The electromagnetic nature of light

[Jeff Root]

Dave,

@Jeff Root - my interpretation of your #27 is that
you seem to be asking two different questions. One is, can you see the
EM field of a single RF photon, and is it sinusoidal? The other is, if you
have a broad-spectrum signal, can you see the sine waves making it up?

Yes. Both questions were raised by Nugatory in post #24, where he said:

> At lower frequencies, we can observe the waveforms with an oscilloscope
> and see the sine wave directly on the screen.

This was surprising to me, so I thought I may have misunderstood what he
meant. He may have been referring to observation of the waveforms of very
large numbers of coherent radio waves, rather than of a "single radio wave",
a single quantum of radio-frequency electromagnetic radiation. I understand
how looking at many examples of a thing can lead to understanding what the
thing itself looks like in general. The more samples that are examined, the
clearer and more detailed the picture one can get of the thing. But in this
case it appeared that Nugatory may have saying that the shape of a crowd
can be observed rather than saying that the shape of humans can be deduced
from looking at many individuals, each of whom is indistinct.

Since it has been my understanding that radio-frequency electromagnetic
radiation is too weak to detect individual photons, and Nugatory explicitly
says that we can see the waveforms with an oscilloscope, I suspect that he
was referring to the shape of the crowd, not the shape of the individuals in
the crowd. If it is possible to infer the shape of the individuals from the
shape of the crowd, I would very much like to know how that can be done.

I have seen the sinusoidal waveforms of artificially-produced signals on
oscilloscopes. I do not know that I have ever seen what I would call a
"sinusoidal" waveform or anything close to sinusoidal in a natural signal.
The "waveform" of natural signals, in my limited experience, is random,
looking more like grass than like a sine wave.

The only reason I ask about broad-spectrum, natural signals is to clarify
the answer to my first question of whether we can observe the waveform
of individual RF photons, and are they sinusoidal.

The fundamental question I have is whether electromagnetic radiation in
general actually has sinusoidal waveform. I believe it does, but that belief
may be based on stories to children. There is certainly some truth to it.
I'm trying to find out how much, from people who know the adult story.

The first you'd have to ask of someone who understands quantum field
theory. Maxwell's equations are classical and only describe classical waves.

The role of theory here is complex and interesting, but I want to cut
through those complexities as much as possible and say that I am asking
about what is observed rather than what theory says. Maxwell's theory
was put forward at the start of the thread as the connection between light
and electromagnetism. Observations of electric and magnetic phenomenon
lead to a theory which connected them with each other and with light. One
of the predictions of the theory is that light has a sinusoidal waveform. I'm
trying to understand if that waveform is what Nugatory observed on an
oscilloscope, or if the sinusoidal shapes he saw were artificial, created as
an intentional result of the design of a circuit or RF source. Since it is my
belief that RF radiation can only be detected with very large numbers of RF
photons, it is not apparent to me how the waveform on the oscilloscope
screen can represent the waveforms of individual RF photons. I am hopeful
that you or Nugatory or someone here can explain to me how the shape of
the trace on an oscilloscope screen can accurately depict the waveform of
individual photons.

My guess would be that the question doesn't make sense - you'd have to be
able to detect parts of a photon and the point of quanta is that you can't do that.

I agree that "parts of a photon" cannot be detected. That is why I question
whether the shape of a trace on an oscilloscope screen can actually represent
the waveform of the individual photons which compose the radiation being
observed. It seems more plausible that it only depicts the waveform of the
crowd of photons, and that would not necessarily be the wave predicted by
Maxwell's equation. It might instead be an artificial waveform of arbitrary
shape. My expectation is that the sinusoidal shape of light waves can be
predicted and inferred from observations, but cannot itself be observed.
So what is Nugatory's oscilloscope actually depicting? My guess is that it
is the cumulative interference of huge numbers of individual RF photons.
The people who designed the experiment know for sure. I expect that
Nugatory knows for sure.

What makes that really interesting, of course, is that interference has been
shown to occur even when only one photon reaches the detector at a time.

The second is a yes, to arbitrary precision given a narrow enough bandpass
filter and a bright enough source. You simply filter out everything except an
arbitrarily narrow frequency band and, the narrower the bandpass the nearer
a pure sine wave you'll pass through.

Can you explain how that is possible? With an incoherent light source, even
if it is filtered to allow only a single wavelength and polarization, the waves
would be out of phase. I'd expect the waveform to be completely random.
Tall grass.

-- Jeff, in Minneapolis

 

[Nugatory]

This was surprising to me, so I thought I may have misunderstood what he
meant. He may have been referring to observation of the waveforms of very
large numbers of coherent radio waves, rather than of a "single radio wave",
a single quantum of radio-frequency electromagnetic radiation.

No, I was referring to the single waveform that is all we're ever working with, whether it's electromagnetic radiation or any of the many other phenomena desribed by the wave equation. I'm not sure where you're getting the idea that the signal contains a large number of waves, whether coherent or not, or that a single quantum is a single wave.
Indeed, any attempt to introduce quantization into a discussion to Maxwell's equations, the speed of light, and the wave nature of electromagnetic radiation suggests a misunderstanding of the relationship between photons and electromagnetic radiation. Single-photon states of the electromagnetic field are not electromagnetic waves (don't be misled by the fact that photons have a frequency - that doesn't mean what it sounds like) and electromagnetic waves cannot be analyzed as a bunch of photons the way a beach can be analyzed as a bunch of grains of sand.
There's a lot to be said for trying to forget that you ever heard the word "photon" until after you have a solid grasp of Maxwell's classical electrodnamics.
(But if you can't bring yourself to do that and also don't want t to take on a graduate-level quantum electrodynamics textbook you might take a look at http://www.physics.usu.edu/torre/3700_Spring_2015/What_is_a_photon.pdf).

Can you explain how that is possible? ... I'd expect the waveform...

Your expectation is wrong. Many posts back I suggested that you google for "Fourier analysis"; this will explain how it doesn't work the way you're expecting.

 

[Ibix]

The fundamental question I have is whether electromagnetic radiation in
general actually has sinusoidal waveform. I believe it does, but that belief
may be based on stories to children. There is certainly some truth to it.
I'm trying to find out how much, from people who know the adult story.

You can write any wave as a sum of sine waves (decomposing an arbitrary wave into a sum of sine waves is what the Fourier transform does). Asking whether classical electromagnetic radiation is "actually" sine waves is a bit like asking whether three is "actually" two plus one. You can certainly represent it that way if you wish.

Regarding the bandpass filter, you would need an infinitely narrow one to pull a pure sine wave out of true white noise. However, real sources typically have some non-whiteness that means you could pull out something very close to a sine wave with a sufficiently narrow filter. Possibly an implausibly narrow one for a real source.

Finally, note Maxwell knew nothing of quantum theory. His equations are purely classical. The sine waves talked about here are not quanta, and you cannot understand quanta of light in terms of Maxwell's electromagnetic field.

 

[ZapperZ]

How was it discovered that electromagnetic radiation is electromagnetic?

-- Jeff, in Minneapolis

I'm going back to your VERY FIRST post here, because this question that I have has not been clearly answered or clarified based on your posts so far.

Question: Do you know that the EM wave function can be derived DIRECTLY by using Maxwell equations, or more specifically, by using two out of the 4 Maxwell equations?

Question: Do you know that once you derived the wave function, you IMMEDIATELY get that the speed of that wave is equal to 1/√(ε₀μ₀), where ε₀ and μ₀ are the permittivity and permeability of free space, respectively, and that is equal to the speed of light in vacuum?

If you are not aware of these, then did what I wrote above answered your question? If you are aware of these, then I do not understand what the issue is here because the derivation drops the answer to your question right onto your lap!

Zz.

 

[vanhees71]

You need all four Maxwell equations. I use SI units here, because they are in this case more to the point answering the historical question. Usually I prefer Heaviside-Lorentz units, but here the SI units serve our purpose better.

The microscopic Maxwell equations are
$$\begin{equation}
\label{1}
\vec{\nabla} \cdot \vec{B}=0,
\end{equation}
$$
$$\begin{equation}
\label{2}
\vec{\nabla} \times \vec{E}+\partial_t \vec{B}=0,
\end{equation}
$$
$$\begin{equation}
\label{3}
\vec{\nabla} \times \vec{B} -\mu_0 \epsilon_0 \partial_t \vec{E}=\mu_0 \vec{J},
\end{equation}
$$
$$\begin{equation}
\label{4}
\vec{\nabla} \cdot \vec{E}=\frac{1}{\epsilon_0} \rho.
\end{equation}
$$
Note the arbitrary constants $\epsilon_0$ and $\mu_0$ which come from the arbitrary choice of the units of charge in the SI being Coulombs or Ampere seconds.

Now to see that there are wave solutions we consider a region in space, where no charges and currents are present, i.e., we set the right-hand sides of the inhomogeneous equations $(\ref{3})$ and $(\ref{4})$ to 0. To get rid of $\vec{B}$ we take the time derivative of Eq. $(\ref{3})$ (with $\vec{J}=0$) and use $(\ref{2})$:
$$\begin{equation}
\label{5}
\vec{\nabla} \times \partial_t \vec{B} -\mu_0 \epsilon_0 \partial_t^2 \vec{E}=-\vec{\nabla} \times (\vec{\nabla} \times \vec{E}) -\mu_0 \epsilon_0 \partial_t^2 \vec{E}=0.
\end{equation}
$$
For the "double curl" we have, using Eq. $(\ref{4})$ with $\rho=0$
$$
\begin{equation}
\label{6}
\vec{\nabla} \times (\vec{\nabla} \times \vec{E})=\vec{\nabla}(\vec{\nabla} \cdot \vec{E})-\Delta \vec{E} = -\Delta \vec{E}.
\end{equation}
$$
Plugging this into $(\ref{5})$ we finally get the wave equation
$$\epsilon_0 \mu_0 \partial_t^2 \vec{E}-\Delta \vec{E}=0,$$
from which we get the phase velocity
$$c=\frac{1}{\sqrt{\epsilon_0 \mu_0}}.$$
Now historically (though using still different units, namely electrostatic units for elecrostatics and magnetostatic units for magnetostatics) Maxwell used the known values of $\epsilon_0$ and $\mu_0$, determind from measurements, comparing the electrostatic and the magnetostatic measures of charge, to determine the speed of the waves, getting a value very close to the value known from meausurements of the speed of light.

You can also derive the same wave equation for $\vec{B}$ and then look for the plane-wave solutions, from which you can find all wave solutions via Fourier transformation. This more detailed analysis also leads to the polarization properties of the electric and magnetic field. The plane waves are all strictly transverse, and that leads to a description of all the polarization properties of light.

Finally after some time H. Hertz for the first time could make and detect electromagnetic waves (in the radio-frequency domain though, i.e., with wavelength in the meter scale) and demonstrate all the properties predicted by Maxwell.

 

[Vanadium 50]

There is no wiggle room. Sin waves.

Pun intended?

 

[HomogenousCow]

Jeff it sounds like you need a good textbook and some mathematical foundations to really satisfy your curiosity. Your issue regarding whether or not electromagnetic waves are "sinusoidal" stems from a lack of mathematical knowledge, the matter itself is really quite trivial; the sinusoidal solutions of the wave equation are essentially the basic building blocks of general solutions in Cartesian coordinates, you could choose some other coordinate system and you would get another set of generally non-sinusoidal functions.

 

[davenn]

I do not know that I have ever seen what I would call a
"sinusoidal" waveform or anything close to sinusoidal in a natural signal.
The "waveform" of natural signals, in my limited experience, is random,
looking more like grass than like a sine wave.

an emphatic NO

because your experience is limited that "grass" noise is just the hiss of zillions of mixed
signals that are too weak to resolve ... just like a "snowy" screen on an old analog TV.

clear signals that are above the noise floor are easily distinguishable

The only reason I ask about broad-spectrum, natural signals is to clarify
the answer to my first question of whether we can observe the waveform
of individual RF photons, and are they sinusoidal.

AGAIN ! ... as you have been told a number of times, forget about photons
You are still trying to mix classical and quantum "views" of EM ... it isn't going to work for you.

and what is YOUR definition of broad spectrum ?
D

 

[anorlunda]

The OP's question has been more than adequately answered.

Thread closed.