I am kind of torn on AI.
I really feel that it will render a lot of humans useless. That of course is terrible not just for the individuals but the human race.
On the other hand, it can be such a great learning tool. We might just be learning for our own personal satisfaction but I guess that that is something.
As I have been on a break I have dug into several topics that I wondered about in schools. Two were related to EMF fields.
One was the solution to Maxwell’s equations in a vacuum yielding the well known traveling wave. The solutions we saw in class always had the form of a sine/cosine wave that exists throughout space. (Ignoring reflected waves here.). Any point in that wave (say a peak) does move at the speed of light. But that always bothered me because 1) that solution exists throughout space and 2) a peak moving at c wasn’t convincing that the wave itself moved at c. And since we only saw steady state solutions, there was no wavefront. ChatGPT clearly showed how to model a condition where an event happens at t=0 and how a wave with a unit function that moves as the light cone does is a valid solution. It also stated that that is not covered in most engineering fields textbooks. So they kind of glossed over an important point.
The second question I had was related. I asked what if an electron appeared in the vacuum of space at t=0. I thought the answer might be one of the following:
1. If that were possible, it would yield an instantaneous presence of the electric field throughout space. That violated causality because the premise of an electron appearing is impossible.
2. Somehow, the inverse square electric field is only instantiated within the causality bubble.
Ai was able to show me it is #2 and that an impulse that spreads out at the rate of c (being scaled by 1/r) would lead and the coulomb (1/r^2) field would be left in its wake. It demonstrated that such a function would satisfy Maxwell’s equation.
It also pointed out one more insight. That electric field has no magnetic field component meaning that the intuition commonly stated that light moves through space because a changing electric field induces a magnetic field and vice versa isn’t really correct because here is a field moving through space at c that doesn’t even have a magnetic component.
We probably didn’t cover that because we had not yet been introduced to the unit and Dirac delta functions at the point we took fields. But without that you lose a significant level of intuition.
I spelled that out because I know there are physicists here who likely knew all of that because you guys just take everything to another level. But, details aside, it is really cool that AI can provide that level of intuition that I would have never known how to get. Or at least it would have taken me a lot longer via Google searches. I know it is mostly just searching and summarizing results but it does a damn good job of that.