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Movpasd t1_j8k0w6r wrote

Before I try to answer your question, I think you're suffering from a (very common!) issue with your approach to physics. I've written a lot about this topic on Reddit before, so I'll link some comments: see here, here, here, and here. Though it's not directly connected to your question, I hope that these can be helpful!

Now to get to your question. I'd start by not trying to understand photons right off the bat. It'll be much easier to first try to understand the electromagnetic field classically, and then try to integrate quantum effects into your understanding. The relationship between photons and the classical field is very tricky, and I find it's the cause of much confusion for physics enthusiasts and students.

In classical/Maxwellian electrodynamics, the electric and magnetic fields are vector fields. That is to say, they are mathematical functions which assign a three-dimensional vector to each point in space. These must obey Maxwell's equations (that's part of the theory).

Wave solutions to Maxwell's equations look something like this. (Shockingly, I couldn't find a clean diagram like this on the Internet, so I had to make one in Paint.) Of course, I can't show you every single vector attached to every single point in space on my diagram, because there's an infinite amount of them, so I've just drawn them for a select grid of points. I'm using the notation where vectors going into the plane are drawn with a cross, and those sticking out of the plane with a dot.

The size of the arrows is meant to represent the relative magnitudes of the fields as they evolve through space, but the actual lengths on the diagram don't matter -- the electric and magnetic fields don't have units of distance.

Hopefully this helps you visualise the idea of wavelength -- let me know if you have follow-up questions!

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Grand-Tension8668 OP t1_j8k7co9 wrote

Thanks a lot for this reply. I've definitely started recognizing what you're trying to say in those other posts, that things really approach a point where you need to trust the math and coming at it the other way around fails to create an accurate understanding of things. (And that our intuitive understanding of what "stuff" is doesn't really hold water in an absolute sense).

I think I'm coming out of this with a less incorrect "mode C" mental model, at least– EM fields change over time / distance (one in the same in this case but whatever) in a cyclical way, so they're waves. We can measure how long it takes for one "wave cycle" to happen, as in the distance traveled as a point oscillates between the electo- part and the -magnetism part. ...Which is certainly still a pretty wrongheaded explanation and I really need to start learning the math of physics in my spare time.

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aiusepsi t1_j8miaub wrote

EM fields in general aren't cyclical (I would usually say 'periodic' for what you mean by that), for example consider the magnetic field surrounding a magnet; that's completely static, so it doesn't change over time, and it just gets weaker with distance from the magnet.

Electromagnetic waves are, mathematically, a lot like lots of other kinds of waves, like sound waves, or waves on the surface of water. All your need is some kind of field, that is, a property which exists at each point, and for the physics of that field to obey a particular form of equation, and waves will exist in that field. For obvious reasons, that kind of equation is called a 'wave equation'.

For sound waves, the field is air pressure. On the surface of water, it's the height of the water's surface. Those are scalar fields, that is, those properties can be described by a single number. EM is a bit different because it's a vector field with two vectors at each point in space. But ultimately, they end up looking very similar.

If you graph out air pressure on one axis and space on the other axis for a sound wave, you get a sinusoid, i.e. it looks the same as graphing y = sin x. And that's exactly what you get if you graph out just the length (i.e. magnitude) of the electric field vector (rather than worrying about the direction of the vector) along the direction the wave is travelling. Just pretend it's a scalar field like air pressure!

Graphing out the magnitude of the magnetic field is basically the same, the electric and magnetic fields vary in the same way in an EM wave, just that the electric and magnetic field vectors are at right angles to each other, and they're both also at right-angles to the direction the wave is travelling.

Anyway, for all of the above, wavelength is just the distance between adjacent peaks on the graph.

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Grand-Tension8668 OP t1_j8morhq wrote

...Well, it's helpful to be reminded that EM fields aren't necessarily changing their properties over time, at least

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Movpasd t1_j8qvfax wrote

I'm very glad you found my reply useful!

If you're set on continuing to teach yourself physics (which I think is a very good, though time-consuming idea), I'd start by making sure you're on top of your high school/A-Level maths and physics (KhanAcademy is a great place for this), and then move onto some first-year university introductory textbooks. You don't have to read them back to front -- start with the first chapter, take your time, do the exercises, and when you get bored switch to a different book. (I really like Griffiths' textbooks, but YMMV.)

A good search term is "introduction to [topic]" or "introductory [topic] textbooks". Good topics to start with would be classical mechanics, electrodynamics, and quantum mechanics. You could then move onto special relativity and statistical physics (my favourite!).

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JTech324 t1_j8l5oiv wrote

I thoroughly enjoyed reading your writing in all those linked comments. You really connect with the reader in their frustration to understand complex topics, and don't sugar coat the fact they very likely will not find comfort in the answers they seek lol.

Do you write anywhere else, like a blog or anything?

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Movpasd t1_j8qwacc wrote

I'm glad you liked my comment! I do have a blog, which I'll link here (assuming there aren't any rules against it -- I can take down my comment otherwise). It's pretty empty at the moment though. I've meant to put down all my thoughts about physics and intuition in one place at some point, but I just haven't gotten around to it. If you liked it, maybe there is an audience for it!

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wooly_boy t1_j8llybf wrote

Ok, so now assuming I understand that radiation is a traveling variation in EM field, how do photons come into play?

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1ndiana_Pwns t1_j8ltc70 wrote

It takes energy to create those little EM waves, right? A photon is a little packet of that energy. The exact amount of energy a photon has is determined by the wavelength of the light, with the relationship being a result of all the math behind light propagation and electromagnetism (thank Maxwell and his equations)

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Movpasd t1_j8qxs6w wrote

It's quite complicated, but I'll try to give a brief answer --

Maxwellian electrodynamics is a classical field theory. When you canonically quantise such a theory, you find that a (sort of*) conserved, discrete quantity pops out, which can be interpreted as "particle number".

This is in line with observations from a century back around black-body radiation that appeared to show quantisation of energy levels.

It's also a satisfying interpretation because certain calculations in QFT have combinatorial properties which allow them to be represented using Feynman diagrams (which you've probably heard of). Together with the path integral formulation, you get a really useful picture of the physics of scattering. But this is mired in complications (renormalisation, confinement (not a problem for photons but it is for quarks), divergences around every corner, ...).

As a side note, instead of starting from the field theory, you can build up a quantum field theory by starting from a particle-based theory; a common approach for effective theories in condensed matter theory, because it's much more tractable mathematically. The fact that QFT unifies classical many-particle and field theories is an advanced form of the "wave-particle duality" you might have heard of.

*: conserved in the free theory

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