Quantum mechanics basically states that, when we examine our Universe for objects the smaller than atoms, we find the "rules" we are used to no longer apply. No matter what we do, no matter how hard we try, we can no longer predict exactly what will happen when we set up an experiment. An atom, for instance, might decay to a lower energy state in one second or two seconds; but it is fundamentally impossible to know which will happen -- we can only speak of the PROBABILITY of one event versus another.
This is NOT because we lack the instruments or the cleverness to do so. It is NOT because the atom "knows" what will happen but "hides" this fact from us. It is because (in our Universe, at least) it is FUNDAMENTALLY IMPOSSIBLE to know with absolute uncertainty.
Let's compare a classical world with a quantum world, using (for this example) a basketball game.
In a classical, "normal" world, a scientist could, if she had enough information, determine with absolute certainty if a shot was going to go through the basket once it left the player's hands. She might have to know a lot of things -- the initial velocity and angle of the shot, the spin of the basketball, how well the hoop bounces, etc -- but she COULD, in theory, make the calculation; and determine, with exact precision, whether or not the basketball would go through the hoop.
In a quantum world, she could NOT do so, no matter HOW MUCH information she collected. She could determine the PROBABILITY of the ball going through the hoop, and that probability might be so high (or so low) that the result would be the same as in a classical world. Or it MIGHT be that she determines that the probability is exactly 50% of it going through -- and that would be the ABSOLUTE BEST that she could do, no matter how much information she was given.
Einstein hated this concept, comparing it to a game of cards. "It seems hard to sneak a look at God's cards. But that He plays dice and uses "telepathic" methods ... is something that I cannot believe for a single moment" is how he described his disgust.
An apocryphal reply from Neils Bohr is "Don't tell God how he should manage His universe."
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