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Comment by gus_massa | Hacker News Reader

I didn't downvote it, but short comments are a very big risk. People may misinterpret it, or think it's crackpot theory or a joke and then downvote.

When in doubt, add more info, like:

But the complete equation is E=sqrt(m^2c^4+p^2) that is reduced to E=mc^2 when the momentum p is 0. More info in https://en.wikipedia.org/wiki/Mass%E2%80%93energy_equivalenc...

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The next section of the wikipedia link discusses the low speed approximation, where sqrt(m^2c^4+(pc)^2) ≈ mc^2 + 1/2 mv^2.

Calling E=mc^2 an "approximation" is technically correct. It's the 0th order approximation. That's just pointlessly confusing. A better word choice would be "a special case".

i think we are venturing into pedantic territory - the point of my comment is that the full derivation is a little harder than just E=mc^2 dimensional analysis

This is why RLHF causes those overly verbose answers to simple questions, it's a fundamentally busted evaluation function so you wind up optimizing for the wrong thing

[Sorry for the dealy.]

In one extreme there are wall of text and in the other extreme very short answers that only the initiated understand (like inside jokes). Somewhere in between there is a sweet spot that helps everyone else to follow the discusion and gain a litle of knowdledge.

(I don't claim I get the best lenght in my comments, but I hope it's good enough.)

What I learnt is that there is a rest mass and a relativistic mass. The m in your formula is the rest mass. But when you use the relativistic mass E=mc² still holds. And for the rest mass I always used m_0 to make clear what it is.

sounds like you had a chemistry education. relativistic mass is IMO very much not a useful way of thinking about this and it is sort of tautologically true that E = m_relativistic because “relativistic mass” is just taking the concept of energy and renaming it “mass”

This is all sort of silly IMO. The equation, like basically all equations, needs context. What’s E? What’s m? If E is the total energy of the system and m is the mass (inertial or gravitational? how far past 1905 do you want to go?), then there isn’t a correction. If m is rest mass and E is total energy, then I would call it flat-out wrong, not merely approximate. After all, a decent theory really ought to reproduce Newtonian mechanics under some conditions beyond completely at rest.

IMO, when people get excited about E=mc^2, it’s in contexts like noticing that atoms have rest masses that are generally somewhat below the mass of a proton or neutron times the number of protons and neutrons in the atom, and that the mass difference is the binding energy of the nucleus, and you can do nuclear reactions and convert between mass and energy! And then E=mc^2 is apparently exactly true, or at least true to an excellent degree, even though the energies involved are extremely large and Newtonian mechanics can’t even come close to accounting for what’s going on.

inertial mass, rest mass, gravitational mass - these are essentially all the same thing. “relativistic mass” is an additional concept where we rewrite energy as mass and is considered archaic

I should have used m_0 to avoid confussion. Anyway, as he sibling comment says, most modern advanced books of special relativity try to avoid the relativistic mass. It's useful for some calculations, like synchrotron, but the problem is that for forward/backward acceleration you must use other number so the relativistic mass add confussion. https://en.wikipedia.org/wiki/Mass_in_special_relativity#His...

Kind of agree. But pervasive downvoting by folks who don’t understand the subject is a form of forum rot. The risk is only that we expose the rot. Not such a terrible risk, because either the owners notice and fix the problem, or the forum continues to rot. In the latter case karma points wont be desirable in the long run.

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