wave functions

The Three Stages of Obsession

Originally posted by okayoongz

‘Jimin was a chronic user of (y/n),

                                           and there was nothing seasonal about his interest.’ 

Featuring: Jimin (bts)
Genre: Fluff
Word Count: 2,006

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@staff i have blocked around ten p0rn bots just this morning, they are actively going through standard art tags, do you have any idea how bad this is? shit’s bad. they’re adding links to art done by minors. that’s fucked up staff. you have some kind of malicious site targeting yours because this wave of bots all function the same.

they are also going through old art posts! as in, not just stuff posted today, stuff posted weeks ago! i am so tired!!

The Analysts as Quantum Theory

INTJ: Wave function because of their Dominate NI in predicting how the future could likely play out.

ENTP: The Uncertainty principle because nothing can ever, EVER be known for certain in an ENTP’s mind.

INTP: Quantum entanglement because an INTP’s goal is to interconnect everything in the possible to know universe together into one logical system.

ENTJ: Uniform field theory because ENTJ’s must have everything perfectly understood and put together in unison.

8

Seems Very Interesting

Part 15

Observer Effect: The theoretical foundation of the concept of measurement in quantum mechanics is a contentious issue deeply connected to the many interpretations of quantum mechanics. A key focus point is that of wave function collapse, for which several popular interpretations assert that measurement, or observation, causes a discontinuous change into an eigenstate of the operator associated with the quantity that was measured.

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Quantum Realities and Voltron

Slav talked about quantum realities in ep 10 and onward, which is a real thing (called the many worlds hypothesis!) where every time a result is determined/a wave function collapses, the universe splits into one version where one result happened, and a version for the other result. So, assuming this confirmed prodigious genius knows what he’s talking about, there is a universe where Slav stepped on a crack and broke his mother’s back, and a universe where he drowned in a puddle.


There’s also a universe where Shiro didn’t disappear, one where the time loop sent Coran and Allura back to Altea, one where Pidge is transported to Matt when she exits the wormhole. One where Zarkon defeats Voltron, or where Zarkon dies, and so on. A universe for all your ships, and all your AUs, and all your fix-it fics and fantasies.

It’s all, very technically, Voltron canon. Just in another quantum reality.

3

Oisín: Wave Function Collapse for poetry

Martin O’Leary took some time out from glaciers and maps to experiment with applying WaveFunctionCollapse to poetry. Despite it’s rough state, it’s remarkably effective at mapping text to a rhyming scheme and meter.

It also outputs GIFs so you can watch the process in action.

Digging deeper, the interesting thing here is applying WaveFunctionCollapse to something that isn’t a grid of pixels. It’s a good demonstration of the flexibility of WFC. Of course, it’s not the only algorithm that can be used in non-obvious ways. But it’s a good reminder that your generative toolbox might have more things in it than you think.

https://github.com/mewo2/oisin

Mathematics

Approximating a square wave using the Fourier series

Cont’d from “Fourier series

Finally! The long-time-coming Fourier approximation of a square wave, as promised in this post.

Let’s start by considering a rectangular square pulse, which we’ll call the function f(x), and define such that

i.e. a square pulse of width π centred at the origin. We’ll let the periodicity be such that f(x) = f(x + 4π), meaning the function has a period of 4π. Graphically this will be a square wave:

To analyse this using the Fourier series we consider only one square pulse:

First, we’ll evaluate the a0 coefficient, the average of the function. We can find this either by inspecting the graph or mathematically. generally, for a periodic function f(x) centred at the origin with period P, a0 is expressed as

In this case, P = 4π, and so

Now, we shall evaluate the an term. There’s a trick we can use here regarding a function’s odd or even properties:

If the function is even, the an term will contain the integral of an even term so it will contribute the Fourier series. However, the bn term will contain an integral of an odd function, which is zero. Therefore, in this case, we can ignore the bn term:

Conversely, if the function were odd, the an term would contain the integral of an odd function and the bn term would contain the integral of an even function. Hence, only the bn term would contribute and we could ignore the an term.

Now, since the function is symmetric in the y-axis it is even and we should analyse the an coefficient.

Using piecewise analysis we can represent the function as the sum of the individual integrals of each respective parts of the function.

Since sin(−x) = − sin(x),

In turn, it can also be inferred that the integral of an odd function centred at the origin between symmetric limits ±ℓ is twice the integral of the same function between half of those limits. Generally, this is,

Now we can obtain a final value for an. We can express an in terms of the sinc function, defined such that

therefore,

Thus, we can substitute these expressions into the Fourier series.

So what does this function look like? Let’s approximate the function by taking the summation to the 7th term.

Clearly we can see that this is not a completely perfect approximation. As we take it to higher orders, we’d expect the function to look more like the original piece-wise function.

wrindwolf  asked:

What are the current quantum mechanics interpretations there are and what are the pros and cons of each one? Note: I might have expressed myself wrongly so to be sure I'll mention two of the interpretations I know of, the Copenhagen interpretation and the Many Worlds interpretation.

Good question! For those of you unaware what these are, these “interpretations” attempt to describe what is happening in quantum mechanics when we can’t directly observe what’s going on. I’ll start with the examples you gave me.

The Copenhagen interpretation is probably the most accepted one, and states that everything exists as a probability wave before being measured. Basically, before you measure a particle, it doesn’t actually have a definite position or momentum, which is pretty weird to think about. When someone observes a probability wave, it ‘collapses’ and looks like a normal particle again. However, this interpretation isn’t very clear as to what an “observation” exactly is.

The many-worlds interpretation is probably the most popular one, and involves the universe constantly ‘splitting’ into different alternate realities every time a quantum measurement is made. This attempts to solve the strange “wave collapse” in the Copenhagen interpretation. However, it doesn’t make as much sense when you think about probability. Basically, why would one ‘branch’ of reality be any more likely to happen than another?

There’s also the De Broglie-Bohm interpretation, which isn’t as well received as the first two. It basically says that particles actually do have definite positions and paths, but they are guided by the wave function. However, this seems fairly redundant, as it would be much simpler to say that the particle and the wave function are the same thing.

There’s a lot more, but these are the main ones. As for me, I prefer the Copenhagen interpretation, as I see it as the most literal interpretation of the math, which is basically all we have to go on. Still, because these can’t really be tested, I can’t put much confidence in any of these. All I know is that quantum mechanics is one of the best models we have to explain what we observe, which is all you can really ask for in a scientific theory.

Thirty-one years ago, Dick Feynman told me about his ‘sum over histories’ version of quantum mechanics. 'The electron does anything it likes’, he said. 'It goes in any direction at any speed, forward and backward in time, however it likes, and then you add up the amplitudes and it gives you the wavefunction.’ I said to him, 'You’re crazy’. But he wasn’t.
—  F. J. Dyson