100 year ago

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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.

On the other hand, while the hydrogen atom is a quantum bound state, the proton became a bound state in world of Gell-Mann's quark model. Thus, the proton can also play the role of quantum bound state. Unlike the hydrogen atom, the proton can be accelerated and its speed can become very close to that of light, as illustrated in this figure:

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 one of the following specific isssues.
1. Further Contents of E = mc²
2. Covariant Model
3. Lorentz Boost
4. Feynman's Decoherence
5. Infinite Number of Partons
6. Boiling Quarks and Phase Transition
7. Quantum Mechanics of Moving Bound States published in J. Modern Physics [13] 138-165 (2022).

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 = cp

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

• Click here for further contents of Einstein's E = mc².
  

• 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.
  

• Its boundary condition can be stated in terms of the spatial coordinates in a given Lorentz frame. Then how about other frames where the spatial and time-like coordinates are mixed? In order to deal with this problem, we need the time-separation variable. Does this variable exist? We are quite familiar with the Bohr radius. It measures the spatial separation between the constituent particles. Then, is there a time-like separation? According to Einstein, the answer is YES. This is the starting point of our plan to construct a harmonic oscillator wave function which can be Lorentz transformed.

• Let us tackle this problem with the following three figures. The first figure is a space-time diagram of the harmonic oscillator wave function. The second figure describes Lorentz boosts in the light-cone coordinate system. The third figure combines quantum mechanics with special relativity by combining the first two figures.

  Dirac 1927 (top) and Dirac (1949)

  Synthesis of the above two figures.

  1. The present form of quantum mechanics. Let us consider a hadron consisting of two quarks bound together by a harmonic oscillator potential. Then, Heisenberg's uncertainty principle applies to position-momentum coordinates, and there are excited states along the space-like directions. As for the time-like (time-separation between the quarks), there are no excitations, but there still exist a time-energy uncertainty without excitation. According to Dirac, it is a c-number time-energy uncertainty relation.

  2. Special relativity. Lorentz boost in the light-cone coordinate system. We are quite familiar with the condition
     (z² - t²) = constant

     in special relativity. This equation gives the hyperbola in the graph. The above equation can also be written

     (z + t)(z - t) = constant.

     The Lorentz boost along the z direction expands (z + t) and contracts (z - t) while keeping the above product constant. This is called Dirac's light-cone coordinate system. The Lorentz boost is now a "squeeze" transformation.

  3. It is then easy to combine quantum mechanics and special relativity. We can now Lorentz-boost quantum mechanics given in the first figure. We can simply squeeze the circle given in the first figure according to the transformation law of special relativity given in the second figure.

• Einstein and Feynman. Dirac talks about them.