Relativistic Quantum Theory (1912.00726v1)

Abstract: The purpose of this paper is to sketch an approach towards a reconciliation of quantum theory with relativity theory. It will actually be argued that these two theories ultimately rely on one another. A general operator-algebraic framework for relativistic quantum theory is outlined. Some concepts of space-time structure are translated into algebra. Following deep results of Buchholz et al., the key role of massless modes, photons and gravitons, and of Huygens' Principle in a relativistic quantum theory well suited to describe "events" and "measurements" is highlighted. In summary, a relativistic version of the "ETH Approach" to quantum mechanics is described.

• The paper introduces an operator-algebraic framework to reconcile quantum mechanics with relativity.
• It refines the operational definition of events and measurements to tackle the quantum measurement problem.
• The work explores the role of massless particles in upholding Einstein causality and illuminating space-time geometry.

Relativistic Quantum Theory: A Framework for Reconciliation

The paper "Relativistic Quantum Theory" addresses the reconciliation of quantum theory with relativity, positing that these two fundamental aspects of theoretical physics rely on one another. Establishing a cohesive framework is imperative to understand the foundational intricacies of quantum mechanics and its compatibility with relativistic principles. The paper introduces an operator-algebraic framework for this purpose, highlighting key conceptual advancements and the incorporation of local relativistic dynamics within quantum theory.

Summary

The paper sets the stage with a poignant reflection on the ongoing confusion and interpretational challenge within the field of quantum mechanics. It acknowledges the measurement problem, a central hurdle whereby concepts such as observation, consciousness, and measurement do not have clear definitions or implications within standard quantum mechanics. The critique signifies the importance of extending beyond mere interpretation to refining the foundational structures of quantum theory.

Core Concepts

1. Framework Introduction: The approach utilizes an operator-algebraic framework to bridge ideas of space-time with quantum mechanics, emphasizing the relations between space-time structure and algebraic formulations. The role of massless particles, such as photons and gravitons, is described as crucial in hypotheses on events and measurements in this context.
2. Events and Measurements: A specific focus is made on understanding 'events' within quantum theory, moving toward an operational definition grounded in algebraic settings. Events catalog the transition from potentiality to observed reality, adhering to the inherent probabilistic nature of quantum mechanics.
3. Locality and Causality: Our comprehension of locality and Einstein causality from the standpoint of relativistic quantum theory is examined. The discussion disentangles the complex relationship and highlights how relativistic conditions are maintained or subtly violated within quantum mechanics paradigms.
4. The ETH Approach: The exploration of a relativistic version of the "ETH Approach" to quantum mechanics posits an evolved framework addressing uncertainties and challenges quantum theory faces. Central to this is the utilization of massless modes and explorations into the dimensionality of space-time and its gravitational interpretations as emergent phenomena.

Implications and Future Directions

The paper's implications are vast, providing a blueprint for future explorations in theoretical physics. By emphasizing the entanglement between quantum theory and relativistic principles, it paves the way for:

• Theoretical Advancements: The operator-algebraic approach introduces new mathematical tools and conceptual clarity, particularly in understanding events and time evolution of quantum states.
• Resolving the Measurement Problem: By rigorously defining events, the potential for resolving the measurement problem within a quantum-relativistic framework is significantly advanced, suggesting that probability and measurement can be fundamentally structured without invoking external mechanisms.
• Space-Time Geometry and Relativity: The exploration of massless particles and their role hints at deeper underlying principles of space-time geometry and interactions, bridging gaps between quantum field theory and general relativity.
• Philosophical Underpinnings: The discussions invoked ask fundamental questions about our interpretation of quantum mechanics and its completeness, challenging existing notions and urging a reconsideration of physical theory foundations.

The paper highlights a pathway toward a comprehensive framework where quantum mechanics can be rigorously aligned with relativistic principles, offering implications that extend across standard physics theories. While extensive work remains to be done, particularly in refining algebraic structures and understanding the operational definitions of events, the paper makes a significant advancement in theoretical physics by proposing a cohesive, operator-algebraic approach to reconciling quantum mechanics with relativity.