Click here for Einstein's E = mc2 derivable from the Heisenberg brackets.

# Planck and Einstein

Max Planck and Albert are two giants in modern physics. We all know what we did for us. What do they have in common? By looking at two different events, they derived the formulas applicable to all.

• Einstein observed the energy-momentum relations are different for massive and massless particles. He then came up with a formula for the energy-momentum relation valid for all speed. This formula is known and Einstein's E = mc2.

• Max Planck saw two different radiation laws for low and high frequencies. He then derived the radiation law valid for all frequencies. In so doing, he came up with "Planck's" constant, which we routinely write as h. Without this constant, you cannot do quantum mechanics.

They were different from most of us. We are interested in how they were different from us. First of all, they used to look at the world differently. In order to tell the difference between them and us, physicists these days have developed the words "birds" and "frogs."

Frogs and Birds
 Frog Bird Frog
 Black body radiation Raleigh-Jeans Planck's formula Wien's law
 Energy Momentum E=p2/2m Einstein's E=(m2 + p2)1/2 E=p

Einstein did not consider internal space-time symmetries of particles when he formulated his special theory of relativity. Let us go back to Newton. He formulated his gravity law for point particles first. It then took him 20 years to work about the law for solid spheres with non-zero radii, such as the sun and earth.

It was not until 1939 when Eugene Wigner formulated his little groups dictating internal space-time symmetries in the quantum world. We can summarize his work in the following table.

 Massive/Slow between Massless/Fast
 Energy Momentum E=p2/2m Einstein's E=(m2 + p2)1/2 E=p
 Spin, Gauge, Helicity S3 S1 S2 Wigner's Little Group S3 Gauge Trans.

• Yes, Einstein is a big bird. On the other hand, did Einstein get his Nobel prize in 1921 his role as a bird. No. He was a frog when did his work on the photo-electric effect.

These days, we talk about air attacks and foot soldiers. We know how important those foot soldiers are. In either case, it is not appropriate to say Gell-Mann and Feynman are frogs. Yet, we can still ask the following question.

 Hillary Clinton in Russia (2009). Frogs and Birds look at the Washington Monument differently.
Hillary Clinton went to Kazan as a bird, and I went there as a frog.

Frogs and Birds. How do they look at the Washington Monument?

• copyright@2016 by Y. S. Kim, unless otherwise specified.