Spyke

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Has anyone named this projection yet?

Recently, I finally started a hobby I've been thinking about for a long time, i.e., designing my own map projections. This one has such a simple but clever idea that I wouldn't be surprised to hear it's an already known one.

Basically, longitude is scaled by the cosine of the corresponding latitude, like in the sinusoidal projection. But then latitude is scaled by its own sine to avoid those sharp poles (and to emphasize the areas near the equator), and a constant to make it a circle.

So, does anyone know a pre-existing name for this? Alternatively, feel free to suggest a new name for it.

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43

Searching for a smooth function that goes from flat zero to exponential growth

Last night an old idea came back to me, an idea about a function where all the derivatives start from zero and then grow smoothly. I thought it would be impossible, but then I found some interesting stuff on Wikipedia. So, I learned to use SymPy and wasted a lot of time with it. Here's a report of my (non-)findings.

(UPDATE: I did some numerical differentiation, which showed that h(x) does have negative derivatives. See details in this comment. A disappointment, although perhaps not a surprising one. It doesn't however, necessarily mean the goal is impossible.)

So, if anyone knows whether such a function exists and what it looks like, please tell me.

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14

Collecting Unruh effect particles

cross-posted from: https://lemmy.world/post/39777765

So, I was reading about the Unruh effect. In short, if I understood correctly, it is about a constantly accelerating observer finding particles in vacuum that an inertial (non-accelerating) observer wouldn't, and relatedly, measuring a higher temperature there than an inertial observer would. This is due to a combination of quantum and relativistic phenomena. There even seems to be recent empirical support for this, but as I was reading about it, I accidentally stepped into some pseudoscience, which left me in an emotional state where I find everything suspicious.

Anyway, even though I technically am a physicist, this is far from my area of expertise. I came up with a thought experiment and would like to ask a couple of questions related to it.

Let's imagine a spacecraft that does a little trip where it goes into open space accelerating enormously, then stops and comes back. My first question is this: would it be (theoretically) possible for the spacecraft during the acceleration to capture some of those particles that from an inertial perspective don't even seem to exist, store them and bring them back as a very concrete evidence of the Unruh effect? If not, why not?

Another question or two: is my intuition correct when I think that if those collected particles were converted into energy, it would in no situation be possible to gather more energy this way than would be spent in the process of accelerating the spacecraft etc? If yes, could one in some sense say that the energy put into the acceleration is what created those particles in the first place?

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4

Collecting Unruh effect particles

So, I was reading about the Unruh effect. In short, if I understood correctly, it is about a constantly accelerating observer finding particles in vacuum that an inertial (non-accelerating) observer wouldn't, and relatedly, measuring a higher temperature there than an inertial observer would. This is due to a combination of quantum and relativistic phenomena. There even seems to be recent empirical support for this, but as I was reading about it, I accidentally stepped into some pseudoscience, which left me in an emotional state where I find everything suspicious.

Anyway, even though I technically am a physicist, this is far from my area of expertise. I came up with a thought experiment and would like to ask a couple of questions related to it.

Let's imagine a spacecraft that does a little trip where it goes into open space accelerating enormously, then stops and comes back. My first question is this: would it be (theoretically) possible for the spacecraft during the acceleration to capture some of those particles that from an inertial perspective don't even seem to exist, store them and bring them back as a very concrete evidence of the Unruh effect? If not, why not?

Another question or two: is my intuition correct when I think that if those collected particles were converted into energy, it would in no situation be possible to gather more energy this way than would be spent in the process of accelerating the spacecraft etc? If yes, could one in some sense say that the energy put into the acceleration is what created those particles in the first place?

View original on lemmy.world
16