# Are EM waves just 'changing mathematical values' of EM field?

Here is my current (rather ignorant) understanding.

If we have an electron, that electron creates (or has) an electric field around it. That electric field is just 'mathematical values' attached to all points in space that tell the magnitude and direction of the EM field created by the electron. So, when we jiggle the electron, the magnitude and direction of the electromagnetic field continuously change at all the points around the electron. And these changing values of the electromagnetic field are what constitute the electromagnetic wave.

How incorrect (or correct) my understanding is?

From a mathematical point of view, your understanding isn't exactly wrong, but I think it is fair to say it is incomplete and lacks some physical interpretation.

If we have an electron, that electron creates (or has) an electric field around it.

First of all, the correct word is has. Charged particles do not create the electromagnetic field, they merely interact with it. Electromagnetic waves are actually a great way of seeing this: they are solutions to Maxwell's equations that can travel through spacetime without needing charges anywhere. They are a great example that the electromagnetic field has degrees of freedom of its own, in the sense that merely saying the charges present in a setup is not enough to determine the electromagnetic field. If you say to me "consider a Universe with no charges anywhere", I can picture a Universe where the electromagnetic field vanishes, but I can also picture a Universe with traveling electromagnetic waves. You didn't give enough information to distinguish between them both.

That electric field is just 'mathematical values' attached to all points in space that tell the magnitude and direction of the EM field created by the electron.

Mathematically, yes (apart from the point I already mentioned that the electron does not create the electromagnetic field). But it is worth recalling that these values have physical meaning. For example, light is an electromagnetic wave.

So, when we jiggle the electron, the magnitude and direction of the electromagnetic field continuously change at all the points around the electron. And these changing values of the electromagnetic field are what constitute the electromagnetic wave.

To be fair, something is a wave if, and only if, it respects the wave equation. The process you are describing is a particular way of creating electromagnetic waves, but it doesn't need to be the only one. Moreover, as I mentioned, these changing values have meaning. Light is an electromagnetic wave, so they are much more physically profound than mere numbers.

How incorrect (or correct) my understanding is?

In my opinion, you're on the right track, but there are still some things that might not be clear. I hope this answer helps, but feel free to ask for further clarification on the comments =)

• Thanks a lot for answering. Firstly, I do realise the physical importance of the mathematical model. Second, is the electromagnetic field not 'due to' charges? i.e charges are mere interactors of electromagnetic field. So if there were no charges in the universe, we could still have the concept of electromagnetic fields? Third, what other ways are to produce electromagnetic fields without 'electron jiggling'? Again, thanks a lot for helping me. Commented Dec 15, 2022 at 5:27
• @RohitShekhawat Nobody can say whether the electron makes the field or the field makes the electron ..... although in advanced QM they prove that a field (EM) can be so excited with energy as to produce a particle (electron or positron). So in this sense the field creates the particle. Commented Dec 15, 2022 at 15:50
• @RohitShekhawat The EM field can transmit energy or forces .... for energy we have real photons and we can observe the individual quanta.... for forces we have virtual photons which we can never observe directly .... we can only measure forces. Commented Dec 15, 2022 at 15:54
• @PhysicsDave that is incorrect. The particle associated with the electromagnetic field are not the electron and positron, but rather the photon. One can argue that the electromagnetic field is more fundamental than the photon due to the Unruh and Hawking effects. Furthermore, charges do not create electromagnetic fields: if there were no charges, the EM field would still have energy and momentum, and hence interact gravitationally Commented Dec 16, 2022 at 0:27
• @RohitShekhawat "we could still have the concept of electromagnetic fields?" yes. We might call it something different, but it would still be there, since it would still interact gravitationally. Just like dark matter. "What other ways are to produce electromagnetic fields without 'electron jiggling'?" Any accelerated charge will radiate, so you don't need to jiggle it. Commented Dec 16, 2022 at 0:30

There is a lot more to this question than you might expect.

You can argue that an electric field is just mathematics. Is it even real? How is energy "stored in an electric field"? talks about that.

But there is something physical going on behind the math. The point of the math is to describe how charges interact with each other.

In classical physics, some particles are charged. That is, they exert forces on each other. If you place one near another, they will accelerate away from each other (two electrons) or toward each other (an electron and a proton). By contrast, an electron and neutron do not exert forces on each other.

The laws are relatively simple as long as the charges hold still. If one charge moves, there is a time delay before the other charge notices the change. The math is simplified if the problem is divided into two parts.

In part 1, a charge creates or has an electric field. The field is a mathematical description that fills all space. It describes how strong the force would be at a point if another charge happened to be there. If the charge moves, the change in the electric field spreads out at the speed of light. A moving charge also generates a magnetic field. These fields carry the "news" that the charge has moved.

In part 2, another charge feels the force of the electric and magnetic fields.

Maxwell's equations are the math that describe all this. For many years, these equations told us everything known about charges and electromagnetic fields.

If you set up some charges and solve Maxwell's equations for that charge distribution, you find the electric field. If you set up a vibrating charge, Maxwell's equations tell you oscillating electric and magnetic fields spread out like a wave. We call this light. If light strikes a charge, the charge feels an oscillating force. If this happens to be in a receptor in your eye, you see the light.

Maxwell's equations describe all the electromagnetism we see in classical physics. They describe a few things we don't see. You can set up empty space and solve for the electromagnetic fields. You can find light that is consistent with this. It propagates from the infinite past to the infinite future with nothing create it. This is a useful approximation for starlight that has left its star far behind. But all light (classically) is caused by the movement of charges.

Likewise, you can imagine magnetically charged particles and figure out the resulting fields from Maxwell's equations. We don't know of any reason why such magnetic monopole particles can't exist. But searches haven't turned up any.

So far, the fields could just be a mathematical trick. Charges and forces are real. But fields? See In what medium are non-mechanical waves a disturbance? The aether?

You can see why fields are a useful trick. We say that light in a distant star generates light. Years later, the light hits the lens of a telescope. We can understand how charged particles in the lens redirect the light. Given the shape of the lens, light can be made to converge toward a focal point. A detector at the focal point can respond to light in a way that generates a permanent record.

It is a lot harder to describe all this in terms of vibrating charges in a distant star setting up vibrations years later in the charged particles of a telescope lens that are just right to set up more vibrations in a detector.

But in quantum mechanics, point particles turn out to be too simple a description. Electrons are sort of like particles and sort of like waves.

It turns out that light is sort of like a particle too. This is a photon. How can a red light photon be different from a blue light photon? It is a little harder to dismiss a particle as a figment of math.

• Thanks a lot for the explanation. I really cant thank you enough for such a detailed answer to my question. Commented Dec 15, 2022 at 10:33