### Probability - All in the mind?

We start with the simplifying assumption that the world is quantum certain. We’ll add quantum uncertainty and worry about its effects later. In a quantum certain universe, the current state of the universe completely determines the future states of the world (or universe). The connection of all the variables may be extremely complicated and may be affected by “a butterfly flapping its wings in Australia”; but the future is certainly determined by the present state of the universe. Now let us try out an experiment in such a universe. I have a biased coin. Initially I do not know what the “probability” of the coin showing up heads is. Without any prior information about the coin, I would say that the probability of the coin showing up heads is half. I then proceed to toss the coin and find that it does indeed show up heads. I repeat the experiment a few times and find that the coin shows up heads 8 times out of 10. This leads me to adjust my probability assessment of the coin showing up heads. Now I show the coin to a friend and ask him to make an assessment of the probability distribution. Again, without any prior information, my friend is going to put the probability at half. I then proceed to flip the coin again. Now here is the point to consider: what is the actual probability of the coin showing up heads – half? Or 0.8? Clearly, my friend’s or my belief should not affect the outcome of the toss at all. Indeed, in a quantum certain world, the end result of this experiment is already decided – only we don’t know what it is. So in this case probability is indeed only in our mind and it has nothing to do with the act of flipping the coin at all. It may be argued that probabilities should not be interpreted as being assigned to a single event but as the statistics arising out of several repetitions of an experiment. However, if the world is quantum certain, why should it be the case that asymptotically the coin will continue to show the same statistical probability of showing up heads 8 out of 10 times? Why may not the predetermined chain of events lead to a completely different statistical behavior in the long run?

Now, let us add quantum uncertainty. This clearly allows probabilities to be “out there” instead of being only a figment of our imagination. However, there is still a problem. Why is it that uncertainties at the level of the tiny atomic/sub-atomic particles so precisely affect and control the probabilities of much more coarse-grained events like coin flips and card selections? How do uncertainties at the quantum level lead to such probability distributions that can be so easily analyzed, like say the probability of picking a king of spades from a pack of 52 cards? Do they infact affect these events at all? Or are these probabilities (of gross events, not quantum events) still only creations of our imagination; a statement of our ignorance of the state of the world?