Is Light a Wave or a Particle?

It’s in your physics textbook, go look. It says that you can either model light as an electromagnetic wave OR you can model light a stream of photons. You can’t use both models at the same time. It’s one or the other. It says that, go look.

Here is a likely summary from most textbooks.

1. Light as a wave: Light can be described (modeled) as an electromagnetic wave. In this model, a changing electric field creates a changing magnetic field. This changing magnetic field then creates a changing electric field and BOOM - you have light. Unlike many other waves (sound, water waves, waves in a football stadium), light does not need a medium to “wave” in.

Oh, that is too simple of an explanation? How about this?

These are one form of Maxwell’s equations. They describe the relationship between the electric and magnetic field (well mostly the last two). If you like, you can use vector calculus on the above equations and then eliminate B to get:

This is the form of the wave equation. So, Maxwell’s equations do say that light is a wave.

2. Light as a particle: The textbook might start off with some experimental evidence from the historic photoelectric effect to show that the wave model of light doesn’t always describe what happens.

It will then say that we can model light as individual “things” (some books actually say particles and others just say photons). These light “things” have energy that depends on the wavelength such that:

Here h is Planck’s constant and λ is the wavelength of the light and f the frequency. With the photon model, a brighter light just produces more photons per second.

Is light a particle or a wave?

Most texts end with something like this:

“Is light a particle or a wave? This is a difficult question - the answer is that in some situations light behaves as a particle and in others it behaves as a wave.”

What's wrong with multiple models?

We always have multiple models for things that we see. However, they are different than this wave-particle model of light. Let’s look at a few other models.

Momentum. When you start looking at momentum, it is almost always (except in the awesome textbook Matter and Interactions) defined as:

This is great. It’s simple and it’s useful. It goes great with the momentum principle that says that the net force on an object is the time rate of change of momentum. Of course, you could also say it is wrong. What if you have a proton moving at 90 percent the speed of light? In that case, you can’t use this definition of momentum with the momentum principle. Instead, you have to use this model:

That’s nice, right? Some people call this the “relativistic momentum”. However, I like to call this just plain momentum. But what does this have to do with two models for light? Well, what if I wanted to find the momentum of a proton going at just 10% the speed of light? Which model would I use? The answer depends on how quickly you want to calculate this and how accurate you want your answer to be. Yes, I know “quick” is relative.

Here is a plot of momentum of a proton as a function of speed for the two models.

You can see that at lower speeds, the two models agree. The faster the proton goes, the less the two models agree.

Gravity. Everyone knows the model for the gravitational force, right? You can write it like this:

No. That is wrong. That model only works when close to the surface of the Earth. The gravitational force is:

That is still wrong, but better. However, we don’t often use the better model for the gravitational force near the surface of the Earth. Why? Because the mg model works well enough. Also, the two models agree on the surface of the Earth just like the two expressions for the proton momentum agree for “slow” speeds.

Quantum Mechanics. I am going to skip many of the very interesting details, but let me just say that I can use the following model the behavior of a super tiny particle in a box. Here is an older post with most of the particle in a box details. Knock yourself out with that.

Or maybe you would like to write it out like this:

This is Schrodinger’s equation and Ψ is called the wave function. It doesn’t give you anything you could directly measure, but from it you could get the probability density - or a description of where a particle is likely to be found (or really, anything else you can know about the particle).

But wait! There’s more. What if you use Schrodinger’s equation to look at a particle in a one dimensional box? Why would you do this? Because it is mathematically simple and because we can use it to explore some of the results of a quantum system. From Schrodinger’s equation, you would find that the particle can only exist at certain discrete energies. This is really one of the key points of quantum mechanics (it’s the quant in quantum).

My favorite quantum analogy is a staircase. For a staircase you can be on one step or the next step but you really can’t be in between steps. In this case, you could say that height is quantized. The same is true for a particle in a box or an electron in a hydrogen atom. There are only certain possible energy levels.

Does this quantum energy model agree with classical mechanics? Yes. If you looked at a tennis ball bouncing back and forth in a typical classroom, you could calculate the quantized energy levels. However, these energy levels are so close to each other that you essentially would never be able to experimentally verify that the ball can only have certain energy levels.

Just to be clear: the quantum model of stuff is just like the other models above. It slowly gives a different result from the classical model of stuff.

Why Do Textbooks Include the Photon Model of Light?

You have been very patient. I know you want to talk about photons, but I had to get the model stuff out of the way. But like I said, just about every introductory physics textbook talks about photons using the photoelectric effect as a basis for this model.

There is a reason for this. Albert Einstein won the Nobel Prize in 1921 in part for his explanation of the photoelectric effect. Of course, Einstein did some other awesome stuff. In particular, the general and special theory of relativity. But the Nobel Prize didn’t mention this - just the photoelectric effect. However, during Einstein’s acceptance speech for the Nobel Prize, he talked about relativity and not the photoelectric effect.

But here is the crazy part (I know, you probably think this whole post is crazy): the photoelectric effect can be explained with a classical wave model of light along with a quantum model of matter. Really, it can. Skipping the details, let me just say (and you can look in your quantum mechanics book to verify this) that if you have a particle with energy E1 and you want it to transition to the energy level E₂ you can do that by adding a time-varying potential such that:

Hey! That looks strangely similar to the equation for the energy of a photon. Yup. If you like, you can use light with a frequency of f to induce the transition from one energy level to another. Even better, it doesn’t matter if this transition is from a higher to lower or lower to higher energy level. This oscillating perturbation can explain both absorption AND emission of light.

What about the photoelectric effect? Well, all the results you see experimentally can be explained if the electrons in the metal can only exist at certain energy levels (quantum model of matter) and the light is a wave. Actually, some of the older quantum mechanics textbooks show this as an example problem.

But then why is the photon model in textbooks? I would say it is because of educational inertia. Who writes the textbooks? If you answer “people”, then you are correct. But where do these “people” learn physics? If you said “textbooks”, that would be a fairly nice answer. So, people learn from textbooks that have photons. Next they write a textbook, so clearly they will have photons in their books. Simple.

Light is Quantized

My main point here is that the photon isn’t what you think it is. It isn’t a tiny little ball of light. It isn’t light as a particle. However, light is still pretty weird. There is a quantum nature to the electric and magnetic fields in light (quantum theory of radiation). But most of the stuff you look at can be explained using a classical wave model of light and a quantized model for matter.

Appeal to Authority: I admit that sometimes, things get confusing. In case any of my arguments don’t make any sense, I will add some opinions from experts (meaning people that know more than I do).

Perhaps the most recent is this quote from W.E. Lamb, Jr’s paper “Anti-photon” - Lamb Jr, Willis E. "Anti-photon." Applied Physics B 60.2-3 (1995): 77-84.:

“It is high time to give up the use of the word ‘photon’, and of a bad concept which will shortly be a century old. Radiation does not consist of particles and the classical, i.e., non-quantum limit of QTR is described by Maxwell’s Equations for the EM fields, which do not involve particles.”

Or maybe you would like a quote from Einstein himself?

“All these fifty years of conscious brooding have brought me no nearer to the answer to the question, ‘what are light quanta?’ Nowadays, every Tom, Dick, and Harry thinks he knows it, but he is mistaken.”

Albert Einstein, letter to Michael Besso 1954.

TL;DR

Yes, this is long. Here are the main points so you don't have to read everything.

• Light is awesome.
• Most models are wrong at some level. However, they slowly converge to other more correct models.
• It is sort of silly to describe light as a particle.
• In fact, just about everything you see in undergraduate physics can be explained with a classical wave model of light along with a quantum model of matter.
• I’m NOT denying that there is a quantum theory of radiation (QTR). For instance, photon anti-bunching can not be described with a classical EM wave.

I wonder if I should put the tl;dr at the beginning. Oh well.

Preemptive Comments

I don’t know why, but I expect some people to not be so happy with this post. In general, people have one of the following two responses to this kind of argument.

Now for some of the comments you might have.

• Are you saying Einstein was wrong? If so, you are crazy. Actually, no. You can describe the photoelectric effect with particles of light. You just don’t need to. Ok fine - Einstein was wrong about the photoelectric effect. He was still a genius and maybe the second greatest physicist that we know of. Newton only edges him out because when he needed new math for his physics, he invented it. When Einstein needed new math, he learned it from mathematicians.
• (This is from my brother Neil, he has a comment and a question) You just hate photons like Steve Jobs hates buttons. Can we still talk about photon torpedoes or are you going to ban those too? I don’t hate photons. Hate is a strong word. But yes, you can still use photon torpedoes - but what about "light torpedoes"? Would that work?
• What about photon momentum? Most introductory textbooks give a nice explanation of how an electromagnetic wave can push on electrically charged matter. I particularly like the explanation in Matter and Interactions II (Wiley: Chabay and Sherwood). In fact, here is my previous explanation of how light can push a comet's tail.
• What about some other particular thing dealing with photons? I will refer you to this very nice paper by David Norwood. There. (The Use and Abuse of "photon" in Nanomechanics - pdf)

Hat Tip to David Norwood. Really, it's his fault that I was thinking about this whole issue. However, he did offer some nice suggestions for this post.