Bootstrap model: Difference between revisions

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The bootstrap principle makes for a logically correct, but conceptually difficult, form of argument. Bootstrap models were much discussed in the 60's and 70's and formed the basis of study of the analytic [[S-matrix]]. Although the [[S-matrix]] has fallen out of favour as a way of studying strong interactions, giving way to [[quantum chromodynamics]], there are a number of important examples of theories which use general principles to derive specific results, starting from [[Einstein]]'s 1905 paper on [[special relativity]]. Similarly the form of the general theory is almost entirely specified from general principles such as the [[cosmological principle]], to the point where only the [[affine connection]] is an arbitrary assumption. Notably that is the part of the theory which Einstein himself tried to modify in his attempts at a [[unified field theory]].

Likewise, the [[quantum logic]] interpretation of [[quantum theory]] as a language for discussing measurement results due to [[Von Neumann]] is a matter of applying general principles of measurement. Putting this together with special relativity leads to the [[Dirac equation]], and ultimately to [[qed]], and bootstrap principles were at the root of the claim that the only possible model for unification is [[string theory]], although in the view of a number of physicists that claim is wrongly founded because string theory violates a vital general principle in that it is not background independent.

Bootstrapping can also be in reference to a method by which one can reach a higher level of understanding by building off of lower levels. For example, one can bootstrap your way to a solution to any quantum mechanical problem using the [[infinite square well]] as your start. This can be proven.{{Fact|date=April 2007}}