For a long time, noise canceling headphones have intrigued me. I do understand the principle of calculating a sound wave to interfere destructively with the noise. It just feels astonishing to me that it can be done quickly enough in such a small space. A great feat of engineering!

Anyway, I just started to wonder about the energy. The original noise carries energy, and so does the canceling wave. Outside the target area they do whatever, but inside it the waves cancel each other (not perfectly, but still). What is left supposedly carries less energy. So where does the rest go?

My guess goes to the usual suspect: the energy is converted to a bit of heat and quickly dissipates to the surrounding air and flesh and plastic and whatever is there. Is this right? And as a funny additional question: how loud would the noise have to be for the headphone wearer to feel this heat?

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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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.

Read the whole strip at: https://thetortoisewebcomic.net/comics/83

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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?

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?

Read the whole strip at: https://thetortoisewebcomic.net/comics/80

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