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Category Archives: Mathematics
What do we do in physics?
Physics is a discipline of science that has become extremely extended. Physics involves both ‘dropping a rock from a tower’ as well as ‘accelerating protons and bring them in collision’. Public has formed a particular vision about physics. I am … Continue reading
Posted in Mathematics, Philosophy, Physics
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Apostasimetry
In this post I will write about geometry. However, I speak about apostasimetry (Greek: apostasi – “distance”, metron “measurement”) as I focus on distance. The concept distance is related to a number that we assign to the gab between two objects, it … Continue reading
Posted in Geometry, Mathematics
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Transformations between inertial systems of reference (download:)
One can derive the Lorentz transformations without specific using the second postulate of relativity. You can find it in this document: Transformations between inertial systems of reference. Ok it is still a draft:) Hope you enjoy it!
Posted in Mathematics, Physics, Relativity, Special Relativity, Transformations
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Raising the power of a 2×2 matrix
The main question here is: given a matrix then what is ? Given is the matrix (1) . . . . It is clear that This can be written as . Note that and . We shall write and . … Continue reading
Posted in Mathematics, Physics, Relativity, Special Relativity, Transformations
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Measuring the speed of light and the speed of the medium.
Let us consider a medium and an observer that is moving through that medium. Say that the magnitude of the velocity of light with respect to the medium is and say that the velocity of the observer with respect to … Continue reading
Posted in Mathematics, Physics, Relativity, Special Relativity
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The escape velocity for the Schwarzschild metric (2).
In the other post The escape velocity for the Schwarzschild metric. we have found the escape velocity , however – this was based on the limit and . Let us return to the radialequation for the Schwarzschild metric given by … Continue reading
Posted in Cosmology, General Relativity, Mathematics, Physics, Relativity, Universe
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Kerr metric and dragging.
The Kerrmetric is given by , where and . We solve the geodesic equation using It is clear that , then for we obtain the equation So there is a solution . Next we look to the equation for and … Continue reading
Posted in Cosmology, General Relativity, Mathematics, Physics, Relativity
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Solving the geodesic equation.
In this post, I will write about the geodesic equation. I suggest a simplified form that is simpler to solve. The geodesic equation is given by , where . We have used the convention that . Then we may write … Continue reading
Posted in General Relativity, Mathematics, Physics, Relativity
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The escape velocity for the Schwarzschild metric.
The Schwarzschild metric is given by where and . The geodetic equation is given by The path for escaping is given by and , so we only need And we obtain the equations So Now it is clear that . … Continue reading
Posted in General Relativity, Mathematics, Physics, Relativity
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The universe as a sphere.
Consider a uniform sphere that has mass and radius . The gravitational energy of an isotropic sphere is given by so using we obtain The energy is given by and defining we obtain where . So Using we can write … Continue reading
Posted in Cosmology, Mathematics, Physics, Relativity, Universe
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