2.) The Polarization of Photons

Preceding this, it has become obvious that there is a limit to the gentleness of observation, and that consequently, the results observed do not provide a quantitative basis for building up quantum mechanics: this requires a new set of accurate laws about the inner workings of nature.

One of the most fundamental of these new laws is the Principle of Superposition of States, a general formulation of which can be formed by considering certain cases, such as the polarization of light.

Experiment shows that when plane polarized light is used for ejecting photo-electrons, there is a preferred direction for the emission of the photons.

Each photon is in a state of polarization, with the problem now being fitting this information into the facts about the resolution of light into polarized components, and recombining them.

If there is a beam of light, shone through tourmaline, which has thqe property of letting through only light which is plane polarized perpendicular to the axis, classical Electrodynamics indicates what will happen with the incident beam with any polarization.

If this beam is polarized perpendicularly, it will go through the crystal, however if it is parallel to the axis, none of it will, while if it is polarized at some angle $\alpha$ to the axis, the percentage equivalent to $sin^2 \alpha$ , will travel through: the question is now, how to make sense of this behavior at the level of individual photons.

A beam of plane polarized light must be comprised of similarly polarized photons, and this presents no difficulty if the incident beam is polarized perpendicularly: we assume that these photons travel through, and ones polarized parallel to the axis are absorbed: however the arbitrarily polarized beam presents a problem. Each of the photons are arbitrarily polarized and it becomes unclear what effect the crystal will have on them. Susskind references this very same experiment using the spin of electrons and some apparatus in Spins and Qubits.

An inquiry about the behavior of an individual photon under these circumstances is generally not precise. Precision requires an experiment performed, which has some bearing on the question, about which one can consider the outcomes.

In this case, the obvious experiment is to take a beam, consisting of a single photon, and observe what takes place behind the crystal: according to quantum mechanics, the result will be that sometimes a photon will be observed there, and other times, it will not.

If one repeats the experiment however, the photon will be observed there roughly $sin^2\alpha$ , of the number of times the experiment was repeated, and $cos^2\alpha$ times, it will be absorbed: these values are statistically equivalent to the expected values from classical theory.

This is the way in which the individuality of photons are preserved, although this is only doable because we abandon the determinism, of classical theory. The most that one can predict is the probability of the occurrence of each outcome.

Thoughts:

Questions about what decides whether the photon is to go through or not and how it changes its direction of polarization when it does go through cannot be investigated by experiment and should be regarded as outside the domain of science.

I disagree highly with this quote, though I accept from the literature/pedagogy that "hidden variables" are not at play/responsible.

Furthermore, we can suppose that an arbitrarily polarized photon may be regarded as being both in the parallel and perpendicular polarization state, which can be considered as a sort of superposition applied to the two states of polarization.

This implies a unique relationship between the states of polarization, which allows for any state of polarization to be resolved into, or expressed as a superposition of two mutually perpendicular states of polarization.

Furthermore, when we introduce the photon to crystal, we are subjecting it to the act of observation, about the nature of its polarization relative to the axis of the crystal: the effect of this observation is to force the photon entirely into one state of polarization, having made a jump there from a superposed state, though which of the two states it will choose, cannot be predicted, and is governed only by probability.

Referenced in

The Principle Of Superposition

An atomic system is comprised of particles (bodies with specific properties of Mass, Inertia), and subject to the laws governing forces acting upon objects. Each component of this system will have various possible motions it could take, and each motion is considered a state. Classically, one can describe this state via the coordinates of the system and the velocities of the components at some point in time, with the complete motion thus being determined.

The Principle Of Superposition

2.) The Polarization of Photons

Preceding this, it has become obvious that there is a limit to the gentleness of observation, and that consequently, the results observed do not provide a quantitative basis for building up quantum mechanics: this requires a new set of accurate laws about the inner workings of nature.

One of the most fundamental of these new laws is the Principle of Superposition of States, a general formulation of which can be formed by considering certain cases, such as the polarization of light.

Experiment shows that when plane polarized light is used for ejecting photo-electrons, there is a preferred direction for the emission of the photons.

This property of light is closely related to its particle nature, requiring each photon being prescribed a polarization: Given a beam of plane polarized light, in some direction, and a beam of circularly polarized light, one must consider the nature of the constituent photons of each beam.

Each photon is in a state of polarization, with the problem now being fitting this information into the facts about the resolution of light into polarized components, and recombining them.

If there is a beam of light, shone through tourmaline, which has thqe property of letting through only light which is plane polarized perpendicular to the axis, classical Electrodynamics indicates what will happen with the incident beam with any polarization.

An inquiry about the behavior of an individual photon under these circumstances is generally not precise. Precision requires an experiment performed, which has some bearing on the question, about which one can consider the outcomes.

In this case, the obvious experiment is to take a beam, consisting of a single photon, and observe what takes place behind the crystal: according to quantum mechanics, the result will be that sometimes a photon will be observed there, and other times, it will not.

This is the way in which the individuality of photons are preserved, although this is only doable because we abandon the determinism, of classical theory. The most that one can predict is the probability of the occurrence of each outcome.

Furthermore, we can suppose that an arbitrarily polarized photon may be regarded as being both in the parallel and perpendicular polarization state, which can be considered as a sort of superposition applied to the two states of polarization.

This implies a unique relationship between the states of polarization, which allows for any state of polarization to be resolved into, or expressed as a superposition of two mutually perpendicular states of polarization.

Referenced in

The Principle Of Superposition