# Why light have angular momentum?

Light carries momentum which is an intrinsic property or ability to move something at least how I interpret it, I got no issue on how it is able to conserve momentum when it is absorbed by another particle say electron. Problem comes when photon starts to spin, is this angular momentum also an intrinsic property like a quantum number or can we control it somehow like using special polarised filter? What is rotating the changing electric field and magnetic field or is it just a quantum state?

The classical (i.e., non-quantized) electromagnetic field can carry angular momentum as well as linear momentum and energy. Therefore the angular momentum of light can be understood classically without having to understand the spin of photons.

The Wikipedia article “Angular momentum of light” discusses the classical approach. One way that angular momentum can be arise is when the electric and magnetic fields in a wave rotate around the direction of propagation (i.e., “circular polarization”).

Of course, the quantized electromagnetic field is a better description of nature than the classical electromagnetic field, so eventually understanding photon spin is a necessity.

In General Relativity the gravitational field can carry energy, momentum, and angular momentum, and this can be understood without discussing gravitons as spin-2 particles.

• G., I quoted you. – HolgerFiedler Dec 24 '18 at 6:55

The title:

Why light have angular momentum?

When studying elementary particle interactions in experiments it became necessary for all particles discovered to have an intrinsic angular momentum, otherwise the interactions would violate momentum conservation a very strong conservation law together with energy and momentum conservation. They were assigned that missing angular momentum as spin and angular momentum conservation in particle interactions is still a law (i.e. as strong as an axiom in mathematics).

Problem comes when photon starts to spin, is this angular momentum also an intrinsic property like a quantum number

It is not spinning, it is an intrinsic property of the photon, which is defined as a zero mass point particle with spin 1 in the standard model of particle physics ,the table was defined by measurements.

or can we control it somehow like using special polarized filter?

Yes , there can be control, as the photon interacts, its spin has a role in the interaction. There is also a superposition:

Photons as quantum entities have wavefunctions which in an ensemble of photons superpose, ( an addition of wavefunctions), and that is how the classical light emerges. This experiment with single photons at a time helps in getting an intuition on the superposition of photons.

A useful graphic is how classical circular polarization of light is built up by a superposition of photons with a corresponding difference in the spin projection (+1 or -1 in the direction of motion of the photon)

What is rotating the changing electric field and magnetic field or is it just a quantum state?

It is just a quantum state whose wavefunction is a solution of a quantized Maxwell equation, which contains the E and B fields so appears in the complex conjugate square of the wavefunction. The probability distributions are affected by the E an B fields

• Hi i did some researchs after reading ur answer and found that if you slow down one of the components such as electric field by a fraction of a wavelength it will become circularly polarised when we traced out the net factor sum, so the electric and magnetic field don't rotate but is actually out of phase. Are you referring to this or something much more advanced? – user6760 Dec 24 '18 at 8:43
• No, I am referring to how the quantum state of a photon builds up the classical electromagnetic wave . The photon does not have an electric or magnetic field that one can manipulate. Only its wavefunction – anna v Dec 24 '18 at 9:15
• An electron could emit lots of photons and each photon has its spin, so” it became necessary for all particles discovered to have an intrinsic angular momentum, otherwise the interactions would violate momentum conservation” does not applies to the photons intrinsic spin.but of course the photon could be given a additional rotation from rotating particles. This angular moment will be conserved. – HolgerFiedler Dec 24 '18 at 10:58
• @HolgerFiedler An electron has to interact with another particle in order for a photon to be emitted, and the total interaction has to conserve angular momentum: 1/2 spin of the electron and the 1 spin of the photon and the spins of the other particles involved have to be summed to get conservation. see this diagram : i.stack.imgur.com/kBXX5.jpg – anna v Dec 24 '18 at 11:27
• An electron could emit say two photons and each of them could be received by another individual electron. Where is there a conservation of the photons intrinsic spins? Photons are “created” from a subatomic particle in different amounts, see electron-electron-scattering and Dans answer and the comment to the question. – HolgerFiedler Dec 24 '18 at 11:38

Photons have an intrinsic spin and additional could spinning.

What is the difference? Simply a photon has a magnetic dipole field component and an electric field component. Taking a snapshot, maybe one see the electric field directed to the top and the magnetic field to the left. Taking a snapshot from another photon (seen in the same direction of movements) one could observe the electric field to the top again, but the magnetic field to right. In addition to the frequency (wavelength, energy content, ..., which are all expressions of the same entity), the relation of these two field components is the only distinguishing feature for photons. This relation is called the intrinsic spin.

If a subatomic particle rotates and emits this time a photon, the photon gets a momentum from the particle and the two field components are rotating. Such a photon has an angular momentum. Get absorbed, this angular momentum over goes to the receiving particle.

As G. Smith wrote:

One way that angular momentum can be arise is when the electric and magnetic fields in a wave rotate around the direction of propagation (i.e., “circular polarization”).

• You are confusing the photon with the classical field. The E and B do not characterize the photon, only the emergent classical em wave from zillions of photons have E and B. The E and B reside in the wave function of the photon which cannot be manipulated, if you look at the link I gave in my answer. – anna v Dec 24 '18 at 9:19
• @annav: Although the quantized em field is usually expressed in terms of the gauge field, one can convert this into the electric field and the magentic field. As such a photon can also be seen as a single excitation of the electric field. Therefore, one can consider the electric field and the magnetic field of a single photon. – flippiefanus Dec 24 '18 at 17:45
• @flippiefanus Ithink this is wrong, look at the last linkin my answer ,link where the electric and magnetic field are in the wavefunction. This means it is expressed in the probability distribution as with the supreposition of the double slit experiment, but an individual photon has only energy and spin and a zero mass. There is no experiment to measure an electric field for a photon . sps.ch/en/articles/progresses/… – anna v Dec 24 '18 at 18:34
• @annav: Any measurement of the electric field would require the exchange of photons. Therefore, one can argue that every experiment in which the electric field is measured involves photons. Without photons one would not be able to measure anything is such experiments. – flippiefanus Dec 25 '18 at 11:39
• @flippiefanus you are confusing the mathematical model of virtual ( exchange) photons with real photons that can be measured in the lab. Virtual photons are unmeasurable, because they are under the integral that gives the probability distribution. Theri only existence is in the mathematics of the model,in contrast to real photons which leave a footprint in the lab. – anna v Dec 25 '18 at 18:21