And how can one bring up Democritus without linking to this? Sorry, Sagan doesn't actually say billions and billions in this clip:
Until Einstein came up with a proper solution to Brownian motion (and it was validated experimentally), there was no firm foothold for atomic theory, or so the authors argue.
When you think about all this research and speculation, keep in mind that no one could see the tiny particles these scientists were speculating about. At that time observations were made with light waves. Since a wavelength of green light is about 5000 times bigger than an atom, light waves were much too big to reveal atoms.The article goes into the history of atomic theory along with the empirical evidence. I thought this was especially cool:
To get an idea of the size disparity, consider ocean waves with a wavelength of ten meters rolling past and hitting the side of a cylindrical lighthouse with a diameter of twenty meters. The waves will bounce off the lighthouse, making circular waves. Looking at these reflected waves, you could find the shape of the lighthouse. Now suppose those same ocean waves crashed into a stick just one centimeter in diameter. Any ripples bouncing off the stick are lost in the ocean wave, useless for revealing anything about the stick. Seeing an atom with light waves was hopeless.
So those scientists in 1900 were making up stories (logically consistent, reasonable stories, but stories nevertheless) about stuff no one had ever seen.
If you have a laser pointer, equipment not available back in Brown's day, you can also see Brownian motion by shining the laser light into a dilute solution of milk and looking at the scattered laser light on a white card after the light passes through the milk. The bright central dot of laser light will be surrounded by twinkling dots of light. These twinkling dots are produced by the interference pattern of all the light scattered by the fat globules in the milk. The pattern changes because the fat globules are in constant motion as they are bombarded with collisions with invisible particles. Those invisible particles are (according to the story of atomic theory) molecules of water in the milk.So by shining a laser pointer through diluted milk, one can observe the underlying random motion of molecules, is that cool or what? And let's not forget that a laser itself is based on the quantization of photons, so this simple experiment is seeing evidence of some of the most profound theories of the Universe that were barely accepted or even known of 100 years ago (Max Planck proposed quantization of energy in 1900 as a fix to the black-body radiation problem).
This leads to the idea that strings, should they be the underlying phoenoma that explain everthing, would exist at a very small scale:
To find the size of a string, scientists need to find the scale at which both quantum mechanics and general relativity apply. To do this, they must consider the size of a quantum black hole. Normal black holes have the mass of a large star or of many thousands of stars, and form by gravitational collapse. They are larger across than a small city. The gravity of a black hole is so great that even light cannot escape across the surface of the black hole, a surface known as the event horizon.The Planck length is pretty important in physics, it pops up a lot (including theological debates). To say that 10-35 meters is small is something of an understatement.
So here's the math. The radius of a black hole is proportional to its mass (R = 2GM/c2 where R is the radius, G is the universal gravitational constant, M is the mass, and c is the speed of light.) The wavelength is inversely proportional to its mass (L = h/Mc where L is the wavelength, M is the mass, h is Planck's constant, and c is the speed of light). These equations can be solved to find the mass of a black hole with a radius equal to its wavelength. (We'll do the calculation to within an order of magnitude so we can ignore factors of 2 or pi (π).) The quantum black hole is found to have a mass of 10-8 Kg or 10 micrograms. If you were to take a strand of hair that's 0.1 mm in diameter and snip off a piece that was as long as one diameter, it would have a mass of about 10 micrograms. If this piece of hair were compressed to 10-35 m in diameter, it would become a black hole with a wavelength of 10-35 m.
These calculations show that the length scale at which both gravity and quantum mechanics are important is 10-35 m. This is an estimate for the size of the loops of string in string theory, the string loops that encircle and bind quantum mechanics and general relativity. This length scale is called the Planck length. The Planck length is 1.6 * 10-35 m.
Another understatement is this sentence:
Several major difficulties complicate efforts to test string theory. The most significant is the extremely small size of the Planck length, which is expected to be close to the string length (the characteristic size of a string, where strings become easily distinguishable from particles).Wikipedia goes on to list some of the ways string theory could be tested. There's not a lot of promising stuff there, but it does show that string theory is not lacking a null hypothesis. Is string theory simply a victim of the lack of empirical evidence that atomic theory lacked in 1900, or perhaps back when Democritus first proposed it (since we are possibly 2000 years away from measuring things at the Planck length). Yes, perhaps. I'll just note that two of my favorite physicists, Richard Feynman and Roger Penrose, are (were) very skeptical of string theory, on the grounds of its lack of testability. Admittedly, Feynman died in 1988 so perhaps he'd be less skeptical of string theory today. Somehow I doubt it, though.