Electrostatics is an approximate model of the electromagnetic reality. In electromagnetic consideration, temporal changes are related with the electromagnetic wave (and energy) propagation. The sources (charges, currents, dipoles) of such waves are always assumed but the fields are more important in the analysis mainly for next reasons: we are not aware of sources, the electromagnetic energy is coming as waves and presents only a history of sources.

Electric and magnetic fields are really an abstraction. In a general dynamic case they cannot even be measured (only the dynamical observables constructed from products of them can be measured). Inspired by Faraday, Maxwell introduced the electric field in a limiting process as follows: You arrange a set-up where an electrically charged particle is kept still (static, non-moving) and then you move a second charge, infinitely slowly (adiabatically, as the term goes) from a place very far away to a place near the first charge. Then you measure the force on this second charged particle and divide the result with its charge and then you get the electric field produced by the first particle at the position of the second particle, also called the test particle. However, the charge of this second particle (the test particle) must be infinitely small, not to perturb the measurement. Clearly, this process is a purely mathematical one and cannot be realised in practice. What can be realised in practice is to measure the (time-varying) linear and angular momentum of a test particle of finite charge, typically the current in an antenna - this is just classical mechanics. But one has to remember that the momenta obtained by the test particle in such an experiment is due to the transfer of momenta carried by the field, and that these field momenta are *second-order* in the fields (typically the electric field vector multiplied by the magnetic field pseudo-vector). So this experiment involves interference (superposition) and everything that follows from it. In fact, this property of the fields were taken over in quantum mechanics where the wave functions (spinors) are fields that cannot be measured directly. See the first chapter in my textbook "Electromagnetic Field Theory" that is available for free in draft version from http://www.plasma.uu.se/CED/Book and also Freeman Dyson's essay on http://www.clerkmaxwellfoundation.org/DysonFreemanArticle.pdf

The clearest demonstration that the electromagnetic field is real is to stand in the sun and feel its effect on you. Light consists of waves in the electromagnetic field, carrying both energy and momentum, and interacting with matter. Action at a distance is an old-fashioned idea that has disappeared from modern physics. While the electric and magnetic fields started as mere bookkeeping devices, it was later understood that these fields were as dynamic as anything we would consider matter, and deserve to be on a more equal footing with it. In fact, the Standard Model of elementary particle physics, which describes all known matter and interactions except gravity, contains nothing but fields. Particles appear as the quanta of the fields, so that electrons are quanta of the electron-positron field, and photons are the quanta of the electromagnetic field. These photons are observable via their interactions with matter, just as matter is observable via its interactions with photons. The electromagnetic force between two electrons is directly attributable to the transfer of momentum when a photon emitted by one is absorbed by the other.

When you stand on the sun you feel the energy, which is the square of the electric field, not the field itself. Dyson discusses this in an admirably clear way in the essay I referred to earlier.

Dyson's essay is brilliant, of course - he is quite a deep thinker, but I find his dimensional argument rather strange, since electric fields are easily measured in Volts/meter, which everyone understands. I would consider anything that is gauge invariant and carries energy and momentum to be "real". If a rock lands on me, I feel the energy and momentum, but the rock carrying it was real. Why should the electromagnetic field, which is also capable of transferring energy and momentum to me, be considered to be any less real? I see the emergence of fields as real physical objects to be the most important conceptual advance to arise from Maxwell's electrodynamics. In quantum field theory, which provides a complete representation of known physics, and thus might be taken as a definition of reality, everything is a field. That means there is no logical basis for considering photons to be less real than electrons. Granted, quantum field theory seems to us to be abstract and remote from what we like to think of as reality, and that was part of what Dyson, who is one of its pioneers, wanted to point out. As he noted, quantum mechanics takes us even further away from normal experience. Bur our perception of reality is largely colored by being big, non relativistic semiclassical bound states accustomed to interacting with other such states. This places us very far from what seems to be the underlying structure of the universe, and prejudices our ideas about what is real.

The point is that here is no way you can measure, observe or sense the electric field *directly* in electrodynamics because the way it was defined (in electrostatics). That's why it's not an observable in the same way as field energy, linear momentum, and angular momentum are. This is the point that Dyson is making in his essay. These latter observables are second-order products of the field (quadratic, bilinear), whereas the field itself is first-order (linear) and has the same standing in electrodynamics as the wave-function (or spinor) has in quantum mechanics. In fact, it is perfectly alright, as for instance Majorana did, to consider the EM fields to be photon wave functions and hence Maxwell's theory a first-order quantum theory. And you cannot measure a wave function directly. If you consider fields/wave functions to be real physical objects, it's fine with me. I am of a different opinion. As Feynman was supposed to have put it: "You just shut up and calculate". As long as you calculate correctly and get the same results, both views of the fields are acceptable.

For me, the fact that photons can be detected at least as readily as charged particles (and much more readily than neutrinos) is sufficient to establish their reality. I certainly accept the fact that opinions on what it all means vary widely among physicists, and it is interesting that classical physics is enough to raise such questions. I was most surprised by Dyson's stance, since local quantum field theory did more than anything (short of supersymmetry, which remains to be seen) to place matter and gauge fields on comparable footing. I assume the objections raised about the reality of electromagnetic fields must apply to the other gauge fields as well, for similar reasons, but an interesting followup question might be - is the Higgs field real? (I would say yes.)

Photons represent (quantised) energy, an observable that is second-order in the field. Photons do not represent the field itself.

Let me emphasise that I am talking about what is *observable*, i.e what can be directly measured in an experiment. I am not talking about what is "real". That's an entirely different thing, related to your own subjective opinion about reality and touches upon things like religion. The electric field cannot be measured directly in an experiment. Whether a person considers an unobservable quantity to be real or not be real is up to that person's own opinion. This is not what Dyson (and I) discuss. We discuss the physics.

In that case, I am even more puzzled, since what does an antenna respond to if not the electric or magnetic field interacting with it? The response is linear in the field and certainly measurable. I was listening to one last night. Parametrization-dependent objects such as gauge potentials and wave functions would certainly fail the test of measurability (and the electron field, which is both gauge-dependent and Grassman-valued fails even worse), but the electromagnetic field-strength tensor is gauge invariant and has a linear interaction with charged currents, which provides a means of direct measurement.

An antenna is a device with (nearly) free electrons in it. Electrons have charge and mass. The response to an incoming EM field is that the electrons start to oscillate, producing an antenna current that is fed into a receiver and demodulated there. The force that gets them to oscillate is the time derivative of the linear momentum (Newton's second law; Euler's first law). This linear mechanical momentum of the particles is provided by the linear momentum of the incoming EM field. This is what the law of conservation of linear momentum in Maxwell's theory predicts. Hence, the EM field interacts with the antenna (electrons) via the field linear momentum which is the electric field vector cross multiplied by the magnetic field (pseudo-)vector, i.e., a quantity that, in Dyson's (and my) words, is *bilinear* in the fields, *not* linear. Hence, the antenna response is not linear in the fields. The density of the linear momentum carried by the field is also known as the Poynting vector divided by the square of the speed of light. This is known as "Planck's relation".

I am familiar with the details of this description and its derivation. There is a lot of subtlety in the definition of the energy-momentum tensor in the presence of sources, and the fact that any current used to probe a field also acts as a source necessarily complicates measurements. But if I put a known charge in an external electromagnetic field, the Lorentz force equation gives it an acceleration linear in the field. A lot of particle physics experiments are based on this. Also, the current from either an electric or magnetic dipole antenna is proportional to the field strength and is readily measured. The magnitude and direction of both the electric and magnetic fields can be observed in this manner, not just bilinear products. I've used devices for measuring fields myself, so I am completely confident in saying that I have observed and measured them directly.

hi

That does not explain why we can block that from being received by the sensor.

Louis

The definition of electric field is very clear: force by unity of electric charge. And given that the Coulombic force depend of the distance therefore does it the field.

Given that the electric charge is constant and invariant under space-time transformations, it could seem that is the same to speak about force or fields, but isn't. If we have an isolated charge it is stupid to speak about force because this concept needs to have one idea of where it is done. Therefore we could think in a field as a force distributed in the space. So far nothing new in the physics, only in the language or in the concepts. Even they could be quite confuse if we try to define a field only with these ingredients.

What makes important the concepts of fields is that they move or change in space or time. For instance, if you have an electric field in between the plates of a condenser and you move it with a velocity v parallel to the plates what happens is that you obtain a new field: the magnetic field multiplied by something proportional to the velocity. And the miracle comes when both fields, electric and magnetic, can associate orthogonally between them for given a Poynting moment and to be indepent of the sources (electric charges, solenoids,..). The fields are then free and can carry momentum and energy behaving as new particles: photons which are the bricks of the fields. In QED the electromagnetic field is made by oscillators which form the photons and which were the born of the new Quantum Physics when Planck needed to introduce them for solving the problem of the black radiation of matter. But long before, the optics or the electromagnetic radiation could not be understand without the pure concept of electric field or magnetic field, which two faces of the same body.

Therefore it seems that the electric field is one physical entity as the magnetic field. Difficult to define, although much easier than defining electric charge or other fundamental concepts of physics, But what is more clear to understand is the electromagnetic field represented in a monocromatic wave where the electric field transforms in magnetic and so on,

@Scott Yost - You do not measure the magnitude and direction of the electric field with an antenna. You measure the time-varying antenna current. The time variation of the current, i.e. the acceleration of the charges in the antenna, is, according to Newton's 2nd law, due to a force acting on them. This force is the time derivative of the mechanical linear momentum of the charges. This time rate change of the mechanical linear momentum of the charges is in turn caused by the transfer to them from the time rate change of the EM linear momentum. The density of the EM linear momentum (the Poynting vector) is proportional to E cross B. From this physical scenario, and neglecting re-radiation effects, you can calculate what the approximate electric field should have been at one single point on the antenna (usually the phase centre). It's not always the case that this inversion process of "measuring" the electric field gives a unique result.

There are a lot of ways to complicate the description of an antenna, but if I just put a straight wire in an electromagnetic field, only the electric field can accelerate the charges along the wire. The response is linear in the component of the electric field along the wire and independent of the magnetic field: a = qE/m for a free charge in the wire, and independent of the magnetic field. If I measure the acceleration and know the mass and charge, I would say that I have just measured the electric field directly, without having learned anything about B. The EM field also interacts with the fixed charges in the wire, but the fact that they are held fixed implies that external forces are acting on the antenna, so that momentum is not conserved and one could not infer anything about the momentum content of the fields from this measurement.

please read my daft....

https://www.researchgate.net/publication/315825530_Theory_of_Empty_Universe_Second_Draft

Article Theory of Empty Universe (Second Draft)

Dear respected colleagues,

The electrostatic field is the domain of the action of an electrostatic charge. The electric field intensity is the electrostatic force acting upon a unit positive charge located in a specific point in the field where the electric field intensity to be determined. So, as a force per unit charge it is a vector having magnitude and direction. Its magnitude in the field of point charge is determined by Coulombs law where the electric field intensity will decay as 1/x^2 where x is the distance from the point positive charge.

Accordingly at some practical distance, the intensity of the electric field will decay to very small values. This is a very important property of the electric field that it will decay rapidly with the distance from its originating charge.

The other important property is that there is positive and negative electric field intensities as there is two types of originating charges positive charges and negative charges. For visualizing the electric field intensities in a space of electrostatic charges, one has introduced the electric field lines forming electric field maps where the direction of these lines represents the direction of the electric field and their density represent the electric field intensity.

One very important other property is that these field lines are sourced from positive charges and sinking at an equal negative charges.

Which means that one can screen the positive charges by negative charges and vice verse.

In fact all materials are naturally neutral as they are composed of neutral atoms.In the atom the electron cloud around the nucleolus screen its electric field. So the negative charges blocks the electric field by the positive charges and vice verse.

Best wishes

If you read my draft, please read this work...

Article Theory of Empty Universe ( Gravity )

hi

Many interesting comments but none to explain why it is possible to shield the effect of a negatively charged object using a simple neutral wooden ruler. Try the experiment and you will be convinced that there is something real leaving the charged object that goes in all directions at speed c. Then explain what that is.