# 100 year ago These photos are from the public domain.

There are no hydrogen atoms moving with relativistic speeds. Thus, this bohr-Einstein issue is only a metaphysical problem.

After 1950, high-energy accelerators produced protons moving with speed close to that of light, but the proton is not a hydogen atom.

# Feynman's Parton Picture

In 1964, Murray Gell-Mann invented the quark model in which hadrons are quantum bound states (like the hydrogen atom) of more fundamental particles called "quarks."

Five years later, in 1969, Richard Feynman observed that a hadron, when it moves with a speed close to that of light, appears as a collection of infinite number of partons with a wide-spread momentum distribution. Partons interact incoherently with external signals.

It is only natural to regard the parton picture as a Lorentz-boosted quark model. However, since the partons are so different from the quarks, we have been wondering whether they are really Lorentz-boosted quarks.

### Thus, the Bohr-Einstein issue on the hydrogen problem becomes this quark-parton puzzle.

This file is very long. You may be interested in jumping to on of the following specific isssues.

## Further Contents of Einstein's Energy-momentum Relation

Einstein's World  Massive/Slow between Massless/Fast
 Energy Momentum E=p2/2m Einstein's E=(m2 + p2)1/2 E=p
 Helicity Spin & Gauge S3 S1 S2 Wigner's Little Group Helicity Gauge Trans.
 Hadrons, Bound States Gell-Mann's Quark Model One Lorentz- Covariant Entity Feynman's Parton Picture

• According to Feynman, the adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing.

If this is the case, we are doing the same physics whether we do the quark model or do the parton model. Indeed, ever since Feynman presented his parton model in 1969, one of the most pressing problems in high-energy physics has been whether it is possible to formulate a covariant theory which will produce the quark model for slow hadrons and the parton model for fast hadrons, within the framework of the existing rules of quantum mechanics and special relativity.

In this photo, one Feynman admirer is standing in front of Feynman's preterit at the entrance of the Feynman Computing Center at Fermi National Accelerator Center, Batavia, Illinois (June 2003). He has been doing Feynman's physics since 1970.

• According to Ne'eman, Feynman diagrams and the parton model are the two greatest contributions Feynman made. Feynman diagrams are well known and well understood, but his parton model is yet to be understood. Why is it so difficult to understand the parton model? It contains too much physics, including some of the current issues such as decoherence, as well as future issues.

## How can we construct a covariant model for quarks and partons?

Let us start with a hadron consisting of two quarks bound together by a harmonic oscillator potential. The simplest wave function for this two-particle system is is the harmonic oscillator wave function. Can this wave function be Lorentz-boosted?

## Can you boost a quark-model wave function to get a parton distribution?

This figure explains how a Lorentz-squeezed hadron become a collection of partons.

1. As the hadron moves fast, the quark distribution becomes concentrated along one of the light-cone axes. The amplitude of the oscillation becomes larger, indicating that the spring constant appears to become weaker. The particles become free!

2. The momentum distribution becomes also widespread. This is what we see in the world through Feynman's parton model.

3. The number of partons is infinite because free particles have continuous momentum distribution as in the case of black-body radiation.

4. The major axis of the ellipse measures the period of oscillation. As Feynman observed, the interaction time between the quarks is dilated.

We are of course interested to know whether the parton distribution calculated from the covariant oscillator formalism is in agreement with the distribution observed in the real world. This graph will indicate that the answer is YES.

## Boiling Quarks

In his 1972 book on statistical mechanics, said

When we solve a quantum-mechanical problem, what we really do is divide the universe into two parts - the system in which we are interested and the rest of the universe. We then usually act as if the system in which we are interested comprised the entire universe. To motivate the use of density matrices, let us see what happens when we include the part of the universe outside the system.

The Bohr radius is an important quantity in quantum mechanics. It is a space-like separation between two particles. However, if the system is boosted, the time-like separation becomes prominent. This problem goes back to Bohr and Einstein. They met often, but they never discussed this issue. Click here for a story.

Since there are no theoretical tools to deal with this problem, this variable is in the Feynman's rest of the universe.

On the other hand, von Neumann's approach to entropy tells us how to deal with the variable we do not measure. If they are not measured, they appear as an entropy increase. Let us look at this figure. Click here for detailed calculations. The entropy increase means an increase in temperature. This thus leads to the following figure the phase transition from the confined state to a plasma state.

Thus, we are led to the phase transition of the form

## My high-scholl background copyright@2019 by Y. S. Kim, unless otherwise specified.