Force in Modern Physics

We are all pretty sure we know what force is. Gravity, for instance, is a force and gravity needs no further explanation. Newon was the first scientist to state the law of gravity in mathematical terms and for many years we thought that this was the final answer to what the law of gravity really is. Then cam Einstein, who found that Newton's law was only a good first approximation. Einstein's relativity concepts gave us a more accurate computation, which has been proved many times to give the correct answers for orbital and space trajectories.

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By this time, therefore, we should feel reasonably certain that at least we know the answer to how gravity affects massive bodies, so that we can predict any result. Soon after wards, it was noticed that their velocities deviated from those predicted by Einstein. It seemed as though an unknown force, emanating from the sun, slowed them down. To add to the mystery, another anomaly was discovered with several spacecraft when they were sent round the earth in what is called a slingshot maneuver, to pick up speed before going on to various space missions. This time, they picked up more speed than they should have, only four millimeters per second, but easily measured. Of course, in both cases, all sorts of precautions were taken to eliminate errors due to faulty instruments, inaccurate measurements or any other extraneous factors that would have allowed existing theories to remain intact. It seems that we might need another bored young patent clerk doodling on a piece of paper, another Einstein to astound us by finally explaining a very enduring mystery.
And this would just be the mathematics that predicts motions of bodies under the influence of gravity. It would not explain what a force such as gravity actually is, or how it is transmitted. When we see a body falling to the ground under the influence of gravity, what we see is the body, not the force. We can turn for enlightenment to his first law, as given in the Principia Mathematica: "Every body continues in its state of rest or of uniform motion in a right line, unless it is compelled to change that state by a force impressed on it." In order to find out what Newton meant by "impressed force" , his Definitions must be consulted. Definition IV states: "An impressed force is an action exerted on a body in order to change its state, either of rest or of uniform motion in a straight line." Here, the definition is saying exactly the same thing (only the other way round) as the law itself. But the law should have been the result of repeated observations, confirmed and proved by experiments, as laid down by Galileo, not a restatement of the definition. It is clear that the difficulty lies with the definition, not the law. It tries to define what a force is by describing its effect on a body.
Before Newton, many thinkers had tried to define what gravity actually was, from magnetism to circular inertia to Kepler's idea of sweeping, broom-like arms from the sun and Descartes' vortices in a universal ether. Newton avoided this entire quicksand of speculation by concentrating on finding a mathematically expressed law that would fit the observed facts. But this did not enable him to answer two crucial questions: what was gravity (or any other force) and how (or in what medium) was this force transmitted? Newton was especially puzzled by the latter question. If the earth and the other planets are made to go round the sun by the force of gravity, what transmits this force? There is no physical transmitter between the bodies of the sun and the earth. During his entire life, Newton could find no satisfactory solution to this problem of action-at-a-distance. Einstein, in his treatment of gravity in the general theory of relativity, included a fourth dimension in his explanation of how the force of gravity functions. Put very briefly, he suggested that the earth's motion in this four-dimensional continuum was actually in a straight line. In our world of three space dimensions, this motion appears to be curved.
When quantum mechanics was developed quanta, or discrete particles, became involved in everything, even in forces. Quantum theory is very careful not to say that the force of gravity (for instance) consists of its particles, the graviton: it merely suggests that this force is transmitted by the particles. These are weightless and must be imagined as a constant stream between two bodies under gravitational attraction, going at no more than the speed of light.
The concept of force particles is more complex than these comments have suggested. For example, force particles are considered to be "virtual" particles, because they cannot be detected directly by a particle detector, as against "real" particles which can. However, theory indicates that gravitons, for example, can also exist in the "real" form - in which case they must be thought of as waves. Gravitational waves are so weak, however, that they have never yet been detected.
All this will show that even today, we have very little idea of what a force actually is and even its transmission is subject to a lively debate. Further discussion of this subject may be found in Galileo's Shadow, including the way the Higgs Field concept can be brought to bear on the controversy of what a force actually is.