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Mostly Mozart


Posted April 21, 2002

Hello, you're listening to Mostly Mozart on CJLY in Nelson 93.5fm, Kootenay Coop Radio. My name is Tom Clegg. Mostly Mozart is sponsored by the Nelson and Area Tom Clegg Society.

Since this is the last episode of Mostly Mozart for this season, and since there is Mostly No Mozart next season, I figure it's time to tie up some loose ends, like that elusive string theory episode I've been promising to do for the last year and a half. And the episode where I try to define what science is and what it means.

I'm especially looking forward to doing the bit about string theory, because it has been requested so often (yet so politely) by Catherine Fisher, and I happen to know that she is busy with the film festival today, so she won't hear it. And this time she won't get a second chance on Thursday, because our new schedule starts tomorrow -- and as I almost just mentioned, there is No Mostly Mozart on the next schedule.

But before I get to that, I would like to answer a question that I received by email from my most prolific asker by email of questions relating to science: Sherry.

"Why is it that when I walk into the dead sea (the salty one), I feel no unusual resistance against my legs and feet, but when I lay back in the water, I float? Why doesn't it affect how my feet feel when I walk in the water?"

Because it's not the water's "resistance" that makes you float; it's its weight. If the water is unusually heavy, you will float higher than usual. This follows from Archimedes' principle, that buoyancy (the force that pushes you upward, against gravity) is equal to the weight of the water you displace.

Equilibrium (floating) is achieved when the upward force equals the downard force; in other words, when you're floating, your buoyancy equals your weight. Your buoyancy -- the weight of the water you displace -- is the volume of the part of your body that is submerged, multiplied by the density of the water.

Your buoyancy, and therefore your weight, which is constant (for our purposes), is equal to the volume of displaced water multiplied by the density of water. That means that if the density of water increases, then the volume of displaced water must decrease.

In order to decrease the volume of displaced water, you must move upward so that a smaller part of your body is submerged. This is known to the layman as "floating higher than usual."

Here's an experiment you can try:

Fill pot with 4 litres warm water. Put heavy things (coins, bolts) into small jar until it floats reeeeal low in the water (just lid poking above water). Add 1 or 2 kilograms cheapest salt you can find. Stir vigorously (but try not to make a big mess). Water still feels like water -- but jar rises.

(When finished, dump salt water in annoying neighbour's garden, or place in fridge in case something interesting happens.)


You're listening to Mostly Mozart on CJLY in Nelson 93.5fm, Kootenay Coop Radio. My name is Tom Clegg. Mostly Mozart is sponsored by the Nelson and Area Tom Clegg Society.

String theory. Well, I mentioned loose ends a few minutes ago. But these strings don't have ends; they're loops. They're called strings because they are one-dimensional: they have length, but they don't have thickness. Obviously, everyday observable strings do have thickness; but it's the closest analogy we have to a one-dimensional object.

But never mind the exact nature of strings for a minute; the part about string theory that I want to mention is why it exists in the first place. In the last century or so, there have been two major revelations in theoretical physics: quantum physics and relativity.

If you've heard of Schrodinger's cat, you've heard of quantum physics. The idea of Schrodinger's cat is that, although there are some things you just cannot know -- like whether a cat, locked up in a box with a poison pill, is alive or dead -- you can know a lot about the probability. For example, if the poison pill has a 50% chance of being a dud, then there is a 50% chance that the cat is alive. The really funny thing about quantum physics is that if you look very closely at physical processes, you find that every possible situation has a certain likelihood of being true at any given moment. And if you examine smaller and smaller spaces, the events that are probable get more and more bizarre. The upshot is that all of the familiar rules of physics apply only on a large scale. Billions of tiny unpredictable small scale events -- some of which are extremely unlikely -- contribute to a large scale average, which follows the rules.

If you've heard of Einstein, or E=mc2, you've heard of relativity. The general theory of relativity changes our understanding of space. According to Einstein, gravity is not simply a mysterious force field that makes things move through space; it is more accurate to say that heavy objects change the shape of space. For a rough idea of what it means to change the shape of space, consider drawing a straight line on a globe. For example, the equator is a straight line on a globe. However, if you look at it from above the north pole, it's no longer a straight line -- it's a circle. If you unrolled or flattened the globe, then the equator would be a straight line from both perspectives.

Thanks to Einstein, we have equations that describe exactly how the shape of space is changed by the presence of mass. The equations agree extremely well with experiments, which essentially means that they are correct. The problem is that these equations don't agree very well with quantum physics. This might not have bothered Einstein very much, as someone who believed that "God does not play dice with the Universe", but most physicists have accepted it; as far as anyone can tell, quantum physics is true.

Relativity offers nice smooth equations that describe the nature of space with infinite precision. Quantum physics, on the other hand, claims that the nature of space is variable on small scales. Sometimes it works this way, and sometimes it works that way; you can't be sure which way it's going to work at this particular moment -- you can only be sure that, in the end, it will work out to a predictable average.

One point where quantum physics and relativity collide -- or fail to intersect, if you will -- is in a black hole, where gravity is unimaginably large and space is unimaginably small. If you try to combine the equations of quantum physics and relativity, you find unnerving things like that the probability of a certain event is -7. A probability of 0 means it doesn't happen; a probability of 1 means it does happen; a probability of 0.5 means it equally likely to happen or not; but what does a probability of -7 mean? Or a probability of 1,000,000? It doesn't mean anything in quantum physics, and it doesn't mean anything in relativity.

Normally, if you combine two theories and get a contradiction, then it's obvious that at least one of the theories must be wrong. However, in this case, some people have come up with the idea that space does not get arbitrarily small. The universe made of strings, or loops; and the strings have a finite size. String theory promises to avoid the contradiction between quantum physics and relativity, basically by stating that the physical conditions necessary for the contradiction simply don't happen in the universe. Essentially, Quantum and relativity theories are both capable of describing something that doesn't exist. Their descriptions can't be reconciled with each other, but who cares? It doesn't exist, so why should it be described the same way by the two theories?

On that note -- the note of apathy, perhaps -- I will leave you with... ummmm... some music.