Does the Energy Uncertainty Principle Contradict Conservation of Energy?

['AQF]

How can the principle of conservation of energy be reconciled with the Energy Uncertainty Principal, by which a particle always has energy, even if not excited?

 

[quantumdude]

Simple: The law of conservation of energy does not forbid a particle having energy without being excited. It forbids a particle's energy from changing without being excited (or de-excited, as the case may be).
The law of conservation of energy doesn't say that $E=0$. It says that $\frac{dE}{dt}=0$.

 

['AQF]

Still, if you place a particle with 0 energy in a box, and without giving it any energy, the Uncertainty Principal states that there will be some energy anyway. So how does Conservation of Energy hold in this case?

 

[quantumdude]

Are you referring to the infinite well problem? If that is the case then it makes no sense to consider the particle before it was placed in the box. That is because an infinite amount of work would have to be done to get the particle from the outside to the inside.

When you deal with the particle in the box problem, you tacitly assume that the particle was never outside the box.

 

['AQF]

If the particle was never outside the box, then how did it get its energy to begin with?

 

[quantumdude]

You simply assume that the energy always existed. That still doesn't violate conservation of energy, which only speaks of the rate of change of energy with respect to time.

 

[Physics Monkey]

AQF, part of the your problem is that you can't "put the particle into the box with zero energy." If a free particle had zero energy, you would have perfect knowledge of its momentum, which implies complete ignorance about its position. Since you don't know where it is, you can't put it in a box.

 

['AQF]

Thanks for your help.

 

['AQF]

By your answers, is the information in http://www.physlink.com/Education/AskExperts/ae605.cfm
incorrect?

 

[Physics Monkey]

Technically, yes, the article is incorrect. Energy is always conserved. Got to go right now, I'll try to expand on this later.

Edit: There is a thread on this very point in the Quantum Physics section.

 

[quantumdude]

[QUOTE='AQF]By your answers, is the information in http://www.physlink.com/Education/AskExperts/ae605.cfm
incorrect?[/QUOTE]

That article has nothing to do with the particle in a box, which I assume you are treating with quantum mechanics. The article on the other hand pertains to interactions that are mediated by gauge bosons, which are described by quantum field theory. This issue of virtual particles does not arise when external fields are represented by potentials.