Wednesday, July 17, 2013

Spacetime is a Pringle

At least, it (spacetime) is if you throw out Euclid's fifth axiom. Looking at non-Euclidean geometry helped Einstein develop general relativity. We began class, not with general relativity, but a quick overview of what was expected for our presentations (both the Hersheypark presentation and the exponential project presentation). We only spent a bit of time on that, and soon moved on to a lecture on general relativity. General relativity has to do with how mass interacts with spacetime which creates gravity. Spacetime can be thought of as a giant rubber sheet. A mass makes an indentation in that sheet, causing other masses to roll towards it. It also explains gravitational lensing. To relate back to the third sentence, Einstein threw out the third and fifth axioms in looking at general relativity. If you do so, the universe is a sphere. It is like a balloon being blown up, and we are on the outside. This is the expansion of the universe. It was a fascinating talk, and, in my opinion, less confusing than special relativity (though I would rather derive the math for special relativity than general relativity). We then had a lecture on the Standard Model. I had heard the first part before, but the second half really helped me understand how everything relates. I particularly gained a better understanding of quarks, anti-quarks, and various leptons and hadrons.

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Elliot Lipeles then gave a talk. He was involved in the discovery of the Higg's boson. He first told us about all the hardware they have in the LHC. They have to accelerate protons to near light speeds. They then have to detect what happens when the protons crash together. The detectors register about 20 million pictures per second. They cannot possibly afford to store this much data, so it's filtered to about 400 per second. The first stage is all hardware, filtering it to about 100,000. The next stage looks at just a few parameters, narrowing it down to about 5,000. The last stage looks at it much more deeply, getting it down to about 400. Our speaker then told us about why the Higg's boson is important, and what it does with the Higg's field. While he went into a lot of fascinating specifics, there are two general ideas: it can give particles mass, and it can unify the electromagnetic and weak nuclear forces. He then told us about what's next. Finally, he answered questions. I stayed behind an extra half hour or so to hear all the answers. He might have been my favorite guest speaker: he lectured well, in addition to going into the specifics of how he does what he does.

We then had lunch, and it was time for our interest groups. (There are three projects I might talk about: interest groups: the cloud chamber; exponential groups: Benford's Law; Hersheypark groups.) The cloud chamber was working a bit better today, though it was not ideal. Tomorrow we will stick a radioactive source in. I then worked a bit in my exponential groups.  The goal was to generate some truly random numbers. We used a Geiger counter and a radioactive source. We then counted the beeps for a given interval of time, giving us a random range of number from between about 5 and 50. We will then use these random numbers to index in to a long sequence of numbers, like pi (I wrote the code to do this in about 2 minutes). If our numbers were 5, 26, and 13, it would look at the first digit of the first 5 digits, the next 26 digits, and the next 13 digits. I love that Penn has these tools available. 

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