What is the reason two rays originally polarized orthogonally but were rotated to parallel polarization does not visibly interfere even slightly?

The Fresnel–Arago laws by Augustin-Jean Fresnel and François Arago summarise some of the more important properties of interference between light of different states of polarization.

The laws are as follows (as per the translated version of the original report):

1. Two rays of light polarized at right angles do not produce any effect upon each other under the same circumstances in which two rays of ordinary light produce destructive interference.

2. Rays of light polarized in the same plane interfere like rays of ordinary light; so that in these two kinds of light the phenomena of interference are absolutely identical.

3. Two rays which were originally polarized at right angles may be brought to the same plane of polarization -without thereby acquiring the ability to interfere.

4. Two rays of light polarized at right angles and afterwards brought into the same plane of polarization interfere like ordinary light provided they were originally polarized in the same plane.

5. In the phenomena of interference produced by rays which have experienced double refraction the position of the interference bands is determined not only by difference of path and difference of speed, but in some cases, as above indicated, it is necessary to take into account also a difference of one-half a wavelength.

(5th law which was in the original report of experiments by Fresnel–Arago was left behind in later textbooks which may be due to the fact "Some cases, as above indicated" phrase is not well defined so readers may have to read the rest of their report in order to understand what these certain circumstances and cases were.)

When regarding the two constituent orthogonal linearly polarized states of natural light, we can rotate those (for example one component of natural light by sending it through a diagonal polarizer and an orthogonal polarizer in that exact order) to align with each other. So these rays would become parallelly polarized natural light waves with random to a degree phase fluctuations. But as the second Fresnel–Arago law states parallel natural light with phase fluctuations can form a stable visible interference pattern.

So why do two rays which were originally polarized at right angles when rotated to the same plane of polarization, not acquire the ability to interfere visibly (even slightly) despite their polarizations now being parallel? (Is there an explanation as to the change of the wave due to rotation or differences between original orthogonal polarized constituents of natural light that prevent visible interference completely when rotated into parallel polarization?)

Note: This question has been edited several times in light of later revealed facts and for further clarification of the question. However, it is still firmly grounded within the scope of the original query. &Thanks to Farcher for providing Fresnel–Arago original paper.

Natural light can be represented in terms of two incoherent, orthogonal linearly polarised waves of equal amplitude with the relative phase difference varying rapidly and randomly.

Intensity is proportional to $$\vec E_1 \cdot \vec E_2\cos \delta$$ where $$\vec E_1$$ and $$\vec E_2$$ are the two electric field vectors and $$\delta$$ is the phase between them.

A source of natural light can produce the equivalent of two coherent sets of waves by division of wavefront, eg double slit, or division of amplitude, eg Newton's rings which then could produce a visible interference pattern.

If the planes of polarisation are orthogonal, $$\vec E_1 \cdot \vec E_2=0$$, and there can be no interference whereas if the planes are parallel interference can occur.

For the third law, if $$E_1$$ and $$E_2$$ start off orthogonal and then you rotate one of them to make them parallel you would have the relative phase difference, $$\delta$$ varying rapidly and randomly so the time average will produce no interference pattern.

• why should the orthogonal component has these random phase fluctuations while parallel rays have no such fluctuations? Commented Jun 18, 2023 at 10:12
• You can split the vertical component into two coherent wave and have those waves overlap to produce an interference pattern. You can also do the same for the horizontal component but the model used for natural light there is no coherence between the vertical and the horizontal components so whatever you do to them when they overlap there will be no observable ("stationary") interference pattern. Perhaps it is better explained in the Wikipedia article Fresnel-Arago Laws? Commented Jun 18, 2023 at 11:31
• @Farcher I think what the question is not "The orthogonal components can't interfere - why can't they?", but rather "The orthogonal components can't interfere because they are incoherent - why are they incoherent?" Commented Jun 18, 2023 at 11:45
• Natural light is not coherent. But parallely polarized natural light waves can form a stable interference pattern despite incoherence. If we take two constituent orthogonal components of natural light and rotate one of them then we make them parallel. So why can't they form an interference pattern? Yes, they are incoherent, but natural light is also incoherent, yet parallely polarized waves of natural light can form interference. (I have read Wikipedia and that's why I asked here because it doesn't explain the third law regarding the aspect I raised here. I am O.K. with the first 2 laws) Commented Jun 18, 2023 at 12:41
• @Vercassivelaunos I know they are not coherent because they are of different frequencies. My question is when orthogonal components rotated to become parallel why they still can't interfere? Natural light is not coherent but it can form interference patterns. There are no perfect coherent light sources only relative coherence. Sodium lamps. etc that we call monochromatic are still not 100% monochromatic or coherent. Commented Jun 18, 2023 at 12:48

Above is a really good paper/analysis using a 2 arm interferometer (Mach-Zender).

Basically the requirement for interference can be summarized as; the EM field needs to have(or see) 2 available paths when/before creating a real photon. I.E. the virtual EM field is split over the 2 arms.

If only one path is available as in the case where polarizers are orthogonal there is no interference. I.E. the virtual EM field can only span one arm or the other.

The 3rd law shows that trying to combine paths with a final polarizer to show interference is not possible. I.E. the virtual EM field can only span one arm or the other.

• The term “virtual EM field” is not a standard term in physics. Can you clarify what you meant by it? Commented Jun 19, 2023 at 12:43
• @DukeWilliam Are you comfortable with virtual photons? They would be the virtual field ...... Commented Jun 19, 2023 at 17:44
• Virtual photons are temporal disturbances in the electromagnetic field that exist during interactions of electron with the field. But a virtual electromagnetic field is not a well-defined term in physics. I only heard it from you. Commented Jun 20, 2023 at 4:32
• @DukeWilliam I don't think temporal has anything to do with it ... electron interacts with the field and the field interacts with the electron .... hence electrons are iterating with each other thru the virtual E field but we in general we just call it the EM field. If you are looking for a "well defined" explanation of interference you are going to be lost in the woods for a long time. Commented Jun 20, 2023 at 13:36
• @DukeWilliam Many physicists are well invested/entrenched in the idea that the DSE is a great mystery ... it helps to attract naive students into the field and is great at generating sexy headlines for scientific articles ... probably even helps get funding! Now you are going back 200 years to try and make sense of this irrationality... Dirac and Feynman were the last to offer insight, but they both moved on to more important matters .... the nuclear frontier. Today we need physicists in nuclear, climate study, electric vehicles, and way out there is nuclear fusion and quantum computing etc. Commented Jun 20, 2023 at 13:41

You wrote "I cannot understand a non-existing field. There is no information online or offline about the virtual field. Only virtual particles are incorporated into QFT."

Virtual fields are fundamental .... we can't see them directly but evidence is easy to find.

• That Hair excitement is due to statics not because of virtual fields. Why do you want additional overlay of fields over existing ones? Mainstream physics is complex enough without adding any more layers of illusionary constructs. We should try to simplify as possible because human minds are limited. It is easy to get lost if there are too many info variables to process. You know great physicists tend to stick to the most simple formulations of theory which usually turn out to be the most correct ones too. Commented Jun 22, 2023 at 15:52
• I absolutely respect your this notion of virtual fields. I am sure you have your reasons to believe in that. But I am looking to find solutions according to standard, generally accepted useful theories, representations and abstractions. Probably someday in the future Physics may adopt those virtual particle fields if they find it makes the right appropriations to circumstances and empirical results. Until then I like to stick to well-defined accepted theories and concepts in physics, you know. Because of my limited knowledge and understanding of the subject I think that is the best practice Commented Jun 22, 2023 at 15:59
• ....that I can follow. However It not going to do me a lot of help if your every answer is going to be based on virtual fields. Even though you believed in the usefulness of the construct "virtual field", I am sure you can provide answers based on standard model of quantum physics. That will help me and others a lot. You know I don't know physics enough to pass judgement on your virtual particle concept, so I do not like to rely on concepts which has no general consensus among the physics community unless I am absolutely sure. But I respect your position on this. Commented Jun 22, 2023 at 16:11
• @DukeWilliam you can search virtual photon on this site and get about 2000 hits. Commented Jun 22, 2023 at 21:30
• @DukeWilliam you will never find a generally accepted theory about "interference" of light it is apparently one of physics's great mysteries! If you continue searching at papers from 200 years ago you will be lost. 60% of physicists accept the classical explanation as it OK for their needs ..... 30% of physicists have their own explanation (virtual field ?) and 10% of physicists are lost! and wasting time. And the 30% don't want to waste time arguing about it! Commented Jun 22, 2023 at 21:36