The Mechanics of Free Will
t'Hooft makes a good point about quantum theory vs. determinism. Let me elaborate a bit.
Quantum physics can only predict probabilities of events. To many physicists (including t'Hooft) this is very disconcerting. Is it really true that the state of the universe cannot be fully predicted from moment to moment? Or is this a shortcoming of our understanding of the universe? If the next state of the universe is selected by a toss of some transcendental dice, why can't we include the physics of those dice in our theory (and thus make them non-transcendental)? In fact, why not search for dice inside elementary particles?
Suppose that there is a hidden mechanism in every particle. If we don't know about the state of that mechanism, such a particle would behave non-deterministically to us.
Since the beginning of quantum mechanics people have been trying to build theories with hidden variables that would explain the apparent indeterminism of quantum mechanics. Not only have they failed, but it was proven that such theories would be incompatible with experiment.
Well, sort of. In every proof there are some assumptions and one can always try to question these assumptions.
The best example of an experiment whose results cannot be explained using hidden variables is the one with entangled particles. You can create a pair of electrons in such a way that they must have opposite spins (because you start with a state of zero spin, and spin is a conserved quantity). Although you know that the two electrons have opposite spins, you don't know in what direction they are pointing (up/down? left/right?). Until, that is, you measure the spin of one of the electrons. At that point you not only know the direction of the spin of that electron, but you also know in which direction the other one is pointing. Now somebody can measure the spin of the second electron, and their result must agree with yours. It is as if the second electron suddenly learned about the fact that its opposite twin has been measured.
The natural reaction at this point would be to say, "But both electrons had the directions of their spins set from the start, we just didn't know them until we measured them." And there's the rub--they couldn't! The actual direction of the spin would be the "hidden variable", but it isn't. The results of the experiment cannot be explained by assuming that both electrons had a definite direction of the spin. In fact, and I won't be going into details, the results of the second measurement depends not only of the result of the first measurement, but also on how the first measurement was done. The experimenter dealing with the first electron may chose to measure the vertical component of the spin; or, by tilting his magnets, might chose to measure the horizontal component (or any other, for that matter). The really spooky thing is that the results for the second electron depend on the way the first experimenter set up his experiment.
The experimenters may allow the electrons to fly apart for hours or years. When the measurements are done, the electrons may be separated by light years. The decision on how to orient each detector can be made at the last moment. And yet it looks like the second electron will instantly know what the first experimenter did.
No hidden variables could explain this!
There's one tacit assumption in this experiment-- says t'Hooft-- and it seems obvious to us, but isn't: The assumption that the experimenters have free will. We take it for granted that the first experimenter can make the last moment decision about the orientation of his apparatus, and that the decision is free and unpredictable. In a totally deterministic universe that is simply not true! If we consider the experimenters as parts of the experiment, their state is as important as the state of the electrons. The only thing that the experiment shows is that in the system where the first experimenter is bound to make the decision to orient his apparatus vertically, the second experimenter will see a particular result. No "spooky action at a distance"! Just the old-fashioned preordained universe.
The funny thing is that a lot of people protest t'Hooft's interpretation because it contradicts the existence of free will. The fact is that
No physical theory, including traditional quantum mechanics, has room for free will.
It seems like there are still some philosophers who don't understand this fact.
Quantum physics can only predict probabilities of events. To many physicists (including t'Hooft) this is very disconcerting. Is it really true that the state of the universe cannot be fully predicted from moment to moment? Or is this a shortcoming of our understanding of the universe? If the next state of the universe is selected by a toss of some transcendental dice, why can't we include the physics of those dice in our theory (and thus make them non-transcendental)? In fact, why not search for dice inside elementary particles?
Suppose that there is a hidden mechanism in every particle. If we don't know about the state of that mechanism, such a particle would behave non-deterministically to us.
Since the beginning of quantum mechanics people have been trying to build theories with hidden variables that would explain the apparent indeterminism of quantum mechanics. Not only have they failed, but it was proven that such theories would be incompatible with experiment.
Well, sort of. In every proof there are some assumptions and one can always try to question these assumptions.
The best example of an experiment whose results cannot be explained using hidden variables is the one with entangled particles. You can create a pair of electrons in such a way that they must have opposite spins (because you start with a state of zero spin, and spin is a conserved quantity). Although you know that the two electrons have opposite spins, you don't know in what direction they are pointing (up/down? left/right?). Until, that is, you measure the spin of one of the electrons. At that point you not only know the direction of the spin of that electron, but you also know in which direction the other one is pointing. Now somebody can measure the spin of the second electron, and their result must agree with yours. It is as if the second electron suddenly learned about the fact that its opposite twin has been measured.
The natural reaction at this point would be to say, "But both electrons had the directions of their spins set from the start, we just didn't know them until we measured them." And there's the rub--they couldn't! The actual direction of the spin would be the "hidden variable", but it isn't. The results of the experiment cannot be explained by assuming that both electrons had a definite direction of the spin. In fact, and I won't be going into details, the results of the second measurement depends not only of the result of the first measurement, but also on how the first measurement was done. The experimenter dealing with the first electron may chose to measure the vertical component of the spin; or, by tilting his magnets, might chose to measure the horizontal component (or any other, for that matter). The really spooky thing is that the results for the second electron depend on the way the first experimenter set up his experiment.
The experimenters may allow the electrons to fly apart for hours or years. When the measurements are done, the electrons may be separated by light years. The decision on how to orient each detector can be made at the last moment. And yet it looks like the second electron will instantly know what the first experimenter did.
No hidden variables could explain this!
There's one tacit assumption in this experiment-- says t'Hooft-- and it seems obvious to us, but isn't: The assumption that the experimenters have free will. We take it for granted that the first experimenter can make the last moment decision about the orientation of his apparatus, and that the decision is free and unpredictable. In a totally deterministic universe that is simply not true! If we consider the experimenters as parts of the experiment, their state is as important as the state of the electrons. The only thing that the experiment shows is that in the system where the first experimenter is bound to make the decision to orient his apparatus vertically, the second experimenter will see a particular result. No "spooky action at a distance"! Just the old-fashioned preordained universe.
The funny thing is that a lot of people protest t'Hooft's interpretation because it contradicts the existence of free will. The fact is that
No physical theory, including traditional quantum mechanics, has room for free will.
It seems like there are still some philosophers who don't understand this fact.