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Posted by Harvey on July 16, 2004 14:49:13 UTC

I agree that a physical theory does not require a 'definition' of space. For example, a quantum theory of gravity doesn't necessarily lead to a list of axioms such as what you listed. However, if you have a list of the correct axioms of space, then you should be able to derive the fundamental theories that are missing (e.g., quantum theory of gravity) in our fundamental understanding of the universe. The reason is that space is linked to our understanding of matter, energy, gravitation, time, inflation, virtual pair creation, etc. If you have correctly reduced space by a set of axioms, then your axioms must account for the links that exist with these other issues.

For example, if none of your axioms account for the expansion of space (e.g., inflation) and under what conditions this can occur, then your axioms are not about the fundamental properties of space, but are much like the axioms of Euclidean geometry - they might explain some of our everyday observations, but they don't help us understand the topic when it comes to new phenomena (e.g., the curvature of space). In the case of the axioms of Reimannian geometry, they do account for spatial curvature, but they do not account for singularities, inflatons, temporal dimensions, etc.

So, as in this example, in order to have a better understanding of space, we need 'higher mathematics' to help answer fundamental questions. The issue that confronts many quantum cosmologists (among others) is that we lack the mathematics needed to take into consideration all of these space-linked phenomena (e.g., inflation, quantum gravity, etc).

When you say that you've developed axioms of space and yet cannot derive a more fundamental theory, then it is meaningless. Every culture since homo sapiens pondered such issues have provided such 'explanations' of space, but they lack the details to explain the phenomena of space. This is what is wrong with your argument, I think.

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