What does "Internal" mean to us?

There are many small particles in the world. However, many of them are not point particles. The hydrogen atom consists of one-electron circling around the proton with the non-zero radius called the Bohr radius.

The internal structure of this atom is well understood now. However, when this hydrogen atom moves, we still treat this as a point particle. We still do not know how the electron orbit appears to us when the atom moves.

In order to understand the word "internal," let us go to the solar system familiar to us all. We use Newton's gravity law (applicable to two point particles) to describe the orbit of the earth around the sun. Newton's law works well because the distance between the sun and earth is much greater than their radii.

However, the earth is not a point particle, and many interesting things happen on the surface of the earth. Let us consider the following case.

  1. Newton realized that the sun and earth are not point particles, but can be regarded as spheres with their non-zero radii. It took him 20 years to formulate the concept of the center of gravity. He had to formulate a new mathematical device known today as the integral calculus.

  2. The earth is rotatiing, and its radius is not small. Thus, the earth has its own angular momentum which does not depend on the gravitional force from the sun. This angular momentum is one of the internal dynamical vairables.

  3. Again, our earth is not a small sphere. Let us assume for simplicity that the density of the earth is uniform. If we dig the well vertically until it reaches the opposite side of the earth, and we drop a small ball to this well, it will go down until it reaches the opposite side of the earth. It will then come back to you and goes down, according to the same gravity law of Newton. Not many people know this aspect of Newton's gravity law.

Let us go back to Einstein's world. The electron motion of the hydrogen atom is well understood when it is at rest on your desk. How would it appear to you when it moves with a speed comparable to that of light?

  1. Indeed, one hundred years ago, Niels Bohr was worrying about the electron orbit of the hydrogen atom, while Albert Einstein was interested in how things appear to moving observers. The question then is how the hydrogen atom appears to a moving observer.

Bohr and Einstein were friendly to each other and they met occasionally to discuss physics. Did they ever talk about moving hydrogen atoms?

  1. If they did, there are no written records to indicate they ever talk about this issue. If they did not, they are excused.

    Physics is an experimental science. There were and still are no observable hydrogen atoms moving with speeds comparable to that of light. If they are not observable, they are beyond the subject of physics.

  2. This hydrogen problem is the issue of moving quantum bound states in Einstein's world. There are these days many moving bound states. They are the protons in the quark model, and they can be accelerated.

  3. The proton, when it moves with a speed close to that of light, appears like a collection of partons whose properties are quite different from those of the quark. Thus, the the resolution of the quark-parton provides the issue of the Bohr-Einstein issue of the hydrogen atom.