Newtonian mechanics in the accelerated motion of a body is defined on a class or set of reference systems, namely, all reference systems inertial. According to general relativity such a system can be found locally at every point of spacetime. But what determines the existence of such a set of systems?
In general relativity also occurs far from any ground such systems may exist. This is because the space-time becomes flat, the same as that of special relativity, where the class of inertial reference systems represent a preferred class and to some extent independent absolute or the rest of the universe. Equivalently one can think that a body away from mass may acquire inertia, that property of a body that links acceleration forces. This is because the space-time becomes flat and inertia appears to be wholly owned by the body.
The question is whether this is conceptually acceptable. If we postulate that all the properties of motion are expressible in terms of observable and dynamically, then the possibility of an absolute determination of inertial systems clearly goes against our assumption. To some extent we do physics with as little baggage as possible in terms of absolute theoretical gadget. The existence of solutions without mass but with inertial systems in general relativity is against this.
In defintiva, the motivation is to ensure that movements are also dynamically equivalent kinematically equivalent. This is a way of expressing what is sometimes called Mach's principle. This is not true in Newtonian mechanics. To illustrate this let us recall the example of the rotating bucket. The water rises through the bucket wall and sinks into the center of the cube (concavity) means that the cube rotates. In Newtonian mechanics the cube is rotated or accelerated with respect to the class of inertial systems. The forces acting on the water appear absolutely. According to Newtonian mechanics if the whole universe would spin but the cube does not, then not act on the cube strength.
But the whole universe and turn the cube is kinematically equivalent to rotate the cube but the rest of the universe. According to our postulate must therefore also find mechanics to describe these two phenomena as dynamically equivalent. That is, if the universe would spin but the hub must not act a force on the cube that is the same as if the cube turn but the universe.
This hypothesis also provides a new perspective to the problem of
Foucault pendulum. The determination of the angular velocity of the earth that follows from this experiment should be equivalent to the determination of the angular velocity of the earth can be done with cinematic experiments, measuring positions of fixed stars at infinity. This is because movements are also kinematically equivalent dynamically equivalent. In the system comoving reference to a body's gravitational pull than the rest of the universe made of this body is no
The condition seems reasonable: if kinematically we can get moving comoving with the body so that he is at rest relative to us it seems sensible to require that dynamically forces do not act on it. At the end of the day we're trying to kinematics and dynamics are equivalent. Although it seems incredible this is the only condition for establishing the theory.
I mentioned so far is the conceptual basis of the work of Dennis Sciama, English physicist (1926-1999), on the subject. In his article:
On the origin of inertia
masterfully presents a model and theory. The article is a gem, so well written that is, how to proceed, for their beautiful ideas conceptually well founded, for his predictions and simplicity in the presentation.
To impose that condition Sciama considered a homogeneous and isotropic universe fulfilling the Hubble law and in which there is inhomogeneity represented by a gravitational mass M. This is the "rest of the universe" that will act on a mass test, which imposes the above principle. Sciama model presented is a vector theory of gravitation. It is known that a theory of gravitation must be tensorial, but the vector model is used to extract enough interesting physical consequences. Sciama promises tensorial model for a future second job, but to me it is unknown if this work really existed or not.
Because in the universe are moving masses on our test gravitational mass, a vector theory of gravity consist of a field and another gravitomagnetic gravitoeléctrico H E on the mass test - analogous to the Maxwell equations. The total field F = E + H is zero in the comoving mass system test and this condition, F = 0, worth to derive the second law Newton with a nontrivial expression for the inertial mass of our mass (gravitational) test (see equation (5) in the article).
I will not show the mathematical steps here, but are simple. Only require to understand equations similar to those of Maxwell. Strongly strongly recommend reading the article that is not known.
- The consequences of the theory are: (i) the gravitational constant in a space-time point depends on the local matter distribution at that point, (ii) the total energy of a body (gravitational and inertial) is zero ( iii) the principle of equivalence is a consequence of the theory, (iv) the theory to calculate the average density of the universe, (v) to the universe we observe most of the inertia of bodies is generated by masses at distances greater than 100 Mpc, and others mentioned in the article.
- Seeing this, one wonders if they really can general relativity be the correct classical theory of gravitation. The conceptual beauty of Mach's principle, which general relativity is not implemented consistently, is so great that it seems a shame that the universe does not make use of it. What tensorial and more realistic theories must incorporate this principle? How do they differ from general relativity? and what are experimentally refuted? These questions engage us in a second entry in the near future.
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