051 A Quantum Story: Probable Problems in Probability

I’ve been getting quite upset about Schrodinger’s Cat lately. Yes, that stupid cat in the box, the problem goes something like this…

One day, the famous Austrian quantum physicist, Erwin Schrodinger, was particularly bored. He was in his home, smoking a pipe and thinking about what he and his dear friends, Heisenberg and Born, had just come up with, a probabilistic interpretation of the atom (but this is not important to us), when another one of his comrades Albert turned up, together with Max. They were quite upset with Schrodinger and what he’s done with the atom. Albert threw a pair of dice at him and said Erwin should never had let God played with it, while Max just sat there and sulked about how he started this whole mess. Erwin was irked at how the pair was treating his idea, and blew up in a fit of anger. He grabbed his net and went out to catch the first living thing he saw to explain the idea. Unfortunately, the first animal he saw was a cat. He caught it (after having to use some projectile motion to get the cat down from a tree), and locked it up in the box. Then, he went to the pantry to get some radium and arsenic that another friend of his, Curie, had given him for Christmas last year, (he finally found use for those silly things Curie was obsessed with). Using his ingenuity with a spark of madness, he designed a contraption that might kill the captured cat (although at this point, animal rights activists protested violently, but Erwin just tossed his book, “What is Life?” at them, which got them interested for the next few hours). The contraption was designed to kill the cat with a probabilistic contraption. Curie’s radium has a half-life of 1 hour, which means that any given radium atom has a 50% chance of decaying in the next hour to lighter elements. Erwin manages to isolate one particular atom from the bunch and attaches it to a switch, which will be triggered when that atom decays. When the switch is triggered, the cat will be exposed to the arsenic, which will kill the cat. After setting up the apparatus, Erwin asked the pair whether the cat would be dead or alive after an hour. So they discussed and after an hour, Erwin asked the pair for their answer…

Albert: I think the cat has an equal chance of being dead or alive, if only we could open the box and observe the cat
Erwin: But then, the sense of mystery, or as my friend Heisenberg would say, the uncertainty is lost.
Max: Then, what difference would it make if the box were open or closed?
Erwin: Have you seen an electron in an atom?
Albert: Err… No, but we know of its existence from the presence of the negative charge in the atom. Right?
Max: Right, but none of us has actually seen an electron, haven’t we?
Erwin: Excellent, you’re getting the point. Have you seen the cat? Isn’t the cat as uncertain as the electron?
Albert: We have seen a cat before. In fact, we know that the there is a cat in the box, and we also know that it’s there, and we would certainly find the cat in the box when we open it. The only thing is that we are not sure whether is alive and meowing or otherwise…
Max: …whereas in the case of the electron, we don’t even know it’s in the atom or not, because we have never seen it, unlike the cat.
Erwin: Max, Max, Max, you’re not getting the point. Tell me for certain, what is the state of the cat after exactly one hour? Dead or alive?
Max: Well… I can’t say for certain, all I can be certain about is the probability that it is dead or alive which is ½ for both cases.
Erwin: Good, Albert, now tell me, what about the case of the electron?
Albert: Hmm… we know that there is an electron in an atom, but since we cannot see it, we cannot be sure where it is. Wait, that means there is only a probability that it is there, right? Just like the cat in the box… we can only be certain of the probability and not the exact location of the electron.
Erwin: Wonderful, so we say that the cat and the electron are both in a superposition of states, between dead or alive in the first case, and being in one place or another in the latter’s case. Get it?
Max: So, we can only be certain of its probability, right? That is all we can determine with absolute certainty.
Albert: This is outrageous; this means that we cannot calculate where the electron is at any one point of time.
Erwin: Well, technically we can, but only the probability that it is there…
Albert: This doesn’t make sense, I could calculate the exact position, speed, momentum etc…of the book you threw at the activists earlier, given I knew when and where you threw and the initial angle and velocity. But you’re telling me you can’t do the same for an electron even though you knew all its physical states at one point of time.
Erwin: I know it’s hard to accept, but yes it’s true. You cannot tell where the electron is with absolute certainty without using devices to measure it.
Max: Here’s another problem, as Albert suggested earlier, what happens if you open the box, or try to find out where the electron is using measuring devices?
Erwin: Ah, we’ll keep that story for another day, shall we?