D’Alembert’s principle is a much more elegant and conceptually powerful formulation of Newton’s second law of motion by the 18th-century French polymath Jean le Rond d’Alembert, even though, mathematically, the reformulation amounts to a simple algebraic manipulation of Newton’s 2nd law. By defining an inertial force F = - m a , where m is the mass and a is the acceleration of the object, one arrives at the following: The sum of the forces on any mass always sum to zero in the reference frame of the mass. In this perspective, one always imagines oneself as being in the coordinate system of the mass, rather than in an inertial reference frame. Defining an inertial force makes discussion about inertia sensible because it is a well-defined concept. It also makes it easier to see how kinetic energy arises as the integral of the inertial force over displacement and momentum arises as the integral of the inertial force over time. Also one can see how the centrifugal and coriolis
Alexander F Mayer has a very thought-provoking website. The basic idea is the Einstein neglected a small transverse relativistic effect and the consequences of that neglect. He also points out that the notion of a history of the universe is a meaningless statement. I have heard this before, but never understood it until his presentation. The argument is as follows: Mass bends spacetime. Because there is only positive mass, spactime bends in one direction. The distribution of matter is quasi-isotropic. This causes the structure of spacetime over large scales to appear like a 4-sphere with time always orthogonal to surface of the sphere. Time will in general over large distance be pointed in different directions and we will see distant galaxies as aging slower, just as they see us as aging slower. Distant objects will always be redshifted without any motional relativity. The idea of curved spacetime also leads to a horizon for all individuals in the Universe beyond which objects are