The Trauma of Paradoxes of Modern Physics

• How wonderful that we have met with a paradox. Now we have some hope of making progress. (Niels Bohr)

Science appears to be filled with paradoxes, which it itself is a paradox, because true science should be free of paradox. For a true scientist a scientific paradox is thus something unbearable, which requires immediate action, because one paradox is enough to kill a whole theory.

There are logical paradoxes as contradiction between words and there are physical paradoxes as contradictions between theory and observation.

One logical paradox is enough to kill a mathematical theory. Thus Russell's paradox killed set theory as the foundation of mathematics in the early 20th century.

Zeno's paradox (still unresolved) of the arrow which is moving although it is not moving at every instant, triggered the development of Calculus, but with a delay of 2000 years!

One physical paradox is enough to kill a physical theory as a mathematical theory about phenomena of physics, all according to the famous physicist Feynman:

• It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong.

If theory does not at all fit with reality, then something is fundamentally wrong with the theory, not the other way around.

A paradox may be thus devastating to existing theory, while leading to new better theory by focussing on weak points.

Yet, the list of physical paradoxes has remained through the development of modern physics and in fact have multiplied since modern physics is loaded with many more paradoxes than classical rational physics, as if modern physics is irrational. Thus the pillars of modern physics in the form of relativity theory and quantum mechanics are both filled with paradoxes, which have remained unresolved for 100 years. This has formed the deep trauma of modern physics with no escape from ever more paradoxes.

Niels Bohr was a master of handling the many paradoxes of quantum mechanics lifting sophistry to a new level with his "complementarity principle" addressing the wave-particle contradiction with murky statements like:

• The opposite of a correct statement is a false statement. But the opposite of a profound truth may well be another profound truth.

While classical physicists had to come to grips with paradoxes, in one way or the other, modern physicists appear to welcome paradoxes as a sign of deep magical physics as opposed to shallow understandable classical physics.

The first defence line for a classical physicist is to simply deny the existence of a paradox formulated by some renegades. The next is to accept that there is indeed a paradox and then come up with an ad hoc explanation for the contradiction between theory and reality, showing that the contradiction is in fact only apparent, but not really real. If the ad hoc explanation is refuted, a new ad hoc explanation is presented and so on.

For a modern physicist, a paradox thus poses no real problem, but of course it is some kind of nuisance and so occasionally may get some attention. Like the Twin Paradox of special relativity discussed in earlier posts, unresolved since 100 years.

The prime paradox of fluid mechanics is d'Alembert's paradox comparing the prediction of zero resistance to motion through a fluid from potential flow solutions to Euler's equations of slightly viscous flow like air and water, with the observation of heavy resistance increasing quadratically with velocity.

The paradox was formulated by d'Alembert in 1755 but nobody was able to come up with a resolution until the young German fluid mechanician Ludwig Prandtl in 1904 came up with the ad hoc solution to discriminate the zero drag potential solution of Euler's equations because potential flow does not satisfy a no-slip boundary condition coming with a thin boundary layer. With the potential solution thus eliminated form the discussion, the paradox simply disappeared. But the act of discrimination of solutions of the Euler equations of course was not so glorious. Discrimination of prefect exact solutions on formal grounds carries the same weakness as discrimination of good citizens on purely formal grounds.

In 2008 we gave a different resolution of d'Alembert's paradox than Prandtl's, based on the fact that potential solutions of the Euler equations are unstable and thus turn into turbulent solutions with substantial pressure drag. This was not discrimination on formal grounds, but on real grounds; an unstable solution does not persist over time. This opened to a revolution in computational fluid dynamics freed from a perceived necessity to computationally resolve unresolvable thin boundary layers.

You find on this web site, if you are interested and make a search, resolutions of the following paradoxes:

• D'Alembert's paradox and other paradoxes of fluid mechanics.
• The Reversibility paradox of classical and quantum mechanics (Loschmidt's paradox) 
• Paradoxes of special relativity including the Twin paradox.
• Paradoxes of wave-particle and collapse of the wave function of quantum mechanics.

Yes, it is wonderful to discover a paradox and even more wonderful to resolve it!

Physics Illusion 4: Elementary Particles, Quanta and Wave-Particle Duality

• Sound is a wave phenomenon as local variation of a pressure field in air. Sound is not a corpuscular flow of sound particles named phonons flying from source to ear.
• Light is a wave phenomenon as local variation of an electromagnetic field in a vacuum. Light is not a corpuscular flow of light particles named  photons flying from source to eye.

Modern physics dominated by elementary particle physics based on the Standard Model is based the idea of particles as pointlike (or stringlike) carriers of charge and mass (fermions) and forces (bosons).
The Standard Model today consists of a wild  zoo of 61 particles and physicists have since 50 years desperately been seeking alternative models with particles replaced by one-dimensional strings or two-dimensional branes, however without much success.

A pointlike elementary particle is supposed to have a dual wave character as a distributed field in what is referred to as wave-particle duality with the idea that both characters can show up in different situations, like Dr Jekyll-Mr Hyde or schizofrenia syndrom.

The carrier of the electromagnetic force is an elementary particle named photon, by which the propagation of light is described as a stream of photon particles, much like the corpuscular theory of light proposed by Thomas Hobbes in 1643 and adopted by Newton. The corpuscular theory of light was replaced by Huygen's wave theory of light once Newton had faded away and reached a completion with Maxwell's equations (1862) describing virtually all of electromagnetics including light by set of wave equations for electric and magnetics fields, an unprecedented triumph of mathematical physics.

With the formidable success of Maxwell's equations describing light as wave, one would imagine that any corpuscular theory of light could safely be put into the dustbin of scientific garbage, but then Einstein entered the game in 1905, stimulated by the energy quanta suggested by Planck in 1900 to avoid the ultraviolet catastrophe of blackbody radiation, with an idea of light quanta as a corpuscular particle theory of light picked up from the dustbin in an attempt to "heuristically" explain the photoelectric effect.

Einstein's particle idea then combined with the new atom physics in the form of quantum mechanics based on Schrödinger's wave equation, connected by a trick of wave-particle duality invented by Bohr.

Since schizofrenia is a serious syndrome, one may ask what makes modern physicists cling to a  primitive particle theory of light as a stream of photons, when there is an educated wave theory in the form of Maxwell's equations?

Why not get rid of the primitivism of a corpuscular theory of light once and for all? Or is a corpuscular theory of light only a harmless heuristic way of thinking, which we can use if we want to explain things to kids?

No, it is not harmless and in fact the opposite because it creates artificial mysteries draining human and material resources with questions without answers like:

• What is a photon particle?
• How do photon particles travel? 
• What is the speed of a photon particle?
• How do photon particles interact with matter?

To understand how silly these questions occupying physicists minds, let us compare light with sound:

• We know that sound is a wave phenomenon of pressure variations supported by vibrating air molecules. 
• We know that sound is not a stream of sound particles as phonons from source to ear. 
• We know that transfer of sound from source to eardrum is a resonance phenomenon between two resonators (vibrating membrane of loud speaker and eardrum) connected by a medium (air) supporting pressure variations transferring forces from membrane to eardrum.

The analog for light is developed as Computational Blackbody Radiation explaining that blackbody radiation is a resonance phenomenon of electromagnetic waves with a high-frequency cut-off avoiding the ultra-violet catastrophe by finite precision computation. 

In short, there is as little reason to speak about photons as light particles as there is to speak about phonons as sound particles. 

It is true that a simple mathematical model of sound propagation can be formulated as a particle model with sound particles moving along straight lines combined with simple reflection laws:

But this is only a simple mathematics model and does not describe the real physics of propagation of sound as a wave phenomenon. Neither does a particle model for light have anything to do with the real physics of light as wave.

The term elementary particle is thus misleading and should better be replaced by something like elementary wave. Hopefully the zoo of elementary particles can then be reduced to a smaller number of elementary waves. This the basic idea of string theory, which however is set to the excessively small size of Planck's quanta $\sim 10^{-34}$ beyond any physics rationale.

Quantum mechanics is a wave theory for atomic dimensions in which particles serve no purpose.

Science Collapse from Wave-Particle Duality

Physics books generally propagate a concept of wave-particle duality expressing that matter and light on atomic scales can exhibit both wave and particle properties. In particular, the old wave-particle controversy on the nature of light going back to Huygens-Newton, which was revived with the introduction of quantum mechanics, is presented as a Solomonic compromise that light is both particle and wave.

Newton's particle theory of light was replaced by a wave theory expressed by Maxwell's equations in the late 19th century, but particles were reintroduced in the early 20th century by Planck to explain blackbody radiation and by Einstein to explain the photoelectric effect. Light was here seen as a stream of light particles later named photons.

Wave-particle duality was then in the hands of Bohr and his Copenhagen interpretation described as wave-function collapse expressing that Schrödinger's distributed continuous wave function "collapsed" into a singular point/delta function upon observation.

But to be both particle and wave is a logical contradiction like being both square and circular at the same time, and logical contradictions in science are catastrophic. From a contradiction anything can follow and the crisis of physics of today can be seen as a result of this contradiction. The fiction of "wave-function collapse" of Bohr designed to handle the contradiction prepared for the real collapse of physics of today. Wave-particle duality is double-speak and double-speak in science is catastrophical.

Is there then any way of avoiding the collapse? Is it possible to throw out particles once and for all and be happy with only waves in a consistent wave theory? A number of physicists say yes, see Are There Any Photons at All? and Collective Electrodynamics by Carver Mead. It is further possible to describe both blackbody radiation and the photoelectric effect using wave theory.

The evidence for waves is massive while the evidence for particles is almost nil. In particular, wave theory has a mathematical expression in the form of Maxwell's equations and Schrödinger's wave equation as compact general descriptions of electro-magnetics and quantum mechanics. Particle theory has a trivial mathematical expression as straight lines traced by rays of photons. Particle theory is bogged down by infinities from singularities of

point/delta functions.

A physical theory with a non-trivial mathematical expression is very useful. This is wave theory.

A physical theory with a trivial mathematical dress is not useful. This is particle theory.

Recall the late Einstein did not believe in the light quanta or photons he had happened to let in to the inner room of science, as he confessed shortly before his death (1954):

• All these fifty years of conscious brooding have brought me no nearer to the answer to the question, 'What are light quanta?' Nowadays every Tom, Dick and Harry thinks he knows it, but he is mistaken.

Particle theory is behind the idea of DLR/backradition playing a key role in CO2 climate alarmism expressing a collapse of climate science.

What do physicists of today say about the collapse from wave-particle duality? Nothing it seems. Because physics has collapsed?