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Tyger
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I may edit this post considerably so if it interests you, you may want to recheck it from time to time.
Two of the most interesting questions in Physics relate to the value of Electric Charge. Why is it's value quantized and why does it have the particular value of appr. 1/137? This is not an attempt to give an answer to those questions (although many have tried) but an effort to present a new way of looking at Electric Charge that may help others gain some insight that may help them find an answer.
The "modern" viewpoint in Physics is group theoretical and that is how we are going to look at Charge. Imagine a Universe where particles could have any value of charge or mass. What symmetries would be kept or broken in such a universe, and likewise what symmetries would be kept or broken in a universe such as ours where charge and mass are well defined?
In our universe symmetry of scale is broken because particles have well defined masses, so in the other universe it might be kept. We could assemble an apparatus out of particles that have twice the rest energy of the electrons and protons in our universe, it would be half as large because the size of atoms are determined by the electrons mass. but otherwise it would operate identically. So mass is related to symmetry of scale.
The operative question is, "What symmetry is related to the value of Electric Charge?" What symmetry would be kept or broken if Electric Charge could have any value, or if it had another value? There is such a symmetry and I call it "dynamical similarity" because it is an analog of the geometrical similarity we learned about in high school.
Consider a scattering experiment where an Electron is scattered off a fixed target of infinite mass at a 90deg. angle. Do a plot of the trajectory and the phase versus time. Now use a "double mass" electron (obviously a thought experiment) and halve the distances and times. The trajectory and phase plot will be geometrically similar, but of course smaller. Now plot the same experiment with double the charge. No transformation will allow you to superpose the two plots. They are not "dynamically similar". So having a specific (quantized) value of electric charge preserves dynamical similarity. So we can say that for the electromagnetic interaction, at least, dynamical similarity is an important symmetry. Because the coupling constants of the other interactions are supposed to be dimensionless, we might wonder if they preserve this symmetry too?
However this view doesn't, at this stage, help us understand the particular value.
Two of the most interesting questions in Physics relate to the value of Electric Charge. Why is it's value quantized and why does it have the particular value of appr. 1/137? This is not an attempt to give an answer to those questions (although many have tried) but an effort to present a new way of looking at Electric Charge that may help others gain some insight that may help them find an answer.
The "modern" viewpoint in Physics is group theoretical and that is how we are going to look at Charge. Imagine a Universe where particles could have any value of charge or mass. What symmetries would be kept or broken in such a universe, and likewise what symmetries would be kept or broken in a universe such as ours where charge and mass are well defined?
In our universe symmetry of scale is broken because particles have well defined masses, so in the other universe it might be kept. We could assemble an apparatus out of particles that have twice the rest energy of the electrons and protons in our universe, it would be half as large because the size of atoms are determined by the electrons mass. but otherwise it would operate identically. So mass is related to symmetry of scale.
The operative question is, "What symmetry is related to the value of Electric Charge?" What symmetry would be kept or broken if Electric Charge could have any value, or if it had another value? There is such a symmetry and I call it "dynamical similarity" because it is an analog of the geometrical similarity we learned about in high school.
Consider a scattering experiment where an Electron is scattered off a fixed target of infinite mass at a 90deg. angle. Do a plot of the trajectory and the phase versus time. Now use a "double mass" electron (obviously a thought experiment) and halve the distances and times. The trajectory and phase plot will be geometrically similar, but of course smaller. Now plot the same experiment with double the charge. No transformation will allow you to superpose the two plots. They are not "dynamically similar". So having a specific (quantized) value of electric charge preserves dynamical similarity. So we can say that for the electromagnetic interaction, at least, dynamical similarity is an important symmetry. Because the coupling constants of the other interactions are supposed to be dimensionless, we might wonder if they preserve this symmetry too?
However this view doesn't, at this stage, help us understand the particular value.
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