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- Relativistic mechanics?
- Relativistic Mechanics, Time and Inertia | E. Tocaci | Springer.
That answer stood largely unchallenged for two centuries, until the Austrian physicist Ernst Mach flatly declared Newton to be wrong. Nevertheless, the essential idea is simple enough. Inertia—that tendency of massive objects to move at constant velocity—must depend on other bodies, because motion itself must be measured relative to other bodies. Rotations and accelerations along straight paths take place with respect to the reference frame of the distant stars and galaxies.
The centrifugal forces that throw you to the side of an automobile as it rounds a corner arise because you are accelerating with respect to the distant matter in the universe. He asserted that this behavior is determined relative to absolute space.
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Does the law of inertia mean anything in an empty universe? It furthermore went against our human intuition that our experience of the world is fundamental, not contingent. When accelerating downward in an elevator whose cable has snapped, you feel weightless. By the same token, when accelerating upward in an elevator, you feel heavier than usual, as if the gravitational pull of the Earth has suddenly increased.
To explain the origin of accelerations, then, he would need to create a theory of gravitation. Furthermore, because free fall abolishes gravity in an elevator, the origin of inertia cannot be found in the interaction with nearby bodies such as Earth. Einstein hoped that, within the framework of general relativity, the distribution of matter of the universe would fully determine the inertia of material objects.
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As simple as the question sounds, there is as yet no definitive answer. Josef Lense, an Austrian mathematician, later provided relevant astronomical observations. Inevitably, this concept of frame dragging has come to be known as the Lense-Thirring effect. In the paltry gravitational field of the rotating Earth, the predicted amount of frame dragging is enough to displace the axis of an orbiting gyro by only 0. In , New Zealander Roy Kerr, then at the University of Texas, discovered the general-relativistic description of rotating black holes.
Soon physicists recognized that frame dragging can become far more pronounced around extreme astronomical bodies. Several teams have claimed to find observational evidence of frame dragging in the disks around supermassive black holes, although the results are indirect and imprecise. The question of how the distant reaches of the universe give marching orders to a gyroscope spinning on my desk is an altogether trickier issue.
It does not mean that the universe is rotating around some central axis. For true followers of Mach, a gyro should track the bulk matter of the cosmos, and so it should remain stationary with respect to distant galaxies.
Such models can be declared unphysical, however, because they flagrantly contradict observations of the real universe. Nevertheless, as theoretical solutions they demonstrate the difficulties that come with defining inertia purely in relation to other objects. In , however, Harry King, then at the University of Texas, proved that a closed universe—one that is destined to stop expanding and eventually recollapse—can exhibit no rotation. Schmid has concluded that vorticity added to a realistic cosmological model would indeed drag gyroscope axes. In this way, he bypasses the necessity to impose boundary conditions at infinity, the problem that bedeviled Einstein.
The matter distribution of the universe in and of itself determines the behavior of gyroscopes.
Relativistic Momentum – College Physics
In SR they don't, but it's still possible to use co-ordinate systems corresponding to accelerating or rotating frames of reference, just as it is possible to solve ordinary mechanics problems in curvilinear co-ordinate systems. This is done by introducing a metric tensor.
The formalism is very similar to that of many general relativity problems, but it is still special relativity as long as the space-time is constrained to be flat and minkowskian. Note that the speed of light is rarely a constant in non-inertial frames, and this has been known to cause confusion. An example is a rotating frame of reference used to deal with a rotating object.
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The transformation of the metric into the rotating frame leads to "fictitious" forces: Coriolis forces and centrifugal forces. But this is no different from ordinary mechanics.
A simple task is to solve for the motion of a rocket that accelerates "uniformly". What does this mean? We don't mean that its acceleration as measured by an inertial observer is constant. We mean that it is moving such that its acceleration measured in a "momentarily comoving inertial frame" is always the same; this frame is an inertial frame travelling at the same instantaneous velocity as the object at any moment.
If you were on board such a uniformly accelerated rocket, you would experience a constant "G force". The motion of this rocket can be found in several ways.