måndag 12 maj 2014

Why Feynman Said: Nobody Understands Quantum Mechanics

We have always had a great deal of difficulty understanding the world view that quantum mechanics represents. At least I do, because I'm an old enough man that I haven't got to the point that this stuff is obvious to me. Okay, I still get nervous with it.... I cannot define the real problem, therefore I suspect there's no real problem, but I'm not sure there's no real problem.

The (trivial) commutator relation  
  • $px - xp = ih$, 
where $x$ is the position (operator) and $p=\frac{h}{i}\frac{\partial}{\partial x}$ is the momentum (operator), is supposed to play a fundamental role in quantum mechanics,  in particular as the origin of Heisenberg's Uncertainty Principle:
  • $\sigma_x\sigma_p\ge \frac{h}{2}$,
where $\sigma_x$ is the standard deviation in measurements of position $x$, and $\sigma_p$ that of momentum. 

We see that both the commutator relation and Heisenberg's Uncertainty Principle concern the product of position and momentum. But such a product lacks physical meaning. Momentum $p$ has physical meaning and so has position $x$, but their product has no physical meaning.  

Momentum multiplied by velocity has a physical meaning as kinetic energy, but momentum multiplied by position does not. Force multiplied by velocity has a meaning as work.

Quantum mechanics is however obsessed with the product of momentum and position, with the message that because of the commutator relation they cannot both be determined at the same time and spot. The message is that this makes quantum mechanics fundamentally different from classical mechanics where supposedly momentum and position can both be determined.

There are two approaches to physics:
  1. Make it as simple and understandable as possible. 
  2. Make it as complicated and mysterioud as possible.     
Quantum mechanics has developed according to 2 as evidenced by Richard Feynman:
  • I think I can safely say that nobody understands quantum mechanics.
One reason is that the product of momentum and position is given an fundamental role in contradiction to the fact that it has no physical meaning. 

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