Schrödinger's cat is a familiar way of referring to a thought experiment in physics devised by the Nobel prize winner Erwin Schrödinger in 1935. A cat - a macroscopic object - was subjected to the strange rules of the microscopic world of quantum mechanics in order to illustrate how difficult it is to relate the quantum world to the classical world. To understand what is going on we first need a reminder of some of the basic ideas of quantum mechanics.
In quantum mechanics every physical process is associated with a probability amplitude which is a complex mathematical function of which the square gives the probability of obtaining a physical event characterised by a set of numbers: the position of an atom, the momentum of an electron, the polarisation of a photon or the emission of a beta ray by the radioactive disintegration of a nucleus etc.
These probabilities are not calculated by classical rules, but from probability amplitudes. Each amplitude is mathematically described by a vector in a given vector space. The sum of these amplitudes is the state vector of the physical system in question. This leads to a radical revision of the concepts of change in time and space of all possible physical quantities. These can end up being reduced to a set of discrete values such as the energy of the electrons in an atom, and do not have any real classical values in the absence of observation. They lead to a situation summed up by the Berkeley philosophical dilemma: "How can I be sure that my desk exists when I'm not there to see it? ".
According to quantum mechanics, on an atomic scale an object does not exist in the classical sense when it is not being observed, in fact measured by a macroscopic observer (who initially may not necessarily be human). In Young's famous double slit experiment with an electron, the electron only exists as a particle at the moment of impact with the screen, meanwhile it passes simultaneously in the form of waves through the two slits, but it can nevertheless not be considered as a charge spread out continuously through space. All attempts to observe its trajectory will send it into a classical state. All this is further discussed here (in French) and in this video in English.
Deeply dissatisfied with the standard interpretation of quantum mechanics, one of its founders, Erwin Schrödinger, had described a thought experiment showing that if we take bizarre quantum behaviour seriously it should not be confined to the world of atoms but should manifest itself in our daily lives, in contradiction with what everybody actually observes. In this way he was hoping to prove the failure of the orthodox interpretation of Bohr, Born and Heisenberg, the so-called Copenhagen interpretation.
If a radioactive atom is placed in a box with a cat and the box is sealed we obtain a physical situation in which, according to quantum mechanics, a single state vector is to be associated with the system with the cat nevertheless being considered as a classical object. If a detector triggers a hammer to break a vial of cyanide when the atom disintegrates, we end up with a situation identical to the double slit experiment where the state vector is the vector sum of the two probability amplitudes, one for each physical process. In the double slit experiment, an electron or a photon passes through either a slit on the left or a slit on the right; the alternative here is dead cat / live cat.
Standard quantum mechanics FORBIDS a system from spontaneously falling into one of the two previous states without the action of an observer opening the box to determine which of the two alternatives has occurred. This is of course shocking since on a still larger scale it would mean that the Moon would have no real trajectory when there was nobody there to observe it!
The founders of orthodox quantum mechanics had already answered these paradoxes but in a way that left a lot to be desired. Today their arguments have been stated using what is called the theory of decoherence. The cat + atom system is not completely isolated and a small disturbance from the outside is enough to push the system into one of the two states before being observed by a human being.
By extension, we sometimes call a set of entangled quantum particles approaching a macroscopic object and used in place of the cat in an experiment analogous to the one proposed by Schrödinger a Schrödinger's cat. For example, we use photons that can interact with an atom in a given quantum state, which is what was done in the famous experiments of Brune, Raimond and Haroche at the Ecole Normale Superieure in 1996. The atom was in two possible states, excited or non-excited, following the emission of a photon. So we do have the case of an atom disintegrating or not, whereas the photonic Schrödinger's cat could be in two states of polarisation that did indeed correspond to the dead or living state of the cat in Schrödinger's initial experiment. This experiment and others that followed showed that the proposed decoherence mechanism was actually operating.
Do not, however, be under any illusions - there are still many mysteries in quantum mechanics. The solution to the problem of the measurement and the quantum/classical transition is still not complete!
Lecture by A. Aspect