"Topological" properties of photons?

[PhysicsKid0123]

I was wondering, how does a photon look like? What does it look like? I'm taking modern physics at the moment and I'm able to calculate lots of things quite well. Like DeBroglie wavelengths, I'm able to utilize the Schrödinger equation and the Heisenberg uncertainty principle and what not but I don't really have a good sense of visualizing some of the physics.

What exactly are the topological or physical properties of a photon in terms of the space it occupies at a single instant for example? What 'shape' does it have? My understanding, correct me if I'm wrong, there two ways to see photons, classically as propagating waves determined by the poynting vector and described by Maxwell's equations or by quantum physics and Heisenberg uncertainty principle, DeBroglie wavelength etc. So in the classical view, is the photon the waves of the induced oscillating EM fields themselves?To me, when visualizing it, it is simply energy that propagates in a given direction with oscillating EM waves. Does the oscillating energy stored in these field look like or take the form of the graph of traveling waves such as sin(kx-wt)? In the sense that the particle traces out the graph of a sine wave? Or is it just that the photon has oscillating magnetic and electric fields but the energy stored in these fields don't necessarily trace out such a graph. The graph is merely a representing the characteristic of the photon oscillating?

Furthermore, in the quantum view, which is the correct way to be think about it, we say a photon is a massless particle. But what does it look like? Does it even have a shape? Is the shape some kind of probability like the election cloud? All I have is this abstract interpretation of a photon solely described by symbols and math.

One way I think of it is this way: I'm not sure how many of you all have played the game "Halo" in that game there is this weapon called plasma rifle which shoots balls of energy. This is how I see them. Which would make sense when speaking of the work function for some metal when a photon strikes it's surface. But when I try to see it this way I am perplexed by what kind of size would this particle which we call photon have?

All photons are the same, what gives the different types of light we observed is because these photons have energies that oscillate at different frequencies, right? So this is what leads me to think about the photon in this way.

For example, in string theory you would imagine when first hearing about it is that these little 'strings' must be so asbtract but it turns out that they really are like such 'vibrating strings'

 

[Nugatory]

What exactly are the topological or physical properties of a photon in terms of the space it occupies at a single instant for example? What 'shape' does it have? My understanding, correct me if I'm wrong...

OK.

...there two ways to see photons, classically as propagating waves determined by the poynting vector and described by Maxwell's equations or by quantum physics and Heisenberg uncertainty principle, DeBroglie wavelength etc. So in the classical view, is the photon the waves of the induced oscillating EM fields themselves?

There is no such thing as a photon in the classical view, and in the quantum mechanical model photons have no definite position so it makes no sense to ask about their "shape" or the "the space they occupy". It's easy, reading the introductory texts and building on the non-technical meaning of the word "particle" to think of photons as if they are little teeny grains of light, and that a beam of light is a stream of photons moving by in same way that flowing water is a stream of water molecules moving by... But that picture is very misleading.

Until you get to quantum electrodynamics and field theory, you should be thinking about light as a classical electromagnetic wave governed by Maxwell's equations. Photons only come into the picture when this electromagnetic wave interacts with matter, and we observe that the wave's energy is deposited at single points instead of spread out across the entire area illuminated by the wave.

Unfortunately, the mathematical price of admission for QFT is fairly steep. The only decent popularization I know of is Feynmann's "QED: The strange theory of light and matter", which I highly recommend. If you want to go beyond popularizations, I would recommend "Quantum field theory for the gifted amateur": https://www.amazon.com/dp/019969933X/?tag=pfamazon01-20

 

[Khashishi]

Photons have no shape. They refer to a unit of transaction between an emitter and an absorber. They are nothing like classical objects. You'll have an easier time assigning a shape to love or hunger.

As far as I know, it's not possible to detect the passage of a single photon by positioning a detector between the source and target. At best, you can get a photon to go from the source to detector, and another photon from detector to the original target.