We can’t say with certainty which eigenstate the system will fall into when an observation is made; it’s an inherently stochastic process, and the best we can do is assign a probability to different outcomes.

[iii] More recently, dogs have also been recruited for the cause. In quantum mechanics the state is specified by a wave function, which can also be thought of as a collection of numbers.

Mr. Dog–in the alternative where he starts in the yard, not in the living room–runs away to the spaceport, stows away on a rocket, and flies to Mars, completely unobserved the entire time. That’s silly. If we look again immediately thereafter, we’re going to see her under the table 100 percent of the time; the original observation (in the usual way of talking about these things) collapsed the wave function to a table-eigenstate. If we were to describe the wave mathematically, to every point on the pond we would associate an amplitude–the height by which the water was displaced–and that amplitude would sometimes be positive, sometimes be negative. [v]. Email seancarroll@nullgmail.com. The first flying dinosaurs were a failed evolutionary experiment, Dinosaur fossil with preserved genital orifice hints how they mated, Videos of over 200 science talks plus weekly crosswords available exclusively to subscribers, Exclusive access to subscriber-only events. If there were no entanglement, the outside world would still exist, but the alternatives available to Miss Kitty would be completely independent of what was going on out there. But while the process of actually calculating something within the framework of Newtonian mechanics–doing a homework problem, or getting astronauts to the moon–can be ferociously complicated, the underlying concepts are pretty straightforward. While it is a continuation of 125a and b, 125c is a somewhat stand-alone course, suitable for anyone who has mastered the basic tools of quantum mechanics (wave functions, Schrödinger equation, Hilbert space, operators, etc.). It turns out that you can write the same wave function in terms of an amplitude for every possible velocity, completely leaving position out of the description. Now let’s consider the other intermediate step, that we see her stop by the food bowl. Let’s say that we saw Miss Kitty on the sofa. In the early decades of the twentieth century, physicists trying to understand the behavior of matter on microscopic scales were gradually forced to the conclusion that the rules would have to be overturned, and replaced with something else. David Deutsch's original article on decision theory and the Born Rule. To see how this works, let’s complicate our model of feline dynamics just a bit. If we observe Miss Kitty and see that she is on the sofa, we know that she is an eigenstate (100 percent on the sofa) right after we’ve done the measurement. Real cats are messy macroscopic objects consisting of very large numbers of molecules, and their wave functions tend to be very sharply concentrated around something resembling our classical notion of a “position in space.” But at the microscopic level, all this talk of wave functions and superpositions and interference becomes brazenly demonstrable.

Still, it rubs people the wrong way.

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