breaking the speed of light article on howstuffworks.com

As others have said, it's the 'del' operator which -- in Maxwell's equations -- is used to mean divergence (when it comes with a little dot next to it) or curl (when it comes with an 'x' next to it). It also commonly shows up right next to a symbol, in which case it means 'gradient.'

It's probably a little advanced for your current mathematical background, but there's a good book called "Div, Grad, Curl and All That" that provides an explanation that you could probably understand shortly if your high school offers a pre-calculus class. This book is often recommended to college students taking their first electromagnetics classes.

Anyway, the 'divergence' of a function tells you how much 'flux' is leaving an infinitessimally sized point in space. Think of a box that has a bucket of water and a water pump in it... and say there are hoses connecting the pump to a a bunch of water spigots around the outside of the box. Depending on which way the pump is run (to push water out or to suck it in) and how the water spigots are set (to allow a large amount of water flow of a small amount), the water 'flux' of the box could be defined simply as the net amount of water flowing into or out of the box, e.g., 3.5 gallons per minute per box.

Maxwell's equation 'del dot D = rho' means that -- for a really, really tiny box -- if you put a certain amount of charge, 'rho' into the box (an electron, for instance, has a charge of 1.6*10^-19 Coulombs), a certain amount of 'electrical flux' comes out of that box. Just like water spraying out of a hose and moving a baseball that it hits, this flux can 'hit' an electron or another charged particle and cause it to move. Larger charges (large rho) means more flux and an electron will be accelerated (moved) more by such a source.

The fancy mathematics is needed to keep track of exactly which direction all these flux sources act in, how to properly 'add up' many flux sources (the 'del dot D = rho' equation can, with the help of the so-called Divergence Law -- be turned into Gauss's law, which you can find in a high school physics textbook), etc.

Keep in mind that Maxwell's equations assume that quantities such as flux as continuous in nature (any amount of it can occur), whereas -- as you've already learned -- in actuality such quantities can only come in discrete (quantized) versions. As such, Maxwell's equations are only an approximation of what 'really' happens, but since the quantizatoin level is so very very tiny, there's almost nothing you'll see discussed on sci.electronics.design where this fact matters. This usage is referred to as 'classical' electromagnetics, whereas folks who need the quantum physics models deal in 'quantum electrodynamics' (QED). Very few people take QED classes (it's safe to say that 99+% of graduate level electrical engineering students don't!).

---Joel Kolstad

The sun will expand very slowly. There will be plenty of time to move the Earth's orbit out to keep the temperature comfy. It's actually not difficult to do.

John

"That quantum physics test is not very good. I took a course on quantum physics and the test has some issues."

I figured. I mean, what kind of a question is "Which of the following does the neutino apply to?" Whoever made it doesn't really sound like he or she knows what they're talking about. I couldn't say exactly what's wrong with it, but I can sort of tell it's not accurate.

"The sun will expand very slowly. There will be plenty of time to move the Earth's orbit out to keep the temperature comfy. It's actually not difficult to do. "

MOVE the earth's orbit?!?

• neutrino

Yes.

Oh, I don't know... at some point you need to rely on those equations if you want to get any Real Work done. I.e., you can't build a jet or an electric motor or a computer or a doppler radar for a metereologist :-) unless you 'rely' on a set of equatoins that you're convinced adequately model whatever it is you're trying to do.

True, but the power of science and math is that it gives s a precise way to describe what we _think_ is going on, and if those descriptions allow us to _extrapolate_ to make _new predictions_, something has been gained.

It's a common error to thnk that math and science are somehow attempting to explain what 'reality' is. They don't; that's left to the philosophers and the faiths. All that science an math attempt to do is to create _models_ of how the universe _seems_ to be behaving. Whether or not those models are correct... well, at some level, yeah, we'll never know, but at another level, most people are happy with the results!

---Joel Kolstad

The first i ever read about QED was at the very end of "The Cartoon Guide to Physics." That was about 4 months ago, and it took me three months to understand it (I was missing one key little piece of information and so I was thinking on the way to school one day and suddenly got it.) Their chapter on Faraday induction isn't very good, so without the missing info I couldn't really understand anything further into the book.

"I just had to say it" is NOT staying on-topic, and is attempting to interject/proselytize your faith upon me. I do not care what your faith prescribes, and I don't want to hear it.

It is certainly your loss if you don't ingest wine... what did Jesus give to the masses? (Not that I care about that fiction either :)

...Jim Thompson

I'm in 8th grade, not high school yet, so I can't take pre cal yet, nor can I take any science classes other than what I'm in.

Sno-o-o-o-ort ;-)

...Jim Thompson

Its hard to imagine where what we can rely on begins and where it ends. For instance, the emission of a photon violates the law of conservation of energy. The law is of good purpose to, say, my science class, but you can't really depend on it in qed.

umm... that's simple?

Clearly. I certainly can't ply her with liquor ;-)

...Jim Thompson

Try:

Brings back the horrors of Field Theory class. We had a Japanese instructor who was as brilliant as he was unintelligible. Luckily for us, he was junior in seniority so also had to babysit us in the afternoon EE labs. So we came to an understanding: he'd give us really easy Fields tests and everybody would slip out of afternoon labs early. We just faked the lab results, which made much prettier graphs than we could get using the ancient equipment in the lab.

I developed a certain sloppy slide rule technique that produced excellent data point scatter.

John

Dang, that reminds me that it's time to stir the beans. They start to stick towards the end.

John

Topic? This newsgroup has a topic?

John

You should appreciate that this is an engineering newsgroup; the "sci" at the beginning is sort of honorary. Engineers tend to trust the teachings of physics without a whole lot of introspection, because we have more important things to do, like design stuff. And we do deal with the speed of light all the time, as a very practical reality, and it's been dependable so far.

But if you assume that everything is qualitative and everything we know may be wrong, you can't get a lot done. The working position is "well, so far, this theory looks really good, so we'll work with it until somebody proves something better." It's sort of an attitude about life, I guess.

John