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 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 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? 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. May 23 comment Will a spinning object come to rest? That's what I thought -- so the sphere can stop spinning, but does it? May 23 comment Will a spinning object come to rest? I don't think that's the case. If it were, then how does the earth tidally lock the moon? Can't the total angular momentum of the system be preserved in the particles of the sphere while the sphere itself stops spinning? You're absolutely correct for point-particle spheres (though it's not clear what it means for a point particle to spin), but I'm wondering about the internal stresses of macroscopic spheres, and whether there is a force resisting the rotation. Dec 31 comment How does scattering work? @MartyGreen, Kitchi is correct. The original motivation for my question stemmed from considering Rayleigh scattering, but I was wondering how a "particle" moving in a "straight line" can scatter as if it were waving all over the place. Jul 21 comment Why Gravity attracts all objects with the same speed? Great answer. Nitpick, though: you can sometimes prove that two quantities are exactly equal. For example, we know that electrons are identical due to their interference. I can't think of a way to do such a thing measuring gravity, but hey, never say never. Jun 15 comment Can a super-positioned human be used to differentiate between the Copenhagen interpretation and many-worlds? I'm aware that the "photon gun" experiment would be nearly impossible. I'm wondering about the principle of the matter. If it makes you feel any better, you can consider the experiment where the "photon gun" is actually a massive finely tuned table of some sort that the human moves along a sliding track into position, or something along those lines. May 18 comment Where do I start with Non-Euclidean Geometry? I already "know" GR (as in, I can apply the formulas and understand the results), but I want to understand how they work and why. I have a pretty strong math background, so I can move the numbers around and get the right answers, but I don't yet have an intuition as to where the equations come from in the first place, or what they really "mean". Sounds like "Gravitation" might be a good book for me. May 16 comment What's the relationship between an object's color and it's energy? Correct. I'm wondering if you can glean anything about the chemical by knowing only what color it reflects. In other words, what is the minimum difference between chemicals to cause the reflection of different colors; and what does that difference entail. May 16 comment What's the relationship between an object's color and it's energy? Interesting. So what is it, then, that differentiates two teacups in a dark box not interacting with the outside world but wich would reflect different colors? Does it have to do with the configuration of the surface? May 16 comment What's the relationship between an object's color and it's energy? Assume opaque teacups. The question becomes trivial if one absorbs high-energy light and the other reflects it: a better phrasing might be "Assume you have two otherwise-identical materials. One reflects only red light, the other only violet. In darkness, with no light shining on them, can we say definitively that one has more energy than the other?" (Also, if so, what form does this energy take? Potential energy of the electrons orbiting the atoms?) May 16 comment What's the relationship between an object's color and it's energy? Yes, I know. But what is the relationship? Can we say that, all else held equal, the red teapot has "more energy" than the blue? If you have otherwise identical materials, but one is reflecting blue light and the other red, which is more energetic? May 16 comment What's the relationship between an object's color and it's energy? I understand that -- but is there also any relationship (albeit indirect) between the percieved color (reflected light) and the energy (likely w.r.t. electron energy levels in the object)? Feb 28 comment In-flight damage to a supersonic jet Well, this is fiction we're discussing, so there are other environmental factors (read: bullets) assisting in the development of the breach. Am I correct in assuming that a small hole in the canopy would soon cause the canopy to be destroyed? What forces would the pilots undergo in this scenario? What are their chances of survival? Feb 28 comment In-flight damage to a supersonic jet All right, the mask requirement (and the pressurization requirement) are, according to my understanding, necessary due to the altitude, not the speed. Would you be able to breathe without a mask at super sonic speeds in a plane with a cockpit breach but at relatively low altitudes?