Are we quantum mechanical or not?This paper basically proves that the famous Schrodinger's cat experiment, which says the cat is a quantum mechanical wave function is correct. The cat is actually in an entangled state which means the cat is alive and dead at the same time. That's pretty weird! But we an make it even weirder! Imagine, if you will,  that you are taking the place of Schrodinger's cat. We don't want to kill you so we'll modify the experiment in line with Deutsch's proposal and Wigner's interpretation.  The experiment performed above is exactly Deutsch's proposal and the result is that yes, you as the observer are in a superposition of quantum states.
What is you in that previous statement? You only ever remember one set of events. You never have any memory of being in two quantum states. It appears that consciousness can only be associated with one quantum state at a time. However it also appears that your consciousness is associated with every quantum state, viz., your consciousness splits into two versions, one associated with each quantum state. What happens to the various yous? There are two basic interpretations that are famous in quantum mechanics: the copenhagen interpretation and the multi-universe theory.
The Copenhagen interpretation says that when a measurement is made the entangled quantum state collapses. In other words, one of the quantum states disappears and the quantum system 'collapses' to the other state. Any measurement you make now will show the quantum system is in the second state. the other state is gone. If you don't make the measurement the entangled state continues to evolve and you can prove that it is still there by, for instance, making another measurement later.  There has never been any indication that this interpretation is 'wrong' in the eyes of the experimenter who makes the measurement. In any experimenter's view of the universe, this is exactly what happens.
Yes and No. We are not quantum mechanical in our own eyes, but we are in the eyes of others.However, if you are taking the place of Schrodinger's cat, then to me, an observer outside the box, you are in a quantum mechanical superposition of two different quantum states. We can actually prove this. In my eyes you are in a quantum mechanical superposition. In your eyes you are not. So what the heck is going on?
If I understand it correctly, it says that the universe looks different depending on who's looking at it. Now that's really weird, but not quite as weird as you might think. Relativity destroyed the idea that everything looks the same. Depending on how fast you are moving, the order of things happening that you observe compared to someone else can change. Events that are causal won't change, but the order of events that are not causally linked don't necessarily stay in the same order. Whew! That means that causality is not violated. Thank God and Einstein for that.
So the fundamental assumptions that are made in science are the following: locality and free choice. Locality means that two quantum mechanical wave functions can only influence each other when they are in the same place. There is no action at a distance.  Free choice is that assumption that humans have free will. They can decide whether or not to make a measurement and the universe can't know ahead of time what that decision will be.  Or we aren't really running an experiment and it's all predetermined ahead of time.
The paper above is interesting in a couple of ways. First, it carefully defines a measurement as something done by an observer. A measurement means that an observer "extract[s] information from another system by means of some interactions, and store[s] that information in a physical memory." So even if the measurement is made, if it is not communicated to the outside world the quantum states stay in superpositions as far as the outside observer is concerned. Communicate the measurement value (not that a measurement has been made, but what measurement is made) and the superposition is broken. This seems to break the Copenhagen's interpretation of quantum mechanics... The wave function didn't collapse when the measurement is made. The wave function appeared to collapse for the observer in the box, they could predict future measurements that were dependent on the value of the measurement that occurred; but the wave function did not collapse for the observer outside the box. Their measurements were consistent with not having the wave functions collapse in the box. So who is right?
Everybody is right. The person in the box definitely made a measurement. The person outside does not know the results of that measurement, so they don't see the 'collapse'. Either the wave function somehow knows who/what is making a measurement on it when or... The many world's interpretation is correct. We are all quantum states, but consciousness splits and travels down only one path at a time. And you can never get back to the other path.
*Sigh* Yes, Quantum Mechanics is very weird.
Thanks for reading,
 Yes, this is from the Twilight Zone, and it's not a mistake or a pun, it's a possible plot that happens in the real world that is so frigging weird, it must be just from a television show. That it's what scientists think happens in REAL LIFE is the scary part.
 D. Deutsch, Quantum theory as a universal physical theory, Int. J. Th. Phys. 24, I (1985).
E. P. Wigner, Remarks on the mind-body question, in: I. J. Good, “The Scientist Speculates” (London, Heinemann, 1961) and heavily using "On the quantum measurement problem", Caslav Brukner.
 This 'collapse' takes place instantaneously across the universe for all objects entangled together. This would seem to violate Einsteins laws of relativity that say no information can be transmitted faster than the speed of light. It turns out that it doesn't, if you assume the no-cloning-without destroying postulate, which, as far as we can tell is the way the universe works. The no-cloning postulate was proposed as a way to fix this paradox in 1982. It turns out that is was actually proved earlier in 1970 to show that any quantum measurement disturbs the quantum system.
 Side bar on gravity. Newton's theory of gravity assumes that the gravitational forces felt by two bodies was instantaneous and independent of distance: spooky action at a distance as Newton put it. He knew something was wrong with this theory. It turns out he was right, it's just a very good approximation to assume that the force is instantaneously transmitted between the two bodies. Einstein fixed this with his General Theory of Relativity. The forces (actually the warping of the field of space) travel at the speed of light. In most situations, it turns out that this looks like spooky action at a distance. Only in certain extreme conditions (like the orbit of Mercury, which is deep inside the grvity well of the sun) can you actually notice the difference between the two theories. And as Newton suspected, Einstein is correct and his theory is just an approximation of what we can measure. A very good approximation. So far as we can tell, Einstein's theory is exact. Although there are some 'paradoxes' when we try to reconcile it with Quantum Mechanics that hint it might not be complete and that there might be another "Theory of Everything" that would reduce to Einstein's theory in most cases, but explain away these paradoxes in the extreme cases.
 All those philosophers (and physicists) who claim free will doesn't exist need to reconcile their views with this postulate of science. The postulate of free choice says that there does not exist a deterministic universe. It says that the experimenter can choose which measurement to make and nothing that has gone on before can determine which choice the experimenter will make. Of course, if everything is determined ahead of time... then we are just in a simulation and our free will is an illusion. However, free will is an open postulate, you can assume we have it or not. Science works both ways. In one case, the measurements we make are predetermined, in the other case the measurement results are random. In the latter case we have free will. In the former case we don't. In the latter case some predetermined 'hidden variables' are causing the measurements to look random. The philosophy of Occam's razor leads me to believe in the former: Human's have free will and measurements can be made via free choice and their results are randomly distributed. Of course, if you think everything is predetermined and we are living in a simulation, why would this simulation be running? What is being simulated? It could only be different initial conditions. And why would anyone want to simulate that? Or we aren't in a simulation and everything is predetermined. There is absolutely no fun in that. No fun at all. I reject that position on the postulate that humans can have fun.