Beyond Space and Time: Reconciling Relativity with Quantum Interference

Author: Denis Avetisyan

A new analysis reveals that enforcing operational principles-like the ability to observe interference-demands a framework that links subluminal and superluminal realms to fully realize the Quantum Principle of Relativity.

This review demonstrates how operational completeness and the need for a phase-sensitive description necessitate a concrete dynamical bridge connecting subluminal and superluminal sectors within the Quantum Principle of Relativity.

While extending special relativity to encompass superluminal frameworks offers a compelling route toward understanding quantum mechanics, simply postulating kinematics is insufficient. This paper, ‘From Kinematics to Interference: Operational Requirements for the Quantum Principle of Relativity’, dissects the necessary conditions for such a program, arguing that operational completeness-specifically, the reproduction of interference effects in closed loops-demands a phase-sensitive calculus and a concrete dynamical connection between subluminal and superluminal sectors. Establishing this framework isn’t about deriving quantum theory from relativity, but rather clarifying the essential additions needed for a well-defined research agenda. What precise dynamical bridges can consistently reconcile these seemingly disparate relativistic regimes and illuminate the foundations of quantum structure?

Beyond Classical Boundaries: Reimagining the Fabric of Reality

Classical physics, built upon the foundations of Newtonian mechanics and Einstein’s theory of relativity, posits a universe fundamentally structured by spacetime – a four-dimensional continuum where events are ordered and causality reigns. However, this framework encounters significant hurdles when attempting to describe the bizarre behaviors exhibited by quantum phenomena. Experiments reveal instances of quantum entanglement, where particles become correlated in ways that defy classical notions of locality and instantaneous communication, seemingly violating the principle that no information can travel faster than light. Furthermore, the act of measurement in quantum mechanics introduces a fundamental uncertainty, challenging the deterministic predictability central to classical physics. These discrepancies suggest that spacetime, as traditionally understood, may not be a fundamental aspect of reality but rather an emergent property, or an approximation that breaks down at the quantum scale, demanding a revised theoretical basis for a more complete description of the universe.

The inherent restrictions of classical physics in fully describing quantum reality are driving theoretical physicists to investigate frameworks that move beyond established notions of causality. Conventional physics operates under the principle that events are linked within the bounds of light-cone causality – meaning an effect cannot precede its cause. However, explorations into quantum gravity and non-local phenomena suggest this structure may not be fundamental. Researchers are now actively developing models-including those leveraging advanced mathematical tools like non-commutative geometry and modified dispersion relations-that permit the possibility of effects preceding causes, or connections existing outside the conventional light cone. These investigations aren’t necessarily proposing time travel in the conventional sense, but rather a relaxation of the strict causal ordering imposed by spacetime, potentially revealing a deeper, more interconnected reality where the relationships between events are far more complex than previously imagined. This pursuit aims to resolve inconsistencies arising when attempting to reconcile quantum mechanics with general relativity, and to build a more complete and accurate description of the universe at its most fundamental level.

The concept of the light cone, defining the boundaries of causal influence – what events can affect others – is deeply ingrained in classical physics and relativity. However, a truly complete description of physical reality may require abandoning the assumption that these boundaries are absolute. Theoretical investigations suggest that, at the Planck scale or in extreme gravitational environments, influences might propagate outside the light cone, potentially violating conventional causality. This isn’t necessarily a proposal of backwards-in-time travel, but rather an indication that our intuitive understanding of cause and effect, built on macroscopic observations, breaks down at the most fundamental levels. Exploring physics beyond the light cone necessitates developing frameworks where information transfer isn’t strictly limited by the speed of light, opening possibilities for non-local correlations and a revised understanding of spacetime’s very structure, potentially resolving conflicts between quantum mechanics and general relativity.

Reconstructing Spacetime: A Kinematic Foundation

The Quantum Principle of Relativity (QPR) postulates that physical descriptions are not limited to subluminal, or slower-than-light, velocities. Unlike conventional relativistic frameworks which strictly enforce $c$ as an upper bound on propagation speeds, QPR allows for the consistent formulation of physics incorporating superluminal, or faster-than-light, descriptions. This is achieved by relaxing the requirement that all observers must share a common light cone structure. Consequently, QPR necessitates a broadened kinematic framework capable of accommodating reference frames where events are perceived as occurring in temporal orders differing from those observed in standard, subluminal frames. The framework does not claim the physical reality of superluminal propagation, but rather asserts the logical consistency of a physics allowing such descriptions, potentially offering alternative perspectives on spacetime structure and causality.

The foundational Kinematic Layer, as considered within the Quantum Principle of Relativity, centers on the mathematical properties of affine linear maps. These maps, which preserve collinearity but not necessarily distances, provide a generalized description of transformations between spacetime points. Unlike traditional kinematic models reliant on rigid transformations, focusing on affine maps allows for the consistent description of both subluminal and potentially superluminal phenomena. Key properties under investigation include composition of maps, their associated Jacobian matrices determining local distortion, and the resulting impact on event ordering. Specifically, the analysis concentrates on how these maps define permissible coordinate transformations and the implications for defining invariant quantities within the generalized spacetime structure, moving beyond the constraints of Poincaré invariance typically assumed in relativistic models.

Admissible Redescriptions within the Kinematic Layer function as coordinate transformations that extend beyond standard Lorentz transformations, allowing analysis of event perception from differing inertial frames in a generalized spacetime. These transformations, formally defined as affine linear maps, preserve the structure necessary to relate event occurrences as observed by various observers, even when those observers are experiencing relative motion exceeding the light barrier. The utility of Admissible Redescriptions lies in their capacity to define a consistent relational structure between events, regardless of the observer’s kinematic state, enabling the derivation of observable predictions and the construction of a comprehensive spacetime model that accommodates superluminal phenomena. Specifically, these redescriptions allow for the translation of event four-vectors $x^\mu$ between frames, maintaining causal relationships as defined by the underlying kinematic structure.

Preserving Causal Integrity: Superluminal Maps and Their Constraints

Null-cone-preserving maps are mathematical transformations designed to maintain the causal relationships between events even when considering descriptions that allow for superluminal (faster-than-light) velocities. Traditional Lorentz transformations, the foundation of special relativity, ensure causality within the confines of light-speed limitations; however, when extending the framework to include superluminal possibilities, these transformations are insufficient. Null-cone-preserving maps specifically constrain any transformation such that the light cone – defining the boundary of causally connected events – is not “tilted” or altered in a way that would allow for closed timelike curves or violations of causality. Mathematically, these maps ensure that the interval $ds^2 = -c^2dt^2 + dx^2 + dy^2 + dz^2$ remains either negative (timelike), zero (lightlike), or positive (spacelike) after the transformation, preventing signals from propagating backwards in time and thus preserving the fundamental order of cause and effect.

Superluminal Lorentz Maps represent a specific instantiation of null-cone-preserving transformations designed to accommodate velocities exceeding $c$, the speed of light. These maps extend the standard Lorentz transformations by allowing for boosts parameterized by superluminal velocities, while simultaneously ensuring that the causal structure – specifically, the light cone – remains intact. Mathematically, this involves a redefinition of velocity parameters within the Lorentz boost equations, allowing for values greater than one when expressed in conventional units. The resulting transformations maintain the time-like and space-like separation of events, preventing causality violations that would otherwise arise from unrestricted superluminal travel. This approach doesn’t imply physical realizability of superluminal signaling, but provides a consistent mathematical framework for exploring theoretical scenarios involving such velocities without necessarily disrupting the fundamental principles of physics.

The framework of null-cone-preserving maps ensures theoretical consistency by maintaining the fundamental physical constraint of causality even when incorporating superluminal velocities. Traditional Lorentz transformations are limited to subluminal speeds; this approach generalizes those transformations to allow for mathematical descriptions of velocities exceeding $c$, the speed of light, without violating the established principle that no information or energy can travel backward in time. By preserving the null cone – defining the boundaries of past and future causal events – the framework avoids the paradoxes inherent in theories permitting faster-than-light communication, thereby providing a mathematically sound and physically plausible foundation for exploring superluminal phenomena.

Bridging Theory and Observation: A Dynamical Framework

The Dynamical/Bridge Layer functions as the quantum field theory (QFT) scaffolding required to produce finite, measurable statistical predictions within the broader theoretical framework. This layer establishes the rules governing particle interactions and propagators, allowing for the calculation of scattering amplitudes and decay rates. Specifically, it defines the mathematical objects – fields and their associated operators – necessary to compute probabilities for observable events. Without this QFT structure, the theoretical calculations would remain abstract and disconnected from experimental verification, as no concrete relationship between theoretical parameters and observable quantities could be established. The layer’s formalism dictates how to translate theoretical predictions into quantities directly comparable with experimental data, such as particle counts, energy distributions, and cross-sections.

Twin-Hilbert-Space Tachyon Quantum Field Theory (TH-TQFT) postulates two Hilbert spaces, one describing subluminal particle propagation and the other superluminal propagation, linked through a tachyon field. This framework addresses the conventional limitations of QFT by allowing for the exchange of information exceeding the speed of light, not as a violation of causality, but as a distinct sector within the broader theoretical structure. The tachyon field, possessing an imaginary mass, mediates interactions between these sectors, enabling the formulation of observable consequences arising from superluminal influences. Specifically, TH-TQFT utilizes a non-local, time-symmetric propagator, expressed as $G(x-y) = \theta(t_x – t_y)G_{ret}(x-y) + \theta(t_y – t_x)G_{adv}(x-y)$, where $G_{ret}$ and $G_{adv}$ represent the retarded and advanced Green’s functions, respectively, allowing for bidirectional influences and potentially resolving issues with time-ordering in certain quantum processes.

The Dynamical/Bridge Layer’s primary function is to establish a connection between theoretical predictions and observable experimental results. By providing a quantum field theory structure capable of generating measurable statistics, the framework moves beyond purely mathematical consistency checks. This is achieved through the formulation of predictions regarding physical observables – quantities that can, in principle, be measured in an experiment. Specifically, the layer facilitates the derivation of probabilistic distributions for these observables, allowing for a direct comparison between theoretical calculations and empirical data. Successful validation of these predictions confirms the framework’s ability to accurately model the underlying physical reality and distinguishes it from models existing solely as mathematical exercises.

Establishing Operational Completeness: Validating the Framework

A robust theoretical framework necessitates a clearly defined Operational Layer – a set of procedures detailing precisely how to prepare initial states, perform measurements on a system, and collect statistical data from the outcomes. This layer serves as the crucial bridge between abstract theory and concrete experimentation, enabling rigorous tests of reproducibility. Without specifying these operational details – including the precise instrumentation, control parameters, and data analysis techniques – a theory remains untestable and open to subjective interpretation. The Operational Layer, therefore, isn’t merely a technical appendix but a fundamental component of any scientific claim, dictating how evidence is gathered and evaluated, and ultimately, how a theory’s validity is established through repeated, verifiable observation. It demands a precise mapping between theoretical predictions and measurable quantities, allowing for objective confirmation or refutation of the proposed model.

Mach-Zehnder interference presents a rigorous test for any framework aiming to model quantum phenomena, demanding precise predictions of how light waves – described by complex amplitudes – will interact and recombine. This setup crucially relies on the principle of superposition, where the probability of detecting a photon at a given point is determined by the interference of multiple possible paths. Accurate modeling necessitates not only predicting the intensity of the resulting interference pattern, but also its phase dependence – how shifts in the wave’s phase alter the pattern. The sensitivity to phase highlights the need for a composition rule that accounts for the complex nature of quantum states; a simple addition of probabilities is insufficient. Validating a framework’s ability to correctly predict these interference patterns, dependent on both the Product and Sum Rules of combination, therefore serves as a powerful confirmation of its operational completeness and its capacity to describe the fundamental principles governing quantum mechanics, particularly in closed-loop systems where interference effects are paramount.

A truly robust theoretical framework must not only predict outcomes, but also align with established experimental observations – and this work validates its completeness through a detailed analysis of interference patterns. Specifically, the framework’s consistency is confirmed by its ability to accurately reproduce results from Mach-Zehnder interferometry, a process fundamentally reliant on the behavior of $complex\ amplitudes$. The analysis demonstrates that predicting interference requires adherence to both the $product\ rule$ and the $sum\ rule$ for combining these amplitudes, but crucially, reveals that a $phase-sensitive\ composition\ rule$ is essential for describing closed-loop interference. This isn’t merely a mathematical consistency check; it signifies the framework’s operational completeness, indicating its capacity to account for the nuanced wave-like behavior observed in physical systems and paving the way for reliable, reproducible predictions.

The pursuit of a Quantum Principle of Relativity, as detailed in this work, necessitates a holistic understanding of interconnected systems. It’s not merely about extending kinematic principles, but recognizing how operational demands – particularly loop interference – dictate a fundamentally phase-sensitive approach. This echoes Max Planck’s observation: “When you change the way you look at things, the things you look at change.” The article demonstrates how altering the framework – demanding operational completeness and considering both subluminal and superluminal sectors – inherently shifts the required mathematical tools, moving beyond classical descriptions towards the calculus of amplitudes. The structure of these requirements, therefore, fundamentally dictates the resulting theoretical behavior, highlighting the interconnectedness of observational demands and theoretical formulation.

Where Do We Go From Here?

The exercise presented here has not been about deriving quantum theory from first principles, but rather about exposing the minimal scaffolding necessary to require its peculiar features. It’s a subtle distinction. The insistence on operational completeness – on defining what a measurement is, rather than merely postulating its rules – forces a reckoning with the limits of subluminal description. The demand for loop interference, seemingly a technical detail, proves crucial in necessitating a phase-sensitive calculus – amplitudes – that escapes the neat determinism of classical kinematics.

However, the critical bridge remains elusive. This work highlights that simply allowing for superluminal Lorentz maps is insufficient. The true challenge lies in articulating the dynamical mechanism connecting these sectors – the concrete rules governing how information, or its analogue, traverses the boundary. What are we actually optimizing for if not a consistent picture, however strange? To pursue this further necessitates abandoning the comfortable assumption that relativity is merely a constraint, and instead embracing it as a fundamental directive for any viable quantum gravity.

Simplicity, it should be remembered, is not minimalism. It is the discipline of distinguishing the essential from the accidental. The framework outlined here, while demanding, offers a pathway toward a more robust understanding of quantum foundations, one that prioritizes operational rigor and acknowledges the inherent limitations of any localized description.

Original article: https://arxiv.org/pdf/2512.05164.pdf

Contact the author: https://www.linkedin.com/in/avetisyan/