Certainty and uncertainty

A lot of the Uncertainty in quantum mechanics is suspiciously certain. For example, we know an electron will always have its spin up or down, in any direction along which we choose to measure it, and the value of the angular momentum will, accordingly, be measured as plus or minus ħ/2. That doesn’t sound uncertain to me. In fact, it sounds remarkably certain, doesn’t it? We know – we are sure, in fact, because of countless experiments – that the electron will be in either of those two states, and we also know that these two states are separated by ħ, Planck’s quantum of action, exactly.

Of course, the corollary of this is that the idea of the direction of the angular momentum is a rather fuzzy concept. As Feynman convincingly demonstrates, it is ‘never completely along any direction’. Why? Well… Perhaps it can be explained by the idea of precession?

In fact, the idea of precession might also explain the weird 720° degree symmetry of the wavefunction.

Hmm… Now that is an idea to look into ! 🙂


4 thoughts on “Certainty and uncertainty

  1. It can be explained by the idea of rotation on two axes, as per this image: (Google on toroidal electron). Take a look at what Feynman said in lecture 27: field energy and momentum: “Suppose we take the example of a point charge sitting near the center of a bar magnet, as shown in Fig. 27–6. Everything is at rest, so the energy is not changing with time. Also, E and B are quite static. But the Poynting vector says that there is a flow of energy, because there is an E × B that is not zero. If you look at the energy flow, you find that it just circulates around and around. There isn’t any change in the energy anywhere – everything which flows into one volume flows out again. It is like incompressible water flowing around. So there is a circulation of energy in this so-called static condition. How absurd it gets!”

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