|Identical paths with acceleration or gravity|
In physics today, first Craig gave a PowerPoint about Einstein's idea of General Relativity. (Originally we were going to do Special Relativity today and General Relativity tomorrow, but it was switched because General Relativity tied in better with our guest lecturer's topic. Craig talked about the basic properties of space that led Einstein to think about Special and General Relativity, and then related advances by other scientists. The main principle of Einstein's that Craig talked about was was his equivalence principle; that it is impossible to tell the difference between gravity and acceleration in any relatively small area of space-time.
|A model of the space-time curvature caused by gravity|
Then, Bill talked for a short time about exponential phenomena, and different graphs that match different situations. He worked his way up to situations that depend on their own solution (like population, in which the future value depends on the current value) which can be written as exponential functions like y=e^x. The number e is important because on the graph y=e^x, the slope at any point is the y-value. He ended with another equation using e, which I agree with him is "the coolest math equation," e^iπ=-1, which combines irrational, natural constants and the imaginary number i to get simply -1.
|An example of gravitational lensing (Einstein rings)|
After that, we had a guest lecturer, Bhuvnesh Jain, who gave a presentation on Gravitational Lensing. He didn't only talk about gravitational lensing (a phenomenon predicted by Einstein's equations), but also about the universe as a whole--the forces that govern it, what it's made of, and where it's going. He talked about the four main forces that govern our universe; electromagnetism, the strong nuclear force, the weak nuclear force (which all act somewhat similarly) and gravity, which seems to be in a class of its own, as it is very weak but acts over very large distances. Astronomers have also noticed discrepancies (like the fact that our sun orbits the center of our galaxy twice as fast as would be suggested by the amount of detectable matter) that show there is "dark matter" in our universe that we can only see the effects of. There is also "dark energy," the term for the unexplained force that is causing the acceleration in the expansion of our universe, and will ultimately lead to all other galaxies disappearing from view as space-time expands faster than the speed of light. In fact, dark matter and dark energy are so prevalent in our universe that atoms only make up 4% of everything in the observable universe.
After lunch, Bill talked about electromagnetism and the interactions between magnetic and electric fields, leading into our lab. In our lab, we used a cathode ray tube to create a beam of electrons we could then manipulate with fields and measure. The goal was to find the ratio of an electron's charge to its mass, through a series of equations.