Insights Relativator (Circular Slide-Rule): Simulated with Desmos - Insight

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This is an update of my 2006 post (reconstructed in 2014) Relativator: The circular slide-rule for physicists.

This is a circular slide-rule for doing relativistic calculations for elementary particle physics that I learned about from
– an article by Elizabeth Wade ( “Artifact: Relativator”, Symmetry (FNAL/SLAC), 01/01/06
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What a cool gizmo!! :smile:

EDIT: I mean I thought a slide rule was smart, and I was of course aware that there we're specialized versions, but this one takes the biscuit! Unfortunately it's too advanced for me. Still, I'm flabbergasted! (For the record, the likes was from before this EDIT.)
 
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I asked a question here, probably over 15 years ago on entanglement and I appreciated the thoughtful answers I received back then. The intervening years haven't made me any more knowledgeable in physics, so forgive my naïveté ! If a have a piece of paper in an area of high gravity, lets say near a black hole, and I draw a triangle on this paper and 'measure' the angles of the triangle, will they add to 180 degrees? How about if I'm looking at this paper outside of the (reasonable)...
From $$0 = \delta(g^{\alpha\mu}g_{\mu\nu}) = g^{\alpha\mu} \delta g_{\mu\nu} + g_{\mu\nu} \delta g^{\alpha\mu}$$ we have $$g^{\alpha\mu} \delta g_{\mu\nu} = -g_{\mu\nu} \delta g^{\alpha\mu} \,\, . $$ Multiply both sides by ##g_{\alpha\beta}## to get $$\delta g_{\beta\nu} = -g_{\alpha\beta} g_{\mu\nu} \delta g^{\alpha\mu} \qquad(*)$$ (This is Dirac's eq. (26.9) in "GTR".) On the other hand, the variation ##\delta g^{\alpha\mu} = \bar{g}^{\alpha\mu} - g^{\alpha\mu}## should be a tensor...

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