Long-Range Forces

Daniel Krawisz

Newton proposed that all matter is attracted to all other matter via a force that is proportional to the mass of both bodies and which diminishes with the inverse square of the distance. He called this force gravity and used it to explain both the cohesion of the Earth and all Earthbound matter and the motion of the orbits of the planets, which obeyed Kepler's laws.

His proposal was controversial because it violated the principle of localism, which requires that objects cannot interact without being nearby to one another. People had always understood that objects have weight that causes them to fall towards the Earth from any height that anyone had experienced, people did not imagine that this force extended far outwards into the heavens. Although Newton's gravity fell off with distance, in theory it extended to the stars without limit.

By contrast, Descartes had attempted to explain the orbits of the planets by vorticies that spun around the sun and pushed on the planets like a kind of wind and he criticized Newton's theory as a kind of mathematical abstraction which did not necessarily pertain to the fundamental nature of the univrse. Newton's famous statement "I frame no hypothesis" was already a response to this objection. His laws were derived empirically from what had been observed in planetary motion and were not claimed to be statements about fundamental causes. Privately, however, Newton agreed with Descartes that a fundamental theory ought to be local.

As time went on, other long-range forces came to be understood. The electric force appears very similar to gravity but has a key difference: it is proportional to charge rather than mass. This has two important implications. First, the electric force can be either attractive or repulsive. Second, that an electric interaction with a distant charged body can be detected without a telescope because two bodies with a different ratio of charge to mass can be observed to accelerate differently.

The magnetic force also obeys an inverse-square law, but unlike the electric and gravitation forces is proportional to current, which means that two charged bodies do not have a magnetic interaction unless they are both moving.

Despite Newton, it appears that these laws are quite fundamental. They are still a part of the best currently known laws of physics, even while other qualities of matter that were unexplained in Newton's day, such as heat, have long since been explained in more fundamental terms. However, with Einstein's special and general theories, localism was resored and found not to be incompatible with long-range forces.

How is such a thing possible? At the very least, a local theory of long-range forces must admit waves. Imagine two bodies that interact via long-range force. If one of the bodies starts to oscillate, the other body must start oscillating as well because the force on it from the first body is changing with its positoin. However, it cannot start oscillating right away because that would be instantaneous communication with the distant other body. The second body must oscillate, but after a time delay. During this time delay, where are the oscillations? They must be travelling through space, between the two bodies.

Einsteinian theories, those compatible with the special or general theory, all work like this. The force is no longer a true interaction between distant bodies. It is a local interaction with a force field that fills all of space and admits waves. This revised understanding of long-range forces began with the discovery of Maxwell's equations of electromagnetism, a theory that unified the electric and magnetic forces with light, which turned out to be electromagnetic waves. Newton had, of course, studied light but had never imagined that it was so closely connected with his idea of force.

Einstein's special relativity was abstracted from Maxwell's equations and his general relativity was discovered by Einstein in his attempt to discover a set of equations that described gravity in analogy to those of Maxwell. Although Einstein's special and general theories are usually and were originally described as theories of relativity, relativity has been a part of physics since the time of Galileo. Before Einstein's general theory, the principle of relativity was understood to mean that the laws of physics are the same in any inertial reference frame, meaning that two scientists can pass each other and both think that they are standing still and that the other scientist is moving fast. No experiment they could do would elevate one perspective over the other, as long as neither was accelerating.

Einstein's special theory did not change the general idea but it did propose that the speed of light was an exception to the principle of relativity. Thus despite the fact that theories which incorporate Einstein's relativity are called "relativitstic", the special theory was actually less relativistic than the physics of Galileo. Einstein's general theory greatly expanded the principle of relativity to include accelerated reference frames, which could be understood as stationary motion with resistance to a gravitational field.

With the special theory, Einstein emphasized relativity because the principle of relativity had been temporarily disturbed due to an incompatability between Maxwell's equations and earlier mechanics. Both of these theories obeyed the principle of relativity on their own, but had different ways of changing perspectives which, when put together, destroyed relativity. For mechanics, a change in persective was called the Galilean transformation, and for Maxwell's equations it was called the Lorentz transformation. These two theories put together were not relativistic and they implied that some scientist could detect his velocity relative to the speed of light, which was absolute.

Einstein argued, however, that physics really is relativistic by noting that the Lorentz transform can be understood in terms of the principle of relativity, and that all mechanics could be reformulated to be compatible with the Lorentz transform. This argument not only restored relativity to physics but restored localism as well, which had been missing for a much longer time. Einstein emphasized relativity because that was the current crisis in physics in his day, but vindicating Descartes was a more important legacy of the special theory.

The compatibility of long-range forces with localism is, in large part, the story of modern physics. The theories which have made this possible are called gauge theories. Gauge theories describe not just electromagnetism and gravity, but the strong and electroweak forces as well. The gauge theory idea is so big that it bridges classical and quantum physics, all the way to gravitation and curved space. Ideas that go beyond known physics, such as grand unified theories and string theory are also gauge theories. Physics has yet to really move past the gauge theory idea, and it all begins with Maxwell. It is arguably the biggest idea in physics and if not it is certainly one of the two biggest ideas in physics, the other being quantum mechanics.

work in progress

L'Europe va continuer de sombrer dans le socialisme avec des taxes et des réglementations qui tuent à petit feu les innovations, l'accumulation de richesses et les gains de productivité qui font baisser les prix.

Donc on aura, 1) du chômage, 2) des prix élevés (ou quand ils seront bloqués, des pénuries), 3) une montée de la violence car les golems ne comprendront pas, se rebelleront et voudront plus d'Etat.

Je pense qu'on assistera aussi à une perte continue des libertés : des confinements, des réquisitions, des taxes exceptionnelles, des Etats d'urgence dans des proportions plus grandes qu'aujourd'hui, afin de faire tenir le système. Chaque crise sera l'occasion pour l'Etat de renforcer son pouvoir, en faire accepter plus aux citoyens, et garnir sa boite à outils répressif qu'il ressortira à chaque crise réelle ou supposée.

Mes solutions à l'échelle individuelle :

1. investir sur soi (santé, alimentation, sport) car le système de santé est catastrophique et avec les boomers cela va s'aggraver.
2. avoir un job à proximité de son domicile pour ne pas être trop dépendant des réseaux routiers ou ferroviaire.
3. être propriétaire de sa résidence principale
4. diversifier ses actifs : actions, obligation, immo, crypto, métaux en choisissant des valeurs connues et solides, quitte à perdre en rendement
5. avoir une certaine résilience (stocks au domicile, savoir bricoler, jardiner, entretenir ses relations familiales et de voisinage)
6. toujours un onglet ouvert sur le premier forum finance d'Europe occidentale pour être au courant de tout