advanced_tools:renormalization
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advanced_tools:renormalization [2018/08/01 19:35] 94.175.27.127 |
advanced_tools:renormalization [2019/02/03 11:53] jakobadmin |
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| + | <blockquote>Thus, when ignoring gravity, which we can do in considering the physics of individual atoms or elementary particles because the gravitational force is so weak on the scale of atoms and elementary particles, we can simply ignore the infinite ground state energies of systems and calculate energy differences between the ground state and excited states. | ||
| + | This idea is at the heart of the mathematical methods that form the basis of renormalization, described by Glashow when he discusses the numerous divergences that arise in quantum field theory. There is another physical basis for ignoring these infinities. The source of these infinities comes from extrapolating the mathematical algorithms that allow one to perform calculations with the theory down to arbitrarily small scales. But there is no reason to assume that no new physics will be encountered on ever-smaller scales—physics that would require one to change the nature of the calculations at small scales. Theories that make sense are therefore theories that are insensitive to changes associated with possible new physics on arbitrarily small scales—so-called renormalizable theories. In such theories one can discard the arbitrary infinities that arise from unknown effects at arbitrarily small scales with impunity. | ||
| + | <cite>https://inference-review.com/letter/anything-but-standard</cite></blockquote> | ||
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| What does a JPEG have to do with economics and quantum gravity? All of them are about what happens when you simplify world-descriptions. A JPEG compresses an image by throwing out fine structure in ways a casual glance won't detect. Economists produce theories of human behavior that gloss over the details of individual psychology. Meanwhile, even our most sophisticated physics experiments can't show us the most fundamental building-blocks of matter, and so our theories have to make do with descriptions that blur out the smallest scales. The study of how theories change as we move to more or less detailed descriptions is known as renormalization. | What does a JPEG have to do with economics and quantum gravity? All of them are about what happens when you simplify world-descriptions. A JPEG compresses an image by throwing out fine structure in ways a casual glance won't detect. Economists produce theories of human behavior that gloss over the details of individual psychology. Meanwhile, even our most sophisticated physics experiments can't show us the most fundamental building-blocks of matter, and so our theories have to make do with descriptions that blur out the smallest scales. The study of how theories change as we move to more or less detailed descriptions is known as renormalization. | ||
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| + | <tabbox History> | ||
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| + | * [[https://arxiv.org/abs/hep-th/9812203|The Glorious Days of Physics - Renormalization of Gauge theories]] by Gerard 't Hooft | ||
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advanced_tools/renormalization.txt · Last modified: 2019/07/05 14:10 by jakobadmin
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