Written and Illustrated by Ed Witten. (Slides 1 to 10 of 48) 1.. One bit of Physics that most of you have probably seen in high school is the inverse square law of Gravity and Electricity. The force between two charges separated by a distance is (e1 x e2) / r^2
2.. And likewise the forces between two masses is G ((m1 x m2) / r^2). (Slide 2 below.)
That was fine for the first 200 years or so, but just about a century ago the electron was discovered and ever since
3.. Physicists have had to grapple with the singularity of the inverse square law at R = 0 (e1 x e2) / R^2 (Slide 3 above)
4.. This singularity seemed to imply, for instance, that an atom could survive for only about 10^-9 seconds. (Slide 4 below)
This problem, in the case of electricity, was solved in the first half of this century with the development of Quantum Mechanics
5.. The solution is based on the 'Uncertainity Principle' .. everything is a bit fuzzy if expressed in classical terms. (Slide 5 above.) The quantum uncertainity 'smears out' the singularity at R = 0
6.. It turns out though, that quantum uncertainity doesn't solve the problem for Gravity. The analogy between Gravity and Electricity is quite as close as the Inverse Square Laws G((m1 x m2) / R^2) or (e1 xe2) / R^2 suggest ....
7.. In fact, since 1915, Gravity is really described by Einstein's Theory of General Relativity, whose non-linear mathematics is such that quantum uncertainity alone cannot solve the problems of the inverse square law.
8.. This problem is at the center of physics, since in fact physics in our time is based on 2 great theories. Quantum Mechanics of Atoms and Sub-Atomic particles (small) and General Relativity which equals Einstein's Theory of Gravity (large) which are in conflict ---- a conflict which is the modern version of earlier contradictions that led to the upheavals in twentieth century physics .......
9.. This leads us to String Theory. Physicists had the good luck to discover, essentially in the 1970s, that this problem can be overcome in string theory. In string theory roughly speaking one reinterprets an elementary particle not as a point but as a vibrating loop or string. (Slide 9 below)
10.. One of the reasons that this is very rough is that one should include quantum uncertainity on each side. (Slide 10 above) Now one of these strings, just like a violin or piano string, has many different modes of oscillation or harmonics. In the present context one interprets these as different elementary particles.
continues in next post .....