Negative Energy?

[cold.wit]

In nuclear fusion when four protons come together to form two protons and two neutrons making a helium nucleus. The mass is less than the original 4 proton atoms. This is explained by the helium nucleus having the same amount of 'negative energy' equivalent to the mass difference. Now, what is this 'negative energy' precisely...the PE or something else?

[Mr Skeptic]

The zero point of potential energy can pretty much be defined anywhere you like, and it is the energy difference that you can actually measure. However you define your potential, there is less potential energy in two protons and two neutrons than in one helium nucleus -- hence energy gets released fusing them together.

[swansont]

It's related to what we call the binding energy — the energy released when forming a nucleus, meaning it's the energy you'd have to add to break it apart. The mass difference due to this is called the mass defect. As Mr Skeptic has stated, your starting point is arbitrary, since you are interested in differences between two states, so a negative value has no deeper significance.

[Mr Skeptic]

Of course, in practice it is very convenient to define the zero point as when the particles are infinitely far away, because that is something easy to do. Whereas if you try to define the zero point as the closest the particles can get, while it would give a more intuitive answer, is really really difficult to do in practice. For example, with point-like electric particles, the closer you get them the higher the force, and it goes up to infinity which doesn't make sense, and would give you infinite energy at any non-zero distance. Whereas if instead you go for the infinitely far route, the force decreases toward zero.

 

Defining the zero point at infinitely far apart does give the unintuitive aspect of zero being the maximum potential energy and stuff having negative potential energy, although that is easily enough considered as the amount of energy binding the system together.

[cold.wit]

So, it's about the work done on the two protons to bring them together. That would be their positive potential energy. And the negative energy is equal to the work done to break them apart. But what if there are two opposite charges, and in bring them together there is no work done. What will be the negative energy then?

[Mr Skeptic]

Right, if you do that you get positive potential energy (with the zero point at infinity), but that also means that your system will break apart if you let it.

[swansont]

In the case of an attractive force (e.g. opposite charges, or with nucleons), energy can be released when the particles come together. This is often in the form of photons (called gammas in the case of nuclear interactions). So an electron can become bound to a proton, emitting photons as it does so.