Needing a basic clarification with SR

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I am new to understanding the concepts in SR and GR, and one of the main concepts i am having difficulty with is the speed limit. I don't understand why things can't already be moving at the speed of light in certain frames of reference. For instance, from the Earth's frame of reference, isn't it possible for something to be traveling c/2 in one direction and something else to be traveling at c/2 in the exact opposite direction, making the velocity from either object's frame of reference c?
 
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No, look up velocity addition in wikipedia.
 
Thanks!
 
These equations on velocity addition are based off time dilation, correct?
 
jam.muskopf said:
These equations on velocity addition are based off time dilation, correct?

No, they are based on the postulate (or empirical observation) that all observers measure the speed of light to be c, regardless of their frame of reference.
 

Thread 'Euclidean geometry and gravity'

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)...
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Thread 'Is the variation of the metric ##\delta g_{\mu\nu}## a tensor?'

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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