So I bought this neat book by Lisa Randall which explains lots of things that I was confused about and ...

>And now you're not confused?
I'll let you know when I'm finished reading it.

Anyway, I thought I'd share some of the things I larned ... as I larn them.

First off, there's a neat visualization of those tiny, curled up, compact dimensions. We have this curve, as in Figure 1 (like a garden hose, viewed from a distance). What's its dimension? >A garden hose? I'd say it had three dimensions. Well, it's a curve, not a garden hose! To identify the location of a point on the curve we choose some origin (like the red dot) and measure distance from there. How many numbers do I have to give you, to identify a point along the garden hose curve? >I'd say one. Right! So it's a 1-dimensional space. Now we look more closely to see if we can find any tiny, curled up, compact dimensions. See Figure 2? The curve is really a tube which would appear as a curve ... unless you were able to discern that curled up component. >I told you it was a garden hose! Pay attention! At each point along that curve there's actually a 1-dimensional compact space. >1-dimensional? Yes. You can move along the length of the curve of Figure 1, forever (assuming the curve goes on forever), and, if you had the appropriate vehicle, you could also move around the tube. That's 1 extra, compact dimension.

Figure 1 Figure 2

>And arrive back where you started, right?
Right, because it's one of those "curled up" spaces. All together, the surface of the tube is 2-dimensional.

>What's inside the tube? A black hole?
Hey! Have you been reading Randall's book? I'm just on page 142 of about 500 pages.

>And in 142 pages she's just talked about garden hoses?
No!
She's talked about atomic structure, gravity, general relativity, space-time distortions, strings, Heisenberg uncertainty, wave-particle stuff, quantum theory ...

>I can hardly wait until you get to page 500 !
Note that general relativity ain't the same as special relativity

a bit of Gravity

You're looking out of your apartment window at kids playing with marbles on the ground below. You notice that there's a large red marble that seems to be attracting the other, smaller marbles. Sometimes the smaller marbles move like the blue one, and sometimes a marble revolves about the large marble, like the green one and sometimes a marble just falls right into the large red marble ... like the purple one. >That's a gravitational force, right? Well, let's see. We go over our Physics 101 notes, take out our calculator and pen and pencil and determine the law that governs the attraction that the marbles have for each other and ... >That's gravity, right? Actually, the red marble is sitting in a hole. The point is, the space that the marbles move in is warped, bent, distorted by the presence of that big marble. The big marble makes a depression in the ground by its very presence and ... >And that's gravity, right? Well, that's what Einstein says in his General Theory of Relativity. In fact, the presence of a body such as the Sun bends the space about it and comets moving nearby follow that curvature and appear to us to be attracted to the Sun by some force. >And that's gravity, right? Will you stop that!

Figure 3 Figure 4

In fact, even light passing near the sun gets bent by the curvature in space generated by the sun's presence.
Nevertheless, gravity is surprisingly weak. The entire Earth pulls on a paper clip, yet a tiny magnet can lift it.
Why is that?

a few Quanta

We shine a light, say ultra-violet or x-rays, on a metal plate and increase the frequency of the radiation.
At some frequency, electrons start to leap off the surface with a particular energy.
We increase the strength of the x-rays and more electrons jump off, but each has the same energy as before.
More energy in the x-rays but not more energy in the electrons.

>But you do get more electrons.
Yes, but why don't the electrons have greater energy? That's a puzzle, eh?
In fact, the x-rays (and all other electromagnetic radiation) travel in parcels called ...

>Photons!
Yes, photons. And each photon has a fixed amount of energy associated with it (depending upon the frequency of the radiation).
A photon hits the metal and an electron absorbs the photon's energy and flies off the surface ... with a fixed amount of energy.

>Stronger radiation, more photons, more electrons, right?
Yes, but each with the same energy. It's that "particle theory" of light (or other electromagnetic radiation) that's part and parcel of Quantum Physics.
Instead of being a continuous wave of radiation, it's made up of quanta ... the "particles" of light, the photons.
It's sort of like watching a wave roll onto the shore. It looks smooth and continous, but it's made up of particles and ...
>Photons?
No! Water molecules!

Anyway, these photons, with frequency ν, have energy proportional to their frequency, namely E = hν where the constant of proportionality is h.
>H-huh?
That's Planck's constant: h = 6.626 × 10^-34   measured in m² kg / s.

That explains why no electrons jumped off the metal plate until the frequency was large enough.
The photon has to supply at least the energy required to extract the electron from the atoms in the plate and photon energy is proportional to the photon frequency so as we increase the frequency we come to a point where the energy hν is sufficiently large so that ...

>E = hν? But I thought E = mc².
Why not? That'd make E = hν = mc² so we can associate a mass with a particular photon, eh?
In fact, if the frequency of the radiation is ν and its wavelength is λ then ν = c / λ so we can rewrite that magic equation as: E = hν = h c / λ = mc².

>Small wavelength means big energy, right?
Yes, so if we want to "see" things that are the size of λ we'd need lots of energy ... and that means high energy accelerators, like those at CERN.

>In Part I didn't you mention something about a curled up, "extra" dimension whose size was ... uh, about 10^-35 metres?
Yes. Did you see how small h is? Since we can relate lengths like λ with mass and energy and a couple of constants, h and c, then ...

>Then can we get back to membranes?
Sure. Why not.

... and Strings

>What about membranes?
Patience. I'm only up to page 284 of Lisa's book.
>Lisa? You call Professor Randall Lisa?
Pay attention!
>I take it you attended her lecture since it was just around the corner.
Uh ... I missed it.

Okay, we've seen, in Part I, that particles like electrons and such, are really tiny, oscillating strings that support various kinds of waves. Remember Figure 5? However, even those things that we knew as waves (when we were young and naive) are particles ... like light quanta or photons. Indeed, as we head into matter, beyond molecules, into atoms, past a cloud of electrons to the atomic nucleus, we find protons and neutrons which themselves are made up of yet smaller particles called quarks and ...

Figure 5

>I know that one! A flea hath smaller fleas that on him prey; and these have smaller fleas to bite 'em, and so proceed ad infinitum.
Yes, well those particles are pretty small and there are various kinds of quarks and they differ in mass and charge and ...

>And to see them you need a big accelerator, right?
Yes indeedy. The protons and neutrons are called hadrons and they're composed of quarks and there's this HUGE accelerator being built called (would-you-believe) the Large Hadron Collider which (hopefully) will be able to "see" the much smaller particles ...

>Which require much more energy, right?
Yes. I see you're paying attention.

We've run across CERN before when we talked about WWW and Tim Berners-Lee, the primary author of HTML, assisted by his colleagues at CERN (Conseil Européen pour la Recherche Nucléaire), a international scientific organization based in Geneva, Switzerland. In addition to HTML to write web documents, Berners-Lee also invented HTTP (HyperText Transfer Protocol) to transfer web documents and the addressing system, URLs (Universal Resource Locators), in 1990 and ... >http and www as in http://www.   etc.etc. Exactly, and ...

CERN Control Centre

>Instead of hadrons, why not just call them neutrons and protons?
Why not say cars, instead of Fords and Chevys?
Why say Ford when you can say Thunderbird and Taurus and ...
>And Testa Rossa?
That's a horse of a diff'runt hue!
>And what does all this have to do with membranes?
Patience! I'm just on page 284!

and now - taDUM!   Branes

Okay, it's time to talk about membranes ... or simply "branes". In Part I we imagined a collection of 10-dimensional brane-worlds separated by a distance in the direction of an 11th dimension. >And what's in between the branes? It's called ... uh, the Bulk. Well, actually, maybe it's better to think of the entire collection of brane-worlds as constituting the Bulk. That is, the collection of brane-worlds lie in a higher dimensional space called ... >The Hulk? The Bulk! The interesting thing about branes is that those "open" strings must end somewhere, and they end ... >On branes? Hmmm ... you've been reading the book. Some of these open strings might start on one brane and end on another, as in Figure 6. However, "closed" strings don't have to be connected to a brane and may travel in the Bulk. Gravitons, for example, are open strings and do, indeed, travel through the Bulk.

I could wile away the hours         Conferrin' with the flowers         Consultin' with the rain         And my head I'd be scratchin'         While my thoughts were busy hatchin'         If I only had a brane.         With apologies to Scarecrow Figure 6

However, most strings / particles reside on (or in?) a single brane.
In fact, photons of light are constrained to lie in a brane (like the brane we both live in).
That means that we'd never see those other branes 'cause light can't get from there to here.

However (and this is really interesting), gravity can act between branes, from one to t'other, influencing particles on neighbouring branes, affecting ...
>And that explains why gravity is so weak, eh? It's spread over lots of branes while magnetism is concentrated in one brane.
Perhaps, but remember this is just a theory. Besides, even in our our own 10-dimensional brane most of the dimensions are invisible to us.
They're small, curled up, so the dilution of gravity would also be small.
After all, there's little space in that curled up space to accommodate gravitons ... compared to the 4-dimensional space-time we recognize and in which gravity is weak.

>How do you know that those extra dimensions are that small? Maybe they aren't small at all. Maybe there's room for lots of gravitational dilution. Maybe ...
Actually, I understand there's a theory that suggests just that. A much larger "extra" dimension that might absorb lots of gravitational energy, leaving little for our 4-dimensional space-time, hence explaining why gravity is so weak in our 4-D world.

Besides, in addition to gravitons, there may be other objects that travel in the Bulk ... like, maybe guiganos.

>Guiganos? Sounds like an Italian cheese. I've had gorgonzola with a glass of chianti, but ...
Pay attention!
If gravity is "spread" by particles called gravitons, then we can imagine them flying off our brane and passing through neighbouring branes.

>Or worser, they could come from some other brane-world and pass though ours! If gravity is really a warping of space, then ...
Then gravitons from a neighbouring brane would warp our space? Who knows? Maybe ...
>Black holes!
Huh?

>Our brane is very near another brane with lots of gravitons. The gravitons warp our brane creating a hole ... a black hole!
Really, now. I don't think that ...

>Pay attention! When something vanishes into a black hole, in our brane, it ends up in that neighbouring brane!
You've been watching too much Star Trek.

for Part III