Tuesday, November 15, 2011


Yesterday, Cindy asked me to check to see if the Dirca on our property was blooming yet.  Western Leatherwood (Dirca Occidentalis) is a funny little plant that only grows in the Bay Area.  Despite it's persnickety nature--growing only where conditions seem to suit it best--it grows in abdundance on our property and across the street at the Jasper Ridge Biological Perserve. Belonging to a small genus consisting of three species, one which grows in Mexico and the other along the East Coast, Dirca is the only member of its family in our region.  It is slow growing, long lived plant. An individual 5 feet tall may be a centenarian. 

There's pretty much one person that studies Dirca.  It is our first bloomer of the season, budding  understated yellow flowers, beautiful and asymmetrical with their stigma and many stamens hanging well below their pedals.  The flowers appear even before the plant has produced leaves.  Its curiosity lies in its timing. Dirca has bloomed in October. It has also bloomed in January.  A theory has emerged that it may bloom after the first heavy rains of the season.  We had an unusual wet October, which is why I was out looking to see if it had bloomed.

The Dirca hasn't bloomed yet, although it is starting to bud out.  It grows in abundance on our property. They grow on the north face of a gulch cut by Bear Creek. The ground is so soft there that it's almost difficult to walk, and these plants have probably been visited by humans very rarely if ever since our house was built 60 years ago. I found some old, stately individuals as well as some young ones. Dusky footed woodrats have a reputation for pruning Dirca to build their middens, but I didn't find any signs of pruning. I did find some (very) old coke bottles and a rock that looks fire cracked to me.  This would mean there were Ohlone here once.

A lone black oak stands in the soft, moist soil at the edge of the gulch. I found this strange.

Monday, November 14, 2011

The Twin Paradox

My friend posted a video on my facebook wall today lamenting that she had resorted to cartoons to understand physics and still didn't understand.  I have enough hubris that I generally think I can explain anything in understandable terms, so I decided I would take a crack at it here as well!

Let's save the explanation of relativity for another day and just accept the result: an object moving very fast will experience time slowing down relative to a stationary object. The quintessential example is a moving train.  If I stood on a train platform and watched a train zoom by (one of those scary trains that doesn't stop at your station), I would notice that a clock affixed to the outside of the train was ticking more slowly than the watch on my wrist. For a person on the train, time is ticking away at it's normal pace. Time is also ticking away at its normal pace for me on the platform, but when I observe their time, it has apparently slowed down.

Fine, physics is crazy, but that's not a paradox--yet.  The paradox comes from another cherished concept in physics, in fact, another form of relativity. Galilean relativity is the idea that all reference frames moving at a constant velocity are equivalent--there is no physical experiment that you can do to figure out whether the train platform or the train is the one moving so long as neither experiences an acceleration.

So the paradox is this: we take two twins (twin A and twin B), leave one on earth and zip one away on a rocket at near the speed of light.  Twin B turns around after 5 years and returns home. Because of relativity, he's now much younger than his twin brother. But who is to say that the earth wasn't moving while the rocket stayed stationary? In that case, twin A should be younger!

The resolution of this paradox comes from the fact that twin B has to make a u-turn to get home. The act of accelerating means all bets are off when it comes to Galilean relativity.  Twin B is definitely younger. 

By the way, all of this falls into the category of special relativity.  Special relativity is Einstein's earlier, easier and mathematically cleaner theory compared to his General Theory of Relativity. The only difference (ok, so it's a big difference) is that General Relativity incorporates gravity.  Occasionally a nasty rumor arises in high school and undergrad physics classes that special relativity can't handle accelerations. Special relativity CAN handle any crazy acceleration you can think of, thank you very much. General relativity really does only add gravity.

Lauren, if you've made it this far, I should mention this isn't actually the paradox we talked about that one time. That was the EPR paradox, one of Einstein's big objections to quantum mechanics. Another blog, maybe?