Max Planck

 Max Planck and the Speed of Light

Causation and the Quantum

The speed of causality (c, the speed of light) may be closely linked to the quantum speed limit. The limitation of causation may be simply due to Planck. Planck’s distance and time.

The Planck length, usually denoted by lp, is approximately 1.6 × 10⁻³⁵ meters or, more reasonably stated, about 10^-20 times the diameter of a proton. In the system of units known as Planck units, Planck’s length is considered "natural" because it can be defined from three fundamental physical constants: the speed of light, c, Planck's constant, h, and the gravitational constant, G.

Because it is the only length obtainable from the constants G, h, and c, it is expected to play some role in a theory of quantum gravity and causality.

Note that h_b is used for 'h bar' as my math program did not have the correct symbol. h_b is h / 2 * pi.

G = 6.67430(15)×10^-11 m3*kg^–1⋅s^-2

h = 6.62607015 × 10^-34 Kg m² * s^-1

C = 2.99792458 × 10⁸ M s^-1

In some descriptions of quantum gravity, it is at this kind of distance at which the structure of spacetime becomes dominated by quantum effects, giving it a discrete or foamy structure.

There is another important thing to know about Planck’s length, it is related to the smallest wavelength (highest frequency) of light that can be generated as the energy density would generate a black hole and that the quantum and gravitational effects are at the same scale.

The Planck length therefore is expected to be the shortest measurable distance. Imagine an attempt to measure shorter distances, by the usual method of performing higher-energy collisions like they do at the Large Hadron Collider. Accelerating a particle to the energy would inevitably result in a miniature black hole which would swallow whatever it is that you are trying to measure.

Planck’s constant h is derived from h=E/f. Note that physicists usually use v instead of f for frequency but coming from the field of electronics I prefer f. E, of course, is for energy and h = 6.62607015 x 10^-34 Joule seconds. This simple equation came about when they discovered that the energy of photons was emitted in discrete packets and the energy of the photon was directly proportional to the frequency, the higher the frequency then the greater the energy.

But what’s this have to do with the quantum speed limit and causality? Well, everything, so I think. From the above equations we get...

c = l_p/t_p

The Planck values are all explained clearly in this video. The video explores the fundamental lower limits of space and time by considering what would happen if two electrons are squeezed closer and closer together. After discussing the ratio of electric and gravitational forces, Heisenberg's uncertainty principle is combined with Einstein's theory of special relativity to show that at very small distance scales the strength of gravity becomes comparable to the electrostatic force. It is shown that when the two electrons are squeezed to a distance equal to the Planck length, a black hole form, placing a fundamental lower limit on the distances that can be meaningfully probed. It is shown that the Planck length, mass and time can all be derived using dimensional analysis and by combining the fundamental constants of quantum mechanics, relativity and gravity.