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The Quantum-Mechanical Model of an Atom02:45

The Quantum-Mechanical Model of an Atom

Shortly after de Broglie published his ideas that the electron in a hydrogen atom could be better thought of as being a circular standing wave instead of a particle moving in quantized circular orbits, Erwin Schrödinger extended de Broglie’s work by deriving what is now known as the Schrödinger equation. When Schrödinger applied his equation to hydrogen-like atoms, he was able to reproduce Bohr’s expression for the energy and, thus, the Rydberg formula governing hydrogen spectra. Schrödinger...
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According to Albert Einstein (1897-1955), free-falling and feeling weightless are intrinsically linked. If a person were in free-fall under gravity, for example, diving towards the Earth from an airplane, they would feel completely weightless. Similarly, a person descending in a lift may feel partially weightless. Broadly speaking, it is assumed that an object in a uniform gravitational field and an object undergoing constant acceleration in the absence of gravity are under the same...
Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

In 1905, Albert Einstein published his special theory of relativity. According to this theory, no matter in the universe can attain a speed greater than the speed of light in a vacuum, which thus serves as the speed limit of the universe.
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Gauss's Law01:07

Gauss's Law

If a closed surface does not have any charge inside where an electric field line can terminate, then the electric field line entering the surface at one point must necessarily exit at some other point of the surface. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. What happens to the electric flux if there are some charges inside the enclosed volume? Gauss's law gives a quantitative answer to this question.
The Principle of Superposition and the Gravitational Field01:17

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The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a point object is the vector sum of the gravitational forces on it due to various objects. The principle helps calculate the force by listing the individual forces and then vectorially summing them up. However, it should be noted that the principle of superposition is not always apparent. In the presence of a second force, the first force could...
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Calculation of First-Law Quantities II

The first law of thermodynamics establishes that the change in internal energy of a system is given by ΔU = q + w, where q is the heat exchanged, and w is the work performed. For a perfect gas, both internal energy (U) and enthalpy (H) depend solely on temperature. Consequently, for any change of state, whether reversible or irreversible, the internal energy change is determined by integrating the heat capacity at constant volume, and the enthalpy change by integrating the heat capacity at...

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Nonperturbative S-Matrix Renormalization.

Physical review letters·2026
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Related Experiment Video

Updated: Jul 20, 2026

Gradient Echo Quantum Memory in Warm Atomic Vapor
10:00

Gradient Echo Quantum Memory in Warm Atomic Vapor

Published on: November 11, 2013

3D quantum gravity and effective noncommutative quantum field theory.

Laurent Freidel1, Etera R Livine

  • 1Perimeter Institute, 31 Caroline Street, North Waterloo, Ontario N2L 2Y5, Canada. lfriedel@perimeterinstitute.ca

Physical Review Letters
|June 29, 2006
PubMed
Summary

We demonstrate that integrating out gravitational degrees of freedom in 3D quantum gravity yields a braided noncommutative quantum field theory. This theory exhibits symmetry under a kappa deformation of the Poincaré group.

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Last Updated: Jul 20, 2026

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06:42

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • Quantum Gravity

Background:

  • Investigating the interplay between matter fields and quantum gravity in three dimensions is crucial for understanding fundamental physics.
  • Standard quantum field theories often face challenges when incorporating gravitational effects.

Purpose of the Study:

  • To describe the effective dynamics of matter fields coupled to 3D quantum gravity.
  • To analyze the resulting theory after integrating over gravitational degrees of freedom.

Main Methods:

  • Integration over gravitational degrees of freedom in a 3D quantum gravity context.
  • Analysis of the resulting effective field theory.

Main Results:

  • The effective dynamics are described by a braided noncommutative quantum field theory.
  • The theory demonstrates symmetry under a kappa deformation of the Poincaré group.

Conclusions:

  • The study reveals a novel connection between quantum gravity and noncommutative field theory.
  • This framework offers new insights into the structure of spacetime and matter interactions at quantum scales.