 One of the first and in many ways the standard point of view is the so-called Copenhagen interpretation, a term coined by Werner Heisenberg who worked with Niels Bohr in the latter's Copenhagen laboratory in the 1920s. This was largely developed by Bohr Heisenberg and Wolfgang Pauley by around 1927. In the spirit of shut-up and calculate, quantum mechanics is usually presented in the form of postulates containing interpretation only to the extent needed to make experimental predictions. Here are simple versions of some of the main postulates. The wave function postulate says that everything we can know about a system is described by its wave function. The operator postulate says that every measurable physical quantity, say M, is described by an operator M hat, an example being the operator describing a vertical polarization filter. We need the following definitions. The so-called eigenvalues M sub n and eigenstates U sub n of the operator M hat satisfy M hat applied to the state U sub n produces M sub n times the same state. The stationary states and energies of the hydrogen atom are examples we've encountered of eigenstates and eigenvalues. The eigenstates of a vertical polarization filter are vertical polarization with eigenvalue 1 and horizontal polarization with eigenvalue 0. An important math fact is that the eigenvalues are real numbers and the eigenstates are orthonormal, meaning that the projection of one state on another is 0 and the projection of a state on itself is 1. Another important math fact is that any quantum state, any wave function, can be represented as a superposition of the eigenstates of an operator. The amplitudes of those eigenstates are simply the projection of the wave function onto the corresponding eigenstate. The measurement postulate says that the only possible results of measuring the physical quantity M are the eigenvalues of the operator M hat. Moreover, the probability of obtaining the eigenvalue M sub n is the squared magnitude of the projection of the wave function onto the corresponding eigenstate U sub n. What we might call the wave function collapse postulate says that if we measure the value M sub n, then the wave function collapses to the corresponding eigenstate U sub n. If before the measurement the wave function is a superposition of the eigenstates, then after the measurement the wave function is reduced to one specific eigenstate, the one corresponding to the measured eigenvalue. Now this is a very strange picture. As we've mentioned, wave function collapse is not described by Schrodinger's equation and there's no detailed description of what goes on during the measurement. If we measure the system to be an eigenstate U sub 2, say, then somehow the probability amplitude of state U sub 1 becomes 0, the amplitude of U sub 2 becomes 1, the amplitude of U sub 3 becomes 0, and so on, leaving us just with the eigenstate U sub 2. The so-called measurement problem of quantum mechanics is concerned with the question when, where, how, and why does the wave function collapse. It worked people up in the 1920s and continues to do so now, almost a hundred years later. In spite of the spectacular practical success of quantum mechanics, it should therefore not be surprising that people have often questioned and pushed back against quantum weirdness. In particular, 1935 was a big year for this. First a paper appeared by Einstein, Podolski, and Rosen titled, Can Quantum Mechanical Description of Physical Reality Be Considered Complete? Largely motivated by that paper, Schrodinger wrote a paper titled, The Present Situation in Quantum Mechanics. The Einstein-Podolski and Rosen paper presented the so-called EPR paradox, which largely took issue with the wave function postulate. The Schrodinger paper presented the Schrodinger's cat paradox, which largely took issue with the idea of quantum superpositions and the measurement and collapse postulates. We'll consider the EPR paradox in a future video. Here we want to investigate the Schrodinger's cat paradox. Towards this end, consider a single molecule, say a water molecule. Is this described by a quantum mechanical wave function? Sure. How about a system of two molecules? Yeah. Three molecules? Why not? How about a bunch of molecules? Um, yeah, I guess so. Okay, how about enough molecules to form a macroscopic chunk of ice? Well, gee, I don't know about that. Well, why not? It's just a bunch of nuclei and electrons, and those are described by quantum mechanics, right? So shouldn't the entire collection be described by one big wave function? If you deny this, then can you explain how the quantum mechanical wave function concept stops working once we get to a certain number of molecules? If you accept this, then seemingly you have to accept that this system can exist in a quantum superposition of macroscopic states. If one state of the molecules is a chunk of ice, isn't another state a puddle of water? So shouldn't it be possible for the molecules to exist as a superposition of a chunk of ice and a puddle of water? Hmm, that is kind of weird. The cylinder's three-part paper is quite long, but a single paragraph made it famous. This reads... One can even set up quite ridiculous cases. A cat is panned up in a steel chamber, along with the following device. In a Geiger counter, there is a tiny bit of radioactive substance. So small that perhaps in the course of the hour, one of the atoms decays. But also, with equal probability, perhaps none. If it happens, the counter tube discharges, and through a relay releases a hammer which shatters a small flask of hydrocyanic acid. If one has left the entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The wave function of the entire system would express this by having in it the living and dead cat, pardon the expression, mixed or smeared out in equal parts. Presumably, as soon as someone looked into the chamber, that is, made a measurement of the cat's state, they would find the cat either alive or dead. Now a cat that is both alive and dead, until someone looks at it, and then is either alive or dead, is completely absurd. But as Schrodinger pointed out, we don't seem to be bothered by the same scenario when the cat is replaced by an atomic nucleus or a photon. Niels Bohr, the leading champion of the Copenhagen interpretation, denied there was a paradox. In his view, the interaction of a macroscopic measurement system with a microscopic quantum system involves an irreversible amplification that destroys any quantum superposition. Specifically, he claimed, As all measurements thus concern bodies sufficiently heavy to permit the quantum to be neglected in their description, there is, strictly speaking, no new observational problem in atomic physics. The amplification of atomic effects only emphasizes the irreversibility characteristic of the very concept of observation. In this view, the wave function would have collapsed by the time the Geiger counter registered the radioactive decay, and long before the cat was poisoned. There would never be a superposition of alive and dead cat. In the Copenhagen interpretation, there is a clear distinction between the microscopic quantum world and the macroscopic classical world. But the boundary is never clearly identified. Schrödinger's cat paradox raises the question, where is the boundary between the quantum and classical worlds, or is it possible that there is no boundary at all?