## Negative Mass

Mass is related to weight. But, an object still has all of its mass, even in the weightlessness of outer space or in freefall. A bowling ball would still hit the pins, just as hard, in outer space as it does at the local bowling alley.

Is it possible for an object to have a negative mass? How would we recognize such an object? People think that such an object would fall upward. So, things with negative mass might be floating around out in space, negative rocks and negative dust.

But, let me show you that a negative mass would fall downward:

F=-Gm1m2/d2

This is Newton's Law of Gravity. G is a constant. The negative sign is there to show that the force (F) is usually downward. m1 and m2 are the two masses in question, usually the mass of the earth and the mass of some object which is attracted to it (actually they are attracted to each other). And d is the distance between the centers of these two objects. We see that in the case of one of these masses being negative, the negative signs cancel, and the force on this object (F) is positive (upward).

F=ma

This is Newton's Second Law of Motion. It shows the relationship between force (F), mass (m), and acceleration (a). It can be taken to be the definition of mass. We want to restate it as a=F/m, to solve for acceleration. Normally, we have a negative force (downward), and a positive mass, producing a negative acceleration (downward). In the case we are studying (negative mass), we have a positive force (upward), and a negative mass, which produce a negative acceleration (downward). A negative mass falls downward.

We can actually confirm this deduction, by conducting Einstein's elevator thought experiment. Einstein showed that light would be bent by gravity, by arguing that gravity and constant acceleration were equivalent. In an elevator, which accelerates constantly upward in zero gravity, a light beam would curve downward, just like any flying object. This curving of light has been verified by experiment. Well, a negative mass, in the same circumstances, would fall downward, as the elevator accelerates upward.

I guess there's a small problem with weight. The force due to gravity is upward, in the argument above. So, the negative object seems to have a negative weight. Weight is the force due to gravity, after all. But, any way that you measure that weight, spring scale or balance scale, would seem to measure a positive weight. Actually, the balance scale measures mass, but the spring scale measures weight. Apparently, a spring scale only measures the absolute value of the weight.