General relativity uses the coordinates and time that can be somehow curved. Relatively to what they are curved? Relatively to straight line coordinate system?
If so how can we determine this initial rectangular coordinate system? What is straight line, what is perpendicularity? When do we take straight rulers to measure distances along to x,y,z-axis?
The metric isn't measured, because it can't be measured-it isn't a physical quantity, since it can be changed by a change of coordinates-it's used to construct other quantities, that are physical, i.e. that don't depend on the choice of coordinates.
This is the subject of courses on general relativity, so it's not useful wasting time and effort that could be spent learning the subject-e.g. from here: https://arxiv.org/abs/gr-qc/9712019
Anatoly,
There are a number of tensors that all exhibit 'curvature' in some way.
The most familiar ones are the Weyl tensor and the Riemann tensors.
The Riemann tensor tells you how well parallel transport is 'true' and how large the angles in a triangle must be.
The Weyl tensor tells you about the tidal forces along a geodesic and would be measurable, with, say, a Forward Mass sensor.
May I recommend General Relativity by Lewis Ryder?
The metric isn't measured, because it can't be measured-it isn't a physical quantity, since it can be changed by a change of coordinates-it's used to construct other quantities, that are physical, i.e. that don't depend on the choice of coordinates.
This is the subject of courses on general relativity, so it's not useful wasting time and effort that could be spent learning the subject-e.g. from here: https://arxiv.org/abs/gr-qc/9712019
To understand why metric isn't measured consider the example of classical electromagnetic theory. Here the "potentials" (scalar and vector) are not measured, but what is actually measured is the field. Potentials have arbitrariness which disappears in the classical electromagnetic field. Yet, me and you extensively use scalar and vector potentials in our calculations.
In a similar fashion the tests of general relativity, which is basically a theory of gravitation of macroscopic objects such as planets and stars, uses the metric (which is not an invariant quantity) as step for calculation of physical effects of gravitation which are measurable. The list is quite long, but I am quoting a few physical effects which have tested the Einstein's theory of gravitation
for a complete list see: https://en.wikipedia.org/wiki/Tests_of_general_relativity
Dear Sirs,
Metric ds2=gabdxadyb uses differentials from high math. Are they presented in real life? Is it correct?
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