Einstein's Derivation of E=Mc^2

Рет қаралды 909

Жыл бұрын

Einstein's original thought experiment and derivation that a photon has (inertial) mass equal to its energy (E=Mc^2). Taken from his original 1905 paper: "Does the Inertia of a Body Depend on its Energy-Content?"
Original paper (translated to English from German): www.fourmilab.ch/etexts/einst...

Пікірлер: 22

@juliavixen176 6 ай бұрын

Just as a historical note, Thompson, Lorentz, Poincaré, et al. had a bunch of theories about "electromagnetic mass", "transverse mass", "longitudinal mass", etc. which were a complicated mess and... wrong, so they don't get mentioned very often in undergrad physics classes. A funny thing about E=mc² is that Thompson almost derived it from modeling an electic charge moving through a dialectric medium. And Poincaré derived E=mc² just from the recoil of light bouncing around inside a box of perfect mirrors. It's basically this same setup as Einstein used in this video. Everyone forgets about Poincaré. (Actually, a *lot* of stuff in Special Relativity is the same as it is in the Lorentz-Poincaré flavor of aether, but Einstein could do it without requiring an aether. Length contraction was Fitzgerald's idea, time dilation is Poincaré's, "Relativistic mass" had been experimentally measured with cathode rays by Kaufman in 1904, etc. etc. Nobody working in the field was surprised by Einstein's results.)

@physicsalmanac 6 ай бұрын

Thanks for the historical info. As usual, and in accordance with Stigler's Law of Eponymy, only the person who finds the last piece of the puzzle is remembered by history...

@jensphiliphohmann1876 Жыл бұрын

Since when is it known that photons carry not only energy but also momentum?

@kenbirdwell Жыл бұрын

Since 1901 and the Nichols Radiometer experiment.

@physicsalmanac Жыл бұрын

It was already known that light carried momentum since the development of Maxwells equations (mid 1800s). But this is the wave theory of light. For a single photon (particle theory of light) this was developed by Einstein earlier the same year (1905). Regarding this thought experiment, in the actual paper Einstein looked at it from an energy point of view. I modified it slightly because in his version the math and physics is a bit more advanced and requires some knowledge of special relativity.

@martijn130370 3 ай бұрын

super

@physicsalmanac 3 ай бұрын

Duper!

@thomasolson7447 Жыл бұрын

I think it's interesting that the momentum goes to zero. If the momentum goes to zero, doesn't that mean the photon goes in a straight line, without an up and down component? That's where sin lives.

@physicsalmanac Жыл бұрын

It’s not that the momentum goes to 0. It starts off as 0 since the box is initially at rest. Since there are no external forces, momentum is conserved. So it must remain 0 at all times. Yes the photon goes in a straight line… as long as the observer is not accelerating or there is no gravitational field. More specifically, we call this an inertial observer.

@thomasolson7447 Жыл бұрын

@@physicsalmanac there is a conundrum that I am having here. In a unit circle triangle, if one leg is 0, the other leg is 1. The two legs are energy and momentum, mc^2 is the hypotenuse (momentum is on the wrong side so it is a jacketed imaginary value). If momentum can be 0, why can't it be 1 and energy be 0? This would imply v=c. Also, isn't this contrary to everything we are being told about energy? Also, I suppose E= ± m*c^2*sqrt(1-(v/c))^2, factoring out the c in the square root, E= ± m*c*sqrt(c^2-v^2). If we multiply everything by gamma and it is greater than 1, the speed of light also increases. Sorry, you must get a lot of this confusion.

@physicsalmanac Жыл бұрын

I don’t really follow… why are you multiplying the energy by gamma? And why would that increase the speed of light? Energy = 0 means there’s nothing there. So you can’t have non zero momentum and zero energy.

@thomasolson7447 Жыл бұрын

@@physicsalmanac E^2=(m*c^2)^2+(p*c)^2 Oh, I made an error in my previous post. I need to be more careful. E^2=(m*c^2)^2+(m*v*c)^2 m*c^2 looks like a dotproduct, so I thought it might have been the hypotenuse. Solving for E^2 under this equation (instead of the other one I used). ±sqrt(c^2+v^2)*m*c So, looking at that solution, it says at v=0 it is m*c^2. At v=c, it is m*c^2*sqrt(2). So, I take E^2 and make it into a unit vector for: 1=(c/sqrt(c^2+v^2))^2+(v/sqrt(c^2+v^2))^2 The main reason I thought mc^2 was the hypotenuse is because of gamma. 1/sqrt(1-(v/c)^2) Factor out the c. c/sqrt(c^2-v^2) cos(arctan(v/c))=c/sqrt(c^2+v^2) cos(arctan(i*v/c))=1/sqrt(1-(v/c)^2)=c/sqrt(c^2-v^2) I just thought that if I'm multiplying mass by gamma, maybe there should be an 'i' in the original E^2 equation. It looks like something that can be overlooked. I think if normal E^2 was in the numerator, and the 'i' version of E^2 was in the denominator, wouldn't you have tanh(2*arctan(i*v/c))?

@physicsalmanac Жыл бұрын

The momentum in that energy equation is defined with respect to proper time. So p = gamma*mv. as v goes to c, E and p go to infinity. A better way to think of it is if p is very large m becomes insignificant and you can say E = pc. This is the ultra relativistic limit.

@mr.minecraft1176 Жыл бұрын

Yo "Physics Almanac" would you like to work with me on physics?

@physicsalmanac Жыл бұрын

Maybe. What do you have in mind? What do you want to work on?

@mr.minecraft1176 Жыл бұрын

@@physicsalmanac You know.... something odd - I'm tryna mix Quantum Computers and AI together

@physicsalmanac Жыл бұрын

You’re working on that now?

@mr.minecraft1176 Жыл бұрын

@@physicsalmanac yup

@qualquan 11 күн бұрын

Tries to DERIVE m = E/C^2, BUT by assuming that kinetic photon has P = momentum and then ALSO assumes that P = E/C or E = PC. So merely DERIVES his ASSUMPTIONS.. Then refuses to say if kinetic mass = m is nonzero except ask how much does light weigh in his next video.. So far he proves to be self delusional.

@physicsalmanac 10 күн бұрын

Well this is not my derivation, but Einstein’s. So call him delusional, not me. M=E/c^2 is not the same claim as E=pc. So there’s nothing circular here. E= pc was already known experimentally, and explained theoretically. So it’s a perfectly fair assumption to make. I’m not sure what you mean by a kinetic photon…? (Are there non-kinetic photons?) I’m also not sure what you mean by kinetic mass? Do you mean inertial or relativistic mass? Maybe it’s called differently in another language? You can watch the first video in this series where I discuss the different types of masses that have been used in physics over the years. It may clear up some terminology issues.