Thursday, December 4, 2008

The REAL Heisenberg Uncertainty Principle

It's not unusual to hear people make analogies to 'The Heisenberg Uncertainty Principle' when trying to make a point. For example, someone trying to describe how an anthropologist cannot 'not affect' a culture that they come into contact with might say "well, the 'Heisenberg Uncertainty Principle' says that you cannot measure something without disturbing it". While that may be true about the HUP (name shortened easier typing), the HUP is far more profound and mysterious than that !

No one 'understands' Quantum Mechanics. Not Physicists, not anyone. At the most we can understand the mathematics that predicts results the real (Quantum) world, and use the learned 'counter-intuitive' nature of the Quantum world to guide us in describing results (which is different from actually understanding Quantum Mechanics).

Now, when non-Physicists quote the HUP and say that: "one cannot measure something without disturbing it", it is usually said with (non-Quantum) Newtonian Mechanics in mind (because Newtonian Physics is something that we can understand). It does turn out that Newtonian Mechanics also says that 'one cannot measure something without disturbing it'. Any information that we get about an object will rely on the taking of a measurement and the taking of the measurement will disturb the object, e.g. if we shine a light on something in order to see it, the light that we see would have been reflected off of the object, and the act of reflection will give the object a little bump thus disturbing it.

So what is so different about the HUP then ?

Let's say that we want to measure the speed (momentum) and position of a moving object. We bounce a sensor of some kind (like light) off of it and deduce the speed and position of the moving object when the sensor comes back to us. Every time we bounce a sensor off of the moving object, we change its speed proportional to the size and speed of the moving sensor. So as we decrease the mass/speed of the sensor object that we use to measure with, we also disturb by that much less, the object that we are observing.

In Newtonian Mechanics there is no theoretical limit to how finely we hone this down to get as fine a measurement of the moving objects speed and position as we want.

In Quantum Mechanics the situation is more profound. It turns out that certain characteristics of a system are 'paired' in a special way. They are mathematically related as Fourier Transforms of each other. In particular, position and momentum are one such pair.
Because position and momentum are related by a Fourier Transform, in theory (and in practice) it is NOT PHYSICALLY POSSIBLE to know both the position and momentum of an object to an arbitrary precision. The limit of possible simultaneous precision is described by the HUP. The basis of this limit arises from the Quantum Mechanical wave nature of matter (a physical particle is both a 'solid' thing AND a wave).

One surprising result is that since the product of the uncertainties in the position and momentum measurements is a constant, it turns out that if one measured the EXACT speed of a moving particle, the HUP says that it could be ANYWHERE, you cannot know where it is. Conversely, if one measured the EXACT position of a particle, you would know where it is but it's speed could be ANYTHING, you cannot know how fast it's moving.

So the HUP is not quite the appropriate analogy to make with respect to a situation in which an anthropologist is influencing a culture that they are studying !

The 'truth' about the HUP is common knowledge to anyone who's studied physics, but I have many friends and acquaintances who have not, so this is for you because you might not hear about the truth otherwise.

I can't describe the basic mathematics of the HUP any better than it's already been done, so here's an excerpt from a standard text (kind of cropped on the right hand side):

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