Ibayn

Hi,

Regarding your example to explain the Einstein hole argument I am having problems that I wonder if you could clear up before I post something on the talk page. I'm wondering whether you can use as an example of a generally covariant equation a differential equation that actually depends on the coordinates. As another user says it just seems like a textual transformation and seems too easy. It also doesn't follow the logic as Einstein described it, or as Norton describes it. In their case the g is transformed to a whole new form when the coords are transformed from x to x'. It takes on the form g'. Whereas with your example there is no such change in the form of the solution, it's always cos(?). But calling this cos(?) g' anyway, and making the step that Einstein makes,we just end up with cos(x) and exactly the same solution! So Einstein had in mind a GC equation but whose solutions themselves when expressed in a particular coord system were not GC, unlike what your example relies on. I don't think you could ever come up with a generally covariant equation that had in it a derivative over one coordinate which is exactly the same as the derivative over another coordinate, unless it was trivially zero.

Ecce.monkey (talk) 02:43, 11 August 2008 (UTC)

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