If I knew the initial (exact) conditions of the throw of a die, could I throw a 6 with certainty? How does the Heisenberg principle affect my ability to control the outcome? — TW
In the classical view of the world, the view before the advent of quantum theory, nature seemed entirely deterministic and mechanical. If you knew exactly where every molecule and atom was and how fast it was moving, you could perfectly predict where it would be later on. In principle, this classical world would allow you to throw a 6 every time. Of course, you’d have to know everything about the air’s motion, the thermal energy in the die, and even the pattern of light in the room. But the need for enormous amounts of information just means that controlling the dice will be incredibly hard, not that it will be impossible. For simple throws, you could probably get by without knowing all that much about the initial conditions. As the throws became more complicated and more sensitive to initial conditions, you’d have to know more and more.
However, quantum mechanics makes controlling the die truly impossible. The problem stems from the fact that position and velocity information are not fully defined at the same time in our quantum mechanical universe. In short, you can’t know exactly where a die is and how fast it is moving at the same time. And that doesn’t mean that you can’t perform these measurements well. It means that the precise values don’t exist together; they are limited by Heisenberg uncertainty. So quantum physics imposes a fundamental limit on how well you can know the initial conditions before your throw and it thus limits your ability to control the outcome of that throw. How much quantum physics affects your ability to throw a 6 depends on the complexity of the throw. If you just drop a die a few inches onto a table, you can probably get a 6 most of the time, despite quantum mechanics and without even knowing much classical information. But as you begin throwing the die farther, you’ll begin to lose control of it because of quantum mechanics and uncertainty. In reality, you’ll find classical physics so limiting that you’ll probably never observe the quantum physics problem. Knowing everything about a system is already unrealistic, even in a classical universe. The problems arising from quantum mechanics are really just icing on the cake for this situation.