Quantum mechanics and time
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Quantum Mechanics and Time: A Comprehensive Overview
The Role of Time in Quantum Mechanics
Time as a Parameter vs. Position as an Operator
In quantum mechanics, time and position are treated differently. While position is represented by a Hermitian operator, time is often treated as a c-number, a classical parameter. This distinction has puzzled many and led to extensive literature on the subject. However, some argue that this problem is only apparent and stems from the dominant role of point particles in physics, tracing back to classical mechanics .
Possibility and Time: Realist Interpretation
The relationship between possibility and time in quantum mechanics is crucial, especially under a realist interpretation. Non-commuting observables cannot have definite values simultaneously, raising questions about the nature of time in quantum mechanics. This interpretation suggests that possibility and actuality correlate with two different notions of time: parameter-time and event-time .
Emergence of Time from Quantum Events
Time in quantum mechanics and general relativity are fundamentally different. While relativity treats time as observer-dependent and dynamic, quantum mechanics treats it as an independent parameter. A proposed resolution involves extending the classical concept of an event to the quantum domain, defining an event as a transfer of information between physical systems. This approach suggests that time emerges as an observer-dependent property from a sequence of events, giving rise to the flow of time as successive "snapshots" .
Entropic Dynamics and the Arrow of Time
Entropic Time and Quantum Dynamics
Quantum mechanics can be derived using the method of maximum entropy, without relying on classical action principles. In this framework, time is introduced as a device to track change, naturally incorporating an arrow of time. The Schrödinger equation emerges from the coupled dynamics of particles and their associated entropy, with the wavefunction's magnitude and phase having statistical interpretations .
Arrow of Time in Quantum Mechanics
A viable theory of the physical world must include some notion of time, which inherently has an arrow. Time reversibility is not a primary requirement, meaning the direction of the arrow of time can be uniquely defined. This concept is crucial for understanding causality and locality in quantum mechanics, particularly in deterministic interpretations like the cellular automaton model .
Space-Time and Quantum Theory
Discrete Quantum Transitions
The classical notion of continuous time is replaced by discrete quantum transitions in quantum mechanics. This shift, originating from Max Born's work, implies that physical quantities change in discrete steps, leading to quantum uncertainties in time and position. This perspective contrasts with the standard interpretation that relies on classical space-time concepts .
Covariant Quantum Theory
In classical mechanics, time is often given a special role, but it can be treated on the same footing as other variables in a covariant formulation. This approach is natural for relativistic systems and can be extended to quantum mechanics by considering non-instantaneous measurements. This leads to a covariant form of quantum theory, where states are described by "spacetime smeared states," eliminating the need for a special time variable .
Human Experience and the Block Universe
Quantum Theory of Time and Human Perception
Recent theories suggest that dynamics may be a phenomenological consequence of a fundamental violation of time reversal symmetry. This view aligns with the block universe concept, where past, present, and future coexist. It also relates to human experience, where we perceive the present moment and reflect on the past while contemplating the future .
Conclusion
The nature of time in quantum mechanics is a complex and multifaceted issue. From treating time as a parameter to understanding its emergence from quantum events, various interpretations and theories offer insights into this fundamental concept. The interplay between time, possibility, and the arrow of time continues to be a rich area of exploration, bridging the gap between classical and quantum perspectives.
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Space-Time Approach to Non-Relativistic Quantum Mechanics
This paper presents a new approach to non-relativistic quantum mechanics, showing that the probability of an event occurring in multiple ways is the square of a sum of complex contributions, satisfying Schroedinger's equation.
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