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String Theory

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Extra Dimensions

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Introduction to String Theory

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Strings in Curved Spacetime

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Introduction to Superconductors

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Superconductivity (Lectures 1 - 10)

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Supersymmetry (SUSY) and Grand Unified Theory (GUT)

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test

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The Standard Model

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Electroweak Unification (Glashow-Weinberg-Salam)

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Gauge Theories (Yang-Mills)

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Gravitational Force and the Planck Scale

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Introduction to the Standard Model

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Isospin, Hypercharge, Weak Isospin and Weak Hypercharge

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Quantum Flavordynamics and Quantum Chromodynamics

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Special Unitary Groups and the Standard Model - Part 1

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Special Unitary Groups and the Standard Model - Part 2

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Special Unitary Groups and the Standard Model - Part 3

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Standard Model Lagrangian

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The Higgs Mechanism

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The Nature of the Weak Interaction

Topology

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Units, Constants and Useful Formulas

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Last modified: January 26, 2018


Gravitational Time Dilation
--------------------------- 
Clocks which are far from massive bodies (or at higher gravitational 
potentials) run faster, and clocks close to massive bodies (or at lower 
gravitational potentials) run slower. This is because gravitational time 
dilation is manifested in accelerated frames of reference or, by virtue 
of the equivalence principle, in the gravitational field of massive 
objects.

The equivalence principle that states that all accelerated reference 
frames are physically equivalent to a gravitational field of the same 
strength. For example, a person standing on the surface of the Earth 
experiences exactly the same effect as a person standing in a space 
ship accelerating at 9.8 m/sec2 (that is, generating a force of 9.8 
N/kg, equal to the gravitational field strength of Earth at its surface). 
According to general relativity, inertial mass and gravitational mass 
are the same.

A common equation used to determine gravitational time dilation is 
derived from the Schwarzschild metric, which describes spacetime 
in the vicinity of a non-rotating massive spherically-symmetric object. 
The equation is:

T = T₀/√(1 - 2GM/Rc²)

Similarly the length contraction radial to the mass givem by:

L = L₀/√(1 - 2GM/Rc²)

where 

T is the time interval measured by a clock far away from the mass.
L is the length  interval measured far away from the mass.
L₀ is the proper length (length in the vicinity of the mass).
T₀ is the proper time (time in the vicinity of the mass).
G is the gravitational constant
M is the mass of object creating the gravitational field
R is the radial coordinate of the observer
c is the speed of light

Note 2GM/c² is the Schwarzchild radius of M