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The speed of gravity
I am real noob in physics, so sorry if this question is really stupid.
Today in a casual conversation I claimed that if the sun were to instantly disappear, we would have felt it in any way nos ooner than after about 8 minutes(which is the distance in light minutes from Earth to Sun). My friend said that light-wise I am right, but we would instantly have felt the gravitation change. I argued that gravitation doesn't spread faster than light.
Am I right or is he right?
Thanks in advance and sorry again for the noob Q :)
Answer
This question has been asked before: How fast does gravity propagate?
Your friend is definitely wrong, but there's also a problem with your example. General relativity doesn't allow matter to be created or destroyed. (Technically the way to say this is that GR has local conservation of energy-momentum.) If you put in an assumption that matter is destroyed, then the equations of general relativity are not self-consistent, so they don't predict anything. To fix up your example, it would be better to imagine that the sun was suddenly yanked out of the solar system at high speed. In that case, we would feel the change in gravity 8 minutes later, at the same time as the change in sunlight.
General relativity predicts that disturbances in the gravitational field propagate as gravitational waves, and that low-amplitude gravitational waves travel at the speed of light. Gravitational waves have never been detected directly, but the loss of energy from the Hulse-Taylor binary pulsar has been checked to high precision against GR's predictions of the power emitted in the form of gravitational waves. Therefore it is extremely unlikely that there is anything seriously wrong with general relativity's description of gravitational waves.
Why does it make sense that low-amplitude waves propagate at c? In Newtonian gravity, gravitational effects are assumed to propagate at infinite speed, so that for example the lunar tides correspond at any time to the position of the moon at the same instant. This clearly can't be true in relativity, since simultaneity isn't something that different observers even agree on. Not only should the "speed of gravity" be finite, but it seems implausible that that it would be greater than c; based on symmetry properties of spacetime, one can prove that there must be a maximum speed of cause and effect.[Ignatowsky, Pal] Although the argument is only applicable to special relativity, i.e., to a flat spacetime, it seems likely to apply to general relativity as well, at least for low-amplitude waves on a flat background. As early as 1913, before Einstein had even developed the full theory of general relativity, he had carried out calculations in the weak-field limit that showed that gravitational effects should propagate at c. This seems eminently reasonable, since (a) it is likely to be consistent with causality, and (b) G and c are the only constants with units that appear in the field equations, and the only velocity-scale that can be constructed from these two constants is c itself.
High-amplitude gravitational waves need not propagate at c. For example, GR predicts that a gravitational-wave pulse propagating on a background of curved spacetime develops a trailing edge that propagates at less than c.[MTW, p. 957] This effect is weak when the amplitude is small or the wavelength is short compared to the scale of the background curvature.
W.v.Ignatowsky, Phys. Zeits. 11 (1911) 972
Palash B. Pal, "Nothing but Relativity," Eur.J.Phys.24:315-319,2003, http://arxiv.org/abs/physics/0302045v1
MTW - Misner, Thorne, and Wheeler, Gravitation
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