A New Model for Linear Polarizing Filter

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This new single-photon model for a linear polarizing filter shows the same apparent violation of Bell's theorem as current loophole-free experiments. This model also replicates the classical results, including Malus's law. No entanglement of photons, superposition of states or hidden variables are assumed.


The graphic compares Malus's law with the new model.


Contributed by: Herb Savage (August 2022)
Open content licensed under CC BY-NC-SA



Filter model

Inputs: polarization angle of the filter, polarization angle of the photon


if selector then return photon angle generated by the emitter else return 1000 (photon does not pass the filter)

The selector is the same as in [1]: . The experiment is just sensitive to whether or not the photon passes the filter. This is true if the difference between the photon polarization angle and the filter is less than .

Three cases for two synchronized photons passing through two different filters are handled by this selector.

1. The two filters are at the same angle. The selector is deterministic and will always pass or block a photon the same way. Thus the result is always the same.

2. The two filters are at a angle. The two angles at cover all possibilities without overlap, so these two are always opposites.

3. The two filters are at a angle. The two angles overlap 50% of the angles, so if one filter passes the photon, the other filter has a 50% chance of passing the photon.

The case for unpolarized photons is also handled by this selector. The filter covers 50% of the angles, so unpolarized light will always be reduced by 50%.

A photon is emitted with polarization angle selected at random from a distribution centered on the filter angle, with ranging from to . Thus, anything emitted will also pass through another filter with the same angle.

Indications that there really is an emitter

1. The behavior of three polarizing filters. If two linear polarizing filters are at , then no light will pass through the two filters. If a third filter is inserted between the two filters at a angle, then the amount of light that passes through increases. This indicates that the filters cannot be pure passthrough filters.

2. The physical construction of linear filters. Both the Polaroid film polarizing filters and the wire grid polarizing filters have either long parallel molecules or parallel wires. In both filters, these are at to the angle of polarization. Thereby, these act as antennae that absorb and re-emit the photons.

3. Circular polarizing filters behavior. These filters are non-commutative. They only work in one direction. From the opposite direction, they act as a linear filter. This can be explained by their construction, consisting of a linear filter followed by a 1/4 wave plate. If the light goes through the linear filter and then the wave plate, it is circularly polarized. In the other direction, if it goes through the 1/4 wave plate first, the photon is re-emitted by the polarizing filter, which undoes the action of the 1/4 wave plate.

The test of Malus's law [2] is to demonstrate that the average percentage of passthroughs for each angle from to difference in the two filters approaches as the number of repetitions increases.


[1] H. Savage. "Apparent Violations of Bell's Theorem" from the Wolfram Demonstrations Project—A Wolfram Web Resource. demonstrations.wolfram.com/ApparentViolationsOfBellsTheorem.

[2] "Malus's Law" from Wolfram|Alpha—A Wolfram Web Resource. www.wolframalpha.com/input?i=malus+law.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.