I've written a lot of blog posts, but the one that generated the most outrage (by far) was the time I said that the integral of sin(x) from 0 to infinity was 1.https://twitter.com/self_nivk/status/1141921775191617538 …
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I understand why ppl are confused tbh. We physicists are often bad at explaining why we are allowed to use some seemingly unjustified manipulations, or why we just throw out divergent regularisation terms. Physically motivated reasoning work great for us, but for non-physicists
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it rightfully seems like we're pulling out some ad hoc bs and we've thrown away the mathematical foundation. The better way to explain it is to explain generalizations of convergence for infinite sums and integrals, where all the manipulation used can be justified.
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I ask this as a curious mathematician/non-physicist: isn't the unspoken assumption that a periodic function dampens problematic (iff unstated)? Should we not then assume that the integral of sin(x) from 0 to 2*pi is slightly larger than 0 due to slight dampening?
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I understand that, practically, it would be, but is it common practice to actually write that in physics circles, or are people generally OK with saying that integral is exactly zero?
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