Core Concepts

Entangled Relativity, a new theory of gravity, proposes that Planck energy is the only fundamental constant, implying that Planck's constant (ℏ) and Newton's gravitational constant (G) are not constant but vary proportionally to a gravitational scalar field, thus connecting the quantum and gravitational realms.

Abstract

**Bibliographic Information:** Minazzoli, O. (2024). Quantum of action in entangled relativity. *arXiv preprint arXiv:2206.03824v4*.

**Research Objective:** This paper explores Entangled Relativity, a novel theory of gravity, and investigates its implications for fundamental constants, particularly Planck's constant (ℏ) and Newton's gravitational constant (G).

**Methodology:** The author employs a path integral formulation of Entangled Relativity and analyzes the conditions required for the theory to align with standard Quantum Field Theory in scenarios where gravity is negligible.

**Key Findings:** The study reveals that Entangled Relativity can be reconciled with standard Quantum Field Theory by identifying the theory's sole parameter, a quantum of energy squared, as the squared reduced Planck energy. This identification leads to the conclusion that ℏ and G are not fundamental constants in this framework but vary proportionally to a gravitational scalar field.

**Main Conclusions:** The paper posits that the constancy of ℏ is only relevant in contexts where gravity is negligible. It suggests that Entangled Relativity offers a more economical description of gravity compared to General Relativity, requiring fewer fundamental constants. The study also highlights the potential for observational verification of the theory's predictions, particularly the variation of ℏ in strong gravitational fields.

**Significance:** This research challenges the prevailing notion of fundamental constants in physics and proposes a novel connection between quantum mechanics and gravity. It suggests that Entangled Relativity could provide a path towards a more unified understanding of fundamental physics.

**Limitations and Future Research:** The paper acknowledges that the variation of ℏ in the solar system, as predicted by the theory, is extremely small and might pose challenges for experimental verification. Further research could explore the implications of a varying ℏ for other areas of physics, such as quantum entanglement and decoherence.

To Another Language

from source content

arxiv.org

Stats

The relative numerical variation of ℏ between the surface of the Sun and Earth is estimated to be approximately 2.4 x 10^-12.
The largest variation of ℏ in the observable universe is expected between the surface of a neutron star and a distant observer, estimated to be at the level of a few percent for the densest neutron stars.

Quotes

"In Entangled Relativity, the value of κ is determined by its cosmic evolution and by its specific value when it began to stabilize at the onset of the matter era."
"This demonstrates an explicit connection between the quantum and gravitational realms within Entangled Relativity, offering a coherent and simplified perspective on elementary physics."
"Should the variation of ℏ be quantitatively confirmed at the observational or experimental level, it would likely imply that Entangled Relativity is better than General Relativity in order to describe the relativistic laws of physics in general."

Key Insights Distilled From

by Olivier Mina... at **arxiv.org** 10-07-2024

Deeper Inquiries

Answer:
The potential variation of ℏ in strong gravitational fields, as suggested by Entangled Relativity, could have profound implications for our understanding of black holes and other extreme cosmic phenomena. Here's how:
Black Hole Thermodynamics and Hawking Radiation: A core concept in black hole physics is Hawking radiation, where black holes are theorized to emit thermal radiation due to quantum effects near the event horizon. The spectrum of this radiation is fundamentally dependent on Planck's constant (ℏ). If ℏ varies in the intense gravitational field of a black hole, the predicted properties of Hawking radiation, such as its temperature and entropy, would be modified. This could lead to new theoretical challenges and potentially observable signatures.
Black Hole Singularity: The singularity at the center of a black hole, where general relativity predicts infinite density and curvature, is a point of significant mystery and potential breakdown of known physics. A varying ℏ, particularly as it approaches the Planck scale near the singularity, could dramatically alter the physics at play. It might hint at a resolution to the singularity problem, perhaps through modifications to the nature of spacetime itself at such extreme scales.
Early Universe Cosmology: In the very early universe, fractions of a second after the Big Bang, the energy density and gravitational fields were incredibly strong. If ℏ was also varying significantly during this epoch, it could have affected the processes of cosmic inflation, baryogenesis (the creation of matter-antimatter asymmetry), and the formation of the large-scale structure of the universe.
Neutron Star Structure: As mentioned in the context, Entangled Relativity predicts variations in ℏ at the percent level for neutron stars. This could influence the equation of state of the ultra-dense matter within these objects, potentially affecting their stability, mass-radius relationship, and the conditions under which they might collapse into black holes.
Observing the effects of a varying ℏ in these extreme environments would be incredibly challenging. However, it highlights the potential for Entangled Relativity to provide new insights into the most enigmatic objects and events in the cosmos.

Answer:
Incorporating a varying ℏ into existing quantum gravity theories presents a significant challenge and likely requires at least a substantial modification of current paradigms. Here's why:
Fundamental Constant: In most established physics frameworks, including quantum field theory and general relativity, ℏ is treated as a fundamental constant, a fixed parameter of the universe. Changing this assumption has cascading consequences.
Canonical Quantization: As pointed out in the context, canonical quantization, a cornerstone of quantum field theory, relies on a constant ℏ to promote classical variables to quantum operators. A varying ℏ would necessitate a fundamentally different approach to quantizing gravity.
Existing Quantum Gravity Approaches:
String Theory: String theory, which attempts to unify gravity with other forces by postulating fundamental vibrating strings, typically assumes a constant ℏ. Incorporating a varying ℏ would likely require a major reformulation.
Loop Quantum Gravity: Loop quantum gravity, which quantizes spacetime itself, also generally assumes a constant ℏ. A varying ℏ might be interpretable as a changing "quantum of area" or "quantum of volume," but this would require careful investigation.
New Theoretical Frameworks: Instead of forcing a varying ℏ into existing theories, it might be more natural to explore new theoretical frameworks where this variation arises organically. Entangled Relativity, as described in the context, is one such example. Other approaches, like some modified theories of gravity or emergent gravity scenarios, might also accommodate a varying ℏ.
Experimental Guidance: Ultimately, the question of whether ℏ varies and how to incorporate it into a theory of quantum gravity will likely require guidance from experimental or observational evidence.

Answer:
The absence of fundamental units of time and space, as suggested by Entangled Relativity, has profound philosophical implications for our understanding of reality and the nature of measurement:
The Illusion of Continuity: Our everyday experience suggests that space and time are continuous and infinitely divisible. However, if Entangled Relativity is correct, this could be an illusion, a convenient approximation at macroscopic scales. At the Planck scale, the very notions of length and duration might break down, replaced by a more fundamental structure.
Relationalism vs. Absolutism: The lack of fundamental units for space and time lends support to relationalist views of spacetime. Relationalism, often associated with thinkers like Leibniz and Mach, posits that space and time are not absolute entities but rather emerge from the relationships between physical objects and events. Entangled Relativity, with its connection between matter and geometry, seems to resonate with this view.
The Meaning of Measurement: If there are no fundamental units of space and time, what does it mean to measure distance or duration? Our standard measuring tools and units (meters, seconds) would be revealed as convenient macroscopic constructs, not reflections of an underlying, absolute reality. This challenges us to rethink the meaning of measurement and its connection to physical reality.
Emergence of Spacetime: Entangled Relativity suggests that spacetime itself might be an emergent phenomenon, arising from a more fundamental, pre-geometric structure. This echoes ideas explored in other approaches to quantum gravity, such as loop quantum gravity and causal set theory. Understanding how spacetime emerges from a deeper level of reality would be a major breakthrough in physics and philosophy.
Limits of Knowledge: The absence of fundamental units in Entangled Relativity could imply fundamental limits to our ability to measure and comprehend the universe at its most fundamental level. There might be a "blurriness" or indeterminacy inherent in the fabric of reality itself.
In conclusion, Entangled Relativity's suggestion of a universe without fundamental units of space and time challenges deeply ingrained assumptions about the nature of reality. It encourages us to explore relationalist views of spacetime, question the meaning of measurement, and consider the possibility of an emergent spacetime arising from a deeper, pre-geometric order.

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