Remarks on Foundations of Physics

Scientific Paper
Title	Remarks on Foundations of Physics
Read in full	Link to paper
Author(s)	Jozef Kajfosz
Keywords	foundations of physics, basic research, causality, visuality, acton model, gas-like ether
Published	2013
No. of pages	10

Read the full paper here

Abstract

A simple scheme for ordering the facts of physics is presented, and some terms associated with basic research are introduced. Some aspects of this research are discussed and an outline of a simple model as an example of a working hypothesis for explaining the known facts is proposed. <o:p></o:p>

Overview

This ten-page essay is Jozef Kajfosz's statement of method rather than of physics. Written in Polish in 1980, never submitted to a journal, posted on a web site and translated into English in 2013, it proposes a simple geometrical scheme — a triangle of facts — for ordering everything physics knows, uses that scheme to define what a "basic discovery" would be, states three rules such a discovery would have to satisfy, and then offers a deliberately unfinished model of the unknown as an illustration of what obeying those rules might look like.

Kajfosz's complaint is not that any particular theory is wrong. It is that the questions at the foundations of physics have no institutional home. The philosophy of science handles them so formally that it "does not reach the average physicist"; physicists themselves raise them "rarely and reluctantly," at seminars "regarded to be not fully serious," in popular works, or at jubilees — because "an unwritten social code says that it is necessary to be a physicist of a very high rank in order to be allowed to take up such a subject. But it seems that the opposite should be right."

The second and more distinctive theme is visuality. Kajfosz argues that physics since Maxwell has progressively abandoned demonstrative models in favour of pure description, and that this is a real loss of understanding rather than a maturation. He is careful and even generous about the theories he is criticizing, writing that relativity and quantum mechanics "describe perfectly the physical phenomena and this is their paramount significance" while adding that many physicists sense their authors "went a bit too far in their absolutization of the relativity and in their determination of promoting the indeterminism." The paper is an argument for licensing a return to models, not a claim to have found the right one.

The scheme

Facts, causes and the triangle

Kajfosz calls both phenomena and the laws relating them facts, and defines two things about them separately:

"The knowledge of a fact is the awareness of its existence."
"Understanding a fact is an ability to answer the question 'why?'"

A fact is understood when we can point to another fact that is its cause. His worked example is homely: the apple falls because Earth and apple attract; they attract because all material bodies attract.

All facts relevant to physics are then drawn as points inside a triangle, ordered so that a cause always lies lower than its consequence. Horizontal zones run from phenomena at the top, through detailed laws, to general laws below. Because a fact generally has many consequences, moving upward the lines ramify and the density of facts increases; the field of facts narrows downward. From this two research directions follow:

Applied research seeks consequences of known facts and moves up the triangle. A step upward is an invention.
Basic research seeks causes of known facts and moves down. A step downward is a basic discovery.

Crucially, a downward step counts as an increase in knowledge "only if the cause has more consequences than the fact." Kajfosz notes that physics thrives regardless, because consequences can be found and exploited without knowing causes — which is why it advances rapidly while fundamental questions stay open.

The basic area, and the limits of knowledge and understanding

Descending through causes one eventually reaches a fact whose cause is unknown: known but not understood. Kajfosz calls this a basic fact, and the set of all basic facts "determines the recent state of knowledge." The example given is the existence of the law of gravity.

Two lines can then be drawn across the lower part of the triangle: a limit of understanding and, below it, a limit of knowledge, with only the basic facts lying between them. Causal chains intersect the limit of understanding — they are its first segments — but no chain crosses the limit of knowledge. A basic discovery is the discovery of a fact below the limit of knowledge, and it drives both lines downward, changing the set of basic facts.

Extending the picture, Kajfosz posits two further lines representing the ultimate border of human cognition: a limit of comprehension and a limit of cognition, with fundamental facts between them. If research ever reaches them, the basic facts become identical with the fundamental facts, all physical reality follows from that set, and further basic research is meaningless — "the end of the way" physicists had begun to speak about. The conclusion he draws is the essay's sharpest line: "ultimately we might be able to know everything but we never will understand everything." The fundamental facts, by construction, have no "why".

He then flags the scheme's own weak point himself — whether the field of facts really is a triangle, and whether it is closed at the bottom, is an open question, and "not only a purely physical issue" but one touching logic, philosophy, psychology and aesthetics. He also observes that chemistry, astronomy, cosmology, geology and biology have no basic facts of their own: their causal chains descend into physics and terminate at its basic facts, so that the set of basic facts of physics characterizes the state of human knowledge of the universe generally.

Five programmes of work in the "basic area" are listed: systematizing the known basic facts and testing their mutual causal independence; analysing what makes a discovery basic; formulating general rules for facts still unknown; investigating the limits of comprehension and cognition; and formulating hypotheses in the unknown area using the results of the first four.

Three rules for a basic discovery

The paper's operative core is three conditions a proposed new basic fact must meet:

It "must result in the reduction of the number of basic facts or in a substantial increase of the number of known facts."
It "must present an image of reality which is as much as possible simple, symmetric, visual and beautiful."
It "does not have to fulfill any conditions which follow from other basic facts."

Rule 1 follows from his causal criterion: either the count of basic facts drops, or the new fact opens causal sequences containing facts previously unknown. Kajfosz concedes rule 2 is "subjective and can stir up controversy," defending it on the ground that all the great discoveries up to a certain moment were introductions of simple, graspable models. His illustration is that nobody objects to a planetary orbit needing six independent parameters, because their necessity "originates logically from one demonstrative fact that the orbit of the planet is an ellipse." Visuality lets consequences be searched for and checked quickly; the model's value lies in joining many independent parameters into one fact.

He dates the departure from models to Maxwell — "his very beautiful theory, which he treated however purely descriptively in accordance with the maxim hypothesis non fingo" — and says relativity and quantum mechanics continued in that direction. Where visuality is lost, the answer to "why?" degenerates into a form like "because in equation [47] the quantity Q appears with the exponent k", which Kajfosz argues is not understanding at all: "understandable is what penetrates to our conviction, whereas convincing is what can find its way to our imagination."

Rule 3 is the one he thinks is most often violated in practice. Formally it is trivial — basic facts are by definition causally independent — but psychologically it is hard to shake "an erroneous notion that the characteristics of these new facts have to obey some rules or laws which apply to other known facts." Since the new facts lie below the current line of knowledge, "reality below the current line of knowledge can be completely different from reality in the area of facts above this line." The single demand is that the known laws reappear as consequences somewhere above the limit of knowledge.

The acton model

The last third of the paper offers a model "in order to stimulate imagination," explicitly "not a finished model" and one that "in this form interprets only a few basic facts qualitatively." Its four postulates:

Space is filled with objects moving rectilinearly in all directions at constant velocity, named actons (from action).
Actons carry a certain amount of one or a few physical quantities.
Only local interactions between actons exist.
Physical objects are local anomalies of acton density, or of the densities of the quantities they carry.

Two, perhaps four kinds of acton would probably be needed, and their velocity "must be almost certainly the velocity of light" — which requires a privileged state of inertial motion in which the acton flux is isotropic. Kajfosz meets the obvious objection directly: this "seems to contradict the most universally accepted interpretation of the special theory of relativity, but fortunately an alternative interpretation exists," namely the Lorentzian one, in which a privileged inertial state exists but cannot be identified. He cites Jánossy's book at this point, and adds that under his own rule 3 it would even be permissible to violate special relativity at this level provided the Lorentz transformation emerges among the model's consequences.

The quantity carried is most probably momentum. Actons penetrating matter are absorbed or lose part of their momentum, so a "field" around a material object is simply an anisotropy in acton number or momentum; a second object sitting in that anisotropy is struck anisotropically and begins to move — attraction or repulsion. Invoking rule 3, Kajfosz insists that carrying momentum does not oblige actons to carry mass or energy, "since actons are not particles or photons in the sense of presently known physical laws," and that it is better not to identify the carried quantities until particles have been modelled. Locality of the acton interactions — scattering, annihilation, creation, or exchange of carried quantities — is what "explains visually the abstract notion of a field."

He considers and rejects an addition: a second species of slow or stationary passons would make particles easier to build, but yields continuous mass and charge spectra, no necessity for spin, and so many extra assumptions that simplicity and universality are destroyed.

The programme of fitting the model is spelled out in order: first ensure the stability of the homogeneous acton field; then, assuming a density anomaly, choose interactions that make it stable in space and time — that is, create the particle; then model the law of inertia and express inertial mass in the model's parameters; then recover the known interactions. Short-range strong interactions he guesses would come from acton scattering or exchange of carried quantities, whereas inverse-square forces "seem to be caused by absorption of actons."

Conclusions and the author's own caveats

Kajfosz does not claim the model works: "It is not our objective to argue that by means of the proposed model it will be possible to describe all known facts." His claim is only that refusing it — showing no version of it can be reconciled with the facts — "is not a trivial task."

He addresses the historical objection head-on. Gas-like ethers have appeared repeatedly, and Feynman's Lectures cite a 1750 example and reject it for violating the law of inertia. Kajfosz replies that an appropriate velocity dependence of the acton absorption cross-section inside matter would retain the law of inertia, and that a body moving in such a medium "should resist the change of its velocity, which would be a qualitative explanation of the phenomenon of inertia." He further claims that the equivalence of inertial and gravitational mass is "almost obvious" in the model, as is the equivalence of gravity and acceleration; that the statistical character of microscopic interaction and the probabilistic determination of particle positions follow naturally; and that because acton absorption is exponential, the exact force between two bodies expands into a series of decreasing terms, offering "a potential possibility of unification of the electric, weak, and gravitational interactions."

Two admissions close the paper. Developing the acton model "lead[s] to surprising results in the form of very large densities of different physical quantities in vacuum" — he offers no argument for rejecting them in advance, but does not defend them either. And the reason gas ethers have failed before, he suggests, is that in the first stage "it is very hard to maintain the law of energy concervation if for those moving objects all properties of regular particles are being assumed." His escape is rule 3 again: if actons are more fundamental than particles they need not obey particle mechanics, in which case conservation of mass and energy "will probably prove to be a secondary law" appearing among the consequences at the level of particles, with mass and energy being the measure of how actons interact with particles.

Assessment

The methodological half of the essay is its strongest part, and it is largely independent of the model that follows. The triangle scheme is crude — Kajfosz says so — but the definitions it supports are genuinely useful: separating knowledge from understanding, defining basic research as the search for causes rather than the search for precision, and requiring that a proposed cause have more consequences than what it explains. That last requirement is a real and unusually clear criterion, and it would disqualify a great many alternative proposals, including some on this wiki. His conclusion that we may end by knowing everything and understanding nothing follows rigorously from his own definitions and is worth sitting with.

Rule 3 is the essay's most valuable and most dangerous idea at once. It is valuable because it names a real failure mode: proposals for sub-particle reality that hobble themselves by insisting the substrate obey the laws its own consequences are supposed to explain. It is dangerous because, taken without discipline, it licenses anything — a substrate exempt from conservation of energy, from relativity, from particle mechanics, constrained only by the requirement that the known laws re-emerge "somewhere above" the current limit. Kajfosz supplies no criterion for when that re-emergence has been demonstrated rather than promised, and his own acton model illustrates the difficulty: conservation of energy is not shown to emerge, it is deferred to a later stage of work that the paper does not carry out.

The acton model itself is offered explicitly as an illustration, not as a theory, and it should be judged accordingly — but even as an illustration its difficulties are the classical ones. A rectilinear flux absorbed by matter is a kinetic (Le Sage-type) mechanism, and the standard objections to such mechanisms are drag on moving bodies and the disposal of absorbed momentum as heat. Kajfosz addresses the first, with a velocity-dependent cross-section, and does not address the second at all. His claim that the equivalence of inertial and gravitational mass is "almost obvious" in the model is asserted, not derived, and the same is true of the promised unification of electric, weak and gravitational interactions via a series expansion of an exponential absorption law: no such expansion is performed. The "very large densities" he concedes the model produces in vacuum are exactly the kind of result that would need reconciling with measured cosmological energy density before the model could be taken further.

The privileged inertial frame is the model's most direct conflict with established physics, and Kajfosz handles it honestly by pointing to the Lorentzian interpretation of relativity rather than pretending the problem away. That move buys empirical equivalence with special relativity at the level of the Lorentz transformation, but it is a choice of interpretation, not a result, and the essay makes no attempt to show how a specifically acton-based dynamics would reproduce the transformation. Finally, the essay's context should be kept in view: it was written in 1980 as an informal piece by a working experimental nuclear physicist, was never published in a journal, and makes no pretence to completeness — "formalists will be disgusted by understatements, the absence of strict definitions and fragmental character of the topics addressed."