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| | title = Complex Conjugate | | | title = Complex Conjugate |
| | image = complex_conjugate.png | | | image = complex_conjugate.png |
− | | titletext = Fun fact: if you say this every time a professor does something to a complex-number equation that drops the imaginary part, they'll eventually move the class to another room and tell everyone else except you. | + | | imagesize = |
| + | | titletext = Fun fact: if you say this every time a professor does something to a complex-number equation that drops the imaginary part, they'll eventually move the class to another room and tell everyone else except you. |
| }} | | }} |
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| ==Explanation== | | ==Explanation== |
− | This was the second comic with one of [[Randall|Randall's]] [[:Category:Fun fact|fun facts]].
| + | This comic is a joke on the common phrase "Shit just got ''real''", meaning that something has suddenly increased in difficulty so it is now a real challenge. [[Cueball]] is standing in front of a board delivering a lesson, and is about to multiply a wavefunction by its complex conjugate. In mathematics, the product of a complex number and its conjugate removes the imaginary part, effectively making it "real". Accordingly, Cueball dictates that the people who are not skilled enough to leave. |
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− | This comic is a joke on the phrase "Shit just got real", which means "something has suddenly increased in difficulty and become genuinely challenging or dangerous". | |
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− | [[Cueball]] is standing in front of a board delivering a lesson, and is about to multiply a wavefunction by its complex conjugate. A {{w|wave function}} is a mathematical description of a quantum system which uses {{w|complex number|complex}} values - numbers that have both a {{w|real number|real}} part and an {{w|imaginary number|imaginary}} part. Multiplying a wavefunction by its complex conjugate is a common thing to do, as it yields the probability density of where a particle is likely to be found, which is a real-valued function. | |
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− | Complex numbers can be written in the form a + bi, where a is the real part and bi is the imaginary part. i is the imaginary unit, defined so that i² = -1. The {{w|complex conjugate}} of a complex number simply reverses the sign on the imaginary part - so for the number above, the complex conjugate is a - bi.
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− | Multiplying the complex number by its own complex conjugate therefore yields (a + bi)(a - bi). If you multiply out the brackets, you get a² + abi - abi - b²i². The abi cancel each other out, and i² can be replaced by -1. Thus, the result is a² + b², a real number, so "shit just got real" as Cueball promised.
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− | The title text notes that you can make this joke in class every time a calculation is performed that drops the imaginary part from a complex number, but warns that it would be so annoying that the professor will eventually find a way to have the class without you in it. Because nonreal numbers are often considered to have no physical significance, turning them into real numbers to produce a final answer is so common that this joke would quickly become tedious.
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− | The wave function shown on Cueball's board is the {{w|Schrödinger_equation|time-dependent Schrödinger equation}} <math>i\hbar\dfrac{\partial}{\partial t} = \hat{H}\Psi</math>, a {{w|Differential equation|differential equation}} that the {{w|Wavefunction|wavefunction}} Ψ, which determines the possible positions of a quantum particle over time, always satisfies. The {{w|Derivative#Partial_derivatives|derivative}} should be written with ∂Ψ on the top; the omission of the Ψ may be a mistake.
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| ==Transcript== | | ==Transcript== |
− | :[Cueball, holding a marker pen down in one hand, is standing at a whiteboard with two equations, one of which is the time-dependent Schrodinger equation and the other shows what the wavefunction equals, but from there it becomes unreadable. Below is a graph with a bell-shaped curve. There are also other unreadable markings on the board below the second equation and next to the graph.] | + | :[A teacher is standing at a whiteboard covered in equations.] |
− | :Cueball: Okay, anyone who's feeling like they can't handle the physics here should probably just leave now. | + | :Teacher: Okay, anyone who's feeling like they can't handle the physics here should probably just leave now. |
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− | :[In a frame-less panel Cueball is seen writing on the whiteboard. This is seen from the side of the board, so it is just a thin line with a shelf at the bottom for putting the pen on.]
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− | :Cueball: Because I'm multiplying the wavefunction by its complex conjugate.
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− | :Cueball: That's right.
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− | :[Dramatic zoom in on Cueball appears to be writing the final part of his next equation.] | + | :Teacher: Because I'm multiplying the wavefunction by its complex conjugate. |
− | :Cueball: Shit just got ''real''. | + | :Teacher: That's right. |
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| + | :[Dramatic zoom. It appears the teacher is writing on the side of the panel.] |
| + | :Teacher: Shit just got |
| + | :real. |
| {{comic discussion}} | | {{comic discussion}} |
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− | [[Category:Fun fact]]
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− | [[Category:Comics featuring Cueball]]
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− | [[Category:Math]]
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− | [[Category:Physics]]
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− | [[Category:Puns]]
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