If quantum mechanics hasn't profoundly shocked you,
you haven't understood it yet.

Niels Bohr

How it all began

In the 17th century, Newton and Huygens began the great debate about the nature of light. Newton argued that light is a stream of particles. Huygens insisted: light is wave. The authority of Newton prevailed then. Corpuscular theory of light existed until the early 19th century, when Thomas Young conducted a famous double-slit experiment, which explicitly (as it seemed) proved the wave nature of light.

He passed a beam of light through a thin plate with two parallel slits, and the light  struck a projection screen behind them. The interference pattern was formed at the screen. That was what clearly proved the wave theory of light. After all, if light consisted of particles, then the screen would have just two bands, formed of particles passing through the two slits.

But in the late 19th early 20th centuries, again, everything had been turned on its head. Scientists found such optical effects as the Compton effect, photoelectric effect, photochemical reactions. In explaining these phenomena, the wave theory was untenable. Plus, it was found that Young's experiment can be repeated with the flow of electrons to form an interference pattern! Physicists was very upset. In desperation, they began to talk about "wavicles" (wave-particles). But they didn't know then that most mysterious and interesting things was to come.

Mysterious experiments

As it was mentioned above, the double-slit experiment was also performed with the flow of electrons: an interference pattern was formed at the screen. The same picture was shown even in the case when the electrons was stricken one after another! This means that it was not an interaction of electrons with each other. As we know, interference is a phenomenon that occurs when the superposition of two (or more) waves takes place. In this case, there is a superposition of two waves generating by each of the slits. How can electrons flying out each after another capable to cause an interference pattern? Only if each of them passes through two slits at once! But this is not the strangest thing. Scientists put a detector of electrons on one of the slits (or two of them at once, not much) to see which split each electron passes through. And what do you think? Each electron is detected only in one of the slits. But the most important thing is that the interference pattern disappears! The fact of observing an electron causes it to become ordinary particle! How naive Newton and Huygens were :-)

Here is a very good cartoon clearly showing the essence of such experiments:

And here's another example of another experiment from the book by Paul Davies "Superforce":

Suppose that the experimenter turns on the device and, at first, chooses the direction to measure it on the spin orientation of the particle. In practice, such direction is usually the direction of the magnetic or electric field. The experimenter wants to determine the angle between the spin of the particle and the direction of the field. After measurement, he surprisingly finds that the spin is oriented strictly along the field direction. The experiment is repeated several times, but the result is always the same: spin is always oriented along the chosen direction. Suspecting something was amiss, the experimenter is going to change the direction of the external field, but the spin of the particle always follows its direction. And no matter how the experimenter tries to detect the spin being directed at an angle to the original direction, he has nothing. The experimenter is in disarray: the particle looks like it reads his thoughts, because it always indicates the direction that he randomly chooses as a reference point.

Despairing, the experimenter resorts to a devilish cunning specifying two different directions, A and B, and measures the angle between the direction of spin and each of them. Since the spin of a particle, according to an experimenter, can not be simultaneously oriented in two different directions, at least in one case, the spin should make with one of them a certain angle. Accordingly, the experimenter makes the first measurement. The fact that the spin is oriented along the direction of A does not cause him surprise. He makes the second measurement immediately after the first one, so the spin will not have time to reorient itself. Direction B was chosen so that it makes an angle 250В° with the direction A, and the experimenter, having satisfied that the spin is oriented along the axis A, of course, expects that the spin will be directed at an angle of 250В° to the axis B. However, he surprised to discover that nature has outwitted him: the particle is somehow pre-empted him, and its spin, as if by magic, turned out to be oriented along the axis B at a time! In a rage the experimenter once again sets to measure the angle between the direction of spin and the axis A and sees that the spin, as before, is oriented along the axis A.

Uncertainty principle

The above described phenomena are derived from the Heisenberg uncertainty principle, the basis of quantum theory. In brief, its essence lies in the fact that it is impossible to simultaneously determine all the parameters of the quantum system, for example, the momentum (velocity) and the coordinate of the particle. If we fix the velocity, then we can not know exactly where the particle is. And vice versa. Knowing the velocity, we can not talk about its exact position. We can assess other characteristics probabilistically only. It will never be possible to determine simultaneously both the characteristics of a particle precisely. It is important to understand that it is not about our imperfect tools, but that it is fundamentally impossible. The very act of fixing one of the characteristics makes the other uncertainty. We can say that the particle simply does not have the momentum and position at the same time.

EPR paradox

Einstein could not accept this probabilistic principle. He did not want to lose the certainty and truth. "God does not play dice" - he said. Einstein called quantum mechanics absurd. He believed that physicists simply do not yet know the values of some hidden variables which would allow to avoid uncertainty. Niels Bohr opposed him, arguing that the probabilistic nature of the predictions of quantum mechanics is fundamentally unresolved. Einstein was not alone in his belief (not many people would lose faith in the existence of objective reality). Boris Podolsky and Nathan Rosen taked his side. They, along with Einstein, proposed a thought experiment which was called "the Einstein - Podolsky - Rosen Paradox (EPR paradox). Its essence is as follows. If we can not measure both the momentum and position of the particle, then what prevents us to calculate it indirectly? We take two identical particles and push them against each other. Choose one of the particles to determine its characteristics. We measure the coordinates in a certain time after the collision. We can not determine the momentum at this point. Well, it does not matter. After all, we can measure the momentum of another particle. Knowing that the sum of momentum of the particles before the collision is equal the sum of their momentum after the collision, we calculate the momentum of the first particle. As a result, we know exact the position and momentum of the particle. Cunning, eh? But Bohr did not give up. He suggested that two interacted particles remain connected in some way, so the state of one measured particle is immediately transmitted to another. If we have measured the momentum of the first particle, we can not measure the coordinates of the first particle and the second one neither! Einstein saw a contradiction of his theory of relativity which sets the speed limit transmission of any information (signal) equal to the speed of light.

But these were only thought experiments. The debate so far could not be resolved by the technical complexity of setting real experiments.

Bell's theorem

Much later in 1960s, John Bell pondered over the EPR paradox. He figured out how to put an end to this endless debate of physicists which started by Bohr and Einstein (By the way, they had not lived till that time). Based on the arguments of EPR-comrades, he formalized this debate in certain inequality which was named Bell's inequality (or Bell's theorem). The only thing that remained to do is, as always, to conduct an experiment. If the experiment confirmed Bell's inequality, then Einstein was right, if not, then Bohr. Technically, such an experiment was also yet to be impossible. But, at least, now it was known exactly the following: 1) what to test, 2) what the test would give to science, and 3) that the test was possible in principle.

The end of common sense / "Goodbye objective reality"

A true convincing experiment to test Bell's inequality was only had been done in 1982 by Alain Aspect in Paris. In this experiment the polarization directions of the two photons, emitted by the same atom and moving in opposite directions, was simultaneously measured. Aspects found that the photons was able to instantaneously communicate with each other regardless of the distance between them. The experiment put an end to endless disputes. To quote Paul Davis:

The results left no doubt: Einstein was wrong. Quantum uncertainty can not be avoided. It is an integral feature of the quantum world and can not be reduced to something else. Naive representation of the reality of particles with well-defined properties in the absence of observations on them have failed the test. Aspects had hammered the last nail in the coffin of physics based on common sense.

Again, a small cartoon on this subject:

Whew! Let's go back a little bit ago and remember what Niels Bohr said (the founder of the Copenhagen interpretation of quantum mechanics):

1. Quantum uncertainty is nonremovable in principle.
2. It is impossible to separate the observer from the observed: the very method of observation manifests certain properties of the quantum world.
3. Two or more particles reacting with each other can feel the presence of each other at arbitrarily large distance from each other and behave as a single entity (such particles are called entangled).

Next, physics did whatever they could. Even molecules (just immense objects in terms of quantum world) "tormented" by dispersion on grating diffraction. And even in this case, the interference effect depended on the very amusing magnitud, measure of the experimenter's confidence in the fact that the particle has passed through a certain slit.

We now have such physics.