# What does it really mean that photons are quanta of light?

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Ebi Rogha
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How do you explain photons as quanta of light?

I thought of photons as quanta of light which are the smallest unit of light.
But then I learned a photon can be split into two or even three photons (red-shifted, energy is conserved), and also photon can lose energy and still be a photon (Raman effect, inelastic scattering). Now, I am not sure what it means when it is said photons are quanta of light (smallest unit of light).

vanhees71 and Delta2

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The simplest way to think about photons is that they are massless particles in the standard model of particle physics.

A photon may be emitted by an atom transitioning from one energy level to another, for example. In principle, such a photon could have any energy (depending on the atom and its energy spectrum). There is no minimum or maximum energy for photons.

Photons may also interact with matter (be absorbed or scattered). If a photon is scattered, it may lose or gain energy (in the same way as any particle could).

A full understanding of photons as the quanta of the EM field requires a knowldege of QED/QFT.

Delta2
Summary:: How do you explain photons as quanta of light?
It means nothing more than that one can describe light in quantum mechanical terms by thinking of it as a collection of photons.
I learned a photon can be split into two or even three photons (red-shifted, energy is conserved), and also photon can lose energy and still be a photon (Raman effect, inelastic scattering).
All elementary particles can lose or gain energy through interactions. Some of them can also decay into multiple other particles (and be detected in this way).

Delta2
Ebi Rogha
There is no minimum or maximum energy for photons.
Are photons only defined for visible light?
If so, there should be a minimum and a maximum energy for photons (according to E=h. f).

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Are photons only defined for visible light?
If so, there should be a minimum and a maximum energy for photons (according to E=h. f).
Visibility is purely a function of the human eye. From radio waves to gamma rays it's all electromagnetism.

Klystron and Ebi Rogha
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The most important thing concerning photons is NOT to think about them as little billiard-ball-like localizable particles. They are rather certain states of the quantized free electromagnetic field, called "single-photon Fock states". You are right saying that they are "the smallest unit of light", but also this has to be taken in the right meaning: If you have electromagnetic radiation of a given frequency ##f## then the least amount of radiation energy that can be absorbed by some medium is given by ##h f##. In this sense a photon is indivisible, i.e., it can be detected as a whole or not at all. Nevertheless the photon itself is not localizable, it doesn't even have a position observable to begin with.

On the other hand you are also right in saying that there are processes, where photons are inelastically scattered (indeed Raman scattering on an atom is one possibility). Then, they change there energy and thus their frequency. There are also processes of "non-linear optics", where you can have a reaction, where one photon of a given frequency is absorbed by some medium and two or more photons are emitted by the medium. Of course again energy-momentum conservation ("phase-matching conditions" as the quantum opticians call it) have to hold.

Klystron, weirdoguy, Delta2 and 1 other person
Mentor
Summary:: How do you explain photons as quanta of light?
Here you are: http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf

Any configuration of the electromagnetic field, whether static or dynamic, whether the nice (but not physically realizable) plane waves that we find as possible solutions to Maxwell’s equations or the wave packets formed by superpositions of these plane waves, can be written as a sum of quantized excitations of the field. We call these excitations “photons” or “quanta of light”

vanhees71 and PeroK
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I'd define a photon as a single-photon Fock state. Of course, the plane-wave modes are no states, because they are not normalizable. But you can define a proper single-photon Fock state. It's a quantized wave packet, i.e., something like
$$|\Psi \rangle=\sum_{\lambda \in \{1,-1 \}} \int_{\mathbb{R}^3} \frac{\mathrm{d}^3 k}{\sqrt{(2 \pi)^3 2 \omega_k}} \Phi_{\lambda}(\vec{k}) \hat{a}^{\dagger}(\vec{k},\lambda) |\Omega \rangle,$$
where the ##\Phi_{\lambda}(\vec{k})## are some square-integrable functions and ##|\Omega \rangle## is the vacuum state; ##\lambda## labels the helicity (polarization) states.

weirdoguy, gentzen and PeroK
weirdoguy
It means nothing more than that one can describe light in quantum mechanical terms by thinking of it as a collection of photons.

I would say that this description usually leads people astray because they visualise it the wrong way - that light and photons are like stream of water (say river) and water molecules.

vanhees71
I would say that this description usually leads people astray because they visualise it the wrong way - that light and photons are like stream of water (say river) and water molecules.
I visualize photons as being like waves on the stream formed by the electromagnetic field. For visualization and for their behavior in ordinary light this is fine. For their physical properties in the microscopic domain, this is only a crude approximation, like all visualization of quantum phenomena.

vanhees71
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Nevertheless almost always it's better to think of photons as em. waves than as "particles". For photons one should abandon the particle picture from the very beginning, because it's pretty misleading. The only "particle like" feature is that it can only be either absorbed as a whole or not.

EPR
trainman2001
Am I mistaken or have they "frozen" a laser pulse and photographed it? If that's true, the leading edge of that pulse would contain photons and since they were not moving would that not imply that we could "locate" them?

weirdoguy
the leading edge of that pulse would contain photons

And that is what I was talking about Photons are not like little water molecules that would be contained in any edge of a wave. But I don't know the details of how the notion of photons apply to this particular state of EM field.

vanhees71
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The em. field transmitted by a laser is far from the "naive photon picture". It's really very much a "wave manifestation" of the em. field, known as a coherent (or squeezed) state, i.e., a coherent superposition of photon states with arbitrary number. The photon number for this state is Poisson distributed.

The modern definition of a photon is within QED, and it's an asymptotic free single-quantum state of the em. field (i.e., a Fock state with determined photon number 1).

Besides the photon in this sense is very far from the naive photon picture of Einstein's early 1905 paper, because for this "modern photon" you cannot even define a position observable.

Interested_observer
Nevertheless almost always it's better to think of photons as em. waves than as "particles". For photons one should abandon the particle picture from the very beginning, because it's pretty misleading. The only "particle like" feature is that it can only be either absorbed as a whole or not.
And that it can impart momentum?