maxwell's field as operational concept

Maxwell’s field as an operational concept ( G. Mpantes)

Maxwell’s field as an operational concept (by G.Mpantes)

operasionalism , mathematical field, Faraday’s field, Maxwell’s field

George Bantes: mathematicis teacher www. mpantes. gr .

Introduction

Electricity is a very deep

phenomenon and natural

philosophy is evenly divided

in dealing with it. Electric

theory described a number of electric forces from

the Coulomb’s force to the forces of Ampere, Grassman, Biot-Savart, Laplace,

Weber, Gauss, Clausius , Lorentz having two paths for the study of

electricity, which appear to represent deeper differences that reach to the

roots of human ability for description and understanding of nature.

In one it connects electricity with bodies, and studies mutual

interactions of charged bodies from distance without intermediate, and the

other the electric interaction is by contact through a medium. The contact

should restore the ether, after replaced by the "field". We call them particle

and field electricity respectively.

Along the way, the view of action by contact, prevailed, but the medium

of the contact was abolished, ( the ether) , we talked about waves without

medium of propagation, it led to the notion of immaterial field unrelated to

bodies, a super reality that lies behind everything, Aristotelian and

conceivable without any operationalist verification.

Physics endeavored much with the atomism on electricity, an

undeniable reality, because the electric field theory that had dominated , had

refused it from the beginning! The electric charge was finally accepted as a

deformation of the ether, the deformation occurs on a particular material

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particle, and later when the ether proved nonexistent, electron was a

condensation of the ' field ' that was immaterial .

Wavered physics between mathematics symbols and physical entities ,

in propagating potentials and propagation velocity of electric action , devised

equations whose mathematical treatment created endless debates about the

nature of electricity.

Eventually the medium theories were verified by means of

electromagnetic waves of Hertz, but after several years we learned that the

waves were not as water waves in the sea, they were as material waves

accompanying the electron, they accompanied the photon, they were

probability waves and the light was a swarm of particles, the photons.

But I think that in effort to understand this edge area of nature, the

area of electricity and light, we put to a test the entire philosophical

background of scientific inquiry: The main dipole that emerges in the study of

the electric theory is the dipole , concept – reality, and the (philosophical)

relation of them is operationalism.

Operationalism .

Operationalism is the view that all theoretical terms in science must be

defined only by their procedures or operations.

Operationalism is based on the intuition that we do not know the

meaning of a concept unless we have a method of measurement for it. It is

commonly considered a theory of meaning which states that “we mean by any

concept nothing more than a set of operations; the concept is synonymous with the

corresponding set of operations” (Bridgman 1927,).

Bridgman’s operational analysis explicitly acknowledged that concepts

were inevitably linked to human experience and that they were equivalent to

the actions involved in the formulation and use of the corresponding terms.

“ The logic of modern physics”1 .

“….Hitherto many of the concepts of physics have been defined in terms of

their properties. An excellent example is afforded by Newton's concept of absolute

1 Percy Bridgman publ. MacMillan (New York) Edition, 1927.

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time. The following quotation from the Scholium in Book I of the Principia is

illuminating:

…I do not define Time, Space, Place or Motion, as being well known to all.

Only I must observe that the vulgar conceive those quantities under no other notions

but from the relation they bear to sensible objects. And thence arise certain

prejudices, for the removing of which, it will be convenient to distinguish them into

Absolute and Relative, True and Apparent, Mathematical and Common.

(1) Absolute, True, and Mathematical Time, of itself, and from its own nature

flows equably without regard to anything external, and by another name is called

Duration” .

Now there is no assurance whatever that there exists in nature anything with

properties like those assumed in the definition, and physics, when reduced to

concepts of this character, becomes as purely an abstract science and as far

removed from reality as the abstract geometry of the mathematicians, built on

postulates. It is a task for experiment to discover whether concepts so defined

correspond to anything in nature, and we must always be prepared to find that the

concepts correspond to nothing or only partially correspond. In particular, if we

examine the definition of absolute time in the light of experiment, we find nothing in

nature with such properties.

The new attitude toward a concept is entirely different. We may illustrate by

considering the concept of length: what do we mean by the length of an object? We

evidently know what we mean by length if we can tell what the length of any and

every object is, and for the physicist nothing more is required. To find the length of an

object, we have to perform certain physical operations. The concept of length is

therefore fixed when the operations by which length is measured are fixed: that is,

the concept of length involves as much as and nothing more than the set of

operations by which length is determined. In general, we mean by any concept

nothing more than a set of operations; the concept is synonymous with a corresponding set of operations. If the concept is physical, as of length, the

operations are actual physical operations, namely, those by which length is

measured; or if the concept is mental, as of mathematical continuity, the operations

are mental operations, namely those by which we determine whether a given

aggregate of magnitudes is continuous. It is not intended to imply that there is a hard

and fast division between physical and mental concepts, or that one kind of concept

3

http://www.marxists.org/reference/subject/philosophy/works/en/newton.htm#scholium


does not always contain an element of the other; this classification of concept is not

important for our future considerations.

We must demand that the set of operations equivalent to any concept be a

unique set, for otherwise there are possibilities of ambiguity in practical applications

which we cannot admit.

It is evident that if we adopt this point of view toward concepts, namely that

the proper definition of a concept is not in terms of its properties but in terms of actual

operations, we need run no danger of having to revise our attitude toward nature. For

if experience is always described in terms of experience, there must always be

correspondence between experience and our description of it, and we need never be

embarrassed, as we were in attempting to find in nature the prototype of Newton's

absolute time. Furthermore, if we remember that the operations to which a physical

concept are equivalent are actual physical operations, the concepts can be defined

only in the range of actual experiment, and are undefined and meaningless in regions

as yet untouched by experiment. It follows that strictly speaking we cannot make

statements at all about regions as yet untouched, and that when we do make such

statements, as we inevitably shall, we are making a conventionalised extrapolation,

of the looseness of which we must be fully conscious, and the justification of which is

in the experiment of the future…..….. Also the term "true" or "false" can be attributed

to a sentence only "operationally" ie only with the description of measurements or

operations needed to verify whether or not the proposal is true ...” 2

But what are operations? To take the simplest example, the operation

of counting is a mental operation, but it is an integral part of many “physical”

procedures. He called such crucial non-physical operations “paper-and-pencil”

operations. Bridgman lamented that it was the “most wide spread

misconception with regard to the operational technique” to think that it

demanded that all concepts in physics must find their meaning only in terms

of physical operations in the laboratory. Later he gave a rough classification of

operations into the instrumental, mental/verbal, and paper-and-pencil

varieties..

This view is tested exactly in the concept of field. Bridgman himself

denies it’s physical existence and states that we have not even found,

manipulations linked to the objective substantiation of the field, which to

2 Bridgman, Percy Williams. 1927. The Logic of Modern Physics. New York:

Macmillan.

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convey it in the reality of physics. The reality of the physicist is an

operationalist reality, other realities are not in physics research. They are

studied in the class not in the lab, the class leads us straight to the Platonic

forms.

Conclusion .

It took a long time for the philosophers of science to accept that any

theoretical concept used in a physical theory was not required to have its

counterpart in our experience (logical positivism).

But we say that if we reject operationalism from natural philosophy,

then the guide of the understanding of the world are mathematics, we have

not anything else, and this was the case of Maxwell’s field. If the

experimental results agree with the math results, then the concepts …. follow.

We create concepts ad hoc nor understood nor measured, basically we dress

up maths with physical concepts, talking about logical positivism, a new

intuition etc. This happens throughout the course of the electric field in

electricity. The course of the mathematization of the world has started from

there, even though Bridgman rejects this development:

….we are convinced that purely mathematical reasoning never can yield

physical results, that if anything physical comes out of mathematics it must have

been put in in another form. Our problem is to find out where the physics got into the

general theory 3Bridgman

The concept of the field before Maxwell .

Electrostatic starts from the electric force of Coulomb, who in 1785 , with

the help of the torsion scales which devised himself, verified Priesley 's law

that:

“The repulsive force between two small balls charged with the same

kind of electricity, is inversely proportional to the square of the distance of

their centers”.

.... Whatever the cause of electricity, we can explain all phenomena on the

3 The Logic of modern physics p169

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assumption that there are two electric fluids, portions of the same fluid is repelled

and attracted with the portions of other fluid ........ Coulomb

The Coulomb force then mentioned among the portions of the fluid , ie

between molecules of the electric fluid , called charges and is known from

high school:

The type of this force that resembled

the type of Newton's gravity, gave in electricity

an old mathematical background to solve practical problems .

. The two central mathematical concepts of electrostatics is the field and the

potential. These help us to solve practical problems of calculation of electric

power in the bodies , and ... there it stops. In each point of a charge, we

define a vector E ( force exerted at each point of the fluid round the

charges ) .Thus the force exerted between the loads q1 and q2 is F = Eq2

where E is the field of q1 and the force F, Coulomb’s force. But beware , we

measure the force and we define the field.

Next , the mathematical result of the electrostatic field, is a function of

the potential U associated with the intensity from the time of Lagrange by

of calculating the electrostatic field with much

simpler steps from the calculation of E. This magnitude is numeric and it’s

physical ' interpretation ' is that any electric or other preservative system, is

considered that it is accompanied by an imaginary energy storage, the

potential , from which it is pumped the energy that moves charges through

( 2 ) . When the system generates work, it finds it on the storage of potential

so the potential energy decreases in the amount of energy produced. The

opposite happens when we give the system energy outside.

The field then before Maxwell is a simple mathematical representation,

just as was the Newtonian gravitational field. Has no status independent of its

source, is not material and does not connects evolutionary the events in

space and time.

This mathematical approach of the field will not remain the same today

as the field has become the reality of the natural world. In field

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electromagnetism theory constructed by the Faraday and Maxwell, fields are

basic physical entities and may be examined without reference to material

bodies . Today mathematical expressions Poisson and Gauss ( potential and

field ) became realities without changing anything in the formulas. The pulsed

electric and magnetic fields can be moved in space in the form of radio waves

and other types of electromagnetic radiation.

The pre-history of Maxwell’s electric field .

Michel Faraday revolutionized physics in 1830 with its lines of force

and the field as a physical entity . He managed to support the overthrow of

this on a careful experimental basis. Between 1864 and 1873 James Clerk

Maxwell achieved a similar breakthrough only with clear thinking4. The starting

point of his theory, were the experimental results of Coulomb, Ampere, and

Faraday that until 1864 expressed the laws of electromagnetism in integral

form, according to the mathematics of their time and the ending point were the

electromagnetic waves.

With the formulation of Coulomb's law, which resembled Newton's

gravitational force that led to the mechanical triumphs from earthly to

heavenly things , the ' electricians ' set themselves the target to build the

electric theory on the same philosophy of action at a distance, with no

assumption about intermediate medium, believing in similar developments in

electricity

These researchers described all phenomena , grounding a complete

electrical theory, considering the electricity consists of charged particles ,

rendered magnetism an electrical phenomenon exactly as we now interpret it,

interpreted the induction with their electrons , measured the forces between

currents, between moving electrons, between accelerated electrons, ... and

then were forgotten.

Eventually the British school of physics dominated, giving a strong and

coordinated ideological struggle. It’s central philosophy was the Maxwell field

4 I believe that with Maxwell’s work starts this "the now widely noticeable arrogance

of mathematical physicists to give priority in formalism against experimental events”…

George Galeczki

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which were implementing the program of electric philosophy of Faraday, on

the idea of action by contact through a medium.

But the reader should understand that the discoveries of the first half

of the 19th century, that began in France and spread to Germany, centered

Gauss and his students (Weber, Riemann..), was not a secondary stream in

physics. It remained for almost the entire 19th century, the central line of

thinking.

We will begin recounting our story with the philosophy of the great

British experimenter Michael Faraday.

The origin of Maxwell’s field .

The origin of Maxwell’s field are the Faraday’s lines of force. These

lines are used to explain the action of forces from a distance. Faraday, the

great experimenter philosopher, was the first to conceive the concept of the

electromagnetic field. He distinguished, a reality of another class from that of

matter ( electrotonic state), it was something real that was taking place in

electric and magnetic phenomena. It was capable of carrying influences from

place to place without being treated like a mathematical structure as the

gravitational field of its time. In his opinion, the phenomena of electricity and

magnetism should be accessed through the field rather than through the

charged bodies and currents . In other words , according to Faraday, when a

current flows through a conductor , the most important aspect of this

phenomenon was not the electric current , but the fields of electric and

magnetic forces distributed to the round from the area of the current.

In 1835 for wrote for intermediate particles that their contact transfers

electrical activity:.... It seems probable and possible that the magnetic action can be transmitted at a

distance , through the action of intermediate particles in a way that similarly the

forces of static electricity are transferred in distance. Interfering particles , we

assume for the moment, that they are in a special situation that I often express

( without much success ) the term electrotonic situation….Faraday

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This Farady’s view became conviction for many generations of

physycists, after the domination of mechanical models in electricity.

How is manifested this reality for Faraday?

With lines of force which he imagined to fill all space .

Physicists were used to illustrate the magnetic forces, scattering iron

filings on a piece of paper and observing the lines formed by the action of a

magnet underneath the paper .. These lines submitted to Faraday the idea of

magnetic lines of force with which , he claimed, we can get informations not

only on the direction of the magnetic force but also on its size. The intensity

of the field, characterized by the density of field lines per unit area , vertical in

it’s direction.

..... I do not perceive in any part of space whether (to use the common phrase)

vacant or filled with matter can help myself , anything but forces and the lines in

which they are exerted …Faraday5

Later in the study of dielectric media he introduced electric field and

electric lines of force, wherein the reduction or the increase of the density of

these lines was describing the behavior of dielectric.

Faraday’s lines of force were the transport routes of action of the

intervening medium in electric and magnetic phenomena.

For example how work the lines of force in the law of Coulomb;

In Faraday’s view, the medium intervenes between the electrified balls

- whatever it is - manifests attractions and tensions which are presented in

"squinting " or " contraction " of the lines of force, also in mutual repulsions

and lateral pressures ( densification or dilution ) . So when they end up in

the other ball , these deformations are transmitted to it and move it . When

the field is more powerful the lines of force are more and we have a more

intense effect . The lines of force exert mechanical actions! The idea of this

spreading action from point to point through a medium with the effect of

adjacent and contiguous particles were applicable to every area of physics in

Faraday’s theory.

He believed in “possible and probable physical existence of lines of force

for gravitation, electrostatics magnetism”

5 Experimental researches in electricity

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He indulged in the speculation that light and radiant heat were tremors

of the lines of force: “ a notion which, as far as it is admitted, will dispense with the

ether , which in another view is supposed to be the medium in which these vibrations

take place” ….Faraday

Thus, the lines of force become an independent reality, they are the "

nerves " of the medium, which moved charged and magnetized bodies.

“…Instead of an inviolable action at a distance between two electrified

bodies, the Faraday considered the entire space between the bodies taut and full of

mutual driven off loops ..... The concept of dynamic lines are in my opinion one of the

biggest services Faraday to science ... JJ Thomson

“..... The view consolidated views of Faraday delivers a real existence in the

dynamic lines in the sense that they exist as an independent entity ....” Grimsehl-Tomaschek

....” As a result of the researches of Faraday and Maxwell we regard the properties

of charged bodies as due to lines of force which spread out from the bodies into the

surrounding medium” ... E.W. Barnes, Scientific theory and religion )

It is better to imagine (to understand Faraday) that these ' energy

pathways ' did not appear there simultaneously with the iron filings, but there

were like landscape around the magnet, and now drifted filings in their

topography . This image, intuitively touch better in our imagination than the

idea that around the magnet there is nothing and that all phenomenon is

created by placing the iron filings. This is the reason why the medium

theories eventually passed through the consciousness of physicists.

Instead of an intangible action at a distance between two electrified bodies ,

Faraday regarded the whole space, between the bodies as full of stretched mutually

repelent springs. The conception of lines of force is in my opinion one of the greatest

of Faraday’s many great services to Science ….J.J.Thomson 6

But what are these springs? How they can transfer energy? In

Faraday’s field , where mathematics are missing, physical processes become

Aristotelian qualitative descriptions :

“….According to Ampere the existence of a magnetic field is inseparably

connected with the motion f charged bodies. But according to Faraday the magnetic

6 Today this seems to be becoming rather excessive for celebrating the philosophy of

the field rather than the Faraday. The greatest service Faraday's science is vast experimental

work in which we met the electrical phenomena, not their interpretations

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field is associated , not with the motion of charges, but with the motion of the tubes

(of lines of force) attached to them;and since the tubes are flexible, there is every

reason to suppose that the tubes might move without the charges….N.Campbell, modern electricity theory Bambridge”

They are qualitative descriptions as Albert O’Rahily says7:

…we obtain the expression of the force -vector at any point. We then draw

the tangent-lines of this vector as a useful graph. To strengthen our belief we call

them “tubes” . Next we endow them with “flexibility” and declare that they “might

move without the charges” from which we started. Then we pick out one prtion of the

force on moving charges and call it “magnetic force” and similarly attribute to it

flexible independently moving tubes. Finally we declare that this double system of

tubes is “the only important theory which has ever been proposed to explain

electricity magnetism and light……Alfred O’ Rahily

Today we know that the lines of force are not so a service to science,

as a contribution to the educational process. The natural assumption which

underscores (the ether) has been removed. The situation described in the

following passage, brings us back to the operationalism in definition of

concepts in physics.

…any explanation of this kind which attributes mechanical properties to tubes

of force is highly artificial as there is no evidence for their existence. Nowadays

physicists are becoming more and more inclined to shun such explanations; so the

mechanical explanation of the interaction of electrically charged bodies is rapidly

falling into disuse. It still lingers in text-books, however, and it is important to

recognise its arbitrariness…Piley 8

Faraday, being purely experimental with little knowledge of theory,

could not perceive an electric field with the purely mathematical way. So he

introduced the lines of force and he believed in their material substance. .

Maxwell continued and described mathematically exactly the ideas of

Faraday's lines of force , the field that intervenes in electrical phenomena .

The lines of force became field and were installed as an absolute ( materials

in genesis ) reality.

7 Electromagnetic theory by Alfred O’ Rahily Dover8 Electricity Oxford 1933

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…We are unable to conceive of propagation in time, except either as the

flight of a material substance through space or as the propagation of a condition of

motion or stress in a medium already existing in space …Maxwell9

The school of Cambridge .

In prevalence of theories of electric medium which began with the

intuitive interpretations of Faraday, the main protagonists apart from him, was

the whole "school of Cambridge " ( as Tait , W.Thomson, Heavyside, etc

himself Maxwell) which is founded on mathematics of Green, Stokes and W.

Thomson, in which (school) dominant belief was that any physical action is

based on dynamics. (very Anglo-saxon!)

….I am never satisfied if I can not construct a mechanical model of

something. Then only I can understand. And this is why I could not capture the

electromagnetic theory ...... I had not a moment of peace or happiness in relation to

electromagnetic theory from November 1846 ... W. Thomson

Thomson, began to investigate the proportions of electrical

phenomena and flexibility. These surveys showed a picture of the spread of

electrical and magnetic activity. He made the suggestion that they spread like

the spreading the elastic displacement in an elastic solid. He was unable to

promote his instructions connecting the ideas of Faraday to the

mathematical proportions had invented. So towards the end of his life in 1896

after the failure of login electromagnetism with mechanical models wrote:….A single word characterizes my efforts on scientific research over the past fifty

years. I do not know anything more about the electric and magnetic force , the

relationship of the ether of electricity and matter than I knew and I taught my students

fifty years ago ....W Thomson..

Maxwell was the one who showed the " electrotonic ¨ Faraday's

situation can be represented by mathematical symbols borrowing ideas from

the researches of Thomson .

Maxwell received the torch of the " school of Cambridge " whose

electrical philosophy presented in December 1864 at the presentation of his

book ' A dynamic theory of the electromagnetic field . " He then said:9 Treatise…p.492

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…It happens a tuple of phenomena in electricity and magnetism lead to the

same conclusion as that of Optics, namely that there is an ethereal medium that

permeates all bodies and is differentiated only by their presence. That the parts of

this medium are tucked in motion by electric currents and magnets, that this

movement can spread from one part of the medium to another through forces

generated from the connections of these parts, that the influence of these forces

generated deformation dependent upon the elasticity of these connections , and

finally as a consequence of all this, it is possible to show the energy of this medium in

two forms , one as kinetic energy of the parts and the other as dynamic energy of its

connections as a result of their elasticity …Maxwell

So then we see that we are leading to the assumption of a complex

structure capable of a multitude of movements , but also having such

connections, that the movement of one region depends according to specific

relations with the movement of other parts, which moves associated with

forces that are born from the movement of the joined elements thanks to their

elasticity . Such a mechanism should be the object of the general laws of

dynamics.

Later Maxwell described the field in a mathematical way, expressing

the laws Faraday (induction) Ampere and Gauss, which were expressed in

integral form, in a system of partial differential equations, where the theorems

of Stokes, Green and divergence were dressed with physical metaphors and

changed the world. But still believing that these metaphors were real, as the

lines of force of Faraday. Now they constituted the field.

So there are two tendencies in Maxwell’s work: the first is the attempt

to explain electrical actions by the properties of the hypothetical medium

which is their carrier and the second is a purely mathematical description by

means of partial differential equations based on the assumption of certain

vectors specifying the electric and magnetic state of a body. Electricity

accordingly exists in two entirely different forms: the electric substance within

the conductor and the electric field in free space.

…The electric field is the portion of space in the neighbourhood of electric

bodies, considered with reference to electrical phenomena… MaxwellThe space all around a magnet pervaded by the magnetic forces is termed

the field of that magnet…..Livens

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The space within which the ether is sensibly disturbed and within which

sensible ponderomotive forces are exercised ..is called the electrostatic

field….Drude…There is said to be an “electric field” in a region which is traversed by lines

of force…Bragg ..In the near action theory the field strength is a reality which exists even

when the reacting bodies are removed … Hertz…E is not the actual strength of the electric field at the point where the charge

e is situated, but rather the field-strength that would exist at that point if the charge e

were not present at all…Planck We must suppose that it E exists at all points about q even when our test

charge is not present; but we can prove it’s existence only by bringing the test charge

toy Q…White….... The idea of Faraday's force field -the field- has fundamentally changed

our picture of the world ... B. Bavik

Maxwell continued and described mathematically exactly the ideas

of Faraday’s lines of force, the field that intervenes in electrical phenomena

and was installed as an absolute (material in genesis) reality. The essence of

the above field approaches in Faraday's perception is the assumption that

when there is not second charge the lines of force exist and move towards

infinity . But without the second charge they are nonexistent. The flow of

Gauss in the Coulomb field is fantastic, it is a mathematical trick to simplify

the results. But in Faraday’s scope becomes real, is the material factor that

produces the phenomena. How believable are they?

…Any statement which is made about the electric field in the neghbourhood

of a charged body cannot strictly speaking be taken to mean more than that a second

charged body, if placed there , would behave in a particular way…the physical reality

of the magnetic pole remains as questionable as that of the electric field ..J. Piley

Even more decisively Leech, carries us back to pre- Faraday period...... The electric field variables φ and E are not subject to direct observation but their

values can be derived from observations in material systems. A clear understanding

of this fact could prevent questions about the nature of these variables. Their reality

should be attributed as follows: to be considered as mathematical entities whose

importance lies in the possibility to use them to describe and predict observable

changes in the behavior of exclusively material systems ..... Leech

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Mathematical entities…but the mathematical entities became basic

concepts of real word.

….it follows that the (Maxwell’s) equations form a consistent scheme,

independently of the hypothesis from which they have been derived,…independently

of any physical interpretations which may be assigned to the various terms of the

equations….we may if we please to discard Maxwell’s interpretation. James Jean

Here Bridgman says:

…there would seem to be no necessary inherent in the requirements of the

model itself , that all the mathematical operations should correspond to recognizable

processes in the physical system. Nor is there any more any reason why all the

symbols appearing in the fundamental mathematical equations should have their

physical counterpart, nor why purely auxiliary mathematical quantities should not be

invented to facilitate the mathematical manipulations, if that proves possible…

Bridgman

Well, what is going on? May be the charge produces a change in the

state of the surrounding aether, may be the charge extend into the region

about it, or is something incapable of description in mechanical terms. But

the important point is that if another charge is placed at any point of such

space it will be acted on by a force and accelerated. The issue touches on

philosophy. In operationalist view this important point is the only point.

…I believe that a critical examination will show that the ascription of physical

reality to the electric field is entirely without justification. I cannot find a single

physical phenomenon or a single physical operation by which evidence of the

existence of the field may be obtained independently of the operations which

entered into the definition ….i do not believe that the additional implication of

physical reality has justified itself by bringing to light a single positive result , or can

offer more than the pragmatic plea of having stimulated a large number of

experiments , all with persistently negative results…..the electromagnetic field is an

invention and is never subject to direct observation. What we observe are material

bodies with or without charges-including eventually in this category electrons- their

positions, motions and the forces to which they are subject. Bridgman

Sources .

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1. Electromagnetic Theory : Alfred O’ Rahily. Dover Publications Inc. New

York

2. A Treatise on Electricity and magnetism : James Clerk Maxwell, Dover

Publications Inc. New York

3. Electromagnetic Waves : F.W.G. White, Methuen &Co. LTD. New York –

John Wiley & sons Inc.

4. Lectures on Electromagnetic theory: L. Solymar , Oxford University press

5. Foundations of electromagnetic theory John R. Reitz, Addison Wesley

publishing company

6.Aether and Electricity: Sir Edmund Whittaker , Harper Brothers , New

York

7. Electrodynamics: Arnold Sommerfield, Academic Press New York and

London

8. Electrodynamics and relativity, E.G. Cullwick, Longmans, Green and CO.

9. Electromagnetism: Hohn C. Slater and Nathaniel H. Frank, Dover

Publications Inc. New York

10. Το ηλεκτρομαγνητικό πεδίο ως εκτελεστική έννοια www.

mpantes.gr

George Mpantes mathematics teacher .

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There are the lines of gravitation force , those of electrostatic induction, those of

magnetic action I don’t perceive in any part of space whether (to use the common phrase)

vacant of filled with matter in which they are exerted…Faraday10

The man who processed and refined with mathematical modeling of

the views of Faraday, Maxwell wrote:

…We are unable to conceive of propagation in time, except either as the

flight of a material substance through space or as the propagation of a condition of

motion or stress in a medium already existing in space …Maxwell11

So there is a reality in the area round of charges and currents in the

work of Maxwell and Faraday..in theories of action by contact, the intensity of the field is a reality that exists even

though the reactive charges are removed ...... P. Hertz

even

.... The theory of Maxwell continues to yields a shelf existent reality to the vector E

independent of the presence of the test (second) charge ...... Abraham-Becker

10 “Experimental resresearches in electicity” 11 Treatise…p.492

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maxwell's field as operational concept

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