Gravitational Reduction of the Wave Function: A Bohmian Perspective Using Quantum Trajectories

Core Concepts

This paper explores the concept of gravity-induced wave function reduction through the lens of Bohmian quantum mechanics, utilizing the intuitive framework of Bohmian trajectories to define the reduction time and critical parameters for the transition from quantum to classical behavior.

Abstract

Bibliographic Information:

Rahmani, F. (2024). Gravitational reduction of the wave function through the quantum theory of motion. arXiv preprint arXiv:2409.09655v2.

Research Objective:

This paper aims to provide a novel perspective on gravity-induced wave function reduction by employing Bohmian quantum mechanics and analyzing the quantum motion of both point particles and objects.

Methodology:

The study utilizes Bohmian trajectories to analyze the dynamics of quantum systems under the influence of gravity. By examining the deviation between nearby trajectories, the authors derive a condition for equilibrium between quantum forces and quantum gravitational forces. This condition is then used to determine the critical width for the transition between quantum and classical behavior. The reduction time of the wave function is estimated based on the period of oscillation of the particle or object within its quantum distribution.

Key Findings:

• The study establishes a relationship between the mass of a particle or object and the critical width of its wave packet for the transition from quantum to classical behavior.
• The research demonstrates that in a gravity-dominant regime, particles and objects exhibit oscillatory motion within their quantum distribution, with the period of oscillation proportional to the reduction time of the wave function.
• The authors derive approximate analytical expressions for the reduction time of both point particles and objects, consistent with previous findings in standard quantum mechanics.

Main Conclusions:

The study concludes that Bohmian quantum mechanics offers a valuable framework for understanding gravity-induced wave function reduction. The intuitive nature of Bohmian trajectories provides insights into the underlying processes governing the transition from quantum to classical behavior.

Significance:

This research contributes to the ongoing debate surrounding wave function collapse and its connection to gravity. The Bohmian perspective offers a fresh approach to this fundamental problem in quantum mechanics.

Limitations and Future Research:

The study primarily focuses on non-relativistic systems and utilizes a fixed background metric for gravity. Future research could explore the implications of relativistic effects and a dynamic spacetime on wave function reduction within the Bohmian framework. Additionally, investigating the role of environmental decoherence in this context could provide a more comprehensive understanding of the transition to classicality.

Stats

For a proton, the critical width derived from the Bohmian approach is approximately 10^6 cm.
For a tennis ball with a radius of 4 cm and a mass of 57 g, the critical width is approximately 10^-17 cm, and the reduction time is approximately 10^-6 s.
For a wave packet with an initial width of 10^-2 cm, the critical mass is approximately 10^-15 g.
For a ball with a size of 5 cm and a mass of 100 g, the reduction time is on the order of 10^-23 s.
For a flea egg with a size of approximately 0.5 mm and a mass of about 10^-5 g, the reduction time is around 10^-11 s.
For a proton, the estimated reduction time is approximately 10^15 s.

Quotes

"In gravity-induced wave function reduction, the mass of an object serves as a criterion for determining the boundary between the classical and quantum worlds."
"In Bohmian quantum mechanics, it is possible to study the quantum motion of the particle or object, which allows for a more intuitive visualization of the problem."
"What is discussed as the collapse time of the wave function in standard quantum mechanics is related here to the period of the particle’s oscillatory motion."

Key Insights Distilled From

Gravitational reduction of the wave function through the quantum theory of motion

by Faramarz Rah... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2409.09655.pdf

Deeper Inquiries

How might the incorporation of quantum field theory and curved spacetime, as opposed to a fixed background metric, affect the results and interpretations presented in this paper?

Incorporating quantum field theory (QFT) and a dynamic curved spacetime, as opposed to the fixed background metric used in the paper, would significantly complicate the analysis of gravity-induced wave function reduction within the Bohmian framework. Here's how:
1. Backreaction and Quantum Fluctuations:

Fixed Background: The paper assumes a static gravitational field generated by the quantum probability distribution. This neglects the backreaction of the particle's motion on the spacetime geometry.
Dynamic Spacetime: In a QFT framework with curved spacetime, the particle's presence and motion would influence the spacetime curvature. This backreaction would be especially important near the critical width where quantum gravitational effects are strong. Additionally, quantum fluctuations of spacetime itself would need to be considered, adding further complexity.
2. Field-Theoretic Description:

Point Particles: The paper treats particles as point-like objects.
QFT: A full QFT treatment would require describing particles as excitations of quantum fields that permeate spacetime. This introduces new degrees of freedom and necessitates a more abstract mathematical framework.
3. Interpretation of Trajectories:

Bohmian Mechanics: Bohmian mechanics relies on well-defined particle trajectories.
QFT in Curved Spacetime: In QFT, the concept of a particle trajectory becomes more ambiguous, especially in the presence of strong gravitational fields or when considering particle creation and annihilation.
4. Conceptual Challenges:

Unification: Combining QFT and curved spacetime consistently remains a major challenge in theoretical physics (quantum gravity). The paper's approach, while insightful, would need significant modification to be reconciled with a full theory of quantum gravity.
Potential Implications:

Modified Critical Width: The critical width for wave function reduction might be altered due to the backreaction of the particle on spacetime and the influence of spacetime fluctuations.
Revised Reduction Time: The estimated reduction time could change significantly when considering the dynamic interplay between the particle and the gravitational field.
New Insights: A full QFT treatment might reveal novel mechanisms for wave function reduction or modify our understanding of the transition between quantum and classical behavior in strong gravity regimes.

Could environmental decoherence, rather than gravity, be the primary driver of wave function reduction, and how would a Bohmian approach account for this alternative explanation?

Yes, environmental decoherence is a compelling alternative explanation for the apparent wave function reduction, often considered more relevant than gravity for most systems. Here's how it works and how Bohmian mechanics incorporates it:
Environmental Decoherence:

Entanglement with Environment: Quantum systems are rarely isolated. Interactions with the environment (e.g., stray photons, air molecules) lead to entanglement between the system and its surroundings.
Effective Loss of Coherence: This entanglement effectively "buries" the quantum superposition of the system into a much larger entangled state. The system's individual coherence is lost, even if the overall superposition persists.
Classical-like Behavior: The system, entangled with the environment, behaves as if it has collapsed into a specific state from the perspective of a local observer, even though no true collapse has occurred.
Bohmian Perspective on Decoherence:

No True Collapse: Bohmian mechanics, like many interpretations, doesn't require a true collapse of the wave function. The universal wave function continues to evolve unitarily.
Effective Collapse: Decoherence, in the Bohmian view, leads to an effective collapse. The particle's trajectory becomes strongly correlated with one of the branches of the wave function that has become entangled with the environment.
Guidance Equation: The Bohmian guidance equation still governs the particle's motion, but the effective potential (including contributions from the environment) guides the particle towards a specific branch of the wave function, mimicking a collapse.
Distinguishing Gravity and Decoherence:

Experimental Challenges: Distinguishing between gravity-induced reduction and decoherence experimentally is extremely difficult. Both predict very similar outcomes for most systems.
Extreme Environments: Gravity might play a more dominant role in extreme environments like black holes or the very early universe, where gravitational effects are significantly stronger.
In summary: Bohmian mechanics can accommodate environmental decoherence as the primary driver of effective wave function reduction. The particle's trajectory becomes correlated with a specific branch of the wave function due to interactions with the environment, leading to classical-like behavior without invoking a true collapse.

If the reduction time of a proton's wave function is so long, what implications does this have for our understanding of the stability of matter and the universe as a whole?

The extremely long reduction time for a proton's wave function, as predicted by some models of gravity-induced collapse, has minimal direct implications for the stability of matter or the universe as we understand it. Here's why:
1. Decoherence Dominates:

Ordinary Matter: In the context of everyday matter, environmental decoherence is the dominant mechanism for suppressing macroscopic quantum superpositions. The gravitational self-interaction of a proton is far too weak to induce a collapse on timescales relevant to atomic or nuclear processes.
Stability Intact: The stability of atoms, nuclei, and matter, in general, is primarily governed by electromagnetic, strong, and weak nuclear forces, along with the Pauli exclusion principle. These are unaffected by the extremely slow hypothetical gravitational collapse of individual protons.
2. Cosmological Timescales:

Proton Lifetime: While protons are theorized to have a very long lifetime (much longer than the current age of the universe), their eventual decay is predicted by Grand Unified Theories through processes unrelated to gravity-induced wave function collapse.
Universe's Evolution: The evolution and large-scale structure of the universe are primarily driven by gravity acting on macroscopic scales, along with the expansion of spacetime. The incredibly slow hypothetical collapse of individual proton wave functions would have a negligible impact on these cosmological processes.
3. Theoretical Considerations:

Model Dependent: It's important to note that the extremely long reduction time for protons is a prediction of specific models of gravity-induced collapse. These models are still speculative and not part of established physics.
Quantum Gravity: A complete understanding of the interplay between gravity and quantum mechanics likely requires a full theory of quantum gravity, which remains an active area of research.
In conclusion: While the concept of gravity-induced wave function collapse is intriguing, its predicted effects on protons are too weak and occur over timescales far too long to have any practical consequences for the stability of matter or the evolution of the universe as we observe it. Decoherence plays a far more significant role in shaping the quantum-to-classical transition in our everyday world.