Einstein's Proof of E=mc²
Why Physics Stack Exchange recommends it
Physics Stack Exchange users link it as a short, intuitive derivation of mass-energy equivalence when explaining or questioning why E=mc\u00b2 holds.
Recommended by 2 people across 2 different months, 2012 to 2018.
What it is
A roughly two-minute minutephysics animation by Henry Reich that walks through Einstein's thought-experiment style argument for why E=mc\u00b2 holds. It uses a simple setup involving light emission and the classical kinetic energy formula to show that losing energy means losing mass.
What people said
Recommends Ord · 2012-07 · Physics Stack Exchange · on “Why did we need relativity to derive $E=mc^2$?”
@SachinShekhar this video ( [this video] ) manages to derive E=mc^2 perfectly well using 1/2*m*v^2. Also, I know that classical and relativistic doppler effects are different (which is why I said *similar* result and not *the same* result); my question is, isn't the classical doppler effect sufficient to discover that when things lose energy they also lose mass, even if the equation derived wouldn't be exactly E=mc^2?
Recommends Phineas Nicolson · 2018-12 · Physics Stack Exchange · on “$E=mc^2$: Why does the speed of light constant affect the Energy or Mass of an object?”
$E=mc^2$ doesn't 'determine how much energy is created when a mass m is converted into energy', it states the mass of a system of energy $E$, or the energy of a system of mass $m$. Minutephysics did a nice video on it [this video]
Cites Earth is a Spoon · 2012-07 · Physics Stack Exchange · on “Why did we need relativity to derive $E=mc^2$?”
Direct answer without arguing about your points (thanks for showing [this video] which is origin of problem): Classical physics can't answer such problems if you forcefully apply your point 2 ( classical doppler effect can't cause lesser energy loss ). With classical physics, we start like this: m is constant, so there must be change in v. If not, we need to in-invent physics. Mind it, particle mass is constant in classical physics and has higher priority than v. Special Theory of Relativity wasn't introduced to create E=mc^2. It was introduced because classical physics failed to explain relativistic phenomena due to wrong understanding of space and time scales. New "Spacetime" scale was introduc
Cites Sophomore_Jinx · 2016-04 · Physics Stack Exchange · on “The mass-energy equivalence is a principle which can not be derived from anything?”
Not duplication) I couldn't find the answer for the general case, instead of the special case that I already seen in Youtube I hyperlinked. I will fully satisfy with not only a mathematically rigorous proof, but also just any argument. For example, I was impressed by the thought experiment(in Youtube : [this video] ) arguing the equivalence principle for the special case that the rest mass of an object actually turned out to be a part of total energy of the object. Is there any argument like that, but for the general case that the total energy(= rest E's + kinetic E's + potential E) of a system must be the total mass of the system which determines the amount of gravitational attraction and resist