- One hundred years ago, Bohr and Einstein met
occasionally to discuss physics.
- Bohr was interested in the electron orbit of the hydrogen atom, and was wondering why
the hydrogen energy levels are discrete.
- Einstein was worrying about how things look to moving observers.
They then must have talked about how the hydrogen appears to a moving observer. The electron orbit later became a standing wave producing a discrete energy spectrum. Then, how the standing wave appears to moving observers. Did Bohr and Einstein discuss the issue of how this standing wave looks to a moving observer. If they did, there are no records on this.
If they did not, they can be excused. The hydrogen atom moving with a relativistic speed was unthinkable at that time. Even these days, there are no hydrogen atoms fast enough to be relativistic.
Y. S. Kim, Phys. Rev. Lett. 63 , 348 (1989).
- Bohr was interested in the electron orbit of the hydrogen atom, and was wondering why the hydrogen energy levels are discrete.
- However things are different these days. There are protons moving with
a speed close to that of light. Like the hydrogen atom, the proton is a
bound state of more fundamental particles called the "quarks." Thus, it is
a standing wave like the hydrogen atom. Unlike the hydrogen atom, it is a
charged particle that can be accelerated.
Click here to see how it is possible to
study the proton in order to study the moving hydrogen atom.
- In 1964, Gell-Mann observed that the proton is a quantum bound state
three quarks, when it is on the table.
- In 1969, Feynman observed that the same proton appears as a collection partons whose properties appear quite different from those of the quarks.
- In 1964, Gell-Mann observed that the proton is a quantum bound state three quarks, when it is on the table.
- The question then is the quark model and the parton model are two
limiting cases of one Lorentz-covariant quantity. In order to answer this
question, we have to construct a wave function that can be Lorentz-boosted.
Many years before the quarks and partons, Paul A. M. Dirac and Hideki Yukawa worried about bound-state wave functions that can be Lorentz boosted. They used the harmonic oscillator wave functions to study this problem. The harmonic oscillator and the bound-state hydrogen atom have different energy levels, but share the same quantum mechanics. Furthermore, the oscillator wave functions are frequently used for the quark model.
- Indeed, it is possible to construct the Lorentz-covariant harmonic
oscillator and its wave functions. It is then possible to use diagrams
to illustrate their transformation properties. You are invited to the
this webpage for the details of
how one covariant wave function can explain both the quark model and
the parton model.
Wigner's Little GroupsIn 1939, Eugene Wigner published a paper dealing with the internal space-time symmetries. This apprach allows to study the above-mentioned Lorentz-covariant wave functions more systematically. In addition, the covariance of the little groups lead to the following interesting conclusions.
Gauge Transformations: A particle at rest has three
rotational degrees of freedom. A massless particle has one
helicity degree of freedom and gauge degrees of freedom. The
question then is whether they are two different manifestations
of one covariant entity, as Einstein's energy-momentum relation
gives two different relations for massive and massless particles.
- Neutrino polarization
as a consequence of Gauge Invariance.
- Lorentz Group: All I said on this webpage are based on
symmetry of the Lorentz group. I made a very heavy investment in
this subject. You may
click here for my latest book on all these items.
- The mathematical tools developed for my high-energy physics is
directly applicable to optical sciences.
Click here for my latest book on this subject.