Re: [Phys-l] EM, is it energy

[John Denker <jsd@av8n.com>]

On 11/30/2007 08:57 PM, carmelo@pacific.net.sg wrote:

> Actually, I have also come across many books explaining that  
> conservation of energy is violated in quantum physics. For example, we  
> can "borrow" energy from uncertainty principle...

I've come across many books that say Elvis is still alive,
and that cigarettes are good for you.

1) There is no way to apply the Heisenberg uncertainty principle
 to energy.  It applies to things like p and x, where the
 momentum p is canonically conjugate to the coordinate x.
 There is no variable that is canonically conjugate to E.
 This is related to the fact that the energy spectrum is
 bounded below;  it would be hard to have a Gaussian
 distributed "packet" of energy.

2) That's nonsense twice over, because even when there is
 a valid uncertainty principle, e.g. for momentum, you
 can't "borrow" momentum from the uncertainty principle.

The physics of the uncertainty principle is also deeply
related to the physics of the zero-point motion.  Now
it turns out that the zero-point motion obeys the same
equation of motion as any other motion.  Really it does.
You have to be a little bit more careful, because the
motion is smaller and you can't get away with classical
approximations that you might otherwise get away with
... but the rule in QM, as Feynman and others have
observed, is that the closer you look the more accurately
the fundamental laws are upheld.  This is really quite
remarkable, and quite unlike most other subjects, where 
the closer you look the more warts and dirt you find.