How Fast Is It - 04 - General Relativity I - Geometry (1080p)
Δημοσιεύτηκε στις 13 Δεκ 2015
Text at http://howfarawayisit.com/documents/
In
this segment of the “How Fast Is It” video book, we cover the geometry
of general relativity. We start with the Elevator Thought Experiment,
and show how it represents a gravitational field and how it predicts the
bending of light. This sets the stage for the Equivalence Principle.
This leads to the reconciliation of Newton’s two definitions for mass.
Which, in turn, leads to the idea that the existence of a mass bends
space. To understand the bending of space, we cover the basics of
Euclidian and non-Euclidian Riemann geometry. We include spherical and
hyperbolic geometries along with the nature of their respective
geodesics. We actually measure geodesic deviation above the Earth. For a
fuller understanding, we cover the definition of metrics and curvature
in terms of tensors. With the general Riemannian Curvature Tensor in
hand, we find the subsets that reflect the behavior of space within a
volume. We then cover how Einstein mapped this geometry to space-time to
produce the Einstein Curvature Tensor. And finally, we describe the
Energy-Momentum tensor that identifies the nature of a volume of
matter-energy, which is the source of the space-time curvature. Setting
these equal to each other with an appropriate conversion factor gives us
Einstein’s general relativity field equations.
In
this segment of the “How Fast Is It” video book, we cover the geometry
of general relativity. We start with the Elevator Thought Experiment,
and show how it represents a gravitational field and how it predicts the
bending of light. This sets the stage for the Equivalence Principle.
This leads to the reconciliation of Newton’s two definitions for mass.
Which, in turn, leads to the idea that the existence of a mass bends
space. To understand the bending of space, we cover the basics of
Euclidian and non-Euclidian Riemann geometry. We include spherical and
hyperbolic geometries along with the nature of their respective
geodesics. We actually measure geodesic deviation above the Earth. For a
fuller understanding, we cover the definition of metrics and curvature
in terms of tensors. With the general Riemannian Curvature Tensor in
hand, we find the subsets that reflect the behavior of space within a
volume. We then cover how Einstein mapped this geometry to space-time to
produce the Einstein Curvature Tensor. And finally, we describe the
Energy-Momentum tensor that identifies the nature of a volume of
matter-energy, which is the source of the space-time curvature. Setting
these equal to each other with an appropriate conversion factor gives us
Einstein’s general relativity field equations.
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