Einstein Field Equations - for beginners!
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Einstein's Field Equations for General Relativity - including the Metric Tensor, Christoffel symbols, Ricci Cuvature Tensor, Curvature Scalar, Stress Energy Momentum Tensor and Cosmological Constant.
Comments
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Great lecture
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After 51:00 you need to understand partial derivatives in curved space.
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Metric Tensor at 49:45
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At 46:15 the Kronecker Delta is introduced. Yes, in these equations it amounts to little more than a kludge.
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In 45:20 do not confuse the indices '1' & '2' with the exponent, which, in this case is 2.
It is unfortunate that indices are written as rightside superscripts when exponents already occupy that corner. -
At 18:47 the dφ on the left means 'rate of change' and the dφ in dφ/x means 'height,' i.e. 1, in this case.
Don't confuse the two altogether different uses of dφ.
Also, the dx under dφ, means '10,' whereas the dx to the right of dφ means '5.'
We mathematicians often ambiguate use and mention. cf Quine: Mathematical Logic; Use versus Mention. -
I understand that calculus is used wherever things are changing or moving. However, what I don't understand is why so MUCH calculus and derivatives are being used. I understand that there is no other way to derive the field equations, and I have done calculus, but in all my life, no one has ever explained why so much of it is used in physics. Please help
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The equivalency principle is not quite ideal, you have to deal with the tidal force, except for the single point there is no effects of tidal force. Maybe we can treat everything as a mass point.
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At 54:28, it was said if the height of the field is 2 m, it matters not what field of reference we're talking about...it will always be 2m.
That cannot be true because a measuring stick appears a different length in different frames of reference(accelerated frames of references). The height of a field is the same thing a measuring stick. Both will appear different lengths when viewed in an accelerated frame of reference. -
Right then, gonna have to break this video down into 10 minute sessions to prevent too much blood loss from my ears.
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I literally cheered in the end of the video!!!! hooray
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Too bad this is not available in book form.
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At 55:25 is the Vnm in top line related to the Vm in second line and Vn in third line? Looks to me like an unfortunate visual effect but with no logical link? W, V, T are all tensors then suddenly Vm is a vector?
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This is an excellent video. I did not follow voice over around 50:50. First why does gmn reduce to delta(mn) in flat space? But more importantly there is no delta (rs) in the equation to take out terms when r not equal to s. What did I miss?
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great video explained very clearly the way math science should be
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I finally got through the first hour of the lecture after weeks of watching lol. I have a book on tensor analysis and it does a horrible job explaining practical uses for tensors. I love your explanations. So far I can derive the first five equations in this video.
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I finally got through the first hour of the lecture after weeks of watching lol. I have a book on tensor analysis and it does a horrible job explaining practical uses for tensors. I love your explanations. So far I can derive the first five equations in this video.
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So, what helped me grasp the concept of spacetime was to view it as bubbles in a liquid. The bubbles being a 'mass' that bent 'spacetime' (the surrounding liquid). It makes sense to me, rather than the trampoline anology, but I'm not 100% sure if this notation would be necessarily correct. Any thoughts?
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"Curly" Dees haha. Great video.
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zed axis you say? cute :))
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