:Agora Laboratory and Class:       

Part IV
The structure of the Agora Laboratory and Class
Corneliu I. Costescu

1. The scientific method can be simply and substantially improved when we apply it to the basic concepts.
2. The basic concepts have changed in the past, they will inevitably change again.
3. A graduate student should have the opportunity to practice how to renew a basic concept, through a semester-long class fully devoted to a single basic concept change from the past.

I. Introduction

The Agora laboratory and class combines in a functional way the old debating method with the scientific method. Involving the debating process slows down considerably the application of the scientific method and hence, it cannot be applied to any topic where the scientific method is applied. We can apply it only to revising and renewing of a few and essential basic concepts. Our Agora laboratory and class would slowly and systematically revise a basic concept, the diffraction of light/ the structure of a light beam, for the beginning, and attempt/ propose to complement the current view with a more detailed view.

Generally, for a chosen basic concept, the student would act, for the whole semester (one time in four years of study), as in this visual (visual 1). Here a student looks into a basic concept, hypothesizing and experimenting (applying the scientific method), and debating again and again, until he/ she finds details that could answer the how-can-it-be-like-that question. Notice that the student combines the systematic search for details (the scientific method) with the systematic debating - the old Greek method that is most adequate for basic concept development, towards answering the how-can-it-be-like-that questions. In addition to these activities, the student would study an example of passing from a basic view to a more detailed view on a phenomenon/ concept (the growth of the kinetic theory of heat/ statistical mechanics specifically the work of Boltzmann, for instance), and would produce a term paper.

We have tried this procedure, as a personal enterprise, for the concept of light diffraction/ the structure of the light beam, for many years, and we consider that this type of inquiry works and that it is fun. First we identified the existing points of view and sought their advantages and weaknesses. The hardest part of it is to escape from the existing points of view, and find a different one worse at the beginning and better in the end. In doing so, we talked to, and debated with anybody willing to listen ... From this experience, one gets the reputation of a person with an obsession. We regard the Agora Laboratory and Class as an opportunity for a graduate student (and for anybody who would take the class) to attempt answering in the most possible honest way what he/she really believes about the basic concept.

It is fun to compare the Agora type of study with the regular class, let us call it the Educational Assembly Line. Here, as you know, the student learns in few lectures the basic concepts, and then, for the rest of the semester he or she goes into many applications. We know that this method is very useful and productive, and we do not wish to discredit it in any way just a comparison. But we need to say that it has a weakness that needs to be corrected. Indeed, never in his/her career does the student find the necessary time to convince himself or herself of the details of some basic concepts. As a result, mysteries lurk around, which considerably limits the applications. Never after the college does a person find the necessary education and time to convince himself/ herself of the details of some basic concepts. As a result, the basic concepts become frozen for hundreds of years leading to crises of meaning in science and society.

We believe that the Agora procedure can generate great ideas, wisdom and tolerance on a large scale, since it deals with fine aspects from our background. We believe that any science or philosophy should be designed to include a scheme for the renewal of its own basic concepts.

II. A 14-week Agora Laboratory and Class

A. Prerequisites to the Agora Laboratory and Class what to look for and what to expect (2 weeks).
- The debating method as a slow but powerful synthetic study of a single concept for years. The scientific method as a quick analytic study of an intricate phenomenon in the microscopic world. Combining the scientific method and the debating method the method of how-can-it-be- like-that.
- Mystery and prosaic concepts in physics and in the childrens play. A case study: passing from a mystery concept, the thermodynamic theory of heat, to a prosaic concept the kinetic theory of heat. Our case: a study of the concept of light diffraction/ the structure of a light beam.
- Making simpler a complex issue: Judging the necessity of revising/ renewing of a basic concept is a very difficult task when we start from analyzing the content/ meaning of that concept, but it is very simple if we start from the need to apply a new method of analysis (the debating method in combination with the scientific method the Agora Laboratory and Class) to it.
- The mechanism of the Agora Laboratory and Class: a) Identifying and debating the main lines of thought, b) Experimenting and debating, c) Writing and debating a paper on the structure of light/ the mechanism of light diffraction, d) Writing and presenting one speech regarding the structure of light/ light diffraction.

B. A case study regarding how to renew a basic concept: the rise of the kinetic theory of heat - L. Boltzmann (2 weeks).
- Identifying and debating the main lines of thought for heat before Maxwell and Boltzmann.
- Identifying and debating the approach by Maxwell and his predecessors.
- Identifying and debating the approach by Boltzmann.
- Two lessons related to Boltzmans work: the mystery lesson, and the prosaic lesson

C. Revising the diffraction of light and the structure of the light beam ( 4 weeks).
- Experiments with light diffraction.
- Identifying the existing main lines of thoughts. Experimenting and debating.
- Debating and experimenting on the strength and the weaknesses of the following structure of a light beam.

The quantitative description of diffraction patterns in electromagnetic optics (w) and quantum mechanics (qm) relies on the capability of the wave/ wave function of particle(s) to diffract in the vicinity of the diffracting edges and to interfere in the space before the screen/ detector. Our extended analysis of old experiments suggests a complementary view. a) The diffracted light is generated by reflection and refraction of light in terminal shapes of the edges hit by light (and not by wave behavior around the edges). b) The light-screen interaction is essential for the formation mechanism of the diffraction pattern (and not the interference of waves/ wave function in free space). c) Consequently a new structure for the light beam is necessary, one structure in free-space and a different one in condensed matter. We propose such a dual structure. A full application to the quantitative description of edge, corner, slit and double slit diffraction is described. The possibility of application/ extension to related phenomena, and the consequences for other basic phenomena are suggested.

The proposed structure for the light beam is different in free space and in condensed matter. (i) In free space the light beam is a collection of sequences of equidistant bursts of finely dispersed matter (finely DM) that travel freely, in straight lines. The shape of the bursts, the distance between bursts and the length of a sequence of bursts may vary, depending of their source characteristics. The distribution of the sequences in the plane perpendicular to their movement (transverse section) also depends on the light source. It can be a gaussian distribution for a laser. (ii) Upon the quasi-periodical arrival of the bursts at the surface of a body, they transform themselves in forced asymmetric collective longitudinal electron oscillations (CLEO) in the surface layer. The action of the bursts on the electron can take place by momentum transfer. (iii) A CLEO interacts with the finely DM of thermal radiation and throws bursts in the two directions of electron oscillation. If the material is transparent, these asymmetric CLEOs propagate through the body as a light beam. The propagation is sustained by the action of the oscillating electrons on the neighboring electron population through the action of locally generated bursts. Hence, the light beam in condensed matter is primarily a propagating CLEO whose propagation is intermediated by locally generated bursts. In a metal, where there are many quasi-free electrons and hence, the electron oscillations propagation is strongly damped.

The bursts generated by a CLEO upon its arrival on a surface toward free space, will travel freely in the surrounding free space. As described above at (i), these burst become the light beam in free space. In this frame, the transparency of a piece of glass is not due to free space light penetrating through the glass. Indeed the free space light bursts disappear at the surface of the glass by transforming themselves into CLEOs. In turn the CLEOs propagate on their own other side of the glass and hence, are the carrier of the light beam through condensed matter. Hence, the transparency is essentially due to the propagaton of CLEOs.

The above structure of the light beam was found to alternatively and clearly describe, both physically and mathematically, the light diffraction patterns. Upon hitting diffracting material edges, the bursts of the initial light beam generates CLEOs in those edges and hence, they become a source of extra beams toward the screen. At a point on the screen, there is a time delay between the arrival of bursts from the initial beam and from the beam generated in a diffracting edge. This time delay is proportional to path differences and hence, at a point on the screen there will be an interference between the CLEO from the initial (source) beam and the CLEO from the diffracted beam. Therefore, this view is fully adequate for describing clearly, physically and mathematically, a high intensity light diffraction experiment. The experiment of the rare photon diffraction receives a very different face here since the photon appears to be a sequence of bursts coming to the detector. The detection of the photon very likely involves a superposition of the effects of such burst sequences see the paragraph below on the photon detection and the photoelectric effect.

D. Implications for other phenomena and applications (2 weeks).
The treatment of light reflection, refraction, transmission and absorption is feasible and involves a detailed look at interaction of the periodically arrival at a body surface, of the light bursts from free space, with the surface layer and subsurface structures. The structure (geometry and material distribution) of the surface layer needs to be modeled such that the specular reflection and diffuse reflection occur as simple geometrical effect, while the refraction depends on the material electron and mass density. Applying the eqs. (3) at the surface of a body of condensed matter, to describe the periodic action of the incident bursts of the light beam, requires boundary conditions that consider the surface modification and movement. A considerable 3D modeling effort is necessary.

The surface layer structure and optical properties can be revealed from 2D or 3D computational models for reflection and refraction. By applying eqs. similar eqs. (1-5) to reflection and refraction, the surface layer structure, a structure that is responsible for absorption in opaque matter and for refraction, can be established. We hypothesize that the structure involves a very top layer mostly populated by electrons, and a lower layer where the electron and material density changes gradually toward those of the bulk values. The top of the lower surface layer is anisotropic in regard to CLEOs. The case of reflection will help establish the necessary details regarding the material, geometry and dynamics related to the very top layer. The study of refraction will show the properties of the lower surface layer. To allow for the change of the direction we assume that a unit momentum transfer generates stronger electron oscillation on normal direction to the surface layer, than on the horizontal direction. In this case the refraction phenomenon. The CLEO propagation will be bent toward the depth of the body. As the CLEO penetrates toward the bottom of the lower surface layer, the material becomes isotropic and the ray bending ceases.

With the above structure of a light beam, the negative result in the experiment by Michelson-Morley (MM) has a very simple explanation. The beam splitting mirror in the experiment transforms the initial beam of light from the source (sun, bulb, laser, etc) into CLEOs in its body and hence, the light emerging from the mirror is entirely generated by the CLEOs in the mirror (and not by the initial source). As a result the bursts move with the same speed toward the two reflecting mirrors in the MM experiment i.e., the speed of the initial source is irrelevant for the light after the splitting mirror and hence, if the distance is the same the time to return to the splitting mirror is the same and no interference effects occur. Notice that the in this view the speed of light can be larger than the speed of light in the laboratory system, depending on the speed of the MM apparatus frame.

In this picture the photon is only a theoretical construction i.e., it does not exist physically. Indeed, if H is the energy per burst and if T is the time interval between the arrival moments of two consecutive bursts to a point in their path, then Energy = H/T =H is the total energy that passes through a surface in one second if the sequence of bursts is continuous. Since in the interaction with the electrons a burst can loose only a fraction of its energy, then fraction of H , say h would be the average energy absorbed per electron when a CLEO is generated. Hence, the Plank constant could have a very simple physical meaning. The above structure of the light beam also provides the necessary ingredients for a more physical understanding and quantitative evaluation of the event of the photon detection and the related photoelectric effect. ...

The light beam structure described above, the action and the generation of the light beam on a material body, suggests that the polarization of the light beam can be related to correlation between the timing of the burst passage through a plane perpendicular on the beam direction (transversal section). ...

Since the direction of the CLEO propagation is clearly related to the changes in the electronic density and material density, it follows that light dispersion can, similarly to the reflection and refraction phenomena, be naturally analyzed with the above structure of the light beam. ....

We mention that the concepts of CLEOs and bursts of finelly dispersed matter, could offer a mechanism for our concept of electric charge and field and electric current and magnetic field. ... Finally, the concept of bursts of finely dispersed matter can be applied to the production of characteristic X-rays as sequences of burst produced by the proper oscillations of tightly bound electrons, and can be extended to the production of bremsstrahlung radiation as a flow of finely dispersed matter dragged by the slowing down electrons. A model for the inelastic scattering of X-ray can be developed in this frame. The need for such model is also suggested by the following line of thought. A review of the Impulse Approximation (IA) for calculating Compton photon scattering probabilities by bound electrons reveals a paucity of measured, double-differential cross-section (DDCS) data with respect to angle and energy, especially for scattered photon with energies near that of the incident photon energy E. The K-shell DDCSs derived from IA display discontinuities and poorly match available experimental continuous DDCSs between the Compton energy and E. Similar discrepancies with respect to experiment are displayed by the S-matrix results. Because numerical evaluation of IA is so practical and straightforward, we have replaced the electron momentum in the energy-momentum conservation with an ad hoc concept of partial electron momentum to show the feasibility of reducing such discrepancies. In the proposed ad hoc DDCS, called here the blended impulse approximation (BIA), this replacement is combined with the incoherent approximation. BIA removes the undesirable discontinuities in the DDCS, indicates better agreement with existing experimental data, and provides a general DDCS form for incorporating evaluated experimental data. We suggest that the ad hoc concept of partial electron momentum could also be used, with similar benefits, in the S-matrix energy-momentum conservation. Further development of BIA requires a measurement of a comprehensive set of DDCSs to help finding an adequate set of shell-dependent expressions for the partial electron momentum. In conclusion we suggest that the concept of partial electron momentum seems to have a basic character and powerful resources. It might have a direct physical significance for the photon, or it might even indicate the need for a reviewed mechanism of the Compton effect, different for free and bound electrons.

E. Writing a text and a speech related to the Agora Laboratory and Class (4 weeks).
- Write a very short critical paper on the Agora Laboratory and Class.
- Write and debate a five-page paper on the structure of light.
- Write and present a persuasive speech regarding the structure of light.


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