The Planck Length is a mysterious constant in modern physics which is often credited as being the smallest allow length in nature or a sort of resolution of the Universe. In reality, this length is derived from considering a particle who’s reduced Compton wavelength is comparable to its Schwarzschild radius; the first being an idea from Quantum Mechanics and the other a concept from General Relativity. We will see from this definition that the Planck Length is a scale where both QM and GR effects are important – the scale at which Quantum Gravity dominates! This can be seen in the formula for the Planck Length which includes Planck’s Constant, Newton’s Gravitational Constant and the constant Speed of Light in a Vacuum.

Theories such as M-Theory and Loop Quantum Gravity attempt to explain such regimes, but at present neither are confirmed. This does not prevent us from using other physics to gain insight at to what could be happening at the Planck Length. It is likely that it is the smallest radius a black hole can have and the scale at which every fundamental force of nature becomes unified. We have already shown how the Electromagnetic and Weak Nuclear Force become unified into an Electroweak force, and Grand Unified Theories (GUTs) include the Strong Nuclear Force in another unification. When the Universe was less than 1 Planck Length in diameter, or less than 1 Planck Time old, it will have had such a high temperature that every fundamental force, including gravity, could have theoretically been unified. As it expanded and cooled, spontaneous symmetry breaking occurred, splitting the forces into the 4 we experience today – however a theory which models how a completely unified force behaves is needed to understand what happens on the Planck Scale.

This video discusses the real meaning and derivation of the Planck Length and Planck Scale and discusses what might modern physics believes happen at and beyond those scales using insight from Particle Physics and General Relativity.

0:00 - Planck Length as a Universal Resolution?
0:34 - Deriving the Planck Length; The Physical Insight
1:07 - Quantum Mechanical Part: Compton Wavelength
2:33 - General Relativistic Part: Schwarzschild Radius and Gravity
3:26 - The Planck Length: A New Regime?
4:02 - Quantum Gravity and Black Hole Considerations
4:44 - Fundamental Force Unification and Symmetry Breaking
5:41 - Early Universe and the Planck Epoch
6:31 - Do Not Think Classically or Quantum Mechanically at this scale