To: Webster Groves who wrote (73842 ) 4/2/2001 4:16:45 PM From: Math Junkie Respond to of 99985 OT Re:"F=ma is currently a fact (a theory "proven" by experiment). " You can't prove a theory by experiment. At most you can confirm its predictions for the range of variables tested. There is no way to know with certainty whether the theory's predictions will continue to be true outside that range. As others have pointed out, F=ma is not even a fact in Newtonian mechanics unless the mass is constant. But is F=d(mv)/dt a fact? According to Richard Feynman's discussion of conservation of momentum in his Lectures on Physics , we can't even say that momentum is always equal to mv: "One of the propositions of Newton was that interactions at a distance are instantaneous. It turns out that such is not the case; in situations involving electrical forces, for instance, if an electrical charge is suddenly moved, the effects on another charge, at another place, do not appear instantaneously - there is a little delay. In those circumstances, even if the forces are equal the momentum will not check out; there will be a short time during which there will be trouble, because for a while the first charge will feel a certain reaction force, say, and will pick up some momentum, but the second charge has felt nothing and has not yet changed its momentum. It takes time for the influence to cross the intervening distance, which it does at 186,000 miles a second. In that tiny time the momentum of the particles is not conserved. Of course after the second charge has felt the effect of the first one and all is quieted down, the momentum question will check out all right, but during that small interval momentum is not conserved. We represent this by saying that during this interval there is another kind of momentum besides that of the particle, mv, and that is momentum in the electromagnetic field. " Feynman goes on to say, "Now in quantum mechanics it turns out that momentum is a different thing - it is no longer mv. It is hard to define exactly what is meant by the velocity of a particle, but momentum sill exists. In quantum mechanics the difference is that when the particles are represented as particles, the momentum is still mv, but when the particles are represented as waves, the momentum is measured by the number of waves per centimeter: the greater the number of waves, the greater the momentum. In spite of the differences, the law of conservation of momentum holds also in quantum mechanics. Even though the law f=ma is false , and all the derivations of Newton were wrong for the conservation of momentum, in quantum mechanics, nevertheless, in the end, that particular law maintains itself! " [emphasis added] So it sounds like F=dp/dt, where p is momentum, may still be current theory, but there is no guarantee that even that will always be found to be true, or a useful model, in future experiments.