Reimagining Physics — Part 6
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
Entanglement and Nonlocality
As described in Part 2 and illustrated in Figure 6-1, above, experiments show that measurements on entangled systems are random but correlated, even if measurements are simultaneous and spatially separated. This presents an apparent conflict with relativity, which limits the propagation of signals or information to the speed of light. Einstein referred to simultaneous correlations of measurements as “spooky action at a distance.” He suggested that quantum mechanics was incomplete, and that correlations result from “hidden variables,” inherited from the particles’ common source and not accounted for by quantum mechanics. However, Bell’s theorem and Bell-test experiments [1] prove that if we reject superdeterminism [2], as did Bell, then polarizations are randomly instantiated at the analyzers, and their correlation is instantaneous, regardless of spatial separation. Explaining instantaneous correlations within the constraints of relativity and without invoking superdeterminism is the problem of nonlocality.
Quantum Nonlocality — Just The Facts
A typical Bell-test experiment involves a source that emits a pair of photons entangled in polarization. For simplicity, we consider the interaction of the photon pair with vertically oriented polarized analyzers at points A and B (Figure 6–1). The photons are emitted from their source at point O in opposite directions. At time=1, prior to measurement, they are entangled and are superposed, corresponding to their two measurable potentialities. At time=2, the photons interact with the polarized analyzers, at which point the photons’ polarizations are instantiated and measurement results are actualized. At time=3, Alice and Bob check to see if their photon was vertically polarized and passed through the polarizer or horizontal and absorbed. They each have a 50% probability of measuring a vertically or horizontally polarized photon.
If the photon pair is entangled with perpendicular polarizations, and if Bob measures a vertically polarized photon, then Alice measures a horizontally polarized photon. If Alice measures a vertically polarized photon, then Bob measures a horizontally polarized photon. The instantaneous correlation of physically separated measurements at points A and B, graphically illustrates the nonlocality of entangled measurement results. Nonlocal measurement correlations are an empirical fact.
Classical Entanglement
Before addressing how simultaneous measurements can be reconciled with relativity, we first need to understand what entanglement actually means. The Thermocontextual Interpretation (TCI) [3] defines entanglement by:
Physically separated particles are entangled if they share properties linked by a deterministic and thermodynamically reversible connection.
Determinism simply means that a change in one particle correlates to a specific change in the other particle. Thermodynamic reversibility means that there is no dissipation of exergy (i.e. no friction in the link connecting them).
TCI’s definition for an entangled state does not imply a superposed or positive-entropy state (Part 5). It does not imply instantaneous connection over an observer’s reference time (Part 4). But as we will see, the definition does completely describe quantum entanglement. But first, we will consider entanglement of a simple classical mechanical system.
To illustrate classical entanglement, we consider frictionless gears linked together in an open circular chain (Figure 6–2). Any disturbance of one terminal gear is transmitted to the other terminal gear. The terminal gears are linked by a deterministic and thermodynamically reversible connection, and by the definition above, they are entangled.
The deterministic link connecting the entangled gears is frictionless and thermodynamically reversible, but it is still subject to the irreversible arrow of causality (Part 4). The physical interaction involves electrostatic interactions between the gears and their atoms, and the propagation of effects cannot exceed the finite speed of light. If gear A is rotated, gear B will respond a small time later. If gear B is rotated, gear A responds after a short delay. There is a clear distinction between cause and effect. This illustrates the irreversible arrow of relativistic causality, as measured by an observer’s clock across reference time (Part 4).
We now consider what happens over mechanical system time. As described in Part 4, system time is a parameter that determines a system’s state at any arbitrarily selected instant. System time is a complex property of state, spanning reversible mechanical time and irreversible thermodynamic time. For the thermodynamically reversible chain of gears, system time can vary over mechanical time, but it is fixed to a single instant of thermodynamic time.
When we describe the gears across reversible mechanical time, we have the same deterministic link, but the distinction between cause and effect that we observed over reference time disappears. The propagation of effects for the thermodynamically reversible chain of gears is time-symmetrical across mechanical system time. A disturbance of A is transmitted across mechanical system time and affects B, but with time-symmetry, we can just as easily say that the disturbance at B affects A. This expresses the idea of time-symmetrical determinism. Time-symmetrical determinism occurs within an instant of thermodynamic time. It is reversible, and it is independent of the irreversible advance of reference time and the arrow of relativistic causality.
Quantum Entanglement
Classical gears have zero entropy, meaning that they have a single definite measurable state. A quantum analogue would be a zero-entropy pair of entangled photons. A vertically polarized photon can be down-converted to a pair of entangled photons with the same definite vertical polarizations [4]. When contextually defined with respect to vertically polarized analyzers, the entangled pair has a definite measurable state of vertical polarization. As with the entangled gears, the entangled photon pair’s contextual state is definite; it has a single measurable potentiality; and by equation 5–2, it therefore has zero entropy.
Photons are not classical particles, however. This becomes clear when we change the photon pair’s context and thermocontextual state by rotating the polarized analyzers. Measurements of polarization can only be parallel or perpendicular to the analyzers, so rotating the polarizers 45° changes the photon pair from a definite zero-entropy state of vertical polarization to an indefinite superposed state. If a vertically polarized photon encounters one of the rotated polarizers, it has a 50% chance of having a parallel polarization and passing through, and a 50% chance of having a perpendicular polarization and being absorbed. Because the photons are entangled by parallel polarization, the photon pair is a superposition of two measurable potentialities: {//} and {\\}. From equation 5–2, a multiplicity of measurable potentialities means a positive physical entropy.
Measurement randomly instantiates one of the pair’s two potentialities (Part 5), but in either instance, the individual photons are strictly correlated and parallel. Bell’s theorem [5] and measurement results prove that measurement results are objectively random and that the entangled pair’s positive entropy is an objective property of the physical state. There is no classical analogue to this situation because classical entropy is strictly informational, reflecting incomplete information of the classical system’s precise state. The physical entropy of superposed quantum states, not entanglement, is the key distinction between classical and quantum mechanics. But having said that, quantum systems can attain a dissipation-free entangled state, but classical reversibility and entanglement is an unattainable idealization, based on absolute zero surroundings.
The next section shows how the TCI reconciles superluminal correlations with special relativity, which asserts that nothing, even information, can propagate faster than light.
Reconciling Nonlocality and Relativity
Figure 6–3 shows the emission of photons from a source at position O and mechanical time itₘ₀, and their measurements at points A and B at time itₘ₁. Once the photons are emitted, their surroundings are defined by the vertically oriented polarized filters at point A and B, shown in Figure 6–1. The experimental setup contextually defines the photons’ measurable states with vertical or horizontal polarization, creating two microstate potentialities and a positive entropy.
The Figure spans space (horizontal axis) and mechanical time (left axis). The photons are emitted at point O and they encounter the polarizers at points A and B. The blue “cones” illustrate the cones of relativistic causality, expanding from the measurement events at A and B at the speed of light as measured by an observer’s reference clock (Reference time, right axis). Images by the author.
The pair’s entanglement by perpendicular polarization constrains the photon pair’s measurable potentialities to either (↔↕) or (↕↔). When the photon pair encounters and interacts with the filters, one of the pair’s two measurable potentialities is randomly instantiated as a zero-entropy entangled microstate. This then actualizes a definite anticorrelated measurement result in the other photon across a time-symmetrical electromagnetic connection linking the two photons, illustrated by A↔O↔B in Figure 6–3.
Irreversible actualization of the measurement results (Part 5) advances thermodynamic time from t_q to t_q’ and sets mechanical time to a new interval of time symmetry. Superimposed on the diagram are light cones from the measurement events at A and B, advancing across reference time (right axis). Each light cone shows the rate of light propagation from points A and B, and its interior defines the domain of causality from A or B, within the constraints of relativity.
The light cones at A and B show the domains of relativistic causality from each measurement. Alice and Bob reversibly observe their definite measurement results, and Bob transmits his result to Alice via a light signal. Alice receives the results recorded by Bob at point A’, and she is able to verify that Bob’s results are anticorrelated with hers. Alice’s and Bob’s observations of their measurement results, Bob’s transmission of his results, and Alice’s recording of his results are reversibly conducted within the instant of thermodynamic time t_q’.
Whereas Alice and Bob reversibly record their correlated measurement results within a single instant of thermodynamic time, their record of events over reference time is very different. The righthand axis of Figure 6–3 shows the record of Alice’s measurement events at points A and A’, as measured by her reference clock. Alice’s measurement at her reference time tᵣA and her recording of Bob’s measurement result at tᵣA’ are reversibly linked within an instant of thermodynamic time via A↔A’↔B (Figure 6–3), but her reference time ticks irreversibly forward. Even though Bob and Alice cannot receive the other’s results until after they conduct their own measurements, they each conclude the other’s measurement was conducted simultaneously with their own, and that the correlation of results was instantaneous.
The TCI reconciles the instantaneous correlation of spatially separated measurements (nonlocality) and relativistic causality. Relativistic causality and observations are defined across irreversible reference time, as measured by the continuous advance of an inertial observer’s reference clock. Nonlocal measurements are deterministically correlated across time-symmetrical mechanical system time, within a single instant of thermodynamic time. By distinguishing between complex system time and reference time, the TCI explains how the simultaneous correlation of nonlocal measurements can compatibly coexist with relativistic causality, without spooky action, hidden variables, or superdeterminism. It should be emphasized, however, that enganglement and nonlocality can only realized when dissipation is entirely eliminated, and this is generally limited to carefully controlled settings.
[1] https://en.wikipedia.org/wiki/Bell_test
[2] https://en.wikipedia.org/wiki/Superdeterminism
[3] Time and Causality — A Thermocontextual Interpretation, published in Time, Causality, and Entropy
[4] https://en.wikipedia.org/wiki/Spontaneous_parametric_down-conversion
[5] https://www.wired.com/2014/01/bells-theorem/
