Sunday, 6 April 2014

The Weirdness of Quantum Mechanics and Probability


While writing my last post that reviewing the documentary "Infinity and Beyond", the wacky idea of infinity leads me to another just as wacky idea of probability.

Infinity and probability both contain some very counter intuitive concepts.

There's no branch of mathematics that's more counter-intuitive from times to times than probability (perhaps topology comes close).

Here's an example.

After flipping an unbiased coins six times and they all turned up heads in a row, many gamblers would swear - and they bet their saving on it - that the next toss of the same coin will much more likely yield a tail. Many times more.

This seems intuitive. The reasoning is as follow. If nature wants to get an average of a 50/50 chance of a head or tail turning up in any coin toss, after a consecutive number of coin tosses resulting in heads; to give this 50/50 chance principle a chance to work, we should get a tail in the next coin toss. Seems to "make sense".

Well, it's not !

The next coin toss will have exactly equal chance of an outcome of a head or a tail  just as the first coin toss no matter how many heads had came up in the last n number of coin tosses. In other words, after getting 50 heads in the last 50 coin tosses, the chance of the next outcome of getting a head or tail is still 50/50 ! So don't bet on tail in the next coin toss and thinking you're gaining on the odds. Many gamblers in casinos all around the world do that everyday.

Using mathematician jargon, the gambler's mistaken belief is called the Gambler's Fallacy, and the reasoning is based on the Law of Large Numbers. Well, the 'large numbers' here is very large, in principle, the large number can be infinity ∞. So even if the coin tosses has a string of 1000000000000 number of consecutive heads as outcome, that number is still very small relative to ∞. Well, we know the trouble with infinity. It makes "common sense" nonsensical.

Here's a very simple explanation to help you to make the world "make sense" again. The coin doesn't remember. So as far as the coin (or dice, or roulette table) is concerned, every toss is the first toss because it has no memory.

A coin that remembers all its previous outcomes is very spooky. More spooky than what we discussed so far. But then, even if the coin has memories, we wouldn't know how many heads or tails it had turned up before. What about before using the coin to make bets with your friends, you record the number of heads or tails it turn up after a huge number of coin tosses before hand. In other words, you're doing a coin loading. And then you ask your friend to flip the coin and get a better odds for your bets. Well, all this is possible if a coin has memory. But it doesn't. Imagine how spooky if it does.

We just choose a lesser of the 2 weirdos.

Now, let's see what all this got to do with quantum mechanics.

Albert Einstein
Einstein once said, "God does not play dice with the universe",
apparently, God does. It's just God works in a probabilistic way.
Sometimes he plays dice, sometime he doesn't. It's all very mysterious.
Yeah, we live in a casino, the quantum mechanics physicists are gamblers
trying to figure out the outcome of the dice. Good luck to them !

There's no more doubt that nature is written in the language of mathematics. All branches of it. This is reinforced by the fact that quite a number of discoveries of nature were predicted by mathematical discoveries. Some theoretical physicists stated that their maths said something they haven't discovered yet should exist, and then other scientists discovered it later. Examples ranging from EM fields to black holes. You can discover all kinds of weird stuff in nature just by scribbling formula on a blackboard if you have the right stuff (chalk, patience, time, and genius. Don King's hairdo is optional). That's what theoretical physicists do. What could be more magical? Albert Einstein happens to be the best known one (but he didn't see eye to eye with quantum mechanics most of the time).

When quantum mechanics physicists say that the reality is brought into existence by their observation, isn't that what they do since science was invented?

Since probability wave function is so crucial and integral part of quantum mechanics, I wonder if all the counter-intuitive spookiness in quantum mechanics is simply a result born out of the counter intuitive weirdness of probability and infinity in the mathematics of quantum mechanics. We can grasp no more quantum mechanics than we can do so for infinity and probability. And quantum mechanics relies on the 3 most counter intuitive areas of maths: infinity, probability and topology.

Nature is weird because maths is weird.

Too simple a conclusion? Am I missing something?



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