Planck Units - Planck Units Simplify Key Equations

Planck Units Simplify Key Equations

Physical quantities that have different dimensions (such as time and length) cannot be equated even if they are numerically equal (1 second is not the same as 1 metre). In theoretical physics, however, this scruple can be set aside, by a process called nondimensionalization. Table 4 shows how Planck units, by setting the numerical values of five fundamental constants to the number one, nondimensionalizes and simplifies many fundamental equations of physics.

Table 4: How Planck units simplify the key equations of physics
Usual form Nondimensionalized form
Newton's law of universal gravitation
Einstein field equations in general relativity
Mass–energy equivalence in special relativity
Energy–momentum relation
Thermal energy per particle per degree of freedom
Boltzmann's entropy formula
Planck's relation for energy and angular frequency
Planck's law (surface intensity per unit solid angle per unit angular frequency) for black body at temperature T.
Stefan–Boltzmann constant σ defined
Bekenstein–Hawking black hole entropy
Schrödinger's equation - \frac{\hbar^2}{2m} \nabla^2 \psi(\mathbf{r}, t) + V(\mathbf{r}) \psi(\mathbf{r}, t) = i \hbar \dot{\psi}(\mathbf{r}, t) - \frac{1}{2m} \nabla^2 \psi(\mathbf{r}, t) + V(\mathbf{r}) \psi(\mathbf{r}, t) = i \dot{\psi}(\mathbf{r}, t)
Hamiltonian form of Schrödinger's equation
Covariant form of the Dirac equation
Coulomb's law
Maxwell's equations





Read more about this topic:  Planck Units

Famous quotes containing the words units, simplify and/or key:

    “Even in harmonious families there is this double life: the group life, which is the one we can observe in our neighbour’s household, and, underneath, another—secret and passionate and intense—which is the real life that stamps the faces and gives character to the voices of our friends. Always in his mind each member of these social units is escaping, running away, trying to break the net which circumstances and his own affections have woven about him.”
    —Willa Cather (1873–1947)

    “We have grown literally afraid to be poor. We despise anyone who elects to be poor in order to simplify and save his inner life. If he does not join the general scramble and pant with the money-making street, we deem him spiritless and lacking in ambition.”
    —William James (1842–1910)

    “Woe unto you, lawyers! for ye have taken away the key of knowledge: ye entered not in yourselves, and them that were entering in ye hindered.”
    —Bible: New Testament Jesus, in Luke, 11:52.