What Walks Down Stairs Alone or In Pairs?

I'm proofing a physics book and the current chapter is talking about quantum theory and in particular, Planck's quantum hypothesis. Please keep in mind that I failed algebra and I generally suck at any math beyond balancing my bank account. I don't often grasp more than the simplest of equations required in physics, but I get the logic of the theories, so I have these ideas and pictures in my head, but no clue how to illustrate them, or prove them mathematically, nor do I usually know if they've already been illustrated and proven. I'm really just babbling to myself. If an engineer or scientist read this, he'd probably be bored to tears. And I'm not saying any of it is true or false. I'm just thinking onto the screen.

First it talks about Planck's constant (h) and how Planck came up with his formula while trying to make the blackbody radiation curve work out in an experiment. Yay for him. Then it says (in short):

To provide a theoretical basis for his formula, Planck assumed that the energy of the oscillations of atoms within molecules cannot have just any value, instead the energy value is a multiple of a minimum value related to the frequency of oscillation by

E = hf

Sounds like greek until you read it really slow three times, but it put a picture in my head of an atom with its little electrons whipping around the nucleus. I got "oscillations" confused with vibrations and how you measure a wave from peak to peak - the wavelength - but that's a good thing because it made me relate a 2D vibration to a 3D oscillation. The atom in my head was 3D, and frequency of a wave is generally shown in 2D, so I was wondering how you would show a wave measurement in 3D and the idea of a stretched out Slinky came to mind. If you look at a Slinky from the side, it could appear flat like the frequency of a wave measurement. But if you then turned the Slinky toward you sideways (like you can in a CAD rendering or 3D animation), then you would see it's actually a big spiral and instead of there being peaks and troughs in a flat wave measurement, it would still have highs and lows but it's a continuous diameter - a spiral instead of a wavy line. Like seeing an added dimension of a 2D wave.

If you're measuring a wave peak to peak (wavelength), then there is always a trough in between indicating a fraction of the measurement, or 1/2. With a spiral, there are highs and lows, but no flat peaks or troughs to indicate a fraction of a measurement because no matter which way you rotate the spiral, there is no definitive top and bottom to each loop, therefore no way to say "this is the halfway point between this peak and the next" (unless you're measuring with an added dimension... keep your panties on, I'll get there).

Since there are no fractions, would that not indicate whole number multiples measuring oscillations? Looking at it that way though, it'd be just a flat circle (like if the Slinky were coiled up tight and you were viewing it from the end). But stretch it out and you're adding a depth dimension - like say, time? - and now you have a distance from peak to peak to measure one complete oscillation, which would still be a whole number since there is no way to define where a peak or a trough is on the spiral.

When I described this to Mark he said he thinks what I'm describing is a good way to illustrate the measurements of string theory. Unfortunately I can't agree or disagree since I have not yet really grasped string theory, but maybe someday I'll get there and go "oh yeah, that is exactly what I was picturing." :)

But back to the book.

The author says Planck's assumption suggests that the energy of any molecular vibration could be only some whole number multiple of the minimum energy hf:

E = nhf, (n=1, 2, 3...; h = Planck's constant; f = frequency)
(Looks like it says "enuhf" LOL)

where n is a quantum number - quantum meaning discreet instead of continuous; discreet meaning in increments. He uses the analogy of quantum being like a box sitting on stairs, as opposed to continuous being a box sitting on a ramp. The ramp is a continuous incline upwards and you could push the box up it smoothly. You could also push the box up the stairs, but only in measured whole steps (increments - not smooth). Just like jumping from the top of one oscillation of a spiral to the next. Except now I'm thinking the spiral is also continuous if you slide around the curve to get from one oscillation to the next instead of jumping from top to top, so does that mean it can be measured both ways? Maybe sliding from one oscillation around to the next is a better illustration of a stairstep. I dunno. Now I'm confusing myself.

Hmm... that definitely makes me think of time though... like we (as humans) live by sliding the long way around the spiral to go from one oscillation to the next, but if you were going to time travel, you would want to find a way to jump between the tops of the oscillations instead of going around the curve. And folding time might be something like compressing the Slinky until all the tops squish together creating a continuous new pathway (a fast track if you will) altogether - maybe a dimension where gravity is reversed because you're now standing on top of (or outside) the curve instead of lying inside the dip. Maybe standing on the top is like the consciousness of One. God is a compressed Slinky. Great. That must mean the Theory of Everything could be illustrated something like this:

Now imagine the stairs are in an M.C. Escher painting and you're really trippin.

I know, I know... this is why I never touched drugs. Who needs to with an imagination like that?

By the way, here's your daily dose of useless trivia: In 1943, Richard James was a naval engineer (figures - who else understands all this math?) trying to develop a meter designed to monitor horsepower on naval battleships. Richard was working with tension springs when one of the springs fell to the ground. He saw how the spring kept moving after it hit the ground and an idea for a toy was born.

"Slinky" is a Swedish word meaning traespiral - sleek or sinuous. (So if you're reading this Mraz, there's one more Swedish word you didn't know you already knew.)

Slinky debuted at Gimbel's Department Store in Philadelphia, Pennsylvania (hey, I come from there!) during the 1945 Christmas season and then at the 1946 American Toy Fair. Richard, nervous at the first demonstration of his toy, convinced a friend to attend and buy the first Slinky. However, this turned out to be unnecessary as 400 were sold during the 90 minute Gimbel demonstration.

Richard James and Betty James founded James Spring & Wire Company (renamed James Industries) with $500 dollars and began production. Today, all Slinkys are made in Hollidaysburg, Pennsylvania using the original equipment designed and engineered by Richard James. Each one is made from 80 feet of wire and over a quarter billion Slinkys have been sold worldwide.

Thank you to Mary Bellis' About.com page on Slinky for that info. :)

So I guess those last bits are a little out of order and jump around themselves, but what can I say. That's how my brain works. Now I have to go read the rest of the chapter and hope he discusses string theory somewhere so I can see if I was right. Next time I'm tackling particle spin. Come to class prepared.

PS: After reading about springs, which led to Hooke's Law, I've decided there was no "Big Bang" at the beginning of the universe. It was just someone setting a Slinky off down the stairs and we're still going. This is what happens when you've been awake for 48 hours and counting.