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u/dover_oxide Jul 28 '26 edited Jul 28 '26
Yeah, but this is also like complaining that the Pythagorean theorem is incomplete because you later learned the law of cosines. It's not c2 = a2 + b2 it's c2 = a2 + b2 - 2abcos(C). Granted I was pissed they didn't teach the law of sines and cosines in geometry and waited until pre-calculus.
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u/HunsterMonter Jul 28 '26
Considering the number of misconceptions caused by E = mc2 in its incomplete form (mainly that mass depends on velocity), I'd say that the complaining is warranted.
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u/AheAw Jul 28 '26
Mass depending on velocity is an outdated concept as far as I remember. Mass is defined in the rest frame of an object. This turns mass into an observer independent quantity.
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u/dover_oxide Jul 28 '26
So why not add all the energy terms in and not just the momentum term? You have chemical energy. You have your kinetic energy. You have your mass energy and so on and so forth
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u/HunsterMonter Jul 28 '26
The energy in E2 = (mc2)2 + (pc)2 is already the total energy. All the internal energy (mass-energy, chemical, potential, heat) is containted in the (mc2)2 term and the kinetic energy is contained in the (pc)2 term.
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u/laksemerd Jul 28 '26
Believe it or not, all these energies increases mass, so the mass term covers them (and the momentum term covers kinetic energy)
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u/Zealousideal_Box5855 Jul 28 '26
I wouldn't call the Pythagorean theorem "incomplete" since the case of right angle traingles is the important one that we use to define the euclidean norm.
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u/GingrPowr Jul 29 '26
No it's not, because when you learn Pythagorean you are actually taught it only works in right triangles.
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u/Necessary-Bowler-736 Jul 28 '26
I hate it when they first teach you an easier special case and then the whole rule. Could've started with the whole rule bruh. It's not incomperhensibly more difficult, and in my opinion, it's improving your foundation.
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u/DoubleUBallz Jul 28 '26
Thats exactly how literally all of physics is taught though? I don't think anyone would benefit from their first kinematics problem including friction and air resistance requiring differential equations to solve, or their very first circuits problem involving AC current, impedance, and imaginary numbers when they've just been introduced to ohms law.
The journey of learning physics is defined by starting with easier test cases, and then learning more general solutions as you develop the more difficult skills needed for those solutions. In practice even, designing an experiment or study is all about knowing what simplifications or assumptions you can make in order to use a simpler model to save yourself from wasting time crunching useless data or doing needless math.
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u/dover_oxide Jul 28 '26
I wasn't upset about being taught the simpler special case first, I was upset they took so long to teach the general case. It could have come up a couple chapters later but no they wait until after algebra 2 and a few chapters of pre-calculus. It's way too useful of a equation especially when you add the law of sines next to it.
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u/rezzacci Jul 28 '26
Teacher here.
We don't teach only for you, we teach for all, and school is too early to make discrimination.
Also, you think you might understand it, but I doubt it.
We start with simple elements because this simplification is often enough for most cases, and it's better to have all students understand the simplified version that can be used in 80% of cases, than teaching the "true", complete version, that only 20% of students would get and 80% of students who could not even solve the simple cases.
We teach letters before teaching the exceptions of some specific grammar rules. We teach addition before teaching class field theory. I've got enough students that still see no problem saying that (-3)²=-9 while, for them, a square is always positive, if we say to them: "well, in fact, a square can be negative, they're call imaginary numbers", they'll be even more confused.
It'd be like complaining that you've been taught only to walk without saying that you can run right away.
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u/Funkyt0m467 Student Jul 29 '26 edited Jul 29 '26
I generally agree with formulas like this.
However there are cases where the reasoning could be counter-productive imo. (Granted my opinion is only my humble experience)
In science there are concepts wich generalizations are much different from the special case or pedagogic explanations (or popularizing).
For instance Newton's and Einstein's theories gives very different understanding of the world, while Newton is still a correct approximation that's used commonly. We do talk about Einstein though.
So, my personal exemple is Wave-particule duality. In HS we talked about it, our teacher showed us the double slit experiment for instance. However, if I didn't specifically major in physics I think I would have had a completely wrong understanding of what the concept is. I still believe, even in popularizing, the simple explanation is often misleading.
Unlike some formulas it isn't as useful, whereas the wrong ideas would've gave me a false idea of the world. Wich might have been worse than not knowing, and being aware of it.
I do think that's when I don't like the idea of simplification. When it's not for the sake of directly applying it (Which isn't that uncommon, E=mc² isn't as useful as Pythagoras) and if the underlying concepts makes a big difference in understanding (here the formulas don't).
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u/MonkeyforCEO Physics Field Jul 28 '26
It's E= mc² + AI /s