Feasibility of a Relativistic Quantum Gravity Experiment Using Superposition of Rotational Energies

Core Concepts

This paper proposes a novel, genuinely relativistic experiment to test quantum gravity-induced entanglement (QGEM) by exploiting the gravitational effects of rotational energy superposition in macroscopic rotors, pushing the boundaries of current experimental capabilities.

Abstract

Bibliographic Information:

Higgins, G., Di Biagio, A., & Christodoulou, M. (2024). A truly relativistic gravity mediated entanglement protocol using superpositions of rotational energies. arXiv preprint arXiv:2403.02062v2.

Research Objective:

This paper explores the feasibility of a new experimental approach to test quantum gravity-induced entanglement (QGEM) by utilizing macroscopic rotors in a superposition of rotational energy states, thus creating a superposition of mass.

Methodology:

The authors propose a theoretical protocol involving two macroscopic rotors, each with embedded electric and magnetic dipole moments. The protocol utilizes electric fields to prepare a superposition of orientations in the electric dipole moment, which is then coupled to the magnetic dipole moment. Subsequently, magnetic fields are used to spin-up the rotors, creating a superposition of rotational energies and, consequently, masses. The resulting gravitational interaction between the rotors is analyzed for entanglement. The feasibility of the experiment is assessed by considering limitations such as the smallness of the entangling phase, centrifugal deformation of the rotors at high rotational speeds, and decoherence due to radiation emission.

Key Findings:

• The proposed protocol relies on the general relativistic effect of rotational energy gravitating, a feature absent in Newtonian gravity.
• The entangling phase in this scheme is suppressed by a factor of 1/c⁴, making the experiment significantly more challenging than traditional QGEM proposals based on spatial superpositions.
• Preliminary analysis suggests a small parameter regime where the experiment might be feasible, requiring rotors with radii around 0.1 meters and angular velocities around 2π × 1 Hz.

Main Conclusions:

While theoretically possible, realizing this experiment poses a formidable challenge with current technology. Achieving the required coherence times for macroscopic rotors at such high rotational speeds necessitates significant advancements in experimental techniques and mitigating various decoherence sources.

Significance:

This research proposes a novel approach to test QGEM that goes beyond the Newtonian limit, probing the genuinely relativistic aspects of gravity. Successful implementation would provide valuable insights into the quantum nature of gravity and its interplay with general relativity.

Limitations and Future Research:

The proposed experiment requires ambitious experimental parameters, pushing the boundaries of current technology. Further research is needed to explore alternative experimental setups, optimize parameters, and develop techniques to mitigate decoherence sources effectively.

Stats

The entangling phase needs to be greater than 10^-3 to be measurable.
The maximum electric field strength applicable is approximately 10^10 V/m to avoid ionization.
The electric dipole moment considered is 10^3 D.
The maximum magnetic field strength used is 100 T.
The minimum separation between the rotors is 10 µm to allow for electromagnetic shielding.
The duration of the key experimental steps is optimistically set to 10^3 seconds.
The rotors are assumed to be solid spheres with a density of 2.3 × 10^4 kg/m^3 (osmium).

Quotes

"Performing such an experiment would be a more important test than the usual QGEM protocols that operate in the Newtonian regime."
"This protocol would test a genuine interface between general relativity and quantum mechanics in the sense that there is no precise analogue in electromagnetism as it would amount to considering a particle in a state superposition of electric charge which is excluded by superselection rules."
"A sober headed conclusion would be that the parameters we use are extremely ambitious and are not feasible for the foreseeable future."

Key Insights Distilled From

A truly relativistic gravity mediated entanglement protocol using superpositions of rotational energies

by Gerard Higgi... at arxiv.org 11-12-2024

https://arxiv.org/pdf/2403.02062.pdf

Deeper Inquiries

Could alternative experimental platforms, such as superconducting circuits or trapped ions, offer a more feasible route to test this relativistic QGEM protocol?

While superconducting circuits and trapped ions represent cutting-edge technologies for quantum control, their applicability to this specific relativistic QGEM protocol presents significant challenges:
Superconducting Circuits:

Mass-Energy Equivalence: Superconducting circuits excel in manipulating quantum states of charge and flux, but their extremely low mass makes it practically impossible to achieve a meaningful superposition of mass through energy differences. The energy scales associated with superconducting circuits are far too small to produce a measurable gravitational effect.
Rotational Degrees of Freedom: Engineering well-defined and controllable rotational degrees of freedom within a superconducting circuit framework poses a formidable challenge. The protocol relies on precise control over the orientation and angular velocity of macroscopic rotors, which is not a natural strength of superconducting circuits.
Trapped Ions:

Mass Limitations: Similar to superconducting circuits, individual trapped ions possess minuscule mass. While ion traps allow for exquisite control over internal and motional states, achieving macroscopic superpositions of mass-energy remains outside their capabilities.
Rotational Control: Although techniques for rotating ion crystals exist, achieving the high angular velocities and precise control over rotational states required by the protocol would be extremely challenging.
In summary: Both superconducting circuits and trapped ions, despite their strengths in other areas of quantum information processing, face fundamental limitations in addressing the specific requirements of this relativistic QGEM protocol, particularly the need for macroscopic mass superpositions and precise control over rotational degrees of freedom.

How might the inherent uncertainties in measuring gravitational interactions at such small scales impact the interpretation of the experimental results and the ability to conclusively prove quantum gravity-induced entanglement?

The quest to measure gravitational interactions at such small scales is fraught with challenges, primarily due to the extreme weakness of gravity compared to other fundamental forces. These inherent uncertainties can significantly impact the interpretation of experimental results and the ability to definitively claim quantum gravity-induced entanglement:

Background Noise: Isolating the minute gravitational interaction from a plethora of environmental noise sources, such as seismic vibrations, electromagnetic fluctuations, and even Newtonian gravitational influences from nearby objects, presents a monumental task. Even with state-of-the-art shielding and isolation techniques, residual noise can easily overwhelm the signal of interest, making it difficult to extract a clear signature of the effect.
Measurement Precision: Detecting the subtle entanglement generated by the gravitational interaction necessitates measurement apparatuses with unprecedented sensitivity. The entangled states are expected to be extremely fragile, susceptible to decoherence from even the slightest environmental perturbations. Achieving the required measurement precision while preserving the delicate entanglement poses a formidable experimental hurdle.
Alternative Explanations: Even if a signal consistent with the predicted entanglement is observed, conclusively attributing it to quantum gravity-induced entanglement requires ruling out all other possible classical or non-gravitational explanations. This demands meticulous experimental design and rigorous analysis to eliminate any potential loopholes or systematic errors that could mimic the sought-after effect.
In essence: The extreme weakness of gravity at these scales, coupled with the inherent uncertainties in measurement and the need to disentangle genuine quantum gravitational effects from background noise and other influences, makes the interpretation of experimental results a delicate and nuanced endeavor. While observing entanglement consistent with theoretical predictions would be a significant step forward, definitively proving its quantum gravitational origin requires extraordinary experimental precision, careful control over systematic errors, and a thorough examination of alternative explanations.

If this experiment were to be conducted in a space-based environment, what new possibilities and challenges would arise in terms of achieving the required experimental conditions and mitigating environmental decoherence?

Conducting this experiment in the pristine environment of space offers both tantalizing possibilities and unique challenges:
Advantages of Space:

Microgravity Environment: The most significant advantage lies in the near-perfect freefall conditions of space, effectively eliminating the influence of Earth's gravity. This drastically reduces the background noise floor, allowing for much greater sensitivity to the subtle gravitational interactions between the test masses.
Reduced Seismic Noise: Space-based platforms are inherently isolated from seismic vibrations that plague Earth-based laboratories. This further enhances the signal-to-noise ratio, making it easier to discern the faint gravitational signal.
Cryogenic Temperatures: The coldness of space provides a natural environment for achieving cryogenic temperatures, essential for minimizing thermal noise and maximizing coherence times of the quantum systems involved.
Challenges in Space:

Technical Complexity: Designing, building, and operating a sophisticated experiment in the harsh conditions of space presents immense technical challenges. The experiment would require advanced technologies for maintaining ultra-high vacuum, precise temperature control, and shielding from cosmic radiation.
Launch and Deployment: Safely launching and deploying a delicate quantum experiment into space poses significant risks. The experiment must withstand the intense vibrations and accelerations during launch and then be precisely positioned and aligned once in orbit.
Remote Operation and Data Transfer: Operating the experiment remotely from Earth and transmitting large volumes of data back to ground stations introduce complexities in communication and data handling.
In conclusion: While a space-based experiment offers a path towards mitigating some of the challenges faced on Earth, it comes at the cost of increased technical complexity and operational risks. The decision to pursue a space-based approach would involve carefully weighing the scientific benefits against the technological and logistical hurdles.