# Conservation of Energy False?

1. Oct 25, 2005

### '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?

2. Oct 25, 2005

### Tom Mattson

Staff Emeritus
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 $\frac{dE}{dt}=0$.

3. Oct 25, 2005

### '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?

4. Oct 25, 2005

### Tom Mattson

Staff Emeritus
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.

5. Oct 25, 2005

### 'AQF

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

6. Oct 25, 2005

### Tom Mattson

Staff Emeritus
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.

7. Oct 25, 2005

### 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.

8. Oct 25, 2005

### 'AQF

9. Oct 26, 2005

### 'AQF

10. Oct 26, 2005

### 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.

Last edited: Oct 26, 2005
11. Oct 26, 2005

### Tom Mattson

Staff Emeritus