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Quantum Field Theory

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Energy and Momentum, E = mc²

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Entropy and the Partition Function

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String Theory

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Extra Dimensions

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Introduction to String Theory

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Kaluza-Klein Compactification of Closed Strings

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Strings in Curved Spacetime

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Superconductivity

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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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Chiral Superfields

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Generators of a Supergroup

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Introduction to Supersymmetry

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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 Force and the Planck Scale
----------------------------------------

From Newton, F_G = Gm²/r²

Frpm Special Relativity, m = E/c²

From Quantum Mechanics,E = pc

Therefore,

m = p/c

From the Uncertainty Principle, ΔxΔp = h => p = h/r

Therefore,

m = h/rc

The gravitational force becomes:

F_G = Gh²/r⁴c²

The Coulomb force between 2 identical charges, F = ke²/r²

We can write this in terms of the dimensionless Fine 
structure constant, α = e²/hc as follows:

F_C = hcα/r²

Equating F_G = Equating F_C gives:

r = √(Gh/c³α)

  = √(Gh/c³)√(1/α)

  ~ 10l_P

The gravitational force is very small compared to the other
forces.  However, at distances approaching the Planck length
the gravitational and Coulomb forces become comparable. 

At these scales, there is a 'new physics' where quantum
gravity becomes important (indicated by the Planck mass
(energy) ~ 1.22 x 10¹⁹ GeV).