Tuesday, February 01, 2005


With regards to Andy's comment on randomness, we need to keep in mind a little something Quantum Mechanics likes to call Heisenberg's Uncertainty Principle. To simplify this theory greatly, it basically says that the more precisely the position of a single particle is known, the less precisely the momentum can be measured in this exact instant, and vice versa. Since a particle's momentum is directly proportional to the product of its mass and velocity, the more we precisley measure one of these magnitudes, our knowledge of the other magnitudes in a sense, blur.

Let me give you an example here. Let's say we have a positron (don't you just love anti-matter?) traveling at a velocity of about 8.38 x 107 m/s. This velocity is measured to a 0.01% accuracy (which is pretty darn accurate). Since an electron has a mass of about 9.11 x 10 -31 kg, we'll assume a positron has the same mass and the resulting momentum would be about 7.64 x 10 -23 kg m/s. The uncertainty of this momentum(Δρ) is the measured accuracy (0.01%) of the determined momentum, or 7.64 x 10 -27 kg m/s. Using Heisenberg's little constant(h) 6.636 x 10-34 J s, we can derive a change in position (Δx) by dividing h by Δρ. The result is the uncertainty in the particles position which is 8.7 x 10-8 m. Now this may seem small to you, but in particle terms, this is an amount of roughly one thousand atomic diameters.

Every time we try to measure either position or momentum, we disturb the other. So in theory, we could never actually predict the lottery ball's location at an instant in time. Want to see more randomness in action? Send a particle like a photon thru a small slit and predict its location just after coming exiting the slit. Then, if you're really in for a doozie, try and determine if that time the photon acted like a wave or a particle. Even with my luck, I always guess right!

By the way, I think that if we zoomed out on the universe it would look like a fractal. Maybe even the golden fractal! Wouldn't that be ironic?

5 comments:

Andy said...

While it may or may not be correct that we can't predict the location of a lottery ball exactly (it's not a particle, so it won't act exactly the same, and it's defintely not a positron), in order to predict the lottery, you don't need to have the exact position to that level of precision. You only need to know the location close enough to determine the order they will come down the ball chute or whatever. Essentially, the position and velocity can be known to a close enough value to make the prediction possible, especially because the balls move a lot slower than the 8.38 x 10^7 m/s and are a lot heavier than 9.11 x 10^-31 kg suggested for the positron in the above statement. The two cases are not really analogous, and thus not useful for comparison.

Jimmy said...

You may be right, but at some point (yet to be discovered) quantum mechanics will connect to relativity and every single thing in life will be able to be equation-ized. So in theory (pun intended), the lotto balls are analogous to quantum mechanics and uncertainity, we just don't know how yet. And besides, how can you predict where an entire colony of ants are moving to, if you can't predict the movement of just one ant?

Andy said...

Ants? ANTS! I thought we were talking about lottery balls. Are you saying there are ants inside the balls telling them where to go, or maybe the balls are made of ants? This would explain why I haven't hit the Powerball yet.

Jimmy said...

I never thought of that...But now things are becoming a little more clear. The ants are everywhere! Save yourself!!

Kathi's Mind said...

K so, you guys make my head hurt a lot....