Event Horizon » September 4th, 2018, 3:47 am wrote:If gravity is mass, and gravity waves arrived here marginally faster than photons etc did, it would seem to suggest gravity/mass must travel at relativistic speeds. But nothing with mass can do that according to Einstein. Could there be a case for gravitation having a duality to it, and this could get complicated. It would mean a particle that travels at speed C that can be part of a wave or be a particle still conferring gravity either way.
How best can we rationalise this? I'm not a Physicist so pls excuse my ignorance.
Edit: This is why in this incarnation here my moniker is Event Horizon. Once beyond my skull, all information is lost!
Gerard t'Hooft wrote:I think there was some confusion here because in the discussion it should have been stated clearly what is a linear function of what. Secondly, we are talking of mathematical models of physics; if we add all the dirty side effects nothing is linear anymore. In Maxwell's theory, the em fields are linear functions of the charged sources and currents that are around, but if you take into account that these sources back react, then the combined equations become non-linear.
Only in this sense, the question posed is a meaningful one: if we keep the sources and currents fixed, then our mathematical models say that the em fields are linear but the gravity fields are not.
In mathematical terms, this can be explained by the fact that the local gauge group in electromagnetism is Abelian (i.e. the effect of two consecutive gauge transformations does not depend on the order) while in gravity it is non-Abelian (the effect of two consecutive curved coordinate transformations does depend on the order). Physically, this means that gravity carries energy and momentum (although this depends on the curved coordinates chosen), so gravity generates gravity, while em fields are electrically neutral.
All of this did not require the consideration of quantum mechanics. In ordinary quantum mechanics, what I say above is still valid. But now, even the vacuum has vacuum fluctuations of charged particles and they cause non-linearities in light when you include the back reaction of the vacuum.
E = m * c^2
E = m * (1)^2
E = m
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