The Meaning of Relativity
Chandra Pasaribu
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Abstract
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The text discusses the fundamental connection between human perception, concepts of space and time, and the empirical basis of physics. It critiques traditional philosophical views that separate concepts from empirical experiences and outlines the evolution of our understanding of spatial relationships through the lens of general relativity. The importance of recognizing reference bodies in defining space is emphasized, and the paper proposes a shift towards a more grounded and experiential interpretation of physical concepts.
Key takeaways
- If all the components, a µν , of a tensor with respect to any system of Cartesian co-ordinates vanish, they vanish with respect to every other Cartesian system.
- Equations (32) and (33) have a tensor character, and are therefore co-variant with respect to Lorentz transformations, if the φ µν and the J ν have a tensor character, which we assume.
- It follows from the invariance of ds 2 for an arbitrary choice of the dx ν , in connexion with the condition of symmetry consistent with (55), that the g µν are components of a symmetrical co-variant tensor (Fundamental Tensor).
- If we have given a curve extending from the point P to the point G of the continuum, then a vector A µ , given at P , may, by a parallel displacement, be moved along the curve to G. If the continuum is Euclidean (more generally, if by a suitable choice of co-ordinates the g µν are constants) then the vector obtained at G as a result of this displacement does not depend upon the choice of the curve joining P and G. But otherwise, the result depends upon the path of the displacement.
- The unity of inertia and gravi-tation is formally expressed by the fact that the whole left-hand side of (90) has the character of a tensor (with respect to any transformation of co-ordinates), but the two terms taken separately do not have tensor character, so that, in analogy with Newton's equations, the first term would be regarded as the expression for inertia, and the second as the expression for the gravitational force.
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