Archive for October 28th, 2008

Suppose you have some physical process you are want to describe, for example a simple situation where a few particles move around, possibly scatter from each other. Each particle has a few numbers that specify its particular state at a given time. It can have position (specified by 3 numbers), velocity (3 other numbers), electric charge, mass, energy etc. Once you specify those numbers you know precisely what particle you are discussing and what it is doing. If you have a complicated situation, with many particles moving around, you end up having to specify lots of numbers to completely describe the situation.

Let’s look at the inverse problem, suppose you are given a series of such measurements, can you reconstruct the corresponding situation? the trick is that those numbers don’t come labeled, no higher authority gives them names like charge or position, interpretation is completely up to you (as is always the case!). This is not that easy actually, and as we’ll see the results are sometimes ambiguous, so I’ll be generous and let you perform as many thought experiments as you want, even infinitely many. Why not? we are talking about theorist’s favorite experiments, the ones that cost no money.


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