
The dark side of light: negative frequency photons - aquark
http://arstechnica.com/science/2012/08/the-dark-side-of-light-negative-frequency-photons/
======
ChuckMcM
The interesting bit is that solving the equations gives you a solution with a
negative frequency. Generally those negative frequencies are ignored because
for most people a negative light frequency doesn't make sense. But if you
extend the analysis further you get a positive frequency light out of
interactions with that negative frequency light. And the paper talks a bit
about observing those second order effects:

 _"Here, we have shown how the same process generates a second, so-far-
unnoticed peak that corresponds to resonant transfer of energy to the
negative-frequency branch of the dispersion relation. "_

which means the negative frequency light was _something_ but what it means
isn't clear. It could be the tip of a new way at looking at light, or it could
be nothing. Some of the experiments it suggests with respect to gravity waves
are interesting.

~~~
beagle3
At the turn of the 19th century, physicists were quite sure that they had a
complete model of the universe, with just two minor unsolved problems: The
aberration of light / michelson-morley experiment (which required the theory
of relativity to explain), black body radiation (which was eventually
explained by quantum mechanics). Actually solving these unsolved problems
turned physics on its head.

Negative frequency light might be just a weird artifact. Or it might turn
physics on its head. I'd put money on the former, though I hope for the
latter.

edit: fix typo "native frequency" -> "negative frequency"

~~~
cgs1019
Those examples were deviations of reality from prediction/model. This is sort
of the opposite -- the model predicts negative frequency light but we ignore
this because it doesn't match what we thought reality was doing. Now we see
that there is some tangible real-ness to these solutions. It may have
interesting applications, but it wouldn't require us to change the theory
(since the theory already predicts it correctly).

~~~
JonnieCache
There's a lot of this kind of thing about. Black holes and the big bang
arguably started life in this category, no?

------
crusso
I love the way that math reveals ultimate truths. We consider math to be some
abstract thing that we're applying to help explain reality. Instead, it often
appears that the abstraction is somehow the True Reality(tm), and our reality
is really just an imperfect view of Math(tm).

We view math about like we view electromagnetic waves with our eyes. We see
effects of it and reflections and complex interactions of only small parts of
the em spectrum.

It's interesting to wonder if we could develop a way to "see math" in its pure
form.

(Sorry, Friday afternoon speculation... not currently taking any drugs.)

~~~
kjhughes
Math is but a medium for modeling. Any model can have predictive power.

The challenge is in determining which surprising aspects of the model have
faithful correspondence to the domain and which are nonessential artifacts of
the modeling medium.

~~~
jblow
No.

The surprising thing is that the models generate predictions far beyond the
domains they were designed for (and far beyond the original knowledge of the
people making the models), and that the predictions are so mindbogglingly
accurate that there seems to be Something Else going on.

See the Unreasonable Effectiveness of Mathematics link below.

~~~
kjhughes
No?

Surprising thing: Math's not the only modeling medium that can be Unreasonably
Effective.

Unreasonable Effectiveness of Mathematics: Know; saw; upvoted apropos
reference already.

~~~
Sniffnoy
I'm confused by your statement that "Math's not the only modeling medium that
can be Unreasonably Effective", because it's not clear to me what the notion
of a "non-mathematical model" means. (That is to say, it's not clear to me
that you're even correct in the weaker assertion that "Math's not the only
modeling medium.") Can you explain?

~~~
kjhughes
Modeling media besides math: digital electronic circuits, analog electronic
circuits, legos, quantum mechanical phenomena, gears, computer simulation,
wetware, mythology, clocks, BZ reactions, ...

~~~
Sniffnoy
Several of those are, in fact, math. (In particular, computer simulation.) The
others are mostly phsyical models, which I must admit, I had not thought of.
So that yields two; mathematical models (that is to say, formal models) and
physical models (that is to say, real-world models). (The line can perhaps be
a bit blurry in the case of e.g. digital electronic circuits, but, well, I'm
not claiming there's a sharp line.)

That leaves "mythology", which I'm not convinced is a proper modeling medium
at all.

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grueful
Here's the paper (PDF):

[http://physics.aps.org/featured-article-
pdf/10.1103/PhysRevL...](http://physics.aps.org/featured-article-
pdf/10.1103/PhysRevLett.108.253901)

It's about observations & theory where you can get waves in Cherenkov
radiation which propagate against the dominant direction.

------
rcthompson
This reminds me a lot of the observation that the double-slit experiment still
produces interference patterns when you send particles instead of waves, and
them even when you send those particles one-by-one in order to exclude the
possibility of inter-particle interference.

------
gus_massa
I read the original article that is much clearer about the details (
<http://news.ycombinator.com/item?id=4429424> ).

My explanation of the effect is long a bit technical. I hope that it is
intelligible.

(To keep this simple, I will ignore the phases of the waves.)

* * * Complex notation:

First, the equation for the electric field of the light is

    
    
      E = A cos(kz-wt)
    

It's more convenient to write it as a sum of complex exponentials

    
    
      E = A [exp(i(kz-wt)) + exp(i(-kz-(-w)t))] /2
      E = Re( A [exp(i(kz-wt))])
    

By the linearity of the equations, the exp(i(kz-wt)) part and the
exp(i(-kz-(-w)t)) have the same behavior, so you usually write simply

    
    
      "E" = A exp(i(kz-wt))
    

and solve everything as if it where a complex function, but just before
writing the final version or going to the laboratory you must remember that
the other part was there, and that the real physical object is the real part
of the function.

* * * Standard non linearity effects:

If the media is linear but not uniform, there appear other waves that travel
in other direction z' (reflection/refractions). All of them have the same w.

    
    
      "E_tot" = A exp(i(kz-wt)) + A' exp(i(kz'-wt)) 
    

Really all of them have two parts, one with w and the other with -w,

    
    
      E_tot = A/2 [exp(i(kz-wt))+ exp(i(-kz-(-w)t))] + A'/2 [exp(i(k'z-wt))+ exp(i(-kz-(-w)t))]
    

but usually you simply ignore that details, and only put a +cc (complex
conjugate) or Re at the last minute.

If the media is no linear there can appear waves with a different frequency
w'.

    
    
      "E_tot" = A exp(i(kz-wt)) + A' exp(i(k'z-w't)) 
    

(There can appear more than two exponentials.)

Again they have two parts, and the real thing is the real part. It's more
clear to choose w' as a positive number, because (-w') will appear in the
hidden part of the equation.

    
    
      E_tot = Re("E_tot")
    

* * * New non linearity effects in this article:

In this article they use a very sharp pulse in a very non linear material. So,
from the

    
    
      "E" = A exp(i(kz-wt)) 
    

part they get two new exponentials

    
    
      "E_tot" = A exp(i(kz-wt)) + A' exp(i(k'z-w't)) + A'' exp(i(k_n''z-w_n''t))
    

where k' and w' are positive numbers as expected. But k_n'' and w_n'' are
negative numbers!! They get this numbers from the same equation that has k'
and w' as a solution, so all of them appear from the same mathematical term.
They call this negative solution "NRR".

But it is important to remember that the original E has two exponentials, so
you must repeat all the computations with the other part

    
    
      "E*" = A exp(i(-kz-(-w)t))
    

everything is equivalent, so after some recalculations you get

    
    
      "E*_tot" = A exp(i(-kz-(-w)t)) + A' exp(i(-k'z-(-w')t)) + A'' exp(i(-k_n''z-(-w_n'')t))
    

where every k and every w has an additional "-". They call this part "NRR* ".
But now -k_n'' and -w_n'' are positive numbers. We can change the names, and
call

    
    
      k'' = - k_n''
      w'' = - w_n''
    

and now k'' and w'' are positive numbers. So the first part of the solution is
now

    
    
      "E_tot" = A exp(i(kz-wt)) + A' exp(i(k'z-w't)) + A'' exp(i(-k''z-(-w'')t))
    

and the second part is

    
    
      "E*_tot" = A exp(i(-kz-(-w)t)) + A' exp(i(-k'z-(-w')t)) + A'' exp(i(k''z-w''t))
    

And the real physical object is

    
    
      E_tot = ("E_tot"+"E*_tot")/2
    

So we can regroup the term. We exchange the terms with k'' and w'' that have
the wrong signs from on part to the other, because the sum doesn't change.

    
    
      "E_totx" = A exp(i(kz-wt)) + A' exp(i(k'z-w't)) + A'' exp(i(k''z-w''t))
    

and the second part is

    
    
      "E*_totx" = A exp(i(-kz-(-w)t)) + A' exp(i(-k'z-(-w')t)) + A'' exp(i(-k''z-(-w'')t))
    

and as before

    
    
      E_tot = ("E_totx"+"E*_totx")/2
    

Now the interpretation of "E_totx" is straightforward. From the original field
"E" you get three waves, with frequencies w, w' and w'', all of them positive.
And in "E* _totx" is the complex conjugate part, so the final result is real.

And they can measure the three waves.

* * * Notes:

Usually, the A'' coefficient is so small that all this strange part can be
ignored, but they were able to measure it in the laboratory.

One important detail is that k/w, k'/w' and k_n''/w_n''= k''/w'' are all
positive, so they represent waves that travel in the same direction.

~~~
lutusp
At times like this I think it's a shame that HN doesn't support TeX
formatting. It's much easier to follow a mathematical argument with proper
notation.

~~~
im3w1l
mathbin.net

~~~
lutusp
Yes, or any image archive, with appropriate homework in advance of posting. Or
an online LaTeX editor like mine:

<http://arachnoid.com/latex>

But better, there are some very low-impact JavaScript utilities like MathJax:

<http://www.mathjax.org/>

Which allow a pretty seamless interleaving of LaTeX and normal content within
a page. Within a submission one need only enclose the LaTeX content in unique
delimiters, like the often-used $$double-dollar-signs$$.

All this because W3C can't seem to agree on a standard way to render
mathematics in the browser itself -- or more to the point, get the browser
builders to agree to anything they've proposed.

------
phaedrus
This reminds me of P and N silicon; the negative frequency light is like hole
current. (N silicon has "extra" electrons. P silicon has "missing" electrons
that leave "holes", and you can have current where it's the holes that are
moving.)

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WiseWeasel
I still don't get what a negative frequency is. The frequency is the number of
times something happens in a given amount of time. Would a negative frequency
be the number of events that were expected to happen but didn't? If so, how
could this be differentiated from an error in our expectations.

~~~
grueful
Physics often uses the sign of a frequency to indicate the direction of travel
with regard to a reference frame.

E.g. 2 Hz is a wave oscillating two times per second and travelling to the
right, -2 Hz is the same travelling to the left.

In some cases direction isn't really meaningful (standing waves, or the height
or pressure of a medium as seen by a stationary observer). In others, the
direction of propagation can be quite significant.

~~~
stcredzero
Is a -2 Hz wave travelling to the right the same as a 2 Hz save travelling to
the right, but going backwards in time?

Could there be something to John G. Cramer's transactional interpretation of
Quantum Mechanics? Instead of probability waves collapsing instantaneously,
could everything be mediated by photons going backwards in time?

~~~
scoith
The problem with such interpretations is that they violate causality. Check
out Wheeler-Feynman absorber theory for history. Concepts such as collapse of
a wave function aren't necessary when you stop treating the observer in a
special way and start considering observer-particle as a big quantum system.

~~~
TheAmazingIdiot
Causality would not seem to be broken if the effects were shunted to an
adjacent universe. This would directly assume that MWT is indeed true.

------
sponk
How exactly would light at "negative green" frequency be perceived by an
eye/camera, when mixed with an equal amount of regular green? Would it cancel
out, would the negative light have no effect, or would the powers add
constructively?

~~~
rcthompson
The article doesn't indicate what the physical manifestation of negative-
frequency wave would be. It only reports the observation of a positive-
frequency wave that seems to require the transient existence of a negative-
frequency intermediate.

This is similar to how particles like the Higgs boson are not directly
detected in particle accelerators, but are inferred from the directly-
observable particles that they produce. The difference is that physicists are
(I think) pretty sure that the Higgs actually physically exists, if only for a
short time, while the same is not clear for the negative-frequency
intermediate wave described here.

------
nsxwolf
Ok, so, this doesn't mean I can have a light bulb that makes the room dark?

~~~
aortega
You don't need anything fancy like negative frequency light bulb for that,
only a regular light bulb that emits light 180 degree phase shifted to the
already existing light in the room. It's actually impossible to do with a
light bulb because the light that emits is not coherent but you can do it with
a laser if the incoming light is also from a laser, in fact negative and
positive laser interference is the basis for several technologies such as
holograms.

