stochastic fluctuations affect gravity

New Study Explores How Stochastic Fluctuations Can Differentiate Classical and Quantum Gravity

A study recently published in Physical Review Letters suggests an experimental pathway to resolving the fundamental question of whether gravity adheres to classical or quantum mechanics.

Introduction: The Gravity Dilemma

For decades, physicists have grappled with the enigmatic nature of gravity. Unlike the electromagnetic, strong and weak nuclear forces, gravity remains resistant to  unification within the quantum framework.

Alternative Approach: Moving Beyond Graviton Detection

Instead of attempting to formulate a complete theory of gravity or detect individual gravitons—the hypothetical carriers of gravitational force—the researchers adopt an alternative approach.

Serhii Kryhin's Perspective

"In recent years, multiple proposals have emerged aiming to experimentally determine the nature of gravity. However, their execution remains highly challenging. Our goal was to devise a more practical experiment capable of at least falsifying the notion that gravity is classical," stated Serhii Kryhin, a third-year graduate student at Harvard University and co-author of the study.

Reframing the asking Question: Observable Differences Between Classical and Quantum Gravity

Rather than asking whether gravity must be quantized, the researchers reframed the question to seek measurable distinctions: "What observable differences would indicate the necessity of quantizing gravity?"

Quantum vs. Classical Fluctuations

"The concept is straightforward yet has remained overlooked until now. If gravity is inherently quantum, it should facilitate the entaglement of distnat matter due to its long-range nature. Conversely, if gravity is purely classical, such entaglement would be impossible," explained Vivishek Sudhir, Associate Professor at MIT and co-author of the study.

Stochastic Fluctuations in Classical Gravity

The fundamental observation is that if gravity is classical, it must generate unavoidable stochastic fluctuations. These fluctuations arise as a necessary consequence of resolving an inherent inconsistency—without them, classical gravity's determinism would contradict quantum mechanical principles.

Quantum vs. Classical Gravitational Fluctuations

The ingenuity of this approach stems from recognizing that these fluctuations would induce a measurable phase shift in the cross-correlation spectrum, distinguishing classical gravity from its quantum counterpart.

Weak Quantum Fluctuations

"Quantum fluctuations inherently emerge as variations in the dynamic degrees of freedom within general relativity. The key distinction between quantum and classical gravitational fluctuations lies in their magnitude—quantum effects, being relativistic in nature, are exceptionally weak and therefore extremely difficult to detect," explained Kryhin.

Larger Classical Fluctuations

"On the other hand, for classical fluctuations to be theoretically viable and consistent with our current understanding, they would have to be considerably larger," remarked Prof. Sudhir.

Theoretical Model: Interplay Between Quantum and Classical Domains

The researchers present a theoretical model describing the interplay between quantum and classical domains within the Newtonian limit of gravity, where classical gravity and quantum matter coexist.

Quantum-Classical Master Equation

The researchers formulated a quantum-classical master equation governing the joint evolution of quantum matter and classical gravity. Additionally, they derived a Hamiltonian for Newtonian gravity's interaction with quantum masses using two distinct approaches: Dirac's constrained systems theory and the Newtonian limit of gravity.

Modified Newton's Law and Stochastic Effects

Subsequently, they derived a modified quantum Newton's law incorporating stochastic gravitational effects and identified the unique correlation patterns between two gravitationally interacting quantum oscillators.

Markovian Master Equation

Through this mathematical framework, they derived a closed Lindblad equation—a Markovian master equation—governing quantum matter interacting with classical gravity. This equation introduces a parameter,  ε, where ε ≠ 0 Signifies classical gravity and ε = 0 denotes quantum gravity.

Identifying Measurable Quantities

Through their analysis, the researchers uncovered critical insights, establishing that a coherent theoretical model of classical gravity coupled with quantum matter is achievable, challenging earlier claims to the contrary.

Distinct Fluctuations in Classical and Quantum Gravity

Their computations indicate that classical gravity generates fluctuations fundamentally different from those of quantum gravity, with a distinct, experimentally verifiable signature.

Phase Shift in Quantum Harmonic Oscillators

When two quantum harmonic oscillators engage gravitationally, a hallmark phase shift of  π (180 degrees) emerges in their cross-correlation spectrum at a defined detuning from resonance, signaling classical gravity.

Proposed Experiment: The Quantum Cavendish Experiment

To validate these theoretical predictions, the researchers propose a quantum analogue of the historic Cavendish experiment, employing two highly coherent quantum mechanical oscillators coupled via gravity.

Measuring the Phase Shift

The characteristic phase shift could be identified by accurately quantifying the cross-correlation of their movements.

This approach stands out due to its experimental viability. Unlike previous proposals requiring macroscopic quantum superpositions, it leverages correlations between quantum oscillators, achievable with present or near-future technology.

Theoretical Implications: Self-Consistent Interaction Between Gravity and Quantum Matter

Professor Sudhir explained that semiclassical gravity models often disregard the influence of quantum fluctuations of matter on classical gravitational dynamics. In contrast, their framework enables a self-consistent interaction between classical gravity and quantum matter.

Empirical Evidence and Its Potential Impact

Empirical evidence supporting the classical nature of gravity would have far-reaching consequences for our understanding of fundamental physics.

Challenging the Quantum Gravity Paradigm

"The notion that gravity must be quantum is widely accepted, yet its precise implications remain elusive," remarked Kryhin.

Potential Reassessment of Fundamental Physics

"Extensive efforts have been dedicated to formulating a quantized theory of general relativity, leading to the development of string theory as a significant outcome. However, if experiments confirm that gravity is classical, a fundamental reassessment of our ontological understanding of the universe will be necessary."

Challenges Ahead: Formalism Development and Technological Feasibility

While this research provides a fresh taken on a decades-old problem, the team acknowledges that significant hurdles remain, including formalism development, model refinement, and the technological feasibility of the proposed experiment.

Technological Challenges in Sensitivity and Measurement

"Experimentally, achieving the necessary sensitivity for a conclusive test required the precise integration of two gravitating masses, advanced noise isolation, and highly refined measurement techniques," Kryhin concluded.

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gravity from entropy quantum gravity

Gravity from Entropy: A Bold New Theory Bridging Quantum Mechanics and General Relativity

Introduction

Professor Ginestra Bianconi, an applied mathematics expert at Queen Mary University of London, presents a pioneering framework in Physical Review D that could redefine the link between gravity and quantum mechanics.

The Study Overview: Gravity from Quantum Relative Entropy

The study, Gravity from Entropy, presents and innovative framework that derives gravity from quantum relative entropy, offering a potential bridge between quantum mechanics and Einstein's general relativity—two historically conflicting theories.

Challenges in Unifying Quantum Gravity

The Struggle to Integrate Quantum Mechanics and General Relativity

Physicists have long grappled with the challenge of unifying quantum mechanics and general relativity—two foundational but seemingly incompatible theories. While quantum mechanics dictates particle behavior at microscopic scales, general relativity governs gravitational forces on a cosmic level. Bridging this theoretical divide remains one of the greatest challenges in modern physics.

Professor Bianconi's Groundbreaking Framework

Reinterpreting the Spacetime Metric as a Quantum Operator

Professor Bianconi's research introduces a novel framework in which the spacetime metric—central to general relativity—is reinterpreted as a quantum operator. By leveraging quantum relative entropy, a principle from quantum information theory, this approach provides new insights into the relationship between spacetime geometry and matter.

The Role of Entropy and the G-field

Entropic Action and Deviations in Spacetime Metrics

The research presents an entropic action framework that measures the deviation between spacetime metrics and those influenced by matter fields.

Modifying Einstein's Equations and Predicting a Cosmological Constant

This framework modifies Einstein's equations, which, under low coupling conditions—characterized by low energy and minimal curvature—converge to classical general relativity. Crucially, it also predicts a small, positive cosmological constant, aligning more accurately with observed cosmic acceleration than alternative theories.

The G-field and its Role in Gravity and Dark Matter

This theory introduces the G-field, an auxiliary field serving as a Lagrangian multiplier. It not only refines the structure of modified gravitational equations but also provides a new theoretical avenue for understanding dark matter, whose elusive nature remains one of modern physics' greatest challenges.

Wider Implications and Future Directions

Quantum Gravity and the Unification of Theoretical Physics

This research carries significant implications, offering a novel connection between gravity and quantum information theory. It paves the way for a potential unification of quantum gravity while also providing fresh perspectives on the elusive nature of dark matter.

The Emergent Cosmological Constant and Expanding Our Understanding of the Universe

"Our research suggests that quantum gravity originates from entropic principles, with the G-field potentially serving as a candidate for dark matter," states Professor Bianconi. "Furthermore, our model's emergent cosmological constant may bridge the gap between theoretical predictions and observed cosmic expansion."

The Future of This Theory and Its Potential Impact

While further investigation is necessary to comprehensively assess this theory's implications, the study constitutes a pivotal stride toward deciphering the fundamental nature of the cosmos.

Disrupting Traditional Paradigms in Physics

Professor Bianconi's research disrupts traditional paradigms, introducing novel avenues for inquiry. By conceptualizing spacetime as a quantum entity and harnessing entropy within spacetime metrics, this work offers profound insights into gravity, quantum mechanics, and the cosmos.

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quantum penrose inequality and black hole thermodynamics

Quantum Insights Extend Classical Black Hole Inequalities into New Realms

The latest study in Physical Review Letters examines quantum effects on black hole thermodynamics and geometry, offering quantum perspective on two established classical inequalities.

Classical Framework and Quantum Enhancements

The classical framework rooted in Einstein's general theory of relativity has provided significant insights into black holes, but it fails to incorporate quantum phenomena such as Hawking radiation.

The objective of this research was to augment classical theories through the inclusion of quantum effects, improving the comprehension of black hole dynamics.

Research Team

The project was carried out by a team of experts:

• Dr. Antonia M. Frassino, a Marie Curie Fellow at SISSA in Italy
• Dr. Robie Hennigar, Assistant Professor and Willmore Fellow at Durham University in the UK
• Dr. Juan F. Pedraza, Assistant Professor at the Instituto de Física Teórica UAM/CSIC, Spain
• Dr. Andrew Svesko, a Research Associate at King's College London in the UK

The researchers spoke to Phys.org about their study on quantum inequalities and their role in understanding black hole dynamics.

Insights from the Research Team

• Dr. Frassino, explaining the impetus for the research, said, "My interest in black hole thermodynamics originated during my Ph.D. Through this project, we were able to develop universal bounds to aid studies of quantum effects in curved spacetime."
• Dr. Hennigar explained, "I've been researching the impact of quantum effects on black holes for years, and lately, my work has expanded to investigate their role in gravitational singularities."
• Dr. Pedraza explained, "Black holes have been the focus of my research for 15 years, and recent developments in holography have provided a more controlled framework for studying quantum effects in black hole physics."
• Dr. Svesko stated, "Throughout most of my career, I've been fascinated by quantum effects on black holes as a pathway to understanding quantum gravity, and I've now found the right team and method to address this challenge."

The Conjecture of Cosmic Censorship

At the heart of a black hole lies a singularity, a point of infinite density, where the breakdown of quantum mechanics and gravity poses significant challenges to our understanding of physics.

The cosmic censorship conjecture posits that singularities are concealed within the event horizons of black holes, which represent the boundary beyond which light cannot escape the immense gravitational pull.

The conjecture plays a crucial role in maintaining the stability of physical laws in the universe by ensuring that naked singularities are not visible, thereby averting any disruption in our comprehension of physics.

Violations in Classical Physics

In certain cases, classical physics does not uphold cosmic censorship. For instance, in a three-dimensional setting (two spatial dimensions and one temporal dimension), naked conical singularities may emerge.

In these situations, researchers suggest that quantum effects could conceal singularities by forming event horizons. This brings us to the Penrose inequality, which offers a framework for exploring the connection between black hole horizons and spacetime mass.

-The Penrose Inequality, along with its reverse isoperimetric variant-

Penrose Inequality and Its Quantum Extension

The Classical Penrose Inequality

"In broad terms, the Penrose inequality sets a lower bound on the mass present in spacetime, bases on the area of the black hole horizons within that spacetime," the researchers explained.

In other words, the classical Penrose inequality draws a connection between the mass of a black hole and the surface area of its event horizon, placing a lower bound on the minimum mass the black hole can have.

Quantum Penrose Inequality

The quantum Penrose inequality builds on this concept, offering a potential bound on spacetime energy, incorporating both black hole and quantum matter entropy. Efforts to extend this inequality into the quantum domain have been explored in four or more dimensions but face computational challenges.

Reverse Isoperimetric Inequality

A closely related concepts, the reverse isoperimentric inequality, establishes a connection between the volume inside a black hole's event horizon and its surface area. Similar to the Penrose inequality, there is an ongoing effort to extend this principle into the quantum domain.

Previous efforts faced difficulties when applied to three-dimensional scenarios, achieving success only for small perturbations. Additionally, handling strong quantum backreactions has proven to be a significant challenge.

Challenges in Quantum Backreaction

Backreaction is the phenomenon where matter and energy influence the curvature of spacetime, as explained by Einstein's theory of general relativity. Essentially, it describes the reciprocal interaction between matter, energy, and the geometry of spacetime.

Holographic Theory in The Context of Braneworld Cosmology

Braneworld Holography and AdS/CFT Correspondence

In their study of quantum black holes, the researchers applied a framework based on braneworld holography, commonly known as double holography.

Braneworld holography utilizes the holographic principle to derive precise solutions to semi-classical gravitational equations, incorporating backreaction at all levels. According to the researchers, this is the only known approach ot address this issue in three, and potentially higher, dimensions.

The researchers built upon the AdS/CFT correspondence to explore quantum corrections in AdS space. AdS, or Anti-de Sitter space, is a spacetime characterized by negative curvature, often used to study gravitational theories related to black holes. CFT, or Conformal Field Theory, is a quantum field theory that examines the behavior of fundamental particles without the effects of gravity.

The AdS/CFT correspondence proposes a duality that links the study of gravity in AdS space to the behavior of fundamental particles in lower-dimensional spaces. Essentially, this allows us to investigate gravity by analyzing quantum fields in reduced dimensions and vice versa.

Additionally, AdS space affords a well-structured framework for examining black holes and singularities at the boundary.

BTZ Black Holes

Their primary focus was on BTZ (Banados-Teitelboim-Zanelli) black holes, which exist in three-dimensional spacetime within AdS space. BTZ black holes serve as an effective model for exploring quantum corrections and backreaction effects, owing to their simplicity and well-understood properties in the holographic framework.

The holographic method allows the researchers to incorporate quantum backreactions, which represent the influence of quantum matter on the curvature of spacetime.

Expanding Classical Inequalities with Quantum Effects

Quantum Penrose Inequality and Quantum Cosmic Censorship

The researchers effectively expanded the classical Penrose and reverse isoperimetric inequalities to incorporate quantum effects, ensuring their validity for all known black holes in three-dimensional AdS space, even in the presence of any quantum backreaction.

The quantum Penrose inequality proposes a version of quantum cosmic censorship.

Entropy and Quantum Information Theory

"This study presents two bounds that are applicable not only to black hole entropy but also to generalized entropy,  incorporating both the entropy of the black hole and the surrounding matter fields,"

"According to the research, should the entropy of both black holes and matter exceed the overall energy of spacetime, it would lead to the formation of a naked singularity," the team clarified.

Reverse Isoperimetric Inequality and Superentropic Black Holes

The researchers explored how dimensional reduction impacts the inequalities, suggesting the possibility of deriving Penrose-type inequalities for two-dimensional dilatonic black holes but also recognizing the difficulty of obtaining exact solutions for braneworld black holes in higher-dimensional contexts.

Regarding the reverse isoperimetric inequality, the researchers determined that black holes violating this inequality, referred to as superentropic black holes, exhibit thermodynamic instability. Even with the influence of quantum effects, the stability of black holes remains largely dependent on their thermodynamic volume.

Implications for Quantum Information Theory

On the influence of their research on quantum information theory, the researchers explained, "The quantum Penrose inequality and the quantum isoperimetric inequality, both of our results, can be viewed as entropy bounds."

"Entropy is fundamentally tied to information theory, and as such, we offer evidence for intrinsic bounds in quantum information theory when gravity is involved. It is entirely conceivable that these concepts could influence quantum information."

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