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I'm reading Lee Smolin's paper: Lessons from Einstein’s 1915 discovery of general relativity
On p10, he writes:
Any thoughts?
On p10, he writes:
I don't follow why the restriction to relational degrees of freedom necessarily implies that as we get closer to a fundamental theory there should be fewer symmetries.Lee Smolin said:Are there principles that can guide our ongoing search for a more complete understanding of the laws of nature?
One principle that seems reliable is background independence[6]. This says that the laws of nature should be statable in a form that does not rely on the specification of a fixed geometry of spacetime. Einstein’s theory of general relativity satisfies this principle, and it has been a useful heuristic for the search for quantum gravity. Background independence can be understood as expressing Leibniz’s principle of sufficient reason, which states that there should be a reason for every choice made in the formulation of the laws of nature[7]. This underlies the idea that space and time are aspects of relationships among dynamical degrees of freedom. One implication of this principle is that there can be no fundamental symmetries in the laws of nature. Every event in the history of the universe must be describable uniquely in terms of the relational degrees of freedom. This means that the closer we are to a fundamental theory, the fewer symmetries we should have. This may be why our search for larger and larger symmetries is no longer working. [...]
Any thoughts?