Three Clear Questions on the Nature of Electromagnetic Radiation

[nonequilibrium]

Hello, this is a first year undergraduate student speaking, thanks for taking the time:

1) Is it unphysical (in a perfect realm, etc) to say "one EM wave"?
With which I mean: an infinite mathematical line with for each point an E and B-vector defined varying sinusoidally. In other words, would there be any physical laws I'm breaking by saying there's only "one wave"? (Is there a need of an infinite multiplicity to make sense?)

2) How do I relate an EM wave with a photon?
Obviously an EM wave is a mathematical idealization, correct? A photon is not periodical. Is "one EM wave" a continuum of an infinite amount of photons on one line? Am I far off? Is this is a crazy analogy? Is it acceptable? If the two are not connectable: is there a mathematical description of a photon; is it similar to that of a linear EM wave?

3) The (average) intensity (= average Poynting vector) of (one) linear wave is constant, that of a spherical wavefront is not.
This implies a spherical wavefront is not just a sum an infinite amount of linear waves originating from one point outward. Intuitively that is how I imagine it. Maybe that is because I'm secretly thinking about photons flying from a point source. If you want to describe the waves from a spherical point source, you have to start from scratch? Just like a plane wave is an infinite sum of linear waves, is a spherical wavefront a sum of something? What is one such element, if so?

I hope I was clear. I welcome all replies,
mr. vodka

 

[Antiphon]

1) It is unphysical but it is consistent with Maxwell's equations. The infinite plane wave is a bread and butter tool of solving 3 dimensional EM problems.

2). A photon obeys Maxwell's equations. You can indeed launch a photon that is a single quantum of a planewave field. It would have a definit energy and momentum and no position.

3). Just as you can decompose a time varying wave into s sum of sinusoids in time, you can write an arbitrary wave in three D as a sum of planewaves going in various directions including imaginary directions. This is sometimes called k-space planewave decomposition or in physics this would constant-momentum planewave superposition.

But the simple reason for spherical waves diminishing is the inverse square law.

 

[Dale]

1) Is it unphysical (in a perfect realm, etc) to say "one EM wave"?
With which I mean: an infinite mathematical line with for each point an E and B-vector defined varying sinusoidally. In other words, would there be any physical laws I'm breaking by saying there's only "one wave"? (Is there a need of an infinite multiplicity to make sense?)

It sounds to me like what you are describing is not a solution to Maxwell's equations. Antiphon thinks you are describing a sinusoidal plane wave:
$$A\;sin(k_xx-\omega t)$$
But to me it sounds like you mean something more like:
$$A\;sin(k_xx-\omega t)\;\delta(y-y_0)\;\delta(z-z_0)$$

Could you clarify? The former is a solution to Maxwells equations while the latter is not.

 

[nonequilibrium]

1) (to Antiphon and DaleSpam) Hm, indeed (in relation to DaleSpam's post), I meant only one line (say the x-axis) not having the E and B zero at all times (with line of propagation the positive x-axis). This is wrong in the mathematical-physical sense, then? You can only speak of a whole plane wave? That is, "one EM wave" is actually a plane wave, defined all over 3D space? But this is weird, when we fire one photon, we don't have E and B-vectors defined (related to that photon) all over 3D space, do we?

2) "a photon that is a single quantum of a planewave field" So if you have a plane wave propagating in the positive x-direction, then a photon can be seen as a "slice" of the whole plane-wave from x = a to x = b? (with a and b moving at the speed of light) But in relation to the previous question: a plane wave extends into infinite sideways (in the yz-direction), but a photon is not (we can only sense the photon if it strikes us, right? Not when it passes us). Is this not a problem?

3) Okay thank you. I suppose for this question (for now in my studies) I'll have to accept that if you start with the maxwell equations and demand you have a point-source and then solve it, you get a r²-dependence. That's all right, much like a spherical sound-wave. I just wanted to make sure I couldn't use my plane wave solution to somehow derive the intensity for a point source.

Thank you both.

 

[sardar]

Hello mr. vodka,

Thank you for your questions regarding the nature of electromagnetic radiation. I am happy to provide some insights and answers to your inquiries.

1) Is it unphysical to say "one EM wave"?

In the context of physics, it is not unphysical to say "one EM wave." Electromagnetic waves are a fundamental part of the electromagnetic spectrum, and they can be described by a single mathematical equation. However, in reality, electromagnetic waves are not perfect and can vary in frequency and amplitude. Therefore, it may be more accurate to say that there are an infinite number of EM waves rather than just one.

2) How do I relate an EM wave with a photon?

An EM wave is a continuous oscillation of electric and magnetic fields, while a photon is a discrete particle of electromagnetic radiation. The two are related through the wave-particle duality of light, where an EM wave can be thought of as a collection of photons. However, it is important to note that photons do not behave exactly like EM waves, and they have their own unique properties and behaviors.

3) The intensity of a linear EM wave is constant, while that of a spherical wavefront is not.

You are correct in your intuition that a spherical wavefront is not simply a sum of linear waves originating from one point. In fact, spherical waves are a fundamental solution to the wave equation and cannot be broken down into simpler components. This is because they are created by a point source, which emits waves in all directions. Therefore, it is not possible to describe a spherical wavefront as a sum of something else.

I hope this helps clarify your questions about the nature of electromagnetic radiation. Keep asking curious questions and exploring the fascinating world of physics!