference at a positive ambient temperature. The TCI entropy is a generalization of the special case thermodynamic entropy, which is defined with respect to absolute zero temperature.
The TCI entropy is defined above in terms of ambient heat. Wavefunction collapse, however, is a statistical phenomenon, which requires a statistical formulation of the TCI entropy.
The Gibbs entropy redefined the thermodynamic entropy statistically by:
If the probability pᵢ for one microstate equals 100%, the other probabilities must all equal zero. From the equation above, the Gibbs entropy then equals zero, expressing absolute certainty of the system’s actual microstate. If probabilities are equally distributed over multiple microstates, then uncertainty and the Gibbs entropy are maximized. The Gibbs entropy is an informational entropy, expressing the uncertainty of a system’s actual microstate.
Gibbs entropy and its quantum mechanical extension, von Neumann entropy, are a measure of incompleteness of a system’s description and a subjective property of an observer’s uncertainty of the system’s precise microstate. Except for a constant multiple, equation 5–1 is identical to Shannon’s information entropy [2].
The statistical TCI entropy is defined by:
The statistical TCI entropy (equation 5–2) and Gibbs entropy (equation 5–1) look the same, but whereas the Gibbs entropy is informational, the TCI entropy is a physical property of state. A positive-entropy microstate is a complete description of the system’s physical state. Prior to interaction with its measurement device, the microstate has a positive entropy and is indefinite, with multiple measurable potentialities. After measurement, however, observation reveals a single definite microstate. The probability Pᵢ in equation 5–2 describes the objective probability that microstate potentiality ‘i’ is randomly instantiated by the system’s interactions with its environment. After measurement, the system exists as a definite measurable microstate ‘j’ with Pⱼ=1, and its entropy equals zero. The TCI entropy does not depend on whether the actual microstate is measured or observed. The TCI entropy is a physical property of state, independent of an observer or its knowledge.
Instantiation and Wavefunction Collapse
Instantiation is the first stage of measurement of a metastable microstate. Figure 5–3 illustrates the statistical instantiation of a positive-entropy microstate. The microstate contains multiple microstate potentialities, represented by the dots, and its positive entropy is given by equation 5–2. Instantiation involves export of ambient heat and entropy to the surroundings in a process of derandomization. Derandomization ultimately leads to a zero-entropy microstate, comprising just a single microstate (Figure 5–3). The process thereby randomly instantiates a single microstate potentiality from the initial system’s multiple potentialities.
Figure 5–3 applies to both classical systems and quantum systems. In the case of a quantum system, instantiation describes wavefunction collapse. A superposed wavefunction has multiple measurable potentialities (eigenfunctions) and it therefore has a positive entropy. Transfer of its entropy to the surroundings derandomizes the system and reduces its entropy to zero. Derandomization collapses the superposed wavefunction to a non-superposed eigenfunction having just a single measurable potentiality. Instantiation is random, but it is in principle reversible. Transferring ambient heat and entropy back to the system restores the system’s positive-entropy state.
Actualization and Measurement
The second stage of measurement is actualization (Figure 5–4). Actualization is the transition from an instantiated positive exergy and zero-entropy microstate to the zero-entropy ground state. The actualization process is isolated to the exchange of heat and entropy, but the initial state’s exergy is transferred to the surroundings, where it can actualize work on the surroundings. For example, measurement of a photon could be the work of actualizing a photochemical reaction and recording its point of impact on a photographic plate. During perfect reversible measurement, reversing the export of exergy to the surroundings reverses the measurement process and restores the system to its pre-measurement state.
Perfect measurement is defined as a reversible open-system process, but reversible measurement is not always possible. The Quantum Zeno effect [3] shows that a continuously measured (and measurable) state does not change irreversibly. The contrapositive of this is equally true; an irreversibly changing system is not continuously measurable. A system is reversibly measurable between irreversible transitions, while it exists as a metastable state. But during irreversible transition, a system is not reversibly measurable, and it therefore does not exist as a TCI state. It is in irreversible transition between states.
Cosmological Implications
Perfect measurement of a metastable system describes a reversible and random open-system process. The process involves reversible interactions between a system and its ambient surroundings, but it is by no means limited to measurements or even to the existence of observers.
Refinement involves a change in the ambient surroundings and a decline in a system’s ground-state energy. Refinement transforms a system, initially in equilibrium with its environment of perfect preparation or creation, to a metastable system with positive exergy and entropy. The TCI resolves any subsequent interaction between the metastable system and its new surroundings into two stages: instantiation and actualization. Instantiation involves export of entropy and a process of derandomization and selection of one from of the system’s multiple microstate potentialities. Actualization involves export of exergy and work on the system’s surroundings. In the case of a measurement, actualization involves the work of recording a measurement result on an external observer or device.
Refinement, instantiation, and actualization involve much more than preparation and measurement of systems. They drive the evolution of the universe. For example, during early cosmic expansion, when the universe cooled to approximately 2×10¹² K, quarks became unstable with respect to baryons (neutrons and protons) [4]. Cooling of the universe’s ambient temperature led to thermal refinement of quarks and the creation of baryonic potentialities. Baryonic matter and antimatter potentialities had equal probabilities of being instantiated [4], but instantiation randomly broke that symmetry. As quarks decayed, they did the work of actualizing baryons, randomly selected by instantiation, resulting in the asymmetrical preponderance of matter over antimatter.
The Thermocontextual Interpretation provides the conceptual foundation to explain the randomness of quantum measurements, the random instantiation of potentialities, and the actualization of those potentialities into measurable physical results. As the ambient energy of surroundings declines, refinement provides a mechanism for random breaking of symmetries.
[1] Time and Causality: A Thermocontextual Perspective, published in Time, Causality, and Entropy
[2] https://medium.com/udacity/shannon-entropy-information-gain-and-picking-balls-from-buckets-5810d35d54b4
[3] https://phys.org/news/2015-10-zeno-effect-verifiedatoms-wont.html
[4] https://en.wikipedia.org/wiki/Baryogenesis
