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QFTs are effective field theories: they describe interactions at a particular energy scale, smoothing over whatever unknown physics is going on at lower (or som
by nyssos 2y ago
QFTs are effective field theories: they describe interactions at a particular energy scale, smoothing over whatever unknown physics is going on at lower (or sometimes higher) length scales. This makes the strengths of interactions scale-dependent. So in QED, for instance, the fine structure "constant" is actually a few percent larger at the GeV scale than it is at zero energy. Fortunately for us, we only need to measure the fine-structure constant at finitely many energies to calculate its value at any energy scale we like. But this is just because QED happens to be well-behaved. When we try to apply the same techniques to the gravitational constant, we end up with infinitely many free parameters for reasons which are too technical to explain here. Any intro QFT textbook will probably have a rough heuristic argument (I used Srednicki), but we don't actually know with certainty that there's no clever way to get all those higher order terms to cancel - we just haven't found one and have no reason to expect one.
- nico 2y agoThis is one of the most eloquent explanations I’ve read. Thank you Do you have any links to online resources that might go slightly more into the math and the free parameters issue? Without getting too technical with the math too quickly?