Classical explanation for the Fizeau experiment & for Sagnac effect in materials

[DanMP]

Long time ago (late 80's), attending a course about relativity at the university, when the Fizeau experiment was presented as an experimental proof for relativity, I thought: "this can be explained in another way, because, clearly, the number of molecules encountered by the ray of light propagating in the same direction as the water stream is smaller than the number encountered by the ray of light opposite to the direction of the water stream", but the course went on, compelling evidence was presented, so I didn't pursue my idea ... until the autumn of 2011, when "faster than light neutrino" news shook relativity. I learned next year that OPERA results were wrong (due to equipment failures), but my explanation is not, in any way, confronting relativity, so it isn't a problem. I mentioned "faster than light neutrino" only because it was the trigger for this alternative explanation (and much more ...).

 

I think that a non-relativistic explanation (one not using Lorentz transformations) is possible, because the speeds involved are far smaller than c ... and needed, because such an explanation (if proved correct) may become very useful in understanding how light travels through transparent materials.

 

 

 

1. Fizeau experiment: (see Fizeau_experiment on Wikipedia)

 

I will not analyze the actual experiment. I will analyze an imaginary, simplified one. Let's consider a tube of length d, in which water flows with constant speed v. The light propagates through the water in the same direction, from A to B.

                                                      

 

If v=0 light travels from A to B in the time: t₀ =d/(c/n)=nd/c (1)

 

(where c is the speed of light in vacuum and n the refractive index of the water)

 

 

From Raman spectroscopy (see Raman_spectroscopy on Wikipedia), I learned that light appears to interact with the electron cloud of the molecules, basically as follows: an incident photon excites the sample. This excitation puts the molecule into a virtual energy state for a short time before the photon is emitted, most of the time with the same energy as the one absorbed (Rayleigh scattering), but sometimes different (Stokes and anti-Stokes Raman scattering).

 

So, it is possible/plausible to consider that light travels in transparent materials with the speed c between atomic electrons (where is "vacuum") and is delayed only as a result of the time lost when interacting with the electrons in the atoms/molecules.

 

My reasoning is that the electron hit by the photon absorbs it, changing its speed/trajectory, and if it remains in the system (atom/molecule) and cannot reach another stable state, the electron will have to emit the photon as it was, regaining its initial stable trajectory/state. All these happen very very quickly but, due to the large number of electrons/interactions, light travels slower in (transparent) materials than in vacuum.

 

It is logical to assume that if the energy of the photon is bigger, it may take a little longer until the electron, together with the system (atom/molecule), can "decide" (by trial and error) that it can not escape, nor use the energy to reach another stable state, and re-emits the photon, and this is consistent with experimental evidence: red light travels faster than blue light in the same material (see chromatic dispersion).

 

I have to state that the absorption described above is in fact a failed absorption or quasi-absorption, because it is always and very quickly followed by emission. So this is not frequency dependent as normal absorption. Any photon can suffer this quasi-absorption.

 

In my opinion, the electrons in the atoms are still revolving around the nuclei, like in the Bohr model, but their orbits are disturbed by these quasi-absorptions and thus, the best way to manage them is to use the wavefunctions. If you don't agree with my interpretation and/or consider that the atoms/molecules, not their electrons, are absorbing the photons, that's fine too, the demonstration below is still valid, because you can consider the electron/atom/molecule entering into a virtual energy state and then re-emitting the photon, like in Raman scattering above ... but I prefer my interpretation, because it offers better insights

 

I know that this is not the mainstream view, but it is based on accepted facts (it is accepted that electrons, together with the rest of the atom, can absorb and emit photons) and yields good results (it can explain without relativity or aether the Fizeau experiment and Sagnac effect in materials, as you'll see below). Refraction experiments can be made to further test this approach (see at the end).

 

I'm not the only one to consider an absorption/re-emission theory/idea (probably not even the first, although I did it since late 80s). Even our colleagues Strange and swansont wrote something similar (follow the links, especially the second).

 

My model may also explain Huygens proposition (see Huygens–Fresnel principle) that every point to which a luminous disturbance reaches becomes a source of a spherical wave, because the electrons are in constant motion, so the direction of the re-emitted photon is (more or less) random. The photons exhibit wave–particle duality, so Fresnel principle of interference  assures the rectilinear propagation of light. In my mind/model, the wavefront is associated with the moving photons and, in most cases (n>1), their speed is the same with the phase velocity of light in the medium (see more about this at the end).

 

 

 

With the above model/approach considered: t₀=d/c+N₀τ₀ (2)

 

(where N₀ is the average number of interactions for "one" photon between A and B when v=0 and τ₀ is the average time for one interaction, the time between the absorption of the photon and re-emission).

 

Probably the distance covered in vacuum (between electrons) from A to B is not exactly d, but it is a good approximation (see the final result).

 

 

For v>0 light travels from A to B in: t₁=(d-N₁vτ₁)/c+N₁τ₁ (3)

 

N₁vτ₁ is the distance light travels with/inside the atoms/molecules, making the travel in vacuum shorter. This is very important and shows how light is entrained by the matter.

 

N₁τ₁ represents the delay due to interactions, and N₁ is smaller than N₀, because from the moment that light starts from A and the moment of arrival in B, some water flowed off the tube, so there were less interactions. The volume of water in static example is Sd, where S is the area of a section in the tube. Svt₁ is the volume of water that flowed from the tube before the light arrived at B. If in the volume Sd we had N₀ interactions, in Sd-Svt₁ we expect to have:

 

N₁=S(d-vt₁)N₀/Sd=N₀(1-vt₁/d) (4)

 

So, from (3) and (4) we get: t₁=d/c+N₁τ₁(1-v/c)=d/c+N₀(1-vt₁/d)τ₁(1-v/c) (5)

 

From (2) and (1) we have: N₀τ₀=t₀-d/c=nd/c-d/c=(n-1)d/c

 

We can consider/approximate: τ₁ = τ₀because the speed v of the water in the tube is far smaller than c, so the redshift/blueshift is too small to influence τ (or n : in the relativistic approach there is also only one refractive index considered, neglecting redshift/blueshift), and time dilation is also too small at those speeds and can be neglected, so: N₀τ₁=N₀τ₀=(n-1)d/c (6)

 

From (5) and (6) we have: t₁=d/c+(n-1)(d/c)(1-vt₁/d)(1-v/c) that becomes:

 

ct₁/d=1+(n-1)(1-vt₁/d)(1-v/c) and then: ct₁/d+(vt₁/d)(n-1)(1-v/c)=1+(n-1)(1-v/c) so:

 

[math]t_1=\frac{1+(n-1)(1-v/c)}{c/d+(v/d)(n-1)(1-v/c)}[/math]

 

Light appears to travel from A to B with the speed V=d/t₁ and using (7) we get:

 

 

So, the final result is:

 

[math]V=\frac{c}{n}+v(1-\frac{1}{n^2-n(n-1)v/c})\approx \frac{c}{n}+v(1-\frac{1}{n^2})[/math]    

(v<<c, so n(n-1)v/c →0)

 

This result, with n(n-1)v/c, is a better approximation (I calculated in Excel with real values - see Compare-Fizeau.xls attached) than the one obtained using special relativity (see here):

 

[math]V-\frac{c}{n}=\frac{v(1-\frac{1}{n^2})}{1+v/cn}[/math]

 

 

2. Sagnac effect in materials

 

Using the same approach as above, it is very easy to explain Sagnac effect in materials without relativity. Let's consider a fiber-optic conveyor and one segment of the fiber-optic:

 

                

 

The segment has the length d and is moving to the right with the speed v.

 

In each segment like this, there are two beams of light, one traveling from A to B and the other from B to A. Let's analyze their travel time:

 

a. Photons are moving from A towards B

 

In the (inertial) laboratory frame we can see that from the moment they started, in A, the right end of the segment, B, moved, with the speed v, prolonging their travel:

 

 

If t₁ is the photons travel time through the segment (from A to B'), the distance they covered is d+vt₁. Considering, like in Fizeau experiment, that photons travel through the transparent material with the speed c in the vacuum between electrons and suffer a great number (N) of absorptions followed by re-emissions, that take in average a time τ₁ each, and during this time they are carried with/inside the atoms/molecules with the speed of the segment, v, shortening their travel in vacuum from d+vt₁ to d+vt₁-Nvτ₁ , we get:

 

[math]t_1=\frac{d+vt_1-Nv\tau_1}{c}+N\tau_1[/math]   making   [math]t_1=\frac{d-Nv\tau_1+cN\tau_1}{c-v}=\frac{d}{c-v}+N\tau_1[/math]

 

b. Photons are moving from B towards A

 

In the same laboratory frame we can see that from the moment they started, in B, the left end of the segment, A, moved, with the speed v, shortening their travel:

 

 

If t₂ is the photons travel time through the segment (from B to A'), the distance they covered is d-vt₂. Considering, like above, the absorptions and re-emissions and that the photons are carried backwards with/inside the electrons with the speed of the segment, v, lengthening their travel in vacuum from d-vt₂ to d-vt₂+Nvτ₂ , we get:

 

[math]t_2=\frac{d-vt_2+Nv\tau_2}{c}+N\tau_2[/math]   making   [math]t_2=\frac{d+Nv\tau_2+cN\tau_2}{c+v}=\frac{d}{c+v}+N\tau_2[/math]

 

I considered that the number of absorptions/re-emissions, N, is the same for both ways because it was the very same segment, with the same number of molecules, etc., traveled from end to end in both instances. Furthermore, τ₁ and τ₂ are in fact identical, because there is no redshift or blueshift (the emitter is attached to the fiber-optic) and time dilation is not only too small, but also identical, because there are the same molecules moving with the same speed v<<c.

 

So, for each segment we have a time difference between the opposing beams:

 

[math]\Delta t=t_1-t_2=\frac{d}{c-v}+N\tau_1-\frac{d}{c+v}-N\tau_2=d\frac{c+v-(c-v)}{(c-v)(c+v)}=\frac{2vd}{c^2(1-\frac{v^2}{c^2})}\approx \frac{2vd}{c^2}[/math]

 

If we add the contributions of all the segments that form the fiber-optic loop, we get ΔT=2vL/c², where L is the length of the loop, and this is the generalized formula for the Sagnac effect, independent on the refractive index of the material and identical with the one obtained using special relativity (search the case of a flexible loop of optical fiber moving like a conveyor belt).

 

 

As I wrote in the beginning, we should have such a theory for Fizeau and Sagnac, because the speeds involved are far from relativistic. And this approach may be also useful in the understanding of nonlinear optics, like frequency doubling: if an electron is hit by another photon before it re-emits the first one, and still remains in the system (atom, molecule, etc.), it may emit only one photon, with the sum of the absorbed photons energies, in order to regain it's initial stable trajectory/state.

 

This particle approach is not necessarily better than the wave approach. In fact, for a better understanding, both should be employed. See here:

 

At the microscale, an electromagnetic wave's phase velocity is slowed in a material because the electric field creates a disturbance in the charges of each atom (primarily the electrons) [...]The charges thus radiate their own electromagnetic wave that is at the same frequency, but usually with a phase delay, [...]. The light wave traveling in the medium is the macroscopic superposition (sum) of all such contributions in the material: the original wave plus the waves radiated by all the moving charges. This wave is typically a wave with the same frequency but shorter wavelength than the original, leading to a slowing of the wave's phase velocity. Most of the radiation from oscillating material charges will modify the incoming wave, changing its velocity. However, some net energy will be radiated in other directions or even at other frequencies (see scattering – including Raman, as I wrote …).

 

Depending on the relative phase of the original driving wave and the waves radiated by the charge motion, there are several possibilities:

• If the electrons emit a light wave which is 90° out of phase with the light wave shaking them, it will cause the total light wave to travel slower. This is the normal refraction of transparent materials like glass or water, and corresponds to a refractive index which is real and greater than 1.^[24]

• If the electrons emit a light wave which is 270° out of phase with the light wave shaking them, it will cause the wave to travel faster. This is called "anomalous refraction", and is observed close to absorption lines [this is logical with my model: when the electron gets very near to anoher stable state, it is hard to „decide” that it is not quite there and go back, re-emitting the photon with a bigger delay/phase difference] (typically in infrared spectra), with X-rays in ordinary materials and with radio waves in Earth's ionosphere. It corresponds to a permittivity less than 1, which causes the refractive index to be also less than unity and the phase velocity of light greater than the speed of light in vacuum c (note that the signal velocity is still less than c, as discussed above). If the response is sufficiently strong and out-of-phase, the result is a negative value of permittivity and imaginary index of refraction, as observed in metals or plasma.^[24]

• If the electrons emit a light wave which is 180° out of phase with the light wave shaking them, it will destructively interfere with the original light to reduce the total light intensity. This is light absorption in opaque materials and corresponds to an imaginary refractive index. [...]

 

For most materials at visible-light frequencies, the phase is somewhere between 90° and 180°, corresponding to a combination of both refraction and absorption.

 

In the Wikipedia article I quote above, the charges (primarily the electrons) in the material are not (apparently) absorbing photons in order to re-emit them. They are just "shaken" back and forth at the same frequency, and then radiate their own electromagnetic wave that is at the same frequency, but usually with a phase delay. I think that without photons being absorbed, it’s like producing photons/energy without consuming anything … so there must be absorption followed by emission, like I proposed.

 

 

As I mentioned when I presented the model, it is possible to test it further. One way is to fill a chamber (with transparent walls) with different quantities of various gases and measure the refractive index. The first goal is to see if the total time delay, Nτ (=(n-1)d/c), is directly proportional to the number of molecules in the chamber (at the same temperature). Then, after measuring all the gases separately, one can mix them (the ones not reacting with each other), carefully measuring the quantities, and test if the measured refractive index is equal with the one predicted using the model (n=1+( N₁τ₁+ N₂τ₂+ N₃τ₃+ N₄τ₄+ …)c/d).

 

[madmac]

DanMP -- i too am interested in the slowing of light etc in glass water air etc. U mention your own absorption-emission theory -- i dont know enuff about science to comment much -- except that your derivation of the fresnel equation might be say #4, the other 3 giving similar or identical equations (fresnel is #1, fizeau might be #2, Michelson #3).

I daresay that this means that there are praps 4 micro explanations for the 4 macro derivations-equations (i dont remember). I would like to mention my idea here (micro explanation #5 if u like). It contradicts your #4, & in that sense is off topic, but i think that such a comparison  need not be considered completely off topic, especially as sadly everyone else has entirely neglected to give u any input.

I have read Strange's &  swansont's comments in thems links. I find phase velocity & group velocity difficult to understand. I am not violently opposed to the standard idea that photons force the electrons (in glass water air) to vibrate & that this creates a feedback field that slows the photons below c (& increases photon frequency) -- with no actual absorption & no re-emission. I think that (your)  re-emission must be random -- in which case it must be non-compatible with what we see (light appears to go straight)(albeit bending at different angles at interfaces etc, depending on frequency, but then goes straight again) -- i think that re-emission must scatter light very widely.

So what is my own #5. I reckon that light is slowed near mass (ie Einstein was correct)(albeit for the wrong reasons). And i reckon that the micro effect re such slowing is identical for light passing throo mass (where the slowing is of course much stronger). So what is my micro effect. It involves what i call photino-drag.

All photons emit a photino field, it is a part of the photon -- & these fields interact, the electron being simply a confined photon (emitting its own photino field) -- & quarks etc being other forms of confined photons (emitting additional photino fields)(ie from all protons & all neutrons)(neutrons might be charge neutral but that doesnt mean that they have no charge fields)(it means that their fields negate in some fashion)(charge fields being due to photinos)(all EM fields are due to photinos) -- the interactions due to congestion slow the outwards spreading of the photinos, which creates a feedback to the main body of the photon, slowing the photon (due to photino-drag).

A photon can only have the maximum possible velocity of c if in deep outer space well away from any mass (objects) or other photons (radiation) or any photinos (EM fields)(another kind of radiation) -- in other words, c is an impossibility.

Edited November 2, 2018 by madmac

[Strange]

33 minutes ago, madmac said:

I find phase velocity & group velocity difficult to understand.

That does not mean they are wrong!

33 minutes ago, madmac said:

I think that (your)  re-emission must be random -- in which case it must be non-compatible with what we see (light appears to go straight)(albeit bending at different angles at interfaces etc, depending on frequency, but then goes straight again) -- i think that re-emission must scatter light very widely.

This is explained by Feynman's path integral in quantum electrodynamics - this is mathematically more complicated than the wave equations you are struggling with, but conceptually simple. You can find his lectures on this online: http://www.feynman.com/science/qed-lectures-in-new-zealand/ (also available as a book).

[DanMP]

5 hours ago, madmac said:

sadly everyone else has entirely neglected to give u any input.

I appreciate that you replied, but your input is not quite what I expected, especially the last part, with you own "theory" ...

5 hours ago, madmac said:

I think that (your)  re-emission must be random -- in which case it must be non-compatible with what we see (light appears to go straight)(albeit bending at different angles at interfaces etc, depending on frequency, but then goes straight again) -- i think that re-emission must scatter light very widely.

I think I covered this problem where I wrote:

On 8/23/2018 at 3:43 PM, DanMP said:

... so the direction of the re-emitted photon is (more or less) random. The photons exhibit wave–particle duality, so Fresnel principle of interference  assures the rectilinear propagation of light.

 

1 hour ago, Strange said:

This is explained by Feynman's path integral in quantum electrodynamics - this is mathematically more complicated than the wave equations you are struggling with, but conceptually simple

Thank you Strange for your input.

What do you think about my "Classical explanation for the Fizeau experiment & for Sagnac effect in materials" above? I thought that you would like it, because:

On 8/23/2018 at 3:43 PM, DanMP said:

I'm not the only one to consider an absorption/re-emission theory/idea (probably not even the first, although I did it since late 80s). Even our colleagues Strange and swansont wrote something similar (follow the links, especially the second).