Reimagining Physics — Part 4
The Reality of Time and Change — Reimagining Physics Part 1
Physics’ Timeless Universe — Reimagining Physics Part 2
A Thermocontextual Perspective — Reimagining Physics Part 3
What is Time? — Reimagining Physics Part 4
Wavefunction Collapse and symmetry-breaking— Reimagining Physics Part 5
Entanglement and Nonlocality — Reimagining Physics Part 6
The Arrow of Functional Complexity — Reimagining Physics Part 7
What is Time?
For millennia, we recorded time by changes in the sun’s shadow, the seasons, and more recently, clocks. Reference time, as measured by a clock, is the familiar time that structures our lives and the world around us.
Newtonian mechanics defined a second role for time, as a mathematical parameter ‘t’ for an equation of motion. The periodic motion of a frictionless pendulum, for example, can be succinctly approximated by the equation x=sin(t). As an empirical measure of clock time, reference time tracks a pendulum’s changing position over reference clock time (Figure 4–1A). As a parameter for an equation of motion, mechanical system time is an index of the pendulum’s position and a coordinate of its trajectory in spacetime (Figure 4–1B).
(A) A frictionless pendulum sweeps back and forth across a one-dimensional arc as reference clock time advances.
(B) Plot of position = sin(tₘ). The graph represents the pendulum as a trajectory in two-dimensional spacetime. The trajectory shows the pendulum’s position at any instant of mechanical system time. We are free to chose any mechanical time, and we are free to track it by reference time until the pendulum encounters an elastic barrier at its midpoint at time tᵣ.
(C) Mechanical and reference times decouple at time tᵣ. The pendulum and mechanical system time reverse direction as the pendulum retraces its trajectory over mechanical time. The trajectory in C shows the pendulum’s position across reference time, which continues to advance undisturbed.
As long as a system is undisturbed, we can ignore time’s dual roles by letting mechanical time track reference time as a single measure of time. However, if the pendulum is disturbed, such as by encountering an elastic barrier (Figure 4–1C), the two times decouple. The pendulum and its index of position, mechanical system time, reverse direction, while reference clock time continues to advance uninterrupted. The fundamental difference between mechanical time and reference time can no longer be ignored.
Mechanical time is reversible, but thermodynamics challenged the notion of system time as a strictly reversible property of state. The Second Law of thermodynamics introduced the idea of a thermodynamic system time, which is defined by the irreversibility of entropy production and exergy dissipation. Whereas mechanical time is reversible, thermodynamic time can only increase with reference time, and like reference time itself, thermodynamic time has a direction.
Prevailing physical interpretations do not accommodate irreversibility as fundamental. They consequently view irreversible thermodynamic time and reference time as phenomenological manifestations of a single parameter of state defined by reversible mechanical time. The thermocontextual interpretation (TCI) [1], in contrast, recognizes reference time, mechanical system time, and thermodynamic system time as three distinct and equally real components of time.
Thermodynamic Time
The Second Law of thermodynamics defines the thermodynamic arrow of time by the production of thermodynamic entropy, S_TD, given by:
The inequality in equation 4–1 expresses the Second Law, which states that the thermodynamic entropy of an isolated system is constant for a reversible process and increases for any irreversible process. The Second Law of thermodynamics has been thoroughly validated by empirical observations.
The TCI formalizes the Second Law of thermodynamics by Postulate 4:
Postulate 4 (Second Law of Thermodynamics): An irreversible process dissipates exergy to ambient heat.
Postulate 4 defines irreversible change by the dissipation of exergy defined with respect to a fixed ambient surroundings. Dissipation produces ambient heat and entropy, which it the standard expression of the Second Law. The TCI establishes exergy and entropy as physical properties of state, and it establishes the Second Law of thermodynamics as a fundamental law.
The TCI measures a system’s thermodynamic time (t_q) by the irreversible dissipation of its exergy at a fixed ambient temperature. It defines thermodynamic time by:
Equation 4–2, for example, can describe a system’s dissipation by radioactive decay. At time t_ref = 0, the system’s exergy equals its initial exergy, X₀, and t_q equals zero. As t_ref advances toward infinity, the system’s exergy approaches zero, and t_q also approaches infinity. Like exergy, thermodynamic time is a thermocontextual property of state. As a thermocontextual property, it is incompatible with and ignored by the prevailing noncontextual interpretations.
Mechanical Time
Mechanical time is the time of classical mechanics, quantum mechanics, and spacetime. Like thermodynamic time, reversible mechanical time is a physical property of state. In classical mechanics, it is represented by a coordinate on a system’s trajectory in phase space between external disturbances (Figure 4–1B); in relativity, it is represented by a coordinate on the time axis of spacetime; and in quantum mechanics, it is represented by a coordinate of the time-dependent wavefunction. Mechanical time specifies a reversible system’s state at any arbitrarily chosen instant of mechanical time. It can proceed forwards or backwards, independent of any external reference time.
Mechanical time is conventionally defined as a real-valued coordinate, but this is merely a matter of convention. The TCI adopts a different convention, by replacing (i × t), which appears in quantum mechanics, with the mathematically identical (itₘ). ‘i’ is the square root of negative one, t is real-valued time, and itₘ is the coordinate of imaginary mechanical time. Imaginary time is fully compatible with the structure of spacetime, and it leaves all equations of mechanics unchanged.
System Time and Reference Time
Equation 4–2 describes the near-continuous dissipation for a many-particle system’s exergy. For an individual particle, however, dissipation is discontinuous. A particle’s positive exergy reflects its potential for irreversible transition to the ground state, but the particle can persist for a period of time as a metastable state. A particle of uranium 238, for example, can persist metastably for billions of years. As a metastable particle, it does not dissipate exergy or change irreversibly, and it exists as a well-defined state…until it doesn’t. At some point, it spontaneously decays to a more stable state of lower exergy, and this advances its thermodynamic time. A metastable particle therefore requires both mechanical time and thermodynamic time to describe its behavior.
The TCI recognizes system time as a complex property of state. A complex number is described by two components , e.g. (a+bi). ‘a’ is the real (normal) component, and bi is the “imaginary” component. Whereas real numbers can be represented by points on a single axis, imaginary numbers are represented as points on a complex plane spanned by a real and imaginary axis.
System time comprises both real-valued thermodynamic time and imaginary mechanical time. System time is represented by a point on the complex system-time plane (Figure 4–2A). A change over imaginary mechanical time (vertical axis) conserves exergy and describes reversible changes in a state, within a single instant of thermodynamic time, t_qᵢ. A change over real thermodynamic time (horizontal axis) describes the irreversible dissipation of exergy and transition to a more stable state. System time is a mathematical parameter of a master equation, which describes a system’s state at any fixed point of system time. System time is deterministic and independent of reference time.
Figure 4–2B shows the irreversible advance of reference time, whether the system time advances reversibly or irreversibly. Reference time advances across each Δt_rᵢ, which mark irreversible transitions between metastable states. Reference time also advances irreversibly between state transitions, even as the system reversibly exists as a metastable state within a instant of thermodynamic time, t_qᵢ.
Reference time is the time of relativity, as recorded by an observer’s clock and across which velocities are measured. Reference time is also the time across which deterministically related events are sequenced. It distinguishes causes from effects, and it defines the arrow of causality. Like the irreversible advance of an observer’s clock, the arrow of causality has a direction.
The TCI recognizes reference time as distinct from system time. It recognizes reversible mechanical time and irreversible thermodynamic time as distinct components of system time. Noncontextual interpretations, in contrast, cannot accommodate irreversibility, thermodynamic time, or the distinction between mechanical time and reference time. This locks noncontextual interpretations into a fundamentally static model of the universe, in which change is simply the playing out of a static and predetermined script.
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[1] Time and Causality: A Thermocontextual Perspective, published in Time, Causality, and Entropy
