Photons with Wavelengths of One Planck Length: Interaction with Atoms and the Role of Dark Matter

It is well-established in physics that photons with wavelengths of one Planck length would indeed interact with atoms. This fact is supported by the increasing cross section for pair production as the incident photon energy increases. Consequently, even highly energetic photons, such as those with wavelengths of one Planck length, can still have significant interactions.

Pair Production and Photon Energy

The process of pair production, which involves the creation of particle-antiparticle pairs from a highly energetic photon, increases as the photon's energy rises. This means that photons with wavelengths of one Planck length, which are extremely energetic, would still be capable of interacting with atoms through the process of pair production. A one Planck length photon would have an energy equivalent to about (1.224 times 10^{19}) GeV, which is dramatically higher than typical photon energies.

Ultra-High-Frequency Photons and Dark Matter

The interaction of such photons with normal matter raises an interesting question about the possibility of ultra-high-frequency photons as a form of dark matter. However, this proposition faces significant challenges.

Firstly, dark matter is known not to move at the speed of light. If it did, it would escape galaxies, which have escape velocities typically around 500 km/s, which is far below the speed of light. This fact rules out the idea of ultra-high-frequency photons being dark matter. Secondly, the annihilation of particles produced by pair production events would generate a significant amount of gamma rays, making it impossible for such matter to remain undetected if it existed.

In the words of Malcolm Fairbairn, dark matter would not be “dark” if it were composed of photons with such extreme energies. The observation of these gamma rays would allow us to detect the presence of such particles, thus negating the very nature of dark matter.

The Role of Planck Length Photons in the Universe

Photons with wavelengths of one Planck length would probably interact very strongly with normal matter and would not travel far in the universe. For example, a photon with an energy of (1 times 10^{19}) GeV would interact with low-energy photons from the cosmic microwave background (CMB), leading to the production of particle-antiparticle pairs such as top quarks. This process would cause the high-energy photon to lose significant energy very rapidly.

The Planck length, defined as (1.616 times 10^{-35}) meters, is an extremely small unit of length. While it is almost infinitely small, it does exist, and photons with wavelengths in this range would be unimaginably powerful and energetic. Their interactions with normal atoms would be minimal because photons with such small wavelengths would be incomparably massive compared to the Planck length. However, in the mysterious 'Other World' dominated by dark matter and dark energy, the effects of these photons with extremely small wavelengths could be observed. Since dark matter and energy do not react well with ordinary matter, such photons might provide unique insights into the properties of these elusive forms of matter.

Who knows, perhaps the high energy photons with Planck length wavelengths could be linked to the same reason as the enigmatic nature of dark matter and dark energy, providing further clues to the fundamental nature of the universe.