Negative joules can exist in the context of negative work or energy, where work done against a force, such as braking a car, is considered negative. Gravitational potential energy can also be negative when measured from a reference point, like the top of a hill. The concept of negative energy is relative, depending on the chosen reference state, similar to temperature scales that can have negative values. However, mass is always positive, and while theoretical discussions may explore negative flux in certain equations, such scenarios do not hold physical meaning. The discussion emphasizes that negative energy and work are valid concepts within specific contexts.