I Boost Generators: Physical Meaning & Observable Quantities

nicholas_eng
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Do the generators of boosts correspond to anything physical?
So, all of the generators of the Poincare group are associated with pretty well-known physical quantities. Time translation is associated with energy, space translations with momentum, rotations with angular momentum, and boosts... well, boosts are generated by the "generators of boosts". Do they correspond to any observable?
 
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A proper understanding of boosts in the context of your question requires unifying them with rotations; note that the split between what is a "boost" and what is a "rotation" is frame-dependent. When we unify boosts and rotations, we find that there is a relativistic angular momentum tensor that corresponds to the boost/rotation generators. Wikipedia has a brief discussion:

https://en.wikipedia.org/wiki/Relat...e_generator_of_spacetime_boosts_and_rotations
 
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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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