[Colin2B]

….. I don't want to derail ES's question.

I think he has already done that and I haven’t had time to provide him with additional ideas.

@Bored chemist makes some good points, one for one against:

Most "green lasers" you see are actually the beat frequency of an IR beam with itself i.e frequency doubling.

The photodetectors use in experiments like that depicted, typically measure the power, rather than the field strength of the incident light.
Since the power is proportional to the square of the field, (which is why it's always positive), the detector is inherently non linear.

Not a straightforward subject because what we measure is always affected by the way we take the measurements.

This is probably a separate topic.

[Bored chemist]

Photographic film isn't particularly sensitive to x-rays, surprisingly, so Edison invented the fluorescent "intensifying screen" that absorbs incoming x-ray photons and emits large numbers of visible photons which are more efficiently captured by the film. At very low dose rates you can see "quantum mottle" on an x-ray image, each spot corresponding to a single x-ray photon hitting  the screen. So at least the quantum behavior of x-radiation is easy to see

If our eyes were about 10 times better, we wouldn't need to explain quantisation of light in textbooks because we would be able to see it.
I wonder if that would leave us more confused about diffraction or less so.

[Bored chemist]

funded at your expense,

[at your expense]

the vanity of people who cannot admit that their model(s) are not reality itself.

You do know that money is just a model, don't you?

[alancalverd]

If our eyes were about 10 times better, we wouldn't need to explain quantisation of light in textbooks because we would be able to see it.

Related topic:

In my youth, all my dogs were interested in dogs that they saw on television. Even a 9 inch 405 line black and white TV made from an old radar unit. More recently, none have shown any interest in life size, full color HD 45 inch damn near real dogs with hi fi stereo sound.

I think the reason is that the old CRT had enough persistence that it presented a fairly complete and slowly changing image, whereas modern LCD units have negligible persistence and rely on the inertia of the human eye to produce an image. But dogs have much faster visual response and just see individual flickering dots.

[Eternal Student (OP)]

Hi.

...I don't want to derail ES's question....

    That's fine, discuss anything that's even vaguely relevant,  it won't trouble me.   I'm still busy doing housework of one type or another, so I'll apologise in advance for not replying but I'll try and keep up where and when I can. 

Best Wishes.

[evan_au]

Alan & I regularly use beat frequencies to tune musical instruments. I agree that the individual component frequencies still exist, but it doesn’t change the fact that the beat frequency exists and has a physical effect, you can for example get it to excite a tuned resonator.

I have also used beat frequencies to tune a guitar (in my distant youth)...
- If you pluck an open string, you will get a (decaying) sine wave (with a few harmonics).
- If you shorten the adjacent string, you will also get a (decaying) sine wave of almost the same frequency (also with a few harmonics).
- If you now pluck both together, your ears (a logarithmic sound power detector) will detect increasing and reducing power, as the two waves go into and out of phase (the beat frequency at say, 1Hz).
- If you measured this with an FFT over a complete beat cycle (eg 1 second), you would see just the two string frequencies, but not the beat frequencies. You would not see the difference frequency because the microphone is linear.
- The guitar does not resonate at 1Hz, as it doesn't really work much below 50Hz. What you hear are the two audio frequencies exciting the sounding board more and less, cyclically.
- Your ear does not resonate at 1Hz, as it doesn't really work much below 20-50Hz. What you hear are the two audio frequencies exciting your eardrum more and less, cyclically.

This is very different than if you:
- Wiggled your finger tension on the string while playing a string (vibrato - more commonly used on violins = non-linear), which creates a series of frequency-modulated sidebands, close to the natural string frequency.
- Wiggled the volume control while playing a string (amplitude modulation = nonlinear), which creates a pair of amplitude-modulated sidebands, close to the natural string frequency.

Really, I don't see that beat frequencies in a linear medium can excite events at the beat frequency (unless the pianist gets excited because the piano isn't tuned properly!).

PS: People don't tend to use this method of tuning guitars these days - it is too easy to use a crystal-locked electronic tuner which doesn't just tell you that the frequencies differ by 1 Hz, but tells you whether the string is too high or too low in frequency (to 1% of a semitone...). ...assuming you want an equal-tempered scale.

[Eternal Student (OP)]

Hi.

Really, I don't see that beat frequencies in a linear medium can excite events at the beat frequency...

     Rather than worrying about the medium that the frequencies are travelling through or were generated in behaving in a non-linear way, the object which the beat is incident upon can't always respond linearly, in particluar it can't always "keep up" with the speed of oscillations.  An example is an object in the region that is behaving as a damped oscillator while some pair of frequencies that resulted in a beat (an amplitude modulated signal) are incident upon it.

I expect you've seen something like this already but I'll put some rough mathematics down here anyway (I don't know who might be reading this and I need a distraction from housework).

     The object  (the damped oscillator) has this equation of motion:

[Eqn 1]

with b, k constants (b for the damping and k for the spring constant), x= displacement from equilibrium position    and F(t) = driving force which varies with time.   There's an m (a mass term) multiplying the d²x/ dt² usually but I've just divided by m and so my constants k,b and Force F are "per unit mass" if you want to be fussy.

  The oscillator is driven by the vibrations in ...whatever...  the vibrations in the air for your guitar string examples.   So we will take 
      F(t)  =  A(t) .  Cos Ωt 
     With   A(t) =   Cos (ωt+Φ)     (with Φ = some constant)
as usual.     
A(t) describes the oscillating amplitude envelope for the beat incident on our damped oscillator, while the Cos Ωt describes the carrier waves within it.    For a beat,  Ω = π (f₁ + f₂)    and   ω = π(f₁ - f₂),   with f₁ and f₂ being the original two frequencies that generated the beat (where we assume they had equal amplitude, or at least equal where they became incident on our object).   All that matters is that Ω >> ω.  (Minor note: You can set Φ which appeared in the Amplitude wave form to 0 if you like, it doesn't make any difference to what follows).

When Ω >> ω we can solve the equation of motion over a small interval of time  t ∈ (t₀, t₁) such that we can assume  A(t)  ≈  A₀ = constant  while the Cos (Ωt) term shows much more variation.      Over that small interval the equation of motion then becomes:
      A₀. Cos Ωt

Which is the equation of motion for a damped oscillator with a sinusoidal driving force at an angular frequency Ω (which is assumed to be far above the natural frequency of this oscillator).  We have a standard solution for this.  The damped oscillator hardly responds to that driving term and we have that x(t) is almost constant throughout that interval,  x(t) ≈ x(t₀).    For convenience we can take  t₁ - t₀   =  2π/Ω  (then Ωt moves through 2π over our interval but with ω << Ω  we will have that ωt  hardly changes giving us A ≈ A₀ throughout the interval as we wanted).

    If we now consider [Eqn 1] at several  discrete values of time  t₀,  t₁, t₂, .., t_n, ....
where the gap between t_n   and t_n+1   is always  2π/Ω    then we obtain   F(t_n) =  Cos (ωt_n + Φ) . Cos (Ωt₀ + n.2π)   =   c .  Cos(ωt_n + Φ)    with c = constant = Cos (Ωt₀).
We can then imagine a new damped oscillator with displacement y(t) and this equation of motion:
        c .Cos (ω t + Φ)   

[Eqn 2]

Confine your attention to just numerical solutions of this O.D.E.   Since the RHS of [eqn 2] will be precisely the RHS of [eqn 1] at every value t= t_n, we know that numerical solutions of  [Eqn 2], y(t_n) =  f(t_n)  for some function f, will be precisely the same as numerical solutions of [Eqn 1],  x(t_n) = f(t_n)  whenever we take uniform intervals Δt = t_n - t_n-1= 2π/Ω and start the numerical technique at the same place t=t₀.   However, [Eqn 2] is just the equation for a damped oscillator being driven at the angular frequency ω << Ω.   We have an analytical solution for this.   The numerical solution we generate for [Eqn 1] is then well approximated by the anlytical solution y=y(t) for [Eqn 2] evaluated at the points t= t_n.   Finally we make use the earlier paragraph (about x(t) being reasonably constant over the small intervals because the damped oscillator hardly responds to a driving frequency of Ω) and conclude:  The exact solutions of [Eqn 1]  take the form    x(t) =  y(t) + δ(t)    where  y(t) is the exact solution of [Eqn 2]  and  δ(t) is a function that is some small correction,  i.e.  |δ(t)| ≈ 0.

   Anyway, the general idea or the "bottom line" of the argument, is that the damped oscillator will respond as if it is seeing a driving force of the form Cos (ωt)  (as seen in [Eqn 2] ) where ω is the angular frequency of the amplitude modulation.

Best Wishes.

[paul cotter]

"I don't know who is reading this", well I certainly am, I am following your every word. When it comes to the maths of physical realities I am all in- things like set theory, number theory and infinities, not much interest. I have a busy schedule today and have not had time to digest your contribution.

[hamdani yusuf]

This experiment is takes a different approach and might be similar to what you are looking for https://www.sciencedaily.com/releases/2018/04/

I find this statement in the article inaccurate.

Polarization occurs when waves, such as electromagnetic or light waves, rotate. Electromagnetic fields called microwaves have a rotating electric field that turns clockwise or counter-clockwise, and most theories predict that microwaves will affect the rotation of electrons. And yet, experimental studies have shown that electrons seem to be unaffected by microwave polarization. These theory-defying results have long perplexed physicists.

It describes circular polarization. There's another type of polarization called linear polarization. Elliptical polarization can be seen as combination of both.

[hamdani yusuf]

I understand that you can show polarisation of a microwave beam by building a wall with row of parallel wires.
- When the wall is oriented in one direction, it "short-circuits" the E-field and the microwaves are blocked
- Rotate the wall by 90°, and the microwaves get through, as the wires don't short-circuit the magnetic field.

A similar arrangement (on a smaller scale) is used to produce polarised lenses for visible light - there is a grid of long, parallel crystals in the lense.

The microwave gets reflected when it's short-circuited. The metal wires don't absorb much of the energy.
Thinner wires have higher resistance, and generate heat while absorbing some energy.

[Eternal Student (OP)]

Hi.

I find this statement in the article inaccurate....

    The article does seem to be condensed and edited.   You're absolutely right, plane polarisation is possible.   However, this experiment seemed to require circular polarised microwaves, so they (the editor rather than scientists, I suspect) didn't explain anything else.   Later in the article, they do say "circular polarised microwaves" instead of just "polarised microwaves".

The microwave gets reflected when it's short-circuited. The metal wires don't absorb much of the energy.
Thinner wires have higher resistance, and generate heat while absorbing some energy.

   Building a good polarising filter is a problem.    The wires can't be too thick and the gap between the wires can't be too large or too small.    If the gap between the wires is too small then what you have is a wall and that will often reflect the microwaves.  If the gap is too large  (imagine a pair of goal posts as used in football) then plenty of microwaves are just going to get straight through the centre without interacting with the wires at all.
     If the wires are too thick then electrons can oscillate (I'll say up and down) significantly even when the wires are running horizontally.  So that is saying the electrons can move across the wire instead of along the wire.   This tends to block the microwaves regardless of the orientation of the filter.  Meanwhile, if the wires are too thin then what tends to happen is that the gap between the wires has got too large compared to the thickness of the wires and/or the resistance of the wires is too high to allow enough oscillation of the electrons.
    Throughout the whole thing, when electrons are oscillating they are tending to create or emit radiation of the same frequency as that which was driving them.  So the filter itself is generating some microwaves.  It's just that the emitted microwaves are thrown out in all directions fairly uniformly, while the horned microwave generators of the type most people use (I've seen some being used by you, @hamdani yusuf , on a different thread) tend to produce a much narrower beam.  Hence, even with a filter that is about as perfect as you could build it and orientated so as to block the beam, you will still pick up some microwaves at the other side of it.   Hopefully, the microwaves emitted by the electrons in the filter have an intensity that falls off as 1/r².   Meanwhile a good and well focused beam of microwaves shouldn't fall off in intensity with distance travelled.   However, in practice nothing is perfect - you probably don't have perfectly focused parallel beams,  microwaves get absorbed, re-emitted, scattered and generally disrupted by the filter and everything else like the medium (air) that they travel through.
    More generally, I don't suppose classical physics with E and B fields is really going to fully explain what is happening with microwaves and a polarising filter.  At the point of interaction with the filter, I would have thought there must be some genuine photon and atom interactions taking place.  @alancalverd  (and others) have already made some posts on this thread suggesting that since the energy of microwave photons is much lower than light, results like the Ehrenfest theorem and the more generalised correspondence principle will be exhibited.  Specifically, that you will get something that is more easily matched to classical physics.   (This post is too long, I'm ending now.   I'll just make it clear that practical experimentation isn't something that I know much about.  Most of my practicals never worked).

Best Wishes.

[paul cotter]

Hi, Eternal Student, I am still digesting your damped oscillator maths. I also re-read the whole thread to clarify your requirements and I found an error on post #20( shock, horror ). You have c=1/με when it should be 1/sqrtμε. It's possible that you have accounted for this in the subsequent maths but I haven' determined that yet ( i'm rather slow ).

[Eternal Student (OP)]

Hi, thanks and well spotted @paul cotter

   It was a typing error,   
       Where we have used the relationship c = 1/(μ₀ε₀).
 Should have been
       Where we have used the relationship c² = 1/(μ₀ε₀).

Fortunately that was what was actually done.  The original post has now been edited.

Best Wishes.

[DarkKnight]

Hi, thanks and well spotted @paul cotter

   It was a typing error,   
       Where we have used the relationship c = 1/(μ₀ε₀).
 Should have been
       Where we have used the relationship c² = 1/(μ₀ε₀).

Fortunately that was what was actually done.  The original post has now been edited.

Best Wishes.

I find it interesting that Maxwell explained the speed of light in a vacuum as c when space isn't a vacuum nor empty. I also don't understand why Maxwell ignored that the Suns EM field extends all the way to the Earths surface with enough magnitude to illuminate the surface .

[hamdani yusuf]

I find it interesting that Maxwell explained the speed of light in a vacuum as c when space isn't a vacuum nor empty. I also don't understand why Maxwell ignored that the Suns EM field extends all the way to the Earths surface with enough magnitude to illuminate the surface .

What should it be if he didn't ignore it?

[Bored chemist]

I also don't understand why Maxwell ignored that the Suns EM field extends all the way to the Earths surface with enough magnitude to illuminate the surface .

That seems to be one of a long list.
Let's cross one item off it.
https://en.wikipedia.org/wiki/Superposition_principle

[hamdani yusuf]

Throughout the whole thing, when electrons are oscillating they are tending to create or emit radiation of the same frequency as that which was driving them.  So the filter itself is generating some microwaves.  It's just that the emitted microwaves are thrown out in all directions fairly uniformly, while the horned microwave generators of the type most people use (I've seen some being used by you, @hamdani yusuf , on a different thread) tend to produce a much narrower beam.  Hence, even with a filter that is about as perfect as you could build it and orientated so as to block the beam, you will still pick up some microwaves at the other side of it.   Hopefully, the microwaves emitted by the electrons in the filter have an intensity that falls off as 1/r2.   Meanwhile a good and well focused beam of microwaves shouldn't fall off in intensity with distance travelled.   However, in practice nothing is perfect - you probably don't have perfectly focused parallel beams,  microwaves get absorbed, re-emitted, scattered and generally disrupted by the filter and everything else like the medium (air) that they travel through.

The working principle of directional radio antenna is explained clearly in this video by Royal Canadian Air Force.

My model can be thought as an extention to the working principle of antenna, which can be shown clearly here.

It uses antenna array as the source of electromagnetic wave. It's different from wave on water surface and Huygen's principle which treat empty space as wave source.
Directional antenna simply shifts the focus of the beam to a point behind the transmitting antenna, which is used as reference to measure r for intensity attenuation.

[hamdani yusuf]

More generally, I don't suppose classical physics with E and B fields is really going to fully explain what is happening with microwaves and a polarising filter.

If you think that classical physics in electromagnetism is well represented by Maxwell's equations as its mathematical model, then we have known its limitations, especially at microscopic scales. Maxwell treated electric charge as continuum, which can be divided infinitesimally. Millikan's oil drop experiment demonstrated quantification of electric charge. This critical false assumption lead this mathematical model to make wrong predictions on microscopic electromagnetic phenomena.

Moreover, Maxwell's equations say nothing about mass of electric charges, nor electromagnetic forces. These dismissals rendered the mathematical model incomplete.

[hamdani yusuf]

The working principle of directional radio antenna is explained clearly in this video by Royal Canadian Air Force.

Based on this explanation, I've built a model and devised some experiments to test it.

Here's the model I proposed. I'm not really sure if it's new, since it's based on how a dipole antenna work. Can we derive Huygen's principle from equations of antenna? Or can we derive equations of antenna from Huygen's principle?

Investigation on microwave 37 : blocking mechanism

Investigation on microwave 38: blocking mechanism explanation

Investigation on microwave 39: Blocking mechanism evidence

Here's an example how the model can be used to predict experimental results.

Polarization twister design.

Signal splitting.

Asymmetric twister/splitter

[hamdani yusuf]

Perhaps this demonstration can help answering the OP question. Although they happen mostly in infrared range of spectrum.

Natural resonance frequency of molecular vibration

Many Quality Control Laboratories already use online infrared spectroscopy fed to monitor product composition almost in real time and reduce manual sampling and chemical analyses. Each type of chemical bond has unique "fingerprint/signature absorption spectra" which can be used to calculate the concentration of some chemical compounds in the product/sample.