Physics and the Dragon’s Tail

I’m a fan and a subscriber to PBS Space Time. Their formula for the presentation and delivery of information often leads me to huge insights. The video below is about Planck’s constant, Planck’s law, Rayleigh-Jeans law, and the Ultraviolet Catastrophe. I’ve read about these many times, but the insight really clicked when watching this video. This realization has enormously important implications for physics mathematics and physics experimentation.

At 5:00 Matt is talking about Rayleigh-Jeans and the ultraviolet catastrophe. So here is a case where that long tail from the Planck scale to zero or Planck scale to infinity, depending on the metric and the integration becomes a problem. Examine this plot of the function 1/r. That long tail as r approaches infinity, or as r approaches 0 is what I am referring to as the Dragon’s Tail. Note however, there are really no zeros or infinities on this function. It’s just 1/r. Note that 1/r is also the basis for scalar electric potential emitted by point charges.

The function 1/r for 0.1 <= r < 10.

In general relativity the dimensions in spacetime can go to zero and result in a singularity, a point of infinite density. Has it not occurred to scientists to apply the same technique that was employed to solve the ultraviolet catastrophe? If not, why not?

Luis Mujsant

Here are a few of the dragon’s tail issues in GR, QM, and ΛCDM.

  • Ultraviolet catastrophe of Rayleigh-jeans
  • SMBH singularities and wormhole nonsense
  • Ultraviolet divergence of QED
  • Infrared divergence

Ultraviolet Catastrophe of Rayleigh-Jeans

The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium will emit radiation in all frequency ranges, emitting more energy as the frequency increases. By calculating the total amount of radiated energy (i.e., the sum of emissions in all frequency ranges), it can be shown that a blackbody is likely to release an arbitrarily high amount of energy. This would cause all matter to instantaneously radiate all of its energy until it is near absolute zero – indicating that a new model for the behaviour of blackbodies was needed.
The term “ultraviolet catastrophe” was first used in 1911 by Paul Ehrenfest. The phrase refers to the fact that the Rayleigh–Jeans law accurately predicts experimental results at radiative frequencies below 105 GHz, but begins to diverge with empirical observations as these frequencies reach the ultraviolet region of the electromagnetic spectrum. Since the first appearance of the term, it has also been used for other predictions of a similar nature, as in quantum electrodynamics and such cases as ultraviolet divergence.


Ultraviolet Divergence of Quantum Electro Dynamics

In physics, an ultraviolet divergence or UV divergence is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with unbounded energy, or, equivalently, because of physical phenomena at infinitesimal distances.

Since an infinite result is unphysical, ultraviolet divergences often require special treatment to remove unphysical effects inherent in the perturbative formalisms. In particular, UV divergences can often be removed by regularization and renormalization. Successful resolution of an ultraviolet divergence is known as ultraviolet completion. If they cannot be removed, they imply that the theory is not perturbatively well-defined at very short distances.

The name comes from the earliest example of such a divergence, the “ultraviolet catastrophe” first encountered in understanding blackbody radiation. According to classical physics at the end of the nineteenth century, the quantity of radiation in the form of light released at any specific wavelength should increase with decreasing wavelength—in particular, there should be considerably more ultraviolet light released from a blackbody radiator than infrared light. Measurements showed the opposite, with maximal energy released at intermediate wavelengths, suggesting a failure of classical mechanics. This problem eventually led to the development of quantum mechanics.

The successful resolution of the original ultraviolet catastrophe has prompted the pursuit of solutions to other problems of ultraviolet divergence. A similar problem in electromagnetism was solved by Richard Feynman by applying quantum field theory through the use of renormalization groups, leading to the successful creation of quantum electrodynamics (QED). Similar techniques led to the standard model of particle physics. Ultraviolet divergences remain a key feature in the exploration of new physical theories, like supersymmetry.


Infrared Divergence

In physics, an infrared divergence (also IR divergence or infrared catastrophe) is a situation in which an integral, for example a Feynman diagram, diverges because of contributions of objects with very small energy approaching zero, or, equivalently, because of physical phenomena at very long distances.

The infrared divergence only appears in theories with massless particles (such as photons). They represent a legitimate effect that a complete theory often implies. In the case of photons, the energy is given by E=hν, where ν is the frequency associated to the particle and as it goes to zero, like in the case of soft photons, there will be an infinite number of particles in order to have a finite amount of energy. One way to deal with it is to impose an infrared cutoff and take the limit as the cutoff approaches zero and/or refine the question. Another way is to assign the massless particle a fictitious mass, and then take the limit as the fictitious mass vanishes.


Spacetime aether is composed of low apparent energy Noether cores and the assemblies they form. A source, perhaps the dominant source, of low energy Noether cores is ultimately redshifted photons and neutrinos. When a reaction occurs in standard matter, energy transfers to the Noether cores in the aether and they reconfigure and take off like a rocket at the speed of light.


We’ve explored the topic of the dragon’s tail from the 1/r electric potential as r approaches 0 or as r approaches infinity. The dragon’s tail has presented major issues for understanding of nature, due to the mathematical models of physics blowing up with infinities. We have the ultraviolet catastrophe of Rayleigh-Jeans. We have the ultraviolet divergence of quantum electrodynamics. We have Einstein’s singularity in GR. Thankfully, we can rebase science on the geometry of point charges and achieve physically implemented solutions that avoid the dragon and its tail.

J Mark Morris : San Diego : California