Where is the potential energy?

[mjcguest]

The classic explanation I remember from school days regarding potential energy went along the lines
"If you carry a rock from the bottom of a hill to the top, that rock gains potential energy".
(Although I recall no mention made of how can you measure this energy, or whether it was the energy of the matter that the rock is composed of, or something else)

As an example..

If I have two equal sized lumps of matter & anti-matter & let them anhialate, I will release an amount of energy.
If I take those same two lumps up to the top of a mountain and let them anhialate, will I see a larger release of energy? There will be no matter left, so was the potential energy "released"?

Thanks for any clear explanation that can be offered!

 

[Zaphys]

Potential Energy, like all other kinds of it, is a non-directly-percieved mesurable magnitude, so you cannot see it, touch it, hear it... feel it. The great majority of the physics magnitudes are so. You can't see a force itself or feel a friction coeficient, for instance, in the same way you do with space or time.

Concerning your question about matter and anti-matter anhilation the answer is quite simple, sure you just missed this datail I'm going to tell you. Potential and potential energy are magnitudes which are mesured as increments, so what matters in a process is the change of the potential of the system (which has a lot to do with the level zero potential for example). In the example you exposed the system potential still the same after the anhilation so we expect no more energy from it.

Hope this helps, any corrections welcome :)

 

[Doc Al]

The classic explanation I remember from school days regarding potential energy went along the lines
"If you carry a rock from the bottom of a hill to the top, that rock gains potential energy".
(Although I recall no mention made of how can you measure this energy, or whether it was the energy of the matter that the rock is composed of, or something else)

It is a mistake to think that the rock gains potential energy. Instead, the rock-earth system gains gravitational potential energy. (Current textbooks shouldn't be making statements like the one quoted.)

 

[Dale]

If I have two equal sized lumps of matter & anti-matter & let them anhialate, I will release an amount of energy.
If I take those same two lumps up to the top of a mountain and let them anhialate, will I see a larger release of energy? There will be no matter left, so was the potential energy "released"?

As the photons from the anhilation go out to infinity they will be gravitationally redshifted some. The photons at the top of the mountain don't have as far to climb so they will redshift less. Less redshift means more energy, the difference in energy is equal to the work required to bring the lumps up the mountain.

 

[ManDay]

To my knowledge it's not known how gravitation affects antimatter.

But that's irrelevant right here. Just saying. You could as well ask where the potential energy of a traditional mass defect went.

 

[user111_23]

As a kid, I thought energy was some blob of light from objects that does stuff...Definitely wrong lol. Potential Energy is completely intangible, it only tells you how much force you can apply over some distance. It's not a physical quantity like electric current.

I think of PE as an indirect way of measuring Kinetic Energy before an object moves, which I think is more useful. Though I may be wrong.

 

[Cleonis]

It is a mistake to think that the rock gains potential energy. Instead, the rock-earth system gains gravitational potential energy. (Current textbooks shouldn't be making statements like the one quoted.)

Expanding on that:
Two lumps of matter and anti-matter will gravitationally attract each other, so if you release them to free motion they will move towards each other. The further apart from each other they start, the more kinetic energy they will gain in moving towards each other.

In that sense you can say that the potential gravitational energy of matter-antimatter pair of lumps is not lost when they annihilate each other. It's just that in order to annihilate they must touch, and by the time they touch all gravitational potential energy has been converted to kinetic energy.

Cleonis