The speed of Gravity

Discussions on classical and modern physics, quantum mechanics, particle physics, thermodynamics, general and special relativity, etc.

Re: The speed of Gravity

Postby Event Horizon on September 3rd, 2018, 9:26 pm 

Thanks Faradave. That is a response that may improve how I try to visualise these things. There are still a lot of unknowns. I just got to figure the right questions if I can, that's the tricky bit.
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Re: The speed of Gravity

Postby hyksos on September 19th, 2018, 4:33 pm 

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!

You are asking the right questions. I will answer by quoting Gerard t'Hooft. (recent Nobel Prize winner in physics) I have added bold-face to pick out the parts where he addresses you directly.

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.

In Einstein Field Equations it is not "mass" that generates a gravitational field. Instead it is a stress-energy tensor that does this. In other words, the presence of raw energy itself contributes a gravitational field. Because GR is a relativistic formulation, you can willy-nilly convert between Energy and Mass by a factor of c2 In some reduxes in academia, meters and seconds are down-converted into Planck Lengths and Planck Clock ticks. This happens to make c (the speed of light) become a so-called dimensionless constant. In these contexts c = 1

Some mild algebra gives :

Code: Select all
E = m * c^2

E = m * (1)^2

E = m

Gravitational waves do carry energy away from a neutron binary. Because they carry energy, they are energy, and so a gravitational wave will contribute a gravitational field (E=m). We reach the same conclusion that Gerard t'Hooft does above. Gravity generates gravity.
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