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I know energy comes in a number of forms and every form of energy is defined uniquely.

But if I had to give a broad definition of energy, I would define it as "ability of a system to perform work."

Using the above definition doesn't make any sense while trying to explain negative energy. So what does negative energy mean?

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  • $\begingroup$ are you asking about classical negative energy, such as negative potential energy, or about something more exotic resulting, for instance, from negative mass or other kinds of exotic matter? $\endgroup$ – user83548 Sep 5 '15 at 0:32
  • $\begingroup$ There is only one definition of energy and you got it. It's the ability to perform work. $\endgroup$ – CuriousOne Sep 5 '15 at 3:00
  • $\begingroup$ @bruce I am asking about the negetive magnitude of energy as in potential energy. $\endgroup$ – the_random_guy42 Sep 5 '15 at 7:17
  • $\begingroup$ 'Energy is the ability to do work' implies that work is a more primitive idea that has already been defined. Unless you say that energy is work, in which case it's tautology. I think I'd rather have 'energy' as the primitive and define work as something that energy does. $\endgroup$ – rdt2 Sep 5 '15 at 9:32
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If positive work is "work done by the system" then negative work is just "work done on the system". The sign just tells if energy is added to the system or leaving the system.

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An nice example complementing Steeven's answer is the energy levels of the hydrogen atom.

The energy of a hydrogen atom is given by $E_n=-\frac{13.6eV}{n^2}$, where $n=1,2,3...$ (the Principal Quantum Number $n$).

The ground state (lowest possible energy) is $E_1=-13.6 eV$ (for $n=1$). A higher state of energy would be (for example) $E_3=-1.5eV$ (for $n=3$).

To 'kick' the atom from $n=1$ to $n=3$ the following amount of energy is required:

$\Delta E=E_3-E_1$, or $\Delta E=-1.5eV-(-13.6eV)=+12.1eV$.

So the difference between two negative energies is positive here: we need to put in energy to go from $n=1$ to $n=3$.

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