In his How Free Are You?: The Determinism Problem (Oxford University Press, 2002), Ted Honderich (Grote Professor Emeritus of the Philosophy of Mind and Logic, University College London). Devotes a chapter, "Neuroscience and Quantum Theory", to the question of what quantum theory means to the freedom of will. Prof Honderich makes several claims about quantum theory in this chapter, some of which are true and relevant, and some of which are neither. Prof Honderich seems to draw a distinction between the world described by quantum mechanics, i.e. the world of the very small, and the "real" world, that we all experience in our everyday lives, and which is well described by the classical mechanics developed by Isaac Newton and which preceded the quantum mechanics. In particular, he makes two related claims which are particularly troubling:
In support of the second claim, Honderich asks why it is that indisputable cases of indeterminism at the macroscopic level have not been found, e.g. why has no one ever documented a levitating spoon?. He says, "The common answer made to this is that any levitations, for several reasons, are so totally improbable as in some sense or other to be out of the question. It does not quite satisfy me. If it is true that there is indeterminism in the real world, and finding it would get someone a Nobel Prize, I would have expected a little unquestioned progress by now. Some kind of unquestioned progress." (pg 66).
Well, Albert Einstein, who Honderich mentions maintained "the stubborn conviction" that quantum mechanics would ultimately be replaced by a more complete and fully deterministic theory, won his only Nobel prize for the photo-electric effect (not for his theory of relativity) which is a quantum mechanical effect. Many, many Nobel prizes have been awarded in the years since the development of quantum mechanics for experiments concerning of quantum mechanical effects, all of which, were, presumably, performed in the "real" world.
Be that as it may, the likelihood of the typical spoon levitating 1cm while sitting in the typical silverware drawer can be calculated, and indeed, one would find the probability is vanishingly small. But this calculation requires an understanding of quantum mechanics and a facility with mathematics that the average person, even the average college graduate might find daunting. On the other hand, the first of Honderich's claims, that there is no agreement between the quantum and classical mechanics, can be demonstrated to be false using little more than what is, today, called "college algebra". Indeed, not only can it be demonstrated that quantum and classical can agree in their predictions given the right kinds of situations, it was recognized during the development of quantum mechanics that this was a essential requirement for the new quantum theory.
So what follows is a demonstration that quantum mechanics and classical do agree in their predictions, and nothing more than algebra is used. We begin with formulae from the classical mechanics, and then make use of two formulae from the quantum mechanics, none of which are justified, but must be taken on faith. Or better yet, the reader could take what is generally the first 3 semesters of "general" freshman physics and (s)he would see the derivation of all four of these formulae, and, most likely, the following demonstration. In any case, all that is needed to follow what follows is straightforward algebra, and a willingness not to be intimidated by math!
In the early days of quantum mechanics, physicists learned that well understood classical principles were not always reliable guideposts. And yet, it was understood that in the "classical limit", i.e. when a microscopic system - one way to think of quantum mechanics is as the physics of "microscopic systems", by which we mean systems with very, very small distance scales or very, very low energies - can be 'scaled' up to a macroscopic system, predictions about the systems behavior made by quantum mechanics had to match the predications about the system's behavior made by classical mechanics. The same was true of Einstein's new relativity theory - relativity theory applies systems with large distance scales or very high energies - when such a system's energy and velocity tend toward zero, relativistic mechanics reduces to classical mechanics. To put this notion formally, Bohr coined what is now referred to as the "Correspondence Principle":
In the limits where classical and quantum theories should agree, the quantum theory must reduce to the classical result.
A prime example of this was due to Bohr himself. When it became clear that atoms consisted of a positively charged nucleus surrounded by 'orbiting', negatively charged electrons, an immediate problem arose. Classical electrodynamics require that an accelerating charge emit electromagnetic radiation - in the new language of quantum mechanics, an accelerating charge will emit "photons", the quanta of electromagnetic radiation. The problem is, an electron in a uniform circular orbit is under continuous acceleration - a particle is accelerating whenever its motion changes direction, even if its speed is constant. And so it would be continuously emitting photons. But in doing so, the electron would lose energy, and its orbital radius would continuously decrease, and it would eventually spiral into the nucleus where it would annihilate with one of the nuclear protons.
Now as matters of empirical fact, atoms are not continuously emitting radiation and they seem relatively stable - one can calculate how long it would take for an 'classical' atom to self-destruct in this manner, and the answer is on the order of a micro-second, i.e. one one-millionth of second!
So either electrons didn't really 'orbit' the nucleus the way the planets orbit the sun, or the physics of an electron in orbit about a nucleus was fundamentally different than from that of a planet orbiting a star. In fact, both are true, but in the early days of quantum mechanics, classical models were generally advanced as tentative first steps on the path to the understanding the new quantum mechanics. Such was the case with atomic electrons.
Bohr initially proposed that electrons orbited the nucleus just as the planets orbit the sun, but so long as they orbited at certain discrete radii, they would emit no radiation, and would emit radiation only when they jumped from one of these 'quantized' orbits to another smaller orbit. A quantized orbit was a new and radical proposal, but it accounted for the empirical data, and allowed for remarkably accurate predications to be made about atomic behavior. It turned out not to be the whole truth, but for our purposes, it is close enough.
One can 'scale up' an "semi-classical Bohr atom so that it is, to a certain extent, describable by classical mechanics. One can "excite" an electron into an orbital radius much, much larger than is normally the case, and when one does so, the atom is referred to as a "Rydberg atom", after the physicst Johannes Rydberg (1854-1919). In these atoms, the highly excited electrons have properties similar to macroscopic objects orbiting other macroscopic objects, like planets orbiting the sun. One of these properties can be examined using nothing but high school algebra - well a little more than that actually, but not much more!
The force that must hold an electron in orbit about a positively charged nucleus is the electromagnetic or coulomb force, which has been understood since the late 19th century, and is:
Here we assume the atom under discussion is hydrogen, i.e. that there is one proton of charge +e (no neutrons, which are uncharged) and one electron of charge -e, r is the distance between the charges, and the leading coefficients are fundamental constants that guarantee, amongst other things, that the force has the appropriate units (mass*distance/time squared). The negative sign indicates that the force is attractive, i.e. that the proton is "attracted" to the electron and vice versa.
The acceleration an object must undergo to remain in a uniform circular orbit, the "centripetal" acceleration, is:
where a is the acceleration the object must experience toward the center of its orbit of radius r if has a velocity v. And as force is mass times acceleration, the centripetal force must equal the coulomb force:
,
where the mass, m, is that of the orbiting electron. This equation can be solved for the velocity of the electron's orbit (multiplying both sides by r and then taking the square-root of both sides):
.
The time it takes an orbiting object with velocity v to go around a circle of radius r is:
,
which, for an electron orbiting a proton, will be:
.
The frequency of the orbit is defined as one over the period, or:
.
Now the quantization of orbital radius Bohr invoked to avoid having atomic electrons continuously emitting photons and spiraling into the nucleus is:
where 
is Plank's constant (divided by 2p) - you know you're doing quantum mechanics when you see ! - and n is the orbital number (called the "principle quantum number" when you're talking about electrons orbiting in atoms) and is strictly a positive integer - this is the quantization condition! The stuff in front of the n2, i.e. the 
is called the "Bohr radius", and is the smallest possible orbital radius - it's equal to .528x10-10m! - of a single electron orbiting a single proton, i.e. this is more less the size of an unexcited Hydrogen atom. Planets can orbit at any radius from the sun (if their orbital velocity is big or small enough), but atomic electrons are limited to radii that go as the square of the positive integer n. If one plugs this quantized, orbital radius into our orbital frequency equation, one gets:
The frequency of the electromagnetic radiation, in the language of classical mechanics, or photons in the language of quantum mechanics, emitted by a charged particle in a circular orbit is equal to the particle's orbital frequency, which is what we just calculated for an atomic electron in a circular orbit. And the only quantum mechanics involved so far was the formula for the electrons orbital radius! You may not understand the importance of this now, but note that we didn't make any assumptions about the size of n in this derivation! We have simply derived the frequency of the radiation that would be emitted by an electron orbiting at a radius r, which happens to be a function of the principle quantum number n, and is equal to the frequency of the electron's orbit.
Bohr's quantization of atomic electron's orbital radii also quantizes its energy:
is the Bohr radius again, i.e. the smallest possible orbital radius of a single electron orbiting a single proton for which n=1. It is important to note that the energy of an electron orbiting a proton is negative, and that because n is in the denominator, the larger n is, the smaller the fraction 1/n2 is. But because -(n+1)<-n (i.e. -5.2<-4.3), this means that a larger n means a larger energy in addition to a larger orbital radius!
We've said that an orbiting e will emit a photon only when it drops from one orbital level to another, and since 'higher' orbits have higher energy, the electron must lose energy when dropping from a higher orbit to a lower. But energy is conserved, so that 'lost' energy must go somewhere, and it does: it becomes the photon that is emitted when an electron drops from one orbital to another. The energy that is the emitted photon is simply equal to the difference in the energies of the electron's orbitals:
Note that because we defined E1 to be a negative number, the energy of the photon is actually positive!
Now the tricky math starts, because we're going to 'scale' this up to a macroscopic system! Recall that the orbital radius gets larger as n gets larger, so to have a 'macroscopic' radii, n must be very large. To see what happens to the photon energy happens as the initial orbital radius gets very large, we'll let n 'grow without bound', but first, we'll factor out the largest power of n in both the numerator and the denominator:
Now, as n gets larger and larger, any fraction with a power of n in the denominator gets smaller, and if n gets large enough, such fractions will become negligible. Thus:
So, for large n, in dropping from the n+1 orbital to the n, an electron orbiting a single proton will emit a photon of energy equal to 
. The energy of an photon is E=2p(n, and so the frequency of a photon emitted by an atomic electron when it drops from the n+1 orbital to the n orbital will be:
Which is exactly the formula that we derived for the orbital frequency of a atomic electron, i.e. vn!
But what does all this mean? Well, what we have done is the following: we started with two formulae from classical mechanics that allowed us to calculate the orbital speed of an object attracted to another by the electric force. We made no assumptions about the size of the two objects, the force between them, or the orbital radius. We made use of a couple of common sense definitions to turn this velocity into an orbital frequency, and then we claimed that this orbital frequency was equal to the frequency of the electromagnetic radiation that would be emitted if the orbiting object were an electron. We then quantized the orbital radius of the electron, making use of Bohr's semi-classical/semi-quantum mechanical model of the atom, and used this to quantize the electron's orbital frequency, and thereby, quantized the frequency of the radiation that would be emitted by the electron if it were continuously emitting radiation as though it really were a classical system! Then we started over, using another unjustified quantum mechanical formula for the energy of an electron orbiting in Bohr's semi-classical/semi-quantum mechanical model of the atom. We calculated the energy it would lose from dropping from one orbit to the next, and converted this energy into the frequency of the photon that carries this 'lost' energy away from the orbiting electron. Finally, we let the orbital radius grow without bound so that it would be big enough that we might consider it to be classical in size. And lo and behold, the frequencies were the same. That is, the classical mechanics makes a prediction of the about the frequency of the radiation emitted by a classical system, and this is prediction is exactly the same as the prediction made by the quantum mechanics about a 'classically' sized quantum mechanical system.
In yet other words, we demonstrated, at least in one situation, the correspondence of quantum mechanics in the classical limit.