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when it moves as a whole. Therefore momentum, as a mechanical quantity, is difficult to hide. Nevertheless, momentum can be hidden-in the electromagnetic field, for example. This case is another effect of relativity. 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 at one location is suddenly moved, the effects on another charge, at another place, do not appear instantane ously-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 ay, 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 tervening distance, which it does at 186,000 miles a second. In that tiny time he 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 equation 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 mo- mentum besides that of the particle, mv, and that is momentum in the electro- magnetic field. If we add the field momentum to the momentum of the particles, then momentum is conserved at any moment all the time. The fact that the electro- so, for better understanding, the original idea thgy makes that field very real,and magnetic field can possess momentum and ene at there are just the forces between particles has to be modified to the idea that a particle makes a field, and a field acts on another particle, and the field itself has such familiar properties as energy ontent and momentum, just as particles can have. To take another example: an electromagnetic field has waves, which we call light; it turns out that light also arries momentum with it, so when light impinges on an object it carries in a ertain amount of momentum per second; this is equivalent to a force, because if the illuminated object is picking up a certain amount of momentum per second, its momentum is changing and the situation is exactly the same as if there were a force on it. Light can exert pressure by bombarding an object; this pressure is very small, but with sufficiently delicate apparatus it is measurable Now in quantum mechanics it turns out that momentum is a different thing- it is no longer mu. It is hard to define exactly what is meant by the velocity of a particle, but momentum still exists. In quantum mechanics the difference is that when the particles are represented as particles, the momentum is still mu, but when the particles are represented as waves, the momentum is measured by the number of waves per centimeter: the greater this number of waves, the greater the momen tum. 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 deriva tions of Newton were wrong for the conservation of momentum, in quantum mechanics, nevertheless, in the end that particular law maintains itself
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