The dark side of light: negative frequency photons • Hacker News Board

Re: The dark side of light: negative frequency photons

#41

Post by Groxx » Sat, Aug 25, 2012, 5:08 AM UTC

kjhughes wrote: post #39

Sniffnoy wrote: post #35

Earlier quoted context omitted.

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?

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

Many of which are reducible to math. Though I'm not sure what legos have been "unreasonably effective" at predicting.

Re: The dark side of light: negative frequency photons

#42

Post by 6ren » Sat, Aug 25, 2012, 5:45 AM UTC

Variance wrote: post #36

crusso wrote: post #5

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 s…

Since math is just the formalization used to describe quantitative patterns observed, you're already seeing math as purely as it will ever get. Really, it's the other way around--since math is an abstraction of observation, what you observe with your senses day to day is a much more direct and fundamental reality. Math is a language, and reality is what it talks about. Similarly, people who speak English will find th…

The surprising bit is not that it explains the observations that it was modelled on, but that it explains further, unexpected observations that were unknown at that time.

It's not that maths is so great, or even that models are great, but that we were able to model some essence of a phenomenon, beyond what we witnessed.

This happens not because it's a model (you can have as many models/theories as you like), but because we selected that model, usually due to beauty/parsimony/elegance - which amounts to some version of Occam's Razor: to not make a model more complex than needed to explain the observations. (do not multiply elements unnecessarily; given different models that explain the observations, the simplest one is most likely the truest of them). http://en.wikipedia.org/wiki/Occam%27s_razor

The real puzzle (if it's a puzzle) is why Occam's Razor works so well...

Re: The dark side of light: negative frequency photons

#43

Post by jblow » Sat, Aug 25, 2012, 6:34 AM UTC

kjhughes wrote: post #34

jblow wrote: post #33

Earlier quoted context omitted.

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.

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.

Did you read the essay? Actually, both of them? The reason mathematics is considered Unreasonably Effective is because we have never seen anything with similar effectiveness. Ever.

Re: The dark side of light: negative frequency photons

#44

Post by jblow » Sat, Aug 25, 2012, 6:37 AM UTC

kjhughes wrote: post #34

jblow wrote: post #33

Earlier quoted context omitted.

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.

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.

And the point is that it's not about modeling!

What happens is that we invent crazy math that is not supposed to have applicability, then some years go by and it's like, oh my God, quantum mechanics is somehow exactly all about the operation of unit Hermitian matrices... how crazy is that?? etc.

If it were some kind of model that we are able to successively refine, the progress of discovery would look something like a Taylor series, and it would be no surprise that we are eventually able to model phenomena within some tolerance epsilon.

But that is not what is happening! Rather, it's that we discover that some large and sophisticated piece of math, for which we had not thought of any particular applicability, turns out to exactly represent specific advanced physical phenomena. This happens over and over.

Re: The dark side of light: negative frequency photons

#45

Post by JonnieCache » Sat, Aug 25, 2012, 7:43 AM UTC

cgs1019 wrote: post #22

beagle3 wrote: post #11

Earlier quoted context omitted.

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 l…

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 correct…

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

Re: The dark side of light: negative frequency photons

#46

Post by Sniffnoy » Sat, Aug 25, 2012, 7:53 AM UTC

kjhughes wrote: post #39

Sniffnoy wrote: post #35

Earlier quoted context omitted.

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?

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

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.

Re: The dark side of light: negative frequency photons

#47

Post by lutusp » Sat, Aug 25, 2012, 8:00 AM UTC

jblow wrote: post #33

kjhughes wrote: post #31

Earlier quoted context omitted.

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.

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.

> 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.

Yes -- and I can't resist citing antimatter as a perfect example. Dirac's Equation had two symmetrical results (sort of like a quadratic), and Dirac wasn't sure about the physical meaning of one of them. After antimatter was detected, Dirac was asked why he didn't simply predict antimatter himself based on a literal interpretation of his equation's implications. He replied, "Pure cowardice."

Re: The dark side of light: negative frequency photons

#48

Post by lutusp » Sat, Aug 25, 2012, 8:04 AM UTC

gus_massa wrote: post #40

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 exp…

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.

Re: The dark side of light: negative frequency photons

#49

Post by lutusp » Sat, Aug 25, 2012, 8:07 AM UTC

kjhughes wrote: post #39

Sniffnoy wrote: post #35

Earlier quoted context omitted.

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?

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

But those are examples of modeling math, with a superficial layer of physical material. Another way to say it is the degree that these are useful models, is the same degree to which they reflect mathematics. With the possible exception of mythology.

Re: The dark side of light: negative frequency photons

#50

Post by Confusion » Sat, Aug 25, 2012, 11:42 AM UTC

46Bit wrote: post #26

scoith wrote: post #20

Earlier quoted context omitted.

Save me the trouble an learn some basic physics. Read Jackson's Classical Electrodynamics, Chapter 7. If it's too complicated for you, read about waves. See how they propagate in time and space, and pay special attention to what happens to the equation when you change the sign of t. If it's too difficult to imagine, try plotting using a program. And anti-matter is not matter travelling backwards in time. See my post…

From just the book title, I'd like to point out that we have something known as Quantum Mechanics nowadays.

Which is exactly why the book has that title. The book by Jackson is required reading for any physics graduate in a field where EM radiation plays a role.