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 Oct 30 awarded Notable Question Aug 9 awarded Nice Question Jun 16 awarded Popular Question Apr 10 awarded Popular Question Apr 9 revised What's the interpretation of Feynman's picture proof of Noether's Theorem? Typo: two delta x2s in denominator (\partial \dot{x_2} \delta\dot{x_2}) Apr 9 suggested approved edit on What's the interpretation of Feynman's picture proof of Noether's Theorem? Nov 11 awarded Notable Question Jul 2 awarded Curious May 21 awarded Popular Question Sep 13 awarded Yearling Aug 2 accepted How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)? Aug 1 comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)? "This is a crucial property of lagrangians: I can add a total derivative to a lagrangian without changing the equations of motion." That really cool. Can you give an example of how that's useful in a real physical application? Aug 1 comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)? I think you miss the point. I know that the above Lagrangian is broken, but I don't buy that it's completely meaningless. For example, you could look at what happens as you smear the stationary point into a wider and wider interval. Or you could look at $\mathcal{L} = \alpha x^n + \beta v$ starting with $n = 2$ and observe what happens as $n$ goes to 1. Or you could play with similar limits using $v$. I was hoping people would point me towards illustrative interpretations. Of course the Lagrangian is broken, but many seem to think that unbroken means undiscussable. Aug 1 comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)? Thanks. I get this sort of stuff, but I'm still confused. For example, division by zero is not just illogical nonsense. A lot can be said about division by zero. Your result diverges to positive or negative infinity. Following this "logical impossibility" can lead you to infinitesimals. I get that this lagrangian is nonphysical. I know it's nonsense. I'm wondering what kind of nonsense it is. Declaring that energy is now x + v clearly breaks everything, but it's not clear to me that it breaks things so hard that we have to stop talking about them. Aug 1 comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)? Are there any nonclassical motions? I know it's not a physical world -- but what kind of world is it? I don't expect it to behave nicely, but I would expect it to behave somehow. Aug 1 comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)? I get that -- but it's not clear to me what it means for a physical system to "not have a stationary point". I can picture a system that never comes to rest, where everything accelerates off into the distance forever, but that's still a stationary path in a Lagrangian, isn't it? What are the paths taken in a world with an inconsistent Lagrangian? How do I picture such a world? Aug 1 revised How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)? added 78 characters in body Aug 1 comment How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)? Certainly not. I'm trying to understand the formulation in general, and in my experience a good way to understand things is to break them. I was surprised that the lagrangian broke as hard as it did as fast as it did. What sort of world would making $\int dt (x + v)$ stationary correspond to? Jul 31 asked How do I read the simple, but contradictory, Lagrangian ($\mathcal{L} = x + v$)? Jun 10 comment What would happen if the Earth was tidally locked with the Sun? I'm still working on it, among a number of others. It grew a bit, in the telling, and isn't exactly "short" any more. I also seem to have have a bad case of lots of ideas and not enough time... I will certainly let you know if & when I finish it, though.