6th March 2014
The Schrödinger's cat and its gruesome fate is one of the most discussed thought experiments in physics. Looks like the Schrödinger's cat is still inside the box and it is possibly going to die as the time axis approaches infinity. Why can't the Schrödinger's cat get out of the box the way Pixel did?
In quantum mechanics the particle in a box with infinite barrier or equivalently an infinite well, is the most basic analytical problem. The next step is the finite potential well problem. Let us consider these two cases and discuss them in perspective of the information available to the observer or the observer's capabilities. We can think of the infinite well as a problem which can not be solved and the finite potential well as a problem which can be solved given enough information. It is a known fact that a potential well no matter how shallow it is, has at least one state. Therefore an observer in a discrete measurement space will have to make at least one measurement for problem which can be solved with infinitesimal effort. We note that the entropy in this case will be zero. As the observer's capability is reduced the number of measurements go up and consequently for an unsolvable problem the number of measurements become infinite which represents an infinite well.
Therefore if we take away all the information available to the observer to make this single measurement, all of a sudden the observer is inside a box. The basic idea is that it is not that the problem which is more or less complicated, it is the observer making measurements who has less or more information to solve the problem. Less information means that we have to make more measurements to determine a result and hence higher the entropy. So if the observer is inside the box then he can not get out of the box. Or even if he did then it will be in to a bigger box.
Try to do the following. Take a rope and hold one end of the rope in one hand and the other in other hand. Now make a knot without releasing the either end or swapping your hands while tying the knot. What is the shape of the knot? It should be a prime knot. The unknot is a trivial solution.
In quantum mechanics the particle in a box with infinite barrier or equivalently an infinite well, is the most basic analytical problem. The next step is the finite potential well problem. Let us consider these two cases and discuss them in perspective of the information available to the observer or the observer's capabilities. We can think of the infinite well as a problem which can not be solved and the finite potential well as a problem which can be solved given enough information. It is a known fact that a potential well no matter how shallow it is, has at least one state. Therefore an observer in a discrete measurement space will have to make at least one measurement for problem which can be solved with infinitesimal effort. We note that the entropy in this case will be zero. As the observer's capability is reduced the number of measurements go up and consequently for an unsolvable problem the number of measurements become infinite which represents an infinite well.
Therefore if we take away all the information available to the observer to make this single measurement, all of a sudden the observer is inside a box. The basic idea is that it is not that the problem which is more or less complicated, it is the observer making measurements who has less or more information to solve the problem. Less information means that we have to make more measurements to determine a result and hence higher the entropy. So if the observer is inside the box then he can not get out of the box. Or even if he did then it will be in to a bigger box.
Try to do the following. Take a rope and hold one end of the rope in one hand and the other in other hand. Now make a knot without releasing the either end or swapping your hands while tying the knot. What is the shape of the knot? It should be a prime knot. The unknot is a trivial solution.
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Previous Blogs:
The initial state and symmetries
Incompleteness I
Discrete measurement space
The frog in well