Quote:
Originally Posted by Squashed
I think publius has a better handle on the whole state of these affairs but in his absence I will state that length contraction is always a single axis/dimensional phenomenon.
In Special Relativity the length contraction is in the direction of travel which if the travel is along the X-axis then all the length contraction will be evident along the X-axis.
For gravity the length contraction is along the radial vector away from the center of gravity.
So in both cases the length contraction is only evident in one dimension whether this phenomenon actually causes a "density" change, since volume would be affected by length contraction, could be debated.
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Not only are you wrong in both cases it is inmaterial to the case I have made. You appear to be viewing gamma as under the limited viewpoint of apparent changes only. I am not interested in what things appears to look like for a given observer. I am only interested in actual changes of parameters such as the Twin (not a) Paradox in SR and those that lead to the
corrected perihelion of mercury in GR. Let's look at your statements individually.
1) Under SR length contraction only occurs on the X-axis of motion.
Apparent length contraction occurs from the apparent change in distance r from an observer. Imagine a large sphere traveling toward you. Looking down the axis of motion you get the standard length contraction. If you look at the sphere at some angle to this axis then the rate of decrease of r will be somewhat slower such that length contraction is somewhat less. This change in the length contraction decreases at all angles out until you view it at right angles to the direction of motion at which point you see no contraction on that axis. The velocity you use for apparent length contracton is defined by the rate of change in the radius from the observer. The end result of all the effects of the Relativity of Rigidity is always the same as if you assumed no length contraction. Even if solid objects appear to bend to accomplish this. As there are no actuall changes in parameters only changes of units it is of no value to explain the effects I have described.
2) For gravity the length contraction is along the radial vector away from the center of gravity.
I am assuming here that the observer is on the surface of the mass therefore not freefalling. Unlike SR under GR every observer in the universe agrees that time is slower for this observer than one placed higher up in the gravitational potential such as on top of a mountain. This means for our observer on the surface the entire universe appears smaller in all directions compared to the one on the mountain. This remains true even if you are at the center of the mass where you feel no gravitational forces. Although these effects are in line with my ideas here you appear to assume that gravitational effects are limited to SR effects induced by the acceleration of g.