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Related Concept Videos

Principle of Equivalence01:18

Principle of Equivalence

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...
Scalar Notation01:28

Scalar Notation

Scalar notation is a useful method for simplifying calculations involving vectors. When vectors are added or subtracted, their components can be added or subtracted separately using scalar notation. For instance, force, a vector quantity, can be broken down into its x and y components, called rectangular components, and then the magnitude and direction of these components can be determined using trigonometric functions.
Consider a man pulling a rope from a hook in the northeast direction. The...
Equivalent Couples01:28

Equivalent Couples

In mechanical engineering, the concept of equivalent couples plays a crucial role in understanding and analyzing various mechanical systems.
Two couples are considered to be equivalent if they produce the same rotational effect on a rigid body. In other words, the two couples have the same magnitude and act in the same direction, causing the same angular displacement or acceleration in the body.
For instance, consider two couples lying in the plane of the page, with one having a pair of equal...
Couples: Scalar and Vector Formulation01:21

Couples: Scalar and Vector Formulation

One might wonder how the captain of a large ship can navigate through the ocean with just a turn of the steering wheel. The answer lies in the concept of two parallel forces that are equal in magnitude and opposite sense, creating a couple moment.
A couple moment is a rotational force that tends to rotate the steering wheel. The wheel's rotation can either be in a clockwise or anticlockwise direction. The right-hand rule is a helpful method for determining the direction of a couple moment. To...
Equations of Equilibrium in Three Dimensions01:30

Equations of Equilibrium in Three Dimensions

When analyzing structures or systems at rest, it is necessary to ensure they are in equilibrium. This is where the vector and scalar equations of equilibrium come into play. These equations are crucial in ensuring a structure is stable and will not collapse or fall apart. The vector and scalar equations of equilibrium provide a framework for analyzing the forces acting on a body.
According to the vector equations of equilibrium, the vector sum of all the external forces acting on a body must...
Scalar and Vectors01:22

Scalar and Vectors

In mechanics, commonly used terms like force, speed, velocity, and work can be classified as either scalar or vector quantities. A scalar is a physical quantity that can be described by its magnitude alone and does not require any directional components. Examples of scalar quantities are mass, area, and length.
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A Millimeter Scale Flexural Testing System for Measuring the Mechanical Properties of Marine Sponge Spicules
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Published on: October 11, 2017

Equivalence principle for scalar forces.

Lam Hui1, Alberto Nicolis

  • 1Physics Department and Institute for Strings, Cosmology, and Astroparticle Physics, Columbia University, New York, New York 10027, USA. lhui@astro.columbia.edu

Physical Review Letters
|January 15, 2011
PubMed
Summary
This summary is machine-generated.

The scalar equivalence principle, crucial for general relativity, is clarified. It holds unless graviton or scalar self-interactions are significant, impacting objects like black holes.

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Area of Science:

  • Theoretical Physics
  • Cosmology
  • Gravitational Physics

Background:

  • The equivalence principle, linking inertial and gravitational mass, is fundamental to Einstein's general relativity.
  • Recent theories propose modifications to gravity at cosmological scales, often involving scalar fields.

Purpose of the Study:

  • To investigate the validity of the equivalence principle in the presence of a universally coupled scalar field.
  • To determine the conditions under which the scalar equivalence principle may be violated.

Main Methods:

  • Analysis of classical and quantum renormalizations in a scalar-tensor theory of gravity.
  • Examination of self-interaction effects for gravitons and scalar fields.

Main Results:

  • A universal scalar-matter coupling, once postulated, is stable against renormalization in the matter sector.
  • The scalar equivalence principle is violated for objects with significant graviton self-interaction (e.g., black holes) or scalar self-interaction.
  • Galilean symmetry of the scalar field prevents violations due to scalar self-interaction.

Conclusions:

  • The equivalence principle remains robust under scalar-tensor theories, with specific exceptions.
  • Violations are linked to extreme self-interaction regimes, offering potential observational or theoretical constraints.