Yesterday we argued that in a Quantum Field Theory (QFT) of gravity cannot exist, due to incompatible assumptions about the observer's mass. Today I will discuss the analogous situation for non-gravitational interactions such as electromagnetism.
An experiment is still an interaction between a system and an observer, and the outcome still depends on the observer's physical properties. Since the predictions of QFT are independent of the observer's charge and mass, we have still made some hidden assumptions, namely
- The observer's charge is zero, so the observer does not disturb the fields.
- The observer's inert mass is infinite.
What makes the situation different from yesterday is that this double limit exists. Only in the case of gravity, where charge equals heavy mass, are charge and inert mass related. For non-gravitational interactions charge and mass are independent, and we can assume both that charge is zero and that mass is infinite.
However, there is a catch. In reality the observer's mass is large but finite, and QFT is only an approximation, valid for systems where all relevant energy scales are much smaller. But this means that all energy scales must be smaller than the observer's mass, including the energy of virtual particles. So the observer's mass essentially becomes a cut-off which limits the energy of virtual particles.
The fundamental theory has horizontal fuzziness. It can be approximated by QFT without horizontal fuzziness, but too energetic virtual particles must be removed. Otherwise some of them may collide with the detector and displace it, making its location fuzzy. Once quantities have been calculated at a given cut-off, we can let the observer's mass approach infinity, making sure that the observed quantities change consistently. This process is called renormalization.
Renormalization is today a standard part of a physicists toolbox, but it was not always uncontroversal. For two decades after the discovery of quantum mechanics, applying it to fields yielded nonsensical infinite results. In the late 1940s people like Schwinger, Feynman and Tomonaga realized how to extract finite results, essentially by subtracting two infinite numbers. Older physicists like Dirac remained skeptical and found such hokus-pokus unsatisfactory, even if the recipe gives extremely accurate results. My perspective is similar to Dirac's. Renormalization is the price to pay for applying a theory without horizontal fuzziness to a situation where horizontal fuzziness is present.
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