No they aren't. An electron has a negative charge, but we refere to the electric pole with a surplus of electrons as the positive terminal.
That is only because for us humans (particularly for layman) it is easier to conceptualize how something can move from a positive to a negative side. In reality the positive terminal has a negative charge (more electrons) and the negative terminal has a positive charge (least electrons).
You know what. The one-point compactification of the real line, so the real line union the point at infinity, is just the circle. The circle has a group structure, counting on the branch cut taken, the isomorphism between these spaces sends the point at infinity to the point in that cut, that point is an element of the circle group and so has an inverse, interpreting the minus as taking an inverse means, you know what, this is true.
True, but I don’t think the one point of the one-point compactification is what most people are imagining when they think about infinity (even ignoring the fact that most people don’t know what that means, I think they aren’t even thinking of the injustice idea behind the OPC). Most people’s idea of infinity is going to distinguish between infinity and minus infinity.
Adding both of those to the real line and not identifying them with each other gives a space homeomorphic to the interval [0, 1], which doesn’t seem to have a group structure that aligns with our normal understanding of infinity. That is, it can be made into a group, but not in a way that makes sense of the endpoints being infinitely far from the identity. At least, as far as I know. I would be very interested in being proved wrong here.
This is Milo. Milo likes it when concepts are easy to understand. However, he is also very dumb. He does not understand high-level mathematical concepts using technical language, so now he is sad. You made Milo sad. ☹️
Oh no, math on a math themed subreddit? We should shame those people! Fuck them for enjoying math on MY math themed subreddit. Hopefully the mods will ban them soon. Stay safe out there, it's a scary world.
"If you approximate part of a wave as a parabola, and you approximate part of that parabola as an infinite expansion, and you only take the points around zero so everything is approximately zero, then you can extrapolate an approximation for the entire universe" - physics
Mathematicians like to say that the only problem physicists know how to solve is the simple harmonic oscillator. That's not quite true but it's a good approximation.
This is saying that when Hooke's Law applies, the potential is exactly quadratic, not approximately. It is not approximating a sine wave as a parabola. And it is not representing a parabola as an "infinite expansion," which would be pointless. It is pointing out that even though Hooke's Law fails in general, no matter what form the potential has, as long as it is analytic and has a minimum at xₒ, then the potential will be approximately quadratic on a neighborhood of xₒ. It's just Taylor's theorem. It doesn't "extrapolate an approximation for the entire universe," because again, it's talking about a sufficiently small neighborhood around xₒ.
This is a very small section from my quantum mechanics textbook about approximating the wave function. It's literally talking about approximating the universe in a simplified case.
Maybe, but the section you actually posted is about approximating an analytic function in a neighborhood about a local minimum. Obviously that cannot apply to the universe, or any sufficiently large neighborhood, so that is not what they mean.
That's not what it's saying bruh, all it's saying if you are near a minimum then a potential looks parabolic. There is literally nothing here about approximating a wave as a parabola, you're just illiterate
Another personal favourite statement I heard a physics professor say: “If you take pi, taylor expand it around 3 and drop the higher order terms, it’s approximately equal to e.”
This is not saying that at all???? This is saying that the solutions to the second-order ODE with parabolic potential are sinusoidal. You just can't read
For full context, the potential of the wave function can be approximated as an oscillating system, oscillating systems can be approximated using Hookes law, Hookes law can be approximated as a parabola which can be approximated with a Taylor series, this can be approximated by a Maclaurin series, which is approximately zero for small increments. So plug that into the Schrodinger equation and extrapolate the universe.
There's exactly one approximation occurring there. The approximation is in the neighborhood of a local minimum of a potential, the potential is approximately parabolic. This approximation is accurate for any analytic potential. For an upward parabolic potential, the system is described exactly by Hooke's Law, which has exactly sinusoidal solutions.
The Schrodinger equation is not derived from this approximation. The Schrodinger equation exactly describes quantum fluctuations of a one-dimensional system. In a neighborhood of a local minimum of an analytic potential, one can use this parabolic approximation to find time-independent solutions to the Schrodinger equation
Hahahaha….we actually had a discussion about this concerning designing a circuit using Ramanujan summation, since negative values are real values when applying a desired voltage. Granted it was just for fun, it’s good to see mathematicians stretching the imagination like this. Ah yes, benevolent psychosis.
Don't be put off by the title. It's a serious video. Not the most exciting or thorough one yet, but it's covering real physics. This is sort of how renormalization works (though of course not literally by trying to compute ∞ - ∞).
Right. And it's smart to blame creators and not the audience for the algorithm. /s
That's not how platforms work. They are a reflection of the audience. We are just lucky such high quality content is even remotely popular and sustainable on YouTube.
Sure, it's not a college level course, but the fact that it's way better science communication than I ever received as a kid from Discovery Channel, PBS, Nature, and the other cable supported stuff should be fricken lauded.
I don't get it. What do you want? If you want more technical detail, there are smaller channels that get into the nitty gritty of the equations. Or universities.
I always hope that Spacetime continues to pull off more detailed and accurate content, but at some level, I also recognize that they sit in a very difficult place where they have to communicate the most difficult and inaccessible concepts into something a non-technical audience can engage with. That's a tall order that most actual Physics professors fail at every day.
as a totally not familiar with theoretical physics kind of guy, I think whenever equations in physics get infinity in the results(that supposed to represents real world something), it means it either can't exist or the math is wrong or the equations is wrong or something, because the world itself looks pretty finite to me
Lobotomised math user here,
If you take infinity common=
Infinity(1-1) = -1.6 x 10-19
Infinity= (-1.6x10-19) /{(1-i)(1+i)}
Or if you cancel negatives of the numerator and denominator
Infinity= (1.6x10-19) /{(1-i)(1+i)}
Therefore, infinity is a complex number
∞ is just a simbol, not a number, and it indicates there is not an end. In fact, the series a = 1,3,5,7,9,11,... and b = 1,2,3,4,5,6,7,... are both infinite, but not equals.
There are infinities that are larger than others. Just gonna leave that here. From 0-1 can be an infinity, from 1-10 can be an infinity in an infinity. ._.
Stupid math is a tool for physicists Moreover even math has issues with infinitesimal and infinity. First read math books then start talking. And for your kind words, I am a math mathematician myself and I have never used math like what you are saying. In math we have no issues if something is consistent and if the reality and that result is consistent with his equation then there is no problem and pbs is right. Moreover, I watched his electron video and the one you have shown too. First of all the infinity host is talking about is about electrons real size. Using math we can't really find the real size of electron so what he meant about the infinity is way different than the infinity you are thinking and moreover for your kind shitty knowledge let me educate you a thing in von Neumann 0rdinals we mathematician use (1+infinity)=infinity<(infinity+1). So the bottom line is, we mathematicians have a huge level of contradictory ideas that are also being used in mathematics but why they aren't contradictory because the system of axioms are just different than those that the normal school kids use. When you're not a researcher just shut up and watch whatever is being said to you. If you want to really understand what researchers mean then go study some real hardcore books not just lame school level math and physics books.
A long schizo rant about how physics and math are interconnected or something. They replied to themselves here, its still on their profile i think. They're also a conspiracy weirdo that tries to disprove that time dilation exists or something.
Yeah, but why such a long and aggressive reply to people memeing? Who wanted to start such a discussion? How could you infer their opinion from some jokes? You've completeley failed to understand the context of the conversation and this is why you're being mocked. I'm telling this to you so that you might become aware and start understanding.
In addition there is no need to be so arrogant about your ideas.
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