If energy is a scalar quantity, how can it be negative? We are studying electrical potential energy in my high school class. I was originally taught that energy is a scalar identity, but the electrical field equation says that there can be negative potential energy in electrons - how is this possible?
I am thinking of energy in terms of money that can be spent on doing certain actions. if electrical potential energy is the energy needed to place a particle at a certain position against the forces acting on it, I do not understand what negative potential energy would mean.
If an electron and a proton are placed near each other, shouldn't it take the same amount of energy to bring them let's say 2mm closer regardless of charge? Does the negative sign denote something other than energy?
Edit: Some clarification in the second paragraph
 A: A short answer is, in any physical process or equation, Energy as an absolute number has no meaning. It is the energy difference between two states or two objects that determines behavior.
For your electrons and protons, the important fact is that the electron has lower potential energy when close to the proton than it does far away from the proton. You can call this difference
$$E_1-E_0=13.6\; \rm{eV}$$
You can assign numbers to the two states like $E_1= 13.6\; \rm{eV}$, $E_0= 0$...or $E_1= 100 \; \rm{eV}$, $E_0= 86.4\; \rm{eV}$... or $E_1= 0\; \rm{eV}$, $E_0= -13.6\; \rm{eV}$.  These are all equivalent, and the value of $E_1-E_0$ (which is all that is measureable in nature) remains the same.
Here is a video that will probably help you.
A: It does not have to do anything with positive and negative they both have different meanings but they are Energies. Let me take an example in which we have to deal with negative energy as novices get confused what does that actually mean.
Take an example of Gravitational force and electrostatic attractive force. In both the cases the participating bodies have energy with a negative sign which means they are bounded to each other, or in other simple words if we focus on an atom (a similar case) and specifically on an electron we can say that the electron is in 'debt' with certain amount of energy taken from the nucleus that means an external agent has to give some amount of what we call positive energy to free that electron from debt. Now let's come to the actual meaning of energy with a negative sign rather than focusing on analogy.
It actually means that if something has a negative amount of energy (in many cases you will find this energy with negative sign behaving as the potential energy of something) it is bounded to something with an attractive force, but it still has an ability to do work so hence we can still call it as energy as the normal definition of energy perfectly holds here.
A: Negative sign has nothing to do with a quantity being scalar or vector.
Electrons have a negative charge while protons have a positive charge and charge, as you might know, is not a vector quantity, instead it is scalar.
Negative sign in energy means the force operating within the system is attractive in nature.
Energy is a "relative" concept, if I may be not too pedantic. When you have just had your meal, you are high on energy.
When you are starving, you are low on energy, or you can say that you have negative energy in comparison to when you had your meal.
I hope this helps.
