If you took a General Relativity course or read a book on the subject you were probably told the tensors that make up Einstein's field equations are a good thing because they are invariant. What's so special about invariant tensors? Here is a quote from one source:
Wow! Cool! This means I can take a vector (a rank-one tensor), place it in any coordinate system or reference frame (also known as a basis) and it will not be affected by the coordinate system. The only things that will change are the values of the vector's components. The diagrams below show an example of a typical coordinate transformation:
Notice how the vector looks and behaves the same way in the different coordinate systems. However, Einstein's theory of General Relativity would not work if this were really true. If the vector above was a light beam this is what would happen:
The light-beam vector curves if the geometry of the coordinate system is curved. It is not independent of the coordinate system. So technically, it is not a tensor and should not be modeled by tensors. Or, the definition of "tensor" needs to be modified.
The theory of General Relativity claims it is the very geometry of spacetime that causes the light beam to curve. Also, curved spacetime geometry causes other objects that are considered tensors to move along a geodesic or curved trajectory when those objects would move differently in flat spacetime. None of this is consistent with the concept of invariance.
No comments:
Post a Comment