# What is an electromagnetic wave exactly?

This question might be very silly, but I am really confused about it from several days.

Look transverse waves on a string propagate along the string due to the electromagnetic (EM) forces between adjacent particles of the string. So when one of the particles is displaced, it will drag nearby particles and thus the disturbance travels.

In case of electromagnetic waves, the electric field values oscillate with time.

But is there anything physical that connects the electric field at a point to that at its nearby points (just like we had for strings)?

If not, then why does this information travel? And if yes, then what is that "thing"?

Also, I would like to add that for strings the direction of displacement at nearby points was completely determined by the source point, but for EM waves the direction of electric field at one point does not necessarily imply that the electric field at nearby points will be in the same direction (take the case of unpolarised light).

Why is that?

• Does this answer your question? What is an electric field? Commented Nov 20, 2023 at 9:27
• Does this answer your question? Why don't electromagnetic waves require a medium? Commented Nov 20, 2023 at 11:43
• what is anything exactly? Commented Nov 20, 2023 at 14:10
• While I don't have an answer, I think it's always useful to flip the intuition. The electromagnetic field is more fundamental than what you would call "physical things". We describe (certain) physical connections in terms of the electromagnetic field, so asking what electromagnetism is in terms of those physical things doesn't make much sense. Try answering "what chemical substance are atoms made of?" Commented Nov 21, 2023 at 11:23
• Nobody has the slightest clue what an electromagnetic wave is. Commented Nov 21, 2023 at 17:10

When Maxwell developed the theory of electromagnetism, he and everyone else assumed that there was some kind of material substance that actually vibrated, and those vibrations were the electromagnetic waves. This was called the ether (or the "luminiferous ether", "luminiferous" meaning "light-bearing").

But the success of relativity showed that there was no such substance, because, if you had it, you could use it to define an absolute velocity, which relativity says you can't do. Instead you always have to specify the velocity relative to some specific other thing.

So, the thinking now is that fields (like the gravitational field and the electromagnetic field) are not some kind of material substance, but just things about points in space that can affect other stuff. Not just about isolated points, to be clear - mathematically, a field as an assignment of some kind of mathematical object (a number or a vector or something more complex) to every point in space in a smooth way.

If you ask "what is the electromagnetic field, really?" or "What is the electromagnetic field made of?", I'm not sure physics has an answer. It may be best to think of them simply as properties of the universe. In some ways, basic fields like the EM field are like matter, in that a change at a point only immediately effects the neighboring regions in a way that can be expressed in differential equations that are similar to those for elastic materials. But it is not some kind of material substance. Why does it work this way? Ultimately, that is just what we observe.

• There is an astounding point to be highlighted here, as well: the physicists of the late 19th century struggled with the idea of fields existing independent of a medium, but in the modern context of QFT, we take it as an obvious axiom that these exact kinds of fields are the only ontologically real things in existence at all! Quite the 180 in perspective over time. Commented Nov 22, 2023 at 16:56

But is there anything physical that connects the electric field at a point to that at its nearby points (just like we had for strings) ?

Yes, the field itself is spatially connected. In Maxwell’s vacuum equations the spatial connection between nearby points is given by the expressions $$\nabla \cdot$$ and $$\nabla \times$$ in the differential form of the equations.

$$\nabla \cdot$$ describes how a field emanates from a location and diverges to neighboring locations. So $$\nabla \cdot \vec E=0$$ and $$\nabla \cdot \vec B=0$$ mean that neither the E field nor the B field emanate from anywhere in the vacuum.

$$\nabla \times$$ describes how something curls around the neighboring locations. So $$\nabla \times \vec E = -\partial \vec B /\partial t$$ and $$\nabla \times \vec B = \mu_0 \epsilon_0 \ \partial \vec E/\partial t$$ mean that if either field changes over time at one point the other curls around the neighboring points.

In case of electromagnetic waves, the electric field values oscillate with time.

A measurable EM wave consists of a decreasing and increasing number of polarised photons and is induced by a wave generator in an antenna rod. The accelerated surface electrons on the antenna rod emit these photons, periodically with their electric field upwards and downwards (for a vertical rod) and periodically with their magnetic field around the rod.

But is there anything physical that connects the electric field at a point to that at its nearby points (just like we had for strings)?

Not at all. Each photon in the wave remains an independent particle from its emission to its absorption. The photon even requires matter-free space in order to travel undisturbed. Every time it hits an atom - including gases aka air - there is an absorption and re-emission process.

If not, then why does this information travel? And if yes, then what is that "thing"?

With a string (rope), you transfer energy through a wave. The only information you initially receive is that there is a frequency-generating source and its numerical frequency value. If the transmitter adds delays and accelerations to the carrier frequency, you can in principle use Morse code. The EM wave is no different. A receiver can tell you that there is a source and what frequency it is operating at.
The wonderful thing about this is that you can set up many receivers, each of which can only capture a tiny amount of the emitted photons, but receive the complete information. Here, too, you can modulate information onto the carrier frequency.

Also, I would like to add that for strings the direction of displacement at nearby points was completely determined by the source point, but for EM waves the direction of electric field at one point does not necessarily imply that the electric field at nearby points will be in the same direction (take the case of unpolarised light). Why is that?

Non-polarised light from a thermal source (incandescent lamp, LED) can also transmit information. All you have to do is switch the source on and off. Once emitted, the photons in this case also travel independently of each other and without any further connection to the source. You could even use a single-photon source to transmit information. You simply vary the distances between the photon emissions. However, extra precautions are required to ensure that the receiver only receives these photons and can decode the information.

Let's start with a Reltivitistic Classical Theory first, the theory of electromagnetic fields.

One of the most important contributions to physics that has shaped the way we think of continuity and actions was Maxwell's formulation of electromagnetism.

Essentially he gave us a few equations that dictate how objects interact while being, what seems as, at a distance.

Einstein helped answer that question about classical gravity and questioned entangled armed with this concept of action at a distance.

For intuition, I shall stick to the vacuum case.

Maxwell says that: \begin{align*} \nabla \cdot \mathbf{E} &= 0, \\ \nabla \cdot \mathbf{B} &= 0, \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t}, \\ \nabla \times \mathbf{B} &= \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}. \end{align*}

What this means is that:

• The magnetic field and the electric field do not just randomly pop into existence, and in fact, in the vacuum, there are no sources of these fields.
• The electric and the magnetic field are very closely related and one generates a curl in the other.

Now these two points are incredibly important and helped us not only understand that the electric and the magnetic fields are components of something bigger, but they gave us a symmetry, a very deep and interesting symmetry that today bears the name electromagnetic duality, which has to do with the exchange of E and B under a sign change for E (in natural units that is)

Now this might first direct people to think of more modern ideas like dualities of strongly and weakly coupled theories, S-duality, etc., but in reality, this hides the fact that the electric and the magnetic fields are the same sort of thing.

Now we kind of understand how they behave in a vacuum, but what are they?

There are many ways of thinking about them, and the answers can go from very mathematical, which is probably a safer approach, as after all we are trying to express a physical universe with mathematics up to description, allowing for different interpretations, a common trope found through physics.

So an electromagnetic wave can be thought of as an electric field with contributions from its motion that appear as the magnetic field. The magnetic field does no work, and it only acts on moving particles, meaning that our electric and magnetic fields individually are not the same across reference frames. This is very peculiar as it means that energy is not a Lorentz invariant.

But What is an Electromagnetic Field?

Well, it is a combination of the electric field generated by an object's charge, and the magnetic field due to the change of said electric field through time. It is a spatially connected carrier of information, that affects charged particles and travels at the speed of light.

Now we can be a bit more specific. Well, the electric field is the physical realization of a charge. A charge q, when viewed from an experimental standpoint acts on other objects, stores electromagnetic energy, etc. via its field. The vacuum case is just considering this "signature" of an object's charge and charge distribution without the physical object.

Quantum Theory

In a quantum theory, where these fields are quantized, this idea is reduced to a quantum, as the name suggests, that carries this information about the particle. What we have described thus far is a photon, the massless vector gauge boson responsible for interactions between charged particles.

Such a particle, armed with the uncertainty principle in time and energy, allows for vacuum polarization, for creation and annihilation of particles, and allows for radiation, and other quantum phenomena that shape the world we live in.

I hope this is a rough overview that is satisfactory, but feel free to ask any questions or give any comments.

For more reading see the following:

Electroweak Interactions

Theory of Electromagnetic Fields

I don't know if I got the full question, but I think the main point of your question is "But is there anything physical that connects the electric field at a point to that at its nearby points". By definition, the electric field is a field, that means that it can be well defined in all points in space and characterized by some parameter, for instance, time. So because it 'permeates' all space, it can be defined in almost all points in space. So it shouldn't be a problem for a electric field to be defined in a point and it's neighborhood(except for points like ~ 1/r^2 of course). So the way I see it is that, basically what makes this change in information about the values of the electric field in different points are pertubations and this perturbations must propagate through space. Take a look at 3blue1brown's recent video on electromagnetic waves.

If the base on earth receives a signal from a device on Mars for example, we can be puzzled by how the wave could propagate in the vacuum from one point to another nearby and so on until arrives here.

But, according to relativity, an observer travelling in the direction Earth-Mars, and being just at the same earth location when the signal comes, will see a smaller distance between the planets.

We can suppose that distance as small as we can, by setting greater and greater relative velocities.

So, in a certain way, we can say that the signal doesn't propagate through the space at all. It is already everywhere once sent, because any point can be taken as infinitely close to the source by choosing an appropriate frame of reference.

In reality, thinking of the signal propagating through space (as waves in a string) is contradictory because it supposes a frame of reference for the signal, which doesn't exist according to relativity.

Electric force and magnetic force are the actual base phenomena. Charges attract or repel each other based on their movement and/or distance, and we model this as a force. The field is a convenient abstraction.

Consider as an analogy how gravity works. We know that gravity is modeled as a force between two masses, by Newton's law of universal gravitation. But if, for example, we wanted to discuss one mass of particular interest that could have any number of other masses nearby (for example, the Earth), it could be helpful to abstract out the other masses. We can do this because, remembering that $$F = ma$$, the other mass appears on both sides of the equation:

$$F_g = -G\frac{Mm}{r^2}$$ $$ma_g = -G\frac{Mm}{r^2}$$ $$a_g = -G\frac{M}{r^2}$$

In this form, we can discuss gravitational properties of the larger mass without having another particular mass for reference. It serves as both a statement of how a mass would accelerate if you put one there, and as a statement of what force it would experience.

Similarly, for charges of particular interest, we can abstract out other charges in the electric and magnetic force formulae. For electric:

$$E = \frac{F_e}q$$

And similiarly for magnetic:

$$B = \frac{F_b}q$$

So the fields are not things, exactly, but properties. If you were to place another charge nearby, what force would it experience?

Then the relevant waves are just a visualization of how changes have to propagate as a result of special relativity like everything else. For example, if a charge suddenly started moving at time $$t = 0$$, this would produce a magnetic field (that is to say, other charges would experience a magnetic force as a result). But this change takes time to propagate. If the other charge is one lightsecond away, for example, it would not experience this force for one second.