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E&M is far from "simple". It contains special relativity, for starters. Also it is incompatible with thermodynamics: solving this problem is why Planck invented
by wmnwmn 8y ago
E&M is far from "simple". It contains special relativity, for starters. Also it is incompatible with thermodynamics: solving this problem is why Planck invented quantum mechanics. Also point charges have infinite energy: this problem leads to renormalization theory. Also it introduces gauge invariance, an essential but complex part of all modern theories. And lastly, the mathematics of E&M is a big step up from Newtonian theory.
- nonbel 8y ago>"E&M is far from "simple". It contains special relativity, for starters." A theory (which is just a set of assumed first principles and rules of logic) can be simple but allow you to deduce vast complexity from it. In fact, it is ideal for a theory to be as simple as possible. The "game of life" is not really a theory, but it demonstrates that simple rules can lead to surprising complexity: https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life https://en.wikipedia.org/wiki/Conway%27s_Game_of_Life EDIT: I can't begin to imagine why this would trigger a downvote. Are there people out there who prefer complex theories that make things more difficult to understand than necessary? Perhaps because it makes them feel smart or something, I don't know. But that is basically saying you dislike science, because the point of science is to synthesize information into a small set of simple "laws" that allow us to deduce accurate and precise predictions.
- aj7 8y agoI reflexively downvote the game of life. I have never heard of a single useful application or analogy of “finite automata.” Yes, there are speculations about extremely small Planck lengths, by no new physics has panned out. Finally I am sad that one of the greatest computer scientists and polymaths, Ed Fredkin, got sucked into this. We all have weaknesses.
- ckocagil 8y agoSurely you mean cellular automata, not finite automata.
- aj7 8y agoYes, you are right. My ignorance shows, but I am still hanging on to my opinion of cellular automata.
- jle 8y agoGoL wasn't used here because of any value or analogy... it's used as an example of how a simple set of rules can generate complex behavior. GoL can display complex behavior, but it would be a stretch to to say that the rules governing it are complex. If you think GoL is too simplistic, you are agreeing with the original comment.
- ZephyrP 8y ago> I have never heard of a single useful application or analogy of “finite automata.” lol.
- aj7 8y agoIt’s remarkable how many silent downvotes you get when you tweak something that people think is cool. C’mon guys. Refute what I said.
- weedwarrior 8y agoyou are being downvoted because of a problem with the nature of HN echo chamber being a symptom. if the voting/karma system was improved we wouldnt have problems with this kind of downvoting
- tntn 8y agoDyson's statement was about Maxwell's theory, not all of E&M and its interactions with every other physical theory. There are no point charges in Maxwell's theory, for example.
- adrianratnapala 8y agoI think the point is that electromagnetism really is a very complex and knotty phenomenon, and we moderns are spoiled by having (1) Heavyside's deceptively elegant formulas for the theory (which we now call the Maxwell Equations) and, (2) A well oiled pedagogy about how those equations the capture specific phenomena named after the likes of Ampere and Faraday, and (3) Powerful formalisms for studying circuits, optics, transmission lines etc that can mostly be used without going back to the fundamentals. Most of that was not available to Maxwell when he started out, so it's not surprising that he presented his theory in a way that reflected the real complexity of it all.
- jules 8y agoE&M is simple in the sense that the equations that govern the relationship between the charge distribution and the electromagnetic field are quite simple. And the equations governing how charges move in an electromagnetic field are quite simple. I think this is what Dyson has in mind. Understanding the implications and limitations of those equations is not simple at all. An even more blatant difficulty with E&M, related to your third point, is that it is schizophrenic. Given the trajectories of charges it will tell you what the electromagnetic field will be, and given the electromagnetic field it will tell you how charges will move. Unfortunately, these two parts of the theory seem to be incompatible, and the theory will not tell you how fields + charges will evolve in time.
- DoctorOetker 8y agowith schizophrenic you mean a system of coupled differential equations? in that case I wouldn't agree with schizophrenic. or are you referring to the fact that mathematically speaking the system of differential equations is indeterministic due to mathematically perfectly valid advanced potentials? in this case I agree that there may be much more to learn from the Maxwell equations, and I have no qualms with naming this feature (highly) schizophrenic.
- jules 8y agoI mean that the theory splits into two parts: the part that tells you the fields given the charges, and the part that tells you the charges given the fields. For instance, it doesn't tell you what two charges with given initial velocities will do. (not even if you also give an initial electromagnetic field)
- Certhas 8y agoWell, the Lorentz force does though. And that follows from energy conservation and the Maxwell equations, e.g.: https://physics.stackexchange.com/a/77028 https://physics.stackexchange.com/a/77028 So that's not really terribly deep or even true.
- deleted 8y ago[deleted]
- weedwarrior 8y agospecial relativity is also simple, once again its the differential equations that provide a difficult explanation.