07 Feb 2014 No Comments

# Is Light a Wave or a Particle?

When I was in high school and early university thirty years ago it was common to teach that light (and other quantum systems) were waves sometimes and particles at others but never both. It seems that this misconception lives on, as questions put to Physics Stack Exchange often show the asker to have this altogether wrong idea of “sometimes wave, sometimes particle”.

Let’s concentrate on the photon, although the following discussion applies to all quantum particles. Quantum light shows both strong particulate attributes and strong wave attributes at the same time, but it is neither the water sloshing on the beach that one thinks of when one hears the word “wave”, nor is it anything like the tiny billiard ball that “particle” evokes.

There were two answers I gave on Physics Stack Exchange that go to the nub of the question of whether light is “sometimes wave, sometimes particle”. A third answer illustrates the principles spoken about in the other two.

## Question 1: When light is only considered as a particle, is it still considersed to be oscillating electic and magetic waves?

I have my head around wave-particle duality, however people tend to refer to light as either a wave or a particle in different situations. If I were to consider light as a particle am I still regarding it as an oscillating electric wave and magnetic wave? And are these waves a reason we can consider light a wave or is it purely a quantum effect? |

*and the answer, slightly edited, is as follows:*

Purely quantum effect, wave and particle are, at the same time, all roughly correct (although not wave in the sense of being like a water wave and not a particle in the sense of a tiny billiard ball). The idea of “wave sometimes” and “particle sometimes” is pretty outdated. Here’s how I like to think of things.

There is one fundamental object in all of this – this is the second-quantised electromagnetic field.

This one everpresent and everywhere object helps define the behaviours that we witness in our World by interaction with the other quantum fields that fill (and define) space.

It is the communications that are the discrete particles. The interactions of the EM and other field are brought into being by “messages” swapped between the fields. These “messages” we call photons. Just like a telephone call, or a data packet through the internet, these messages are “discrete”. You can’t have half a telephone call! But, just like a telephone call or a data packet, a photon can have different effects depending on which modes of the second quantized EM field make it up and with what superposition weights in those modes it has. The quantum *observables* define the statistical distributions of the outcomes of interactions the second quantized EM field has with the other fundamental fields.

Imagine the EM field in a one photon state: say it is formerly in the quantum ground state and an excited atom has spontaneously radiated into it, *i.e.* sent a “one photon” message to the unique quantum EM ground state. Then the means of the electric and magnetic field observables propagate in space and time precisely following Maxwell’s equations. For the simple one-photon state, the means of the electric and magnetic field observables as functions of position and time wholly and uniquely define the second quantized EM field’s state, in the same way as a simple Poisson probabilitu distribution is uniquely defined by (but is not equivalent to) its mean.

So our second quantized EM field has one “particle” in it, and the means of the $\vec{E}$ and $\vec{B}$ observables wholly define the field in this state. These means fulfill Maxwell’s equations – which are * exactly *the relativistic wave equation for one photon in free space. You can’t get “wavier” than something whose Cartesian components fulfill D’Alembert’s wave equation!

I think this is why Dirac made his famous statement “each photon interferes only with itself” because, unless there is entanglement, foretell the behavior of a classical field by doing the same for each photon and interpreting the probability density as the classical energy density for the corresponding photon states that make it up. His statement is not altogether true because it doesn’t hold with entanglement present. See my answer to the Physics SE question How can we interpret polarization and frequency when we are dealing with one single photon?).

## Question 2: Do Photons interfere when it passes through a slit (one)?

When a light (photons) goes through two slits it creates interference patterns. if the light goes through a “single” slit, does it create interference patterns or does it behave like particles (photons)? is the pattern same for both particles and light waves if it is a “single slit”? In the double slit experiment, if you close one slit (or observe) it is said that light behave as particles (bullets) which means that through one slit light exactly behaves as stream of particles?? |

*and the answer, slightly edited, is as follows:*

I’m not sure how much quantum mechanics you’ve done, I’m guessing you haven’t yet learnt about unitary state evolution through Schrödinger’s equation and measurement through quantum observables; please correct me if I’m wrong and I’ll change my answer accordingly.

First of all, assume you are dealing with a classical wave and then read through the Physics SE answer How can a single slit diffraction produce an interference pattern? and the two articles Section “Single-slit Diffraction” on the Wikipedia page for Diffraction and the Hyperphysics “Fraunhofer Single Slit” Page. These articles will let you understand how something that fulfils the D’Alembert wave equation can show interference when it diffracts from a single slit.

Now for the quantum/wave/particle bit. For now forget about waves, particles and photons and I even want you to forget about the concept of “space” for a minute and understand that there is only one object that begets and shows all the optical behaviours we witness: the second-quantised electromagnetic field.

The only things that are believed to be real in modern physics are this field and other quantum fields like it. There are only a handful of them. When we witness physical phenomena we are seeing *interactions* between these quantum fields.

The second quantised electromagnetic field can be thought of as a infinite gathering of quantum simple harmonic oscillators, one for each classical plane wave mode of Maxwell’s equations. The eigenstates of quantum simple harmonic oscillators are discrete and they are evenly spaced by an amount of energy $h\,\nu$, where $\nu$ is the frequency of the oscillator in question. So each oscillator can change its state disk continuously, by taking up or shedding a whole number multiple of this basic energy “chunk” $h\,\nu$. So the interactions of the electromagnetic field with the other quantum fields in the world is by way of these discrete packets. I like to think of these packets not so much as billiard balls but more like discrete data packets that are swapped between networks on the Internet, thus giving being to “stuff that happens” on the Internet. The quantum fields of the World talk to each other in discrete, chunky, communications, thus giving being to everything that we see happenning around us.

Where are these quantum oscillators? Remember we haven’t even talked about space, I ask you to forget about it! The answer is that they are nowhere in particular and everywhere all at once! For the quantum fields I spoke of *are* the space around us. We don’t need to deal with the mysterious concept of a “void” any more in physics (an idea that actually used to give me nightmares as a child): empty space is nothing more than what we see when the quantum oscillators of the quantum fields of the World are all in their ground states!

Now let’s come right back to Earth and think about our single slit experiment when we do it with “one photon at a time in the experimental kit”. A one photon state is now simply a quantum superposition of one photon states in the quantum oscillators that make up space around our kit. One photon states propagate *exactly* following Maxwell’s equations: you can try your luck reading my answers [here (How can we interpret polarization and frequency when we are dealing with one single photon?)](http://physics.stackexchange.com/a/78949/26076) and [here (Electromagnetic radiation and quanta)](http://physics.stackexchange.com/a/74483/26076), to get more info on exactly how the one photon state fulfils Maxwell’s equations, but it certainly does so just the same, and, to the best of our knowledge, it does so exactly. There is no approximation. To my mind, you can’t get something “wavier” than something that fulfills Maxwell’s equations: the vector components in free space all fulfill the dispersionless D’Alembert wave equation (or, equivalently, Helmholtz’s equation, if we take the time-Fourier transform of our solutions and analyse them one frequency at a time). And yet we’re talking about one “particle”, one photon! So you can’t have anything wavier than a photon and you can’t have anything chunkier that a photon all at once. The quantum field idea really gets rid of the notion that light can’t be a wave and a particle at once. It is both (and likely more, withal, but that is as yet undiscovered physics).

Actually, if you look at my other answers, one photon states behave, in a certain sense, *exactly* like classical light waves: there is a bijective map between the classes of classical solutions to Maxwell’s equations and the class of one photon states, although the interpretation of the meaning of a Maxwell equation solution is a little different in both cases. One photon states are much more like classical states than few photon states: in the latter case we can see the weird behaviours of entanglement and other wholly quantum effects.

So, somewhat ironically, you are actually more likely to witness “classical behaviour” if you do make sure that only one photon is in the kit at once! One photon states diffract and interfere in their passing through slits exactly like the wave fields I asked you to read about at the beginning of my answer.

Here, though, is where one photon propagation differs from shining a strong laser through a slit. The probability amplitude to absorb photon at a given point is what is propagated by Maxwell’s equations (actually it’s a bit more involved than that, but that’s the basic idea). So our one photon state diffracts through the system, and when it reaches the screen, the electromagnetic quantum field undergoes one of its fundamental *interactions* with the other quantum fields, in this case the Fermionic quantum fields that make up, say, the CCD array photographing the interference pattern. So you get a single point on the photographic screen: but if you keep sending one photon “click click click” at a time through the experimental kit, however slowly you do it, those little dots will slowly make up *exactly* the intensity pattern calculated from the classical Maxwell equations for the system.

Question 3: How does the Ocean polarize light?

This is applicable to any interface between dielectric mediums, not only the ocean and air.

I’m going to focus on Chris White’s rewording of the question: “if the photon is only hitting a few molecules in random orientations, how does it know what direction to be polarized?”

because, unless you can delve into Maxwell’s equations, you’re not going to get much joy from anything else. So let’s just accept that, as on the Wikipedia page, there are the Fresnel equations coming from the solution of Maxwell’s equations and that they say that light of different polarisations behaves differently when reflected from a dielectric interface. All of these equations assume that the mediums involved are continuums, with bulk, extrinsic refractive indices. So, given this context, how indeed do continuum ideas square with a photon hitting a few molecules in random orientations?

The answer is that the photon does not just hit a few molecules – it’s not like a billiard ball bouncing off things. A photon propagates following Maxwell’s equations. When light enters a medium, the propagating wave interacts with all of the molecules in its field of influence. In a medium, we don’t just have pure photons, we have a quantum superposition of free photons and exited matter states. And all of the molecules contribute to that quantum superposition. Indeed, an optical photon’s wavelength is about three orders of magnitude longer than the molecular size, so the quantum superposition will involve of the order of $10^9$ to $10^{11}$ molecules even if the light field is focused to its diffraction limited spot. So the photon really does see effectively a continuum.

The particle side of the photon’s nature does not show itself until it is “observed” by being permanently absorbed, e.g. in a photodetector or camera film. Until then, even at the one photon at a time level, the propagation is perfectly well described by the classical Maxwell equations.

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