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The Theory of Probability & Schrödinger's Cat
Transcript of The Theory of Probability & Schrödinger's Cat
Both of these are simple, simple questions when you only look at the surface. whether it is: Should I switch my door? Or: Is schrödinger's cat dead or alive?
What is the theory of probability?
The Theory of Probability
The theory of probability is what measures what is probable. For example, take Plinko from the old game show "the price is right". What should you do? place the disc near the middle? The left end? The right end?
More about Schrödinger's cat
Since the chances of the gunpowder exploding is 50/50, if you repeat the experiment enough times half of the cats will die, and half will live. But you will only see that by checking. So if you repeated this 99 times, and the cat died 49 times, and lived 50, you can already know that it's bad news for kitty once you open up the bunker. But we're talking about the very first time. Once again, you would have no way of knowing if the cat is dead or alive, so reality may not have necessarily chosen yet. This is one of the hugest unsolved mysteries in quantum physics, which is probably why I have been able to write so much about a very simple question. Is the cad dead or alive?
Total on dice pairs of dice probability
2 - 1+1 = 1/36 = 3%
3 - 1+2, 2+1 = 2/36 = 6%
4 - 1+3, 2+2, 3+1 = 3/36 = 8%
5 - 1+4, 2+3, 3+2, 4+1 = 4/36 = 11%
6 - 1+5, 2+4, 3+3, 4+2, 5+1 = 5/36 = 14%
7 - 1+6, 2+5, 3+4, 4+3, 5+2, 6+1 = 6/36 = 16%
8 - 2+6, 3+5, 4+4, 5+3, 6+2 = 5/36 = 14%
9 - 3+6, 4+5, 5+4, 6+3 = 4/36 = 11%
10 - 4+6, 5+5, 6+4 = 3/36 = 8%
11 - 5+6, 6+5 = 2/36 = 6%
12 - 6+6 = 1/36 = 3%
I'm sure some of you in the room already know what this paradox is. This paradox is about a cat in a bunker with either gunpowder, which Einstein used for his version of the theory, or poisonous gas, which schrödinger used. If you put a cat in a bunker with gunpowder which had a 50% chance of exploding and a 50% chance of doing nothing, what happens? Well, that's quite clear, the cat is either alive or dead. It cannot be both. But we won't know until we look, clearly. But what is it if nobody looks?
Let's say you have three doors, and in one is a video game console, and in the others a nice pile of rocks. So you have a 1/3 chance of getting the game console, and a 2/3 chance of getting some fancy rocks. I know whats in which, and tell you need to pick a door. Once you pick a door, I open a door you didn't choose containing rocks. At this point I ask you if you want to switch or stay with the one you picked first. Which should you choose? Switch or stay? The answer all boils down to simple fractions.
Because there is a 2/3 chance of picking some rocks, and only a 1/3 chance of picking the console, at first you hope to pick the rocks. Because if you switch after that, then you now have 2/3 a chance to get the console! to make this clearer, let's say I have 1000 doors. In 999 of them is some leftover lasagna from someones dinner 14 years ago, and in one a lifetime pass to the PNE. if you pick a door, there's only a one in one thousand chance that you picked the life pass, but if I open up 998 doors all containing horrid lasagna, if you switch, you now have a 999/1000 chance to get the life pass, because I knowingly cut down the doors.
Now, dice is an extremely simple probability theory, because dice are already numbered out and separated into sections. Let's be simple and say you have two six sided dice. It's as simple as what numbers add together more. So on two six sided dice, 7 is the most likely to be rolled. Remember that that does not mean that seven is going to be rolled constantly, as even though it is the most likely, it is still only a chance of 16%. As you may have noticed from the picture, this is another bell curve, just like plinko.
You should place the disc near the middle. Since the disc will hit 12 pegs on the way down, it's most likely to hit the peg and go right and left 6 times, than going left 5 times and right 7, or especially going right or left 12 times. This means that the closer you are to the middle, the more likely it will be for you to hit the 10000 space. This is called a bell curve. Also keep in mind that this does not make the chance of you getting the 10000 spot very high, and only about 1/5 of the time would you get it in the center.
Nothing can be dead and alive at the same time, but the whole theory is that before we look, it is. Once we look, we force reality to pick a side, either killing the cat or letting it live. This is the reason it is called a paradox. It can't be alive and dead at the same time, but if reality doesn't decide until we look, is it both dead and alive? In some sort of position between reality? Again, what the cat sees is what happens. so if you were in a bunker with gunpowder that may or may not explode, if it does, clearly you see it explode, and sadly die, but if it doesn't explode, you would not see it explode. You can't see it explode and it doesn't explode, because that makes no sense. It's our observation of the cat that makes nature decide, curiosity killing the cat, or curiosity not killing the cat.