Exploring the Analogy of Negative Energy in Physics: The Jack-in-the-Box Example

[droog]

I seem to recall reading an analogy describing the total mass/energy of a jack-in-the-box. This said that a compressed spring insided a box would "weigh" more than the same when relaxed (albeit immeasurable small). This makes sense given the equivalence of energy and mass. But what if the spring is stretched out (and held out inside the box). Does the box now "weigh" more again due to the energy stored in the streched spring or is the sign preserved making the whole deal "lighter". I'm sure this analogy was given by a respectable physicist when describing negative energy due to gravitational potential - I just can't recall where.

 

[Doc Al]

The elastic PE stored in a spring is given by [itex]1/2 k x^2[/itex], where x is the displacement from its unstretched position. Whether compressed or stretched, the stored energy is always positive.

 

[droog]

The elastic PE stored in a spring is given by [itex]1/2 k x^2[/itex], where x is the displacement from its unstretched position. Whether compressed or stretched, the stored energy is always positive.

OK thanks. So what was the purpose of the example I wonder? I'm sure it was given to show more than just the equivalence of mass and energy. The proposition related to the cancellation of mass/energy within the totality of the universe on account of the "negative energy" contributed by the gravitational attraction of all the mass/energy.