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Newton's Law of Gravitation01:15

Newton's Law of Gravitation

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Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward force was unique to Earth. By the 16th century, Nicolaus Copernicus (1473-1543) put forward the heliocentric theory, which suggested that Earth and other planets orbited the sun, while the Moon orbited the Earth. However, it was Isaac Newton (1642-1727) who linked these two motions together in the 17th century. He reasoned that the force of...
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Principle of Equivalence01:18

Principle of Equivalence

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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...
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Space-Time Curvature and the General Theory of Relativity01:17

Space-Time Curvature and the General Theory of Relativity

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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.
This has been verified in many experiments. However, space and time are no longer absolute. Two observers moving relative to one another do not agree on the length of objects or the passage of time. The mechanics of objects based on Newton's laws of...
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Newton's Law of Gravitational Attraction01:24

Newton's Law of Gravitational Attraction

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Sir Isaac Newton established the universality of the law of gravitational attraction based on empirical evidence and inductive reasoning. He published his work in Philosophiae Naturalis Principia Mathematica ("the Principia") on July 5, 1687.
Newton's law of gravitational attraction is a fundamental law of physics that governs the attraction between objects. It states that the magnitude of the gravitational force between any two objects is proportional to their masses and inversely...
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Measuring Acceleration Due to Gravity01:12

Measuring Acceleration Due to Gravity

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Consider a coffee mug hanging on a hook in a pantry. If the mug gets knocked, it oscillates back and forth like a pendulum until the oscillations die out.
A simple pendulum can be described as a point mass and a string. Meanwhile, a physical pendulum is any object whose oscillations are similar to a simple pendulum, but cannot be modeled as a point mass on a string because its mass is distributed over a larger area. The behavior of a physical pendulum can be modeled using the principles of...
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The Principle of Superposition and the Gravitational Field01:17

The Principle of Superposition and the Gravitational Field

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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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Updated: Apr 26, 2026

Setting Limits on Supersymmetry Using Simplified Models
07:46

Setting Limits on Supersymmetry Using Simplified Models

Published on: November 15, 2013

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Quantum gravity: are we there yet?

Shahn Majid1

  • 1School of Mathematical Sciences, Queen Mary University of London, London, UK.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences
|May 8, 2025
PubMed
Summary
This summary is machine-generated.

This study outlines quantum Riemannian geometry (QRG) for quantum gravity. New models of fuzzy spheres and polygons suggest features of quantum gravity, highlighting remaining challenges.

Keywords:
non-commutative geometryquantum gravityquantum groupsquantum spacetime

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Area of Science:

  • Theoretical Physics
  • Quantum Gravity
  • Non-commutative Geometry

Background:

  • Optimism at the millennium for quantum groups and non-commutative geometry to model quantum spacetime.
  • The challenge of developing a formalism for quantum gravity effects via non-commutative spacetime coordinates.

Purpose of the Study:

  • To outline the formalism of quantum Riemannian geometry (QRG).
  • To present new results for 'baby quantum gravity' models.
  • To discuss the implications and missing elements for a full quantum gravity solution.

Main Methods:

  • Development of a 20-year formalism for quantum Riemannian geometry (QRG).
  • Application of QRG to fuzzy sphere and [Formula: see text]-gon models.
  • Analysis of results to infer features of quantum gravity.

Main Results:

  • New results for fuzzy sphere and [Formula: see text]-gon 'baby quantum gravity' models.
  • Identification of potential features of quantum gravity suggested by these models.
  • Discussion of critical conceptual and mathematical gaps.

Conclusions:

  • Quantum Riemannian geometry provides a framework for quantum gravity.
  • Current models offer insights but are not a complete solution.
  • Further development is needed to fully achieve the goal of quantum gravity.