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**i**,

**j**and

**k**notation and use instead positive and negative signs to denote direction. A scalar value to me is an absolute value. It should have no sign whatsoever. No one can ever have a "negative" speed because that would imply a direction. So why is it that scalar properties like work and potential energy can have negative and positive signs? The concept "negative work" implies to me that work is done in the direction opposite motion (if motion is in the positive direction). Friction does negative work. Since work is associated with a force, and force is a vector quantity, it would almost make sense to me to assign a direction to work. Clearly, "3J" of work is distinct from "-3J" of work - both have different consequences on the motion of the body of interest. If we redefine the axes so that motion is along the negative axis and the force is directed positively, then we still have a negative value for work.

If an object has -3J of gravitational potential energy, this means the object has lost 3J of energy due to its movement in the gravitational field. The problem seems similar to the one with work. Change in PE is associated with a change in position, and position is a vector. This merely denotes that the object's PE is three units to the left of some arbitrary origin. This idea doesn't really denote a direction for the energy (eg. 3J @ NE! - which wouldn't make sense) but it does give the direction of energy transfer (from greater to lesser values of potential energy). So my question is this: how can the negative (or positive) sign be interpreted as giving the direction of a vector quantity sometimes, but not always?