||[Oct. 31st, 2003|08:33 am]
I'm contemplating a thought-experiment conducted on the recent PBS show, "Elegant Universe".
Our careful narrator imagines the following: The sun, whose mass is theorized to be the source of gravity, is suddenly removed from the center of the solar system. The resulting shock wave, drawn as a buckling, uniform "sombrero" moving outward from the coordinate occupied by the sun, then takes eight or so minutes before the earth begins to proceed along the straight, inertial line out of orbit.
I have some problems with the animation presented here. First, although they depict the gravity well quickly rising at the center of the animation to its undeformed value, at some point the animation clearly shows what seems to be a positive deformation in the curvature of space time as it travels outward. This doesn't seem plausible, as it seems to imply negative values for gravitational force radiating outward like a wave. Can gravity be a negative? Why? Secondly, the planets themselves exert some minimal force on each other: after all, isn't it by calculation of the orbits of the then-known planets that it was theorized other masses such as neptune and pluto were discovered, as straight calculation of the forces involved assuming point masses for the planets resulted in slightly inaccurate orbits? (need to investigate whether or not this is a true statement.) Therefore, as the "shock wave" propagates outward, it in turn must be deformed and bent by the mass of each of the planets, so the "sombrero" should begin to break up and (scatter)? Third, the calculations are time dependent, and yet there is a discontinuity in the graph: the mass does not slowly return to zero, but is depicted to un-deform in a uniform, continous fashion. At any point in time, there must be a propagating discontinuity in the force equation to reflect the effect of the inherently unphysical premise of the experiment, that the gravity is "winked" out. Which leads to the most annoying problem with the whole mess: you can never ever really do that experiment. Mass is supposedly conserved, right? Even if mass is being converted to energy by the sun's fusion processes, we never really discuss the mass of the sun as a variable: it is a fixed amount. Granted, the mass lost due to conversion is such a tiny percentage of the total, that even after millions of years I doubt it's going to amount to a noticable change in the significant figures that are reported.
However, one could have done the experiment whereby a point mass begins to approach the sun from the far side, slowly beginning to alter the orbit. It would take another few minutes before the relative change in positions begins to alter the course of the earth. So, to my naive way of thinking, therefore, should there be a form of "inertia" where as something accelerates, the surrounding objects are delayed in influence by a factor related to the speed of light, the distance, and the angle of the incoming object? We have the computational power to simulate this, right? So where's my flash animation?
Furthermore, if the galaxy is accelerating away from the center of the big bang, then should that not mean that the solar system should be slightly deformed away at the angle of the solar system to the center of the universe, since all objects would be accelerated away at a uniform rate but as the mass begins to coalesce into an effective point mass, the pull would be greater but delayed by the distance from the central point?
I detest the performance of thought-experiments which can never be performed, even if you were really, really smart. There's too much wrapped up in what you assume to be the effect of the impossible event, that it outweighs the merit of the conclusions arising from the experiment.