# Angular momentum cut off experiment

## Angular momentum for light and electromagnetic waves

Background and actual explanation

The energy of a photon is directly related to its frequency E=hν and the momentum of a photon is equivalent to the energy divided by the speed of light p = E/c . Photons with different energies carry a different momentum
Besides their momentum, any photon has another characteristic - spin angular momentum which is independent of its frequency.
Spin angular momentum is essentially circular polarization for a photon and has only two possible values: ±h/2π. In an intuitive representation, because this is a quantum characteristic without classical correspondent, the angular momentum is the helical momentum of the photon along its flight path.
The experimental proof that a fascicle of polarized light carries an angular momentum was proved by Beth in 1936.
The circular polarised light passing through a sheet of material change its polarisation and consequently the sheet is rotated with a small angle. In order to amplify the microscopic effect the change of polarisation due to light reflection on a second silvered material sheet is used as in fig.1. The sheets are suspended and have the possibility of rotation.
When incident light, left polarised pass through sheet L, changes its polarisation and become right polarised. Light passes two times through the second sheet l and due to the change of polarization during reflection, arrive again at sheet L with polarisation changed related to initial incident light. In this way passing two times through the sheet L, the effects are added and become more accessible to be measured.

Figure 1. Beth simplified device

If there are emitted N photons which pass once through sheet, there will be an angular momentum transferred to sheet equal with:M =Nh/2pi

Proposed further experiment

A repetition of Beth experiment with microwaves instead of light can differentiate between comportment of light (IR,VIS,UV,Xray, Gamma) and an electromagnetic wave (radio, microwave or terraherz).
According to actual quantum theory, a microwave photon carries the same amount of angular momentum like a light photon.
Consequently when a microwave source with the same power is used instead of light and of course the sheets of materials are changed with a material transparent for microwave, the same effects should be obtained.
The L sheet must be made from a high transparent microwave material already available on the market as example polypyrrole films or microtubules of polyaniline. L sheet can be made sticking two films of polypyrolle, one transparent for microwave and a secondary doped film, having high reflectivity capacity for microwave; this second film is practically the silvered mirror from the light case experiment.
In reality, using a microwave source and adapted layers, the result is completely negative and the sheets are not rotating.
The fundamental difference between a wave and a corpuscle regards the possibility to carry an angular momentum. Light photons (from IR to gamma) having a corpuscular nature can carry a small angular momentum.
Electromagnetic waves do not carry an angular momentum and independent on the rotation of electric or magnetic component of wave, an electron does not have enough time to react at this changes.
Let’s consider that electromagnetic waves hit an electron, in the first semi period, when the electric field E increases, as in fig. 2. In this case the electron will be attracted toward the direction of increasing electric field.

After a semi period, the electric field changes its direction, and of course the electron changes its direction of motion, too, like in fig. 3.

Because the change of electric field direction is made more then 10exp(8) times per second the electron due to its inertia does not move at all.
Consequently an electromagnetic wave can’t produce a macroscopic angular momentum at absorption or reflection.
The detailed interaction between electromagnetic waves and matter will be described in further study.
For the proposed experiment, it is necessary to emphasize that in case of microwaves, the layer of material does not twist.

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