Whittaker and the Super-Potential

220px-Edmund_Taylor_WhittakerE.T. Whittaker – Mathematical Physicist (1873 – 1956)

“What these gentlemen call vacuum isn’t really
nothing but something which is not matter”
(Caroline Ansbach, letter to Leibniz)

Here is a minor fiction, which speaks to mathematical fashion. Once upon a time, in a far away galaxy, there were twin planets, carrying the twins Primo and Ultimo. On giving them some mathematical tools their differences in character become readily apparent.

Primo asserts:

“Oh, what nice tools! I will make the same as you only better!”

Ultimo counters:

“Oh, what nice tools! I will make something different and hope you like it!”

One wonders how deeply people think on their own sayings. Is there any time at all to think in the face of such enormous growth in the scientific literature and bibliographic material?

Do we read others just to differ or only to better?

The exponential growth of bibliography from the 19th century onward should make any sane civilization worry about how to handle the complexity of such a task.

In understanding some of the consequences of this, we consider the cognitive dissonance caused by any the concept of “a vacuum” and that of “nothingness”.

Most people find it difficult to conceive of anything with an existence of any kind between material objects without this “additional” existence being able to exert some kind of resistance or “friction” for that matter.

The famous Michelson-Morley experiment probed exactly that. Was there an Aether existing between substances that supported electromagnetic vibrations of a something?

Let’s look at this from a modern viewpoint. Consider space walks. Such an experience would appear to be one of the utmost freedom, without anything in the vacuum of space impeding us. But think again! How naive that would sound to any person trained in the fundamentals of General Relativity?

In fact, there is nothing really free at all in a situation of “Free Fall”!

I have never heard of any phrase with such an inherently self-contradictory attitude than the expression “Free Fall” as normally used in GR! Surely, no other state of motion is less “free” than the one constrained to move along a precisely tuned Geodesic!

The affront to our freedom lies in the Platonic domain, that line of thought of Einstein himself on the nature of Space-Time. What restricts the motion out there amidst all the nothingness of the world? It is the successor… to “Newtonian potentials”, GR being the
greatest “potential” theory ever made – matter tells space how to curve, space tells matter how to move. The two are co-dependent.

And what exactly is a potential? Is it a bird?, Is it a plane? Is it a tangible thing? Well, it seems that somehow, that it is and it is not. Let us call this intangible existence a state of “something” at the moment.

[Ed. Within the context of electromagnetism and source theory we can see the role of the Green’s function in helping eliminate “the source” in favor of “the potential”. Matter and field are two sides of one indivisible phenomenon.]

One might imagine cartoons appearing on a TV screen and ask if there is any kind of “resistance” to their own motion from the screen itself? What does the image move through if not nothing? Of course, it is a phase relationship of one pixel to its neighbor. Something can move while being itself nothing.

Scientific perspectives can be fluid, as illustrated by a quote in the recent book Contact Geometry and Topology. The first chapter contains the remark (p. 2):

“Since electrodynamics is just a part of mechanics, the discovery made in 2009 can be attributed only to systematic eradication of historical facts from scientific textbooks and monographs.”

I remembered then, in my own college days, never having being informed by anyone on the existence of curl eigenfields nor of the important work by Eugenio Beltrami, mentioned in my previous post. It was as if an invisible hand had erased any memory of it!

It is the Parable of Primo and Ultimo in the context of scientific fashion. When once something is done we make it better or different to the point of forgetting. For institutions that are being paid for teaching you this resembles the art of misdirection used by trickster magicians and card game bluffers.

Your attention is moved to where the educator wanted.

Using this trick, anything or anyone that does not conform to our present axiomatic framework will be cast as marginal and boring. It lies in the realm of specialized techniques, that will only be taught in the extreme situation that we may need to make use of such former wisdom for a demarcated purpose.

This thought causes me to go back a hundred years and check in on the problem of vacuum vs nothingness. The question concerns evidence for “Super-potentials” and Theories of the Aether, due to English Prof. Edmund T. Whittaker. The description of his contribution may be found here.

Whittaker had a certain animosity towards Einstein’s theory of Special Relativity. This was, in part, because Whittaker had invented himself a simple theory in one of his most influential papers in 1904 only that it was superseded by Einstein’s work in 1905 to end up on the shelves.

[Ed. Whittaker appeared to view history through the lens of the Aether and thus took a different perspective. Of course, Einstein was the guy who banished the Aether so perhaps this explains some of the animosity.]

My purpose is to trace the reconciliation of relativistic theories with the previous analysis by Whittaker. It involves recalling his work on the super-potential theory.

The relevant papers are:

1) On the partial differential equations of mathematical physics which develops a general solution of Laplace’s equation through a novel decomposition of the field into two pieces;

2) On an expression of the electromagnetic field due to electrons by means of two scalar potential functions which expresses the electron field in terms of derivatives of two auxiliary scalar potentials

These early works anticipate somewhat the Transactional Interpretation of Quantum Electrodynamics due to John G. Cramer, which itself evolved from the Wheeler and Feynman Source-Absorber theory of photon exchange.

[Ed. Whittaker may perhaps be understood, even if you disagree with his viewpoint, as following a path different from the now conventional Green’s function approach to solving for the field given its sources.]

The Whittaker separation of the electron field into two non-symmetric parts are referred to here as Super-potentials. Their value lies in the fact that both the fields and the first level potentials for such fields can be constructed from an originating potential without any recourse to vector fields. In a different view, these might represent the actual, independent degrees of freedom of the fields, akin to a “basis” or an irreducible representation but not in the ordinary sense of a linear algebra including of course the necessary gauge degrees of freedoms.

Interestingly enough, the first Whittaker scalar, if parametrized in spherical coordinates, shows an interesting periodic structure while the second is akin to a “phase” angle. In the 1930s, H.S. Ruse discovered that the Whittaker scalars represent the Principal Null Directions of the Hertzian tensor in the fully covariant relativistic expression of Maxwell equations due to Heinrich Hertz. This result followed his earlier anticipation of a connection between super-potentials and relativity.

Surprisingly enough, Ruse managed to find a direct association of this basis with the Dirac equation. In fact, the Dirac theory seems possible without explicit use of spinors due to an equivalent form offered by the Whittaker scalars! Little attention seems to have been paid to these facts by the rest of the physics community.

Some fifty years later the connection between Hertzian, Whittaker and relativistic theories was revived by Japanese researcher Prof. Hideki Kawaguchi Prof. Hideki Kawaguchi. Kawaguchi published a series of articles from 1988 to 1995, working from the Hertzian formulation to the standard Lienard-Wiechert potentials, with a connection to the spinorial version of Dirac wave-functions.

Coming back to our previous “vacuum vs nothingness” question, Kawaguchi illustrates the connections on five levels. At the lowest fifth level, where the super-potentials lie, the complexity of radiation reaction shows up in the relations among these potentials in analogy to the Lorentz Force in a more conventional treatment.

The theme of “advanced” waves and signals from the future resurfaces here, underscoring the complexity of any discussion of causality in the electron system. Such considerations, working from advanced waves, led John Cramer to speculate on Retrocausality and a possible series of experiments to look for such effects.

[Ed. The key issue, much like tests of the Bell inequality, is whether any information can be transmitted in such a scheme of advanced and retarded waves. Considerations of relativity would suggest not, much like the lack of any super-luminal signalling potential in the EPR experiments to test Bell and Leggett inequalities.]

This exploration of super-potentials calls attention to an old allegory of Plato. In his defense of “Ideas” as superior to “Things” (the Cartesian “Res Extensa”) Plato considers a grand piece of marble. Before the sculptor starts work, one may conceive of all possible statues being contained in that initial marble. Thus the monolithic marble represents a universe of potentialities from which our consciousness gradually shapes at least one.

This “shaping” procedure in natural law seems to incorporate a kind of “Occam’s Razor” – a principle of economy in the logical structure of theories. Perhaps this has something to do with the super-potential idea as being a level down in the hierarchy, which leads to those layers above.

In contrast, strings, branes, and other popular speculations upon a deeper level, seem to be less constrained and may therefore seem less in tune with Occam’s Razor. According to the ancient meaning of the Greek word “Cosmos” which originates in the verb “Cosme’o” (to decorate) the true meaning of the Cosmos must be “The Jewel”!

The Misanthropic Principle


“What is well known in general, exactly because it is well known, is not known.”

G. W. F. Hegel, “Preface to The Phenomenology of Spirit”

“Defects of empirical knowledge have less to do with the ways we go wrong in philosophy than defects of character do; such as the simple inability to shut up; determination to be thought deep; hunger for power; fear, especially the fear of an indifferent universe”

David Stove, “The Plato Cult and Other Philosophical Follies”

The historical development of modern science carries with it several philosophical underpinnings that while common, often pass unnoticed by becoming parts of a “social cliche”.

The recent Creationist Agenda managed to bring about one such issue which is commonly referred among professional philosophers with the pompous name of the “Three Major Cosmological Indignations of Mankind”

These are attributed to the three major revolutions, the Copernican, the Darwinian and the Freudian. All share a common attribute consisting in a decentralization of the human kind with respect to the rest of the Universe. Although the last may be in doubt due to more recent neurological evidence, it is the second one that presents the most interesting evidence of a self-contradictory attribute in it’s very name by which it became known to a general audience’.

Despite the core of Darwinian teaching, we still prefer to use the term “Evolution”. In doing this, we preserve a place for us in the upper parts of a tree-like diagram of species variation. Implicitly, we enjoy a special place on the upper leaves of that tree for our own intelligence and scientific understanding.

However, one should be reminded that a “tree” structure is in itself an abstract construct that only shows variation. The true nature of the so called evolutionary record is in fact the mere and raw prevalence of one specimen to another.

It is perhaps by a sheer luck that the lack of contact with any possible alien race allows us to show such arrogance by putting ourselves on the top leaves and considering our own science as the best of anything achievable. But just think of a species able to sense all the acoustic and electromagnetic spectrum, what need would it have of all our precious and expensive equipment!

[Ed. Indeed, the Mantis Shrimp is a crustacean found in waters of Thailand with extreme perceptual powers from ultraviolet through infra-red]

Consider also the case where all the massive ingenuity and trickery of nature would have been concentrated on another species like the “Alien” in Scott Ridley’s film, not requiring anything more than its own reflexive power to face all our defenses. If ever on Earth it would have wiped us all out in months if not days!

We are flattered enough by still thinking of ourselves as the culmination of natural history, a kind of self-prize and yet we show no true evidence of such a progress when the issue of social relationships comes about, even in Academia.

There, the same old natural attitude abounds and that is “pre-eminence”.

Multi-Verse Dreaming and the Fredkin-Zuse Ambush

“We are such stuff as dreams are made on;
and our little life is rounded with a sleep.”

W. Shakespeare, “The Tempest“, Act 4, scene 1.

In a previous post on Privateer Science, one phrase caught my attention:

“all physics is an algorithm”

I believe this is worthy of further analysis.

Can we reduce everything to an Algorithmic formulation? Are we living in a digital universe or a simulation? There is much blood spilled over such claims, which makes it interesting to trace their history backwards.

The earliest version was offered by a pioneer of digital computers, Konrad Zuse. In 1967, he published a treatise with the name “Rechnender Raum”, [Ed. in English: Calculating Space], which conceived of the Universe as a set of interconnected parallel processors. The problem of quantum correlations is not there resolved but is attributed to “external” machinery of some sort.

Later, the American physicist Edward Fredkin developed this story. He tried to build a realistic model based upon the conception of parallel automata given by Von Neumann. Later, this became known as “Cellular Automata” as in the computer game “Life”. This philosophy was renamed the “Fredkin-Zuse Hypothesis” in analogy with the famous “Church-Turing Thesis”.

It is unclear how to build the Standard Model as Cellular Automata and how many properties and symbols these should have. Such systems, if properly defined, have a vast number of combinations so any disproof is difficult.

The most recent creative attempt is a book by Stephen Wolfram, “A New Kind of Science”. At 1200 pages, this colossal tome claims that a short collection of Cellular Automata might reproduce the complexity of the Universe as we perceive it.

There remains the problem of consciousness, or freedom of will, and a serious attempt by the Roger Penrose. In his masterpiece, “Shadows of the
, he claims to present a complete and rigorous proof for the non-algorithmic nature of the human mind. The key is the intuitive capability of proof, as shown by mathematicians.

Others think differently, including Marvin Minsky and John Searle.

Let us be dispassionate. Personally, I would not be surprised if these questions turn out to be undecidable!

What is interesting to me is that the history of such claims goes way back in ancient Greek philosophy. Indeed, the allegory of Plato’s Cave, in the “Republic”, describes how people can live chained like prisoners. They perceive the shadows of things as reality projected on the walls of the cave from an external source of light which is always behind their back.

If by accident, or by favor, one of the prisoners ever grasps the
external reality, he finds it impossible to explain it to the rest of his comrades. They still prefer the shadows into which their minds are accustomed from the actual reality. This is the mystery of Life.

Later Plato’s followers and intellectuals like Carneades and the Pyrrhonists established a kind of “Academic Scepticism” which in a sense  precludes the Kantian notion of the ever inconceivable “Being in itself”. Soon after, the Pre-Christian tradition of the Gnostics went a step beyond, by claiming to have discovered an external constructor or “programmer” of our reality in the face of the evil mad god “Demiurge or “Yaldabaoth”  in the effort to also answer the famous “Problem of Evil“.

Strangely enough, modern sociology and anthropology was also influenced vby the notion of simulated reality. This is evident in the works of Roland Barthes, Umberto Eco and Jean Baudrillard, especially the Baudrillard’s
work “Simulacra and Simulation“. In this and similar works, modern sociology sees a kind of “Apo-Semiosis” or designification where the Sign is finally deprived of any need for a signified “true” object to gradually become an empty signifier. This is reminiscent of all the “quantum this and quantum that” hype or the “All Popes and no God” attribute mentioned earlier in this blog.

One of the most important works of fiction that made heavy use of such a paradigm was the 1992 novel “Snow Crash” based on a 3D Metaverse, a kind of fully “Immersive Reality“.

In an acute critic, Richard Rorty mentions that the most important symptom of such a worldview is not so much its artificiality but rather the total lack of inspiration. In another important work by Walter Michaels, titled “The Shape of the Signifier: 1967 to the End of History”, the following phrase still echoes concerns expressed in this blog.

“So a world in which everything – from bitmaps to blood – can be understood as a “form of speech” is also a world in which nothing actually is understood, a world in which what a speech act does is disconnected from what it means.”

The above really sounds so “Quantum” if so “Copenhagen” that one cannot avoid the temptation offered by direct comparison!

And by another stranger coincidence, one can even be tempted to ask of what it would mean if a kind of “Entangled Brains Hive”  could exist where not just two separate dreamers but a myriad of them could tune into one and the same common dream!

Would such a dream be able to materialize and what kind of elusiveness would such a dream matter appeared to have? What would the scientists and intellectuals inside the World Dream conclude on the nature of the Dream-matter? Would it be as elusive as the
wave-particle duality appears to be?

I cannot avoid a last comparison in here with the verses from a very common popular song, the well known “Hotel California

“We are programmed to receive.
You can check-out any time you like,
But you can never leave! “