John Carlos Baez on Nostr: One theory that predicts how the observed charge of the electron changes when you ...
One theory that predicts how the observed charge of the electron changes when you measure it at higher energies is QED, meaning 'quantum electrodynamics'. In its simplest form this theory involves only electrons, positrons and photons.
Approximate calculations in QED predict that the electron charge keeps growing as we measure it at shorter and shorter distance scales... and it becomes *infinite* at a distance of roughly 10⁻²⁹³ meters! For details see page 26 here:
https://arxiv.org/abs/1609.01421
There's a lot to say about this. First, the calculations are approximate so they could actually be wrong, even within the framework of QED. Second, this distance is absurdly small: the Planck length is about 10⁻³⁵ meters, and nobody thinks QED applies to such short distances (or high energies). Third, we already have better theories of particle physics, like the Standard Model, which change the story.
So, my point is *not* that this is a serious problem!
My point is that 1) observed quantities like the electron charge really do change when you measure them at higher energies, 2) renormalization lets us calculate how this works, 3) in practice renormalization works well and makes sense, but 4) sometimes when you extrapolate it to absurdly high energies it seems to go bad. That could be a sign that we're applying renormalization to a theory that's only approximate, and isn't really good for such high energies.
So what does it mean to say a theory, like quantum gravity, is "nonrenormalizable"? It doesn't mean we can't play this renormalization game! It means something goes bad - something *different* than goes bad with QED.
I have to explain this next....
(4/n)
Approximate calculations in QED predict that the electron charge keeps growing as we measure it at shorter and shorter distance scales... and it becomes *infinite* at a distance of roughly 10⁻²⁹³ meters! For details see page 26 here:
https://arxiv.org/abs/1609.01421
There's a lot to say about this. First, the calculations are approximate so they could actually be wrong, even within the framework of QED. Second, this distance is absurdly small: the Planck length is about 10⁻³⁵ meters, and nobody thinks QED applies to such short distances (or high energies). Third, we already have better theories of particle physics, like the Standard Model, which change the story.
So, my point is *not* that this is a serious problem!
My point is that 1) observed quantities like the electron charge really do change when you measure them at higher energies, 2) renormalization lets us calculate how this works, 3) in practice renormalization works well and makes sense, but 4) sometimes when you extrapolate it to absurdly high energies it seems to go bad. That could be a sign that we're applying renormalization to a theory that's only approximate, and isn't really good for such high energies.
So what does it mean to say a theory, like quantum gravity, is "nonrenormalizable"? It doesn't mean we can't play this renormalization game! It means something goes bad - something *different* than goes bad with QED.
I have to explain this next....
(4/n)