Is white light a bunch of photons or a messy electromagnetic wave or both?

Question

I'm a layperson so I hope you'll excuse my naivete. I have this notion that white light is made of many different frequencies. When I think about them being photons I can imagine them all bunched up together kind of overlapping, some blue, red, yellow, etc. When I think of the different frequencies in the electromagnetic field I imagine it more like a sound wave where one single line encodes for many different frequencies (please excuse the imprecise 2D analogy). My question is are either or both of these mental models correct? Or am I basically saying the same thing twice?

Update: to be clear, I'm not talking about the perception of light. Or necessarily white light at all. In the simplest example we could have two wavelengths traveling in the same direction together. Then my question is: Is it one superimposed electromagnetic wave with two frequencies (like sin(x) + sin(2x)) or photons of those two wavelengths? I think I'm realizing that the answer is that it's both. I'm just having a hard time thinking of what happens when that light goes through a prism and gets split up. If it's a single electromagnetic wave with combined frequencies then I guess the two frequencies start to diverge inside the glass due to their interactions with the medium. Maybe I just need to actually take physics courses to understand.

Answer 1

Both.

It is like asking if water is a fluid that flows smoothly or a bunch of molecules bouncing around.

Answer 2

Classically, a light wave is just two fields, the electric and magnetic field, which are both moving sine waves. A field is just a function that is defined for all points in space. To make things simple, we can focus only on the electric field $E(x,t)$. In this classical setting, your superposition model is correct. At $t=0$ we have $$E(x,0)=A_1\sin(kx)+A_2\sin(2kx)$$

Your model of a messy electromagnetic wave is correct and to describe all the things you mentioned, like diffraction, you don't need quantum mechanics at all. You just need to understand what happens to waves when they encounter a medium with different refractive index (=with different propagation velocity). The interactions with the medium can be fairly complicated on a molecular level, but the great thing about optics is that on a macroscopic scale you often just see a modification of the propagation velocity. Maybe some absorption as well.

For completeness sake I will touch slightly on quantum mechanics, or quantum field theory technically speaking. The most "classical-like" state is the coherent state. It is the state created by a laser. It has the least uncertainty in phase and amplitude possible. A coherent state looks something like this:

Imagine we have a detector that can measure the field at a certain point in time. If we measure the field of such a coherent state, we get a normal distribution centered around a sine wave. The variance of this normal distribution is constant, but if we increase the amplitude of the sine wave, the relative variance (variance / amplitude) decreases. In a coherent state we don't have a fixed number of photons. The number of photons is actually probabilistic. For large field strength, we recover a classical wave. We can also have states with a definite number of photons. These are actually harder to make than coherent states. But for these states the amplitude and phase are maximally uncertain. We can no longer interpet these states as a sine wave.

Answer 3

Consider first the wave model. To detect the frequency (energy) of the wave, you must sit at one location for a finite period of time. You measure the passing of peaks and troughs in the electromagnetic spectrum. You may determine that the peaks and troughs are perfectly regular to infinite repeatability. In this case, you are viewing one or more monochromatic waves having identically only one specific frequency. You may instead determine that the peaks and troughs have uncharacteristic irregularities. In this case, you are viewing a (Fourier) combination of more than one wave, each with a different frequency.

In the monochromatic case, you should need to sit only for at least the time needed for one full wave length to pass by you. In the polychromatic case, you should in principle sit for an infinite time to assure that you have captured all possible (infinite number of) wavelengths. Since you cannot know in advance which case you face, you might guess that you are sitting for some time and that you will need to report an uncertainty in your final result for frequencies and wavelength(s) based on how long you sat and measured the peaks and troughs of the passing electromagnetic wave.

One analogy is playing an FM radio (rather than an AM radio). How long the radio samples the incoming wave and how many samples it takes per increment in time before reporting the tune of a violin A string or a piano C key will mark the fidelity of the final report.

White light is a collection of many (lots of) waves, each with different frequencies. A prism acts to refract each frequency wave in a specific directions. Refraction slows down the speed of a wave, changing its wavelength but not its frequency. This happens inside the material. Refraction also changes the direction that an incident wave travels. This happens at the interface between the material and its surroundings. Refraction occurs because a material interacts with a given frequency of an electromagnetic wave in a specifically different way. Electrons in orbitals are "sloshed around", as are free electrons in a "plasmon sea". Ions are vibrated more, as are polar molecular dipoles. Each mode interacts with various frequencies in different ways, changing the angle of travel crossing through the interface and slowing down the travel through the material.

The photon model is rather more complex to consider for the case you are presenting. Suffice to say that a photon is a spatial localization (a packet) of a combination of waves with infinitesimally close frequencies. The spatial extent of the wave packet is defined by the range of frequencies it includes. In perfect principle, a wave packet with only one frequency (a perfectly monochromatic light wave) would extend over infinite space. Correspondingly, a wave packet with infinite frequencies would occupy essentially zero spatial extent. Actual photons are somewhere between in practice.

Answer 4

The human retina contains three types of cone cells. Those cells can see red, green, and blue light. The simplest case occurs when all three of these colors fall on the retina in equal proportions, which your brain interprets as white light. It is also possible that other combinations of the right intensity of colors will be interpreted as white light, but the point is that what you are seeing as white light may well contain far fewer frequencies than assumed.

Answer 5

The physical world does not distinguish between the different view points that we have (waves or photons) that we use to try and understand it. It is what it is. So, all these different ways to model the physical world are just concepts in our minds.

However, there is something to be said for using different formalisms to model the physical world. They serve to provide convenience for calculations within different scenarios. Still the different formalisms should not be mutually inconsistent.

With that said, let's consider the situation with light consisting of multiple frequencies. Unfortunately, to know that a particular beam of light consists of different frequencies is not enough to pin its physical nature down precisely. From a quantum physics point of view, a photonic state can be either pure or mixed and still have the same spectrum. The purity of light affects its ability to produce interference just like the width of its spectrum would. So, for the sake of the discussion, let's assume it is pure.

Just to remove some possible misconception, the fact that light consists of different frequencies does not means that each frequency must be represented by a separate photon. In fact, the superposition of different single photons (with different frequencies) still represents a single photon. (Multiple photons are represent by a tensor product of single photon states.)

Therefore, we can have a single photon with a polychromatic spectrum. So what it really means is that quantum physics is versatile enough to be consistent with our understanding in terms of classical electromagnetic fields when we are just interested in the spectral properties of the light.

Answer 6

Even classically, you must understand that there are infinitely many different possibilities that all look exactly like the same white light to you. Because you only have 3 types of cones in your retina and each one of them actually requires a few photons to trigger, which means essentially 3 degrees of freedom in the human-detectable colour space (unless you happen to be of the rare people who have 4 types of cones). Whereas there are infinitely many degrees of freedom in making up white light, more or less with one degree of freedom per visible frequency.