Solving Mysterious Relativity Paradox: New Derivation of E=mc^2

[jedishrfu]

Interesting new derivation of $E=mc^2$ from an experiment of moving atoms emitting photons.

http://flip.it/AfcjP9 http://flip.it/AfcjP9

But researchers at the University of Glasgow thought of a paradox that would call this basic principle into question. They found instances where moving (but not stationary) atoms spitting out packets of light energy would bring into existence a tiny force that acted like friction, and published research on it earlier this year. A force that exists when an object is moving, but not when it is stationary, violates the core principles of Einstein’s (and Galileo’s) laws of relativity—there isn’t anything special about the laws of physics when something is moving at constant velocity versus when it’s at rest. So, had they accidentally spotted a tiny hole in the most well-accepted theories of physics?

 

[Drakkith]

From the article:

Doing some math and digging into the most basic of modern physics, Newton’s laws, the researchers found the solution to this violation. The light packets and atom both contain momentum, which is mathematically equal to mass times velocity. In high school physics, you always just keep the mass constant and only let the velocity change when calculating a change in momentum. But the researchers thought, well, what if they redo all of the physics of this situation, but allow the mass of the atom to change, too?

This, it turns out, resolves the paradox—the moving atom loses a tiny amount of mass through the emission of energy, eliminating the requirement for a velocity-dependent frictional force. Essentially, they came across Einstein’s most famous equation, E=mc^2, demonstrating that energy and mass are proportional using the basic laws of physics.

“We have employed an entirely non-relativistic analysis to arrive at a paradox the only resolution of which seems to imply the necessity of a central feature of special relativity,” according to the paper published last week in the Journal of Modern Optics. Basically, without using Einstein’s theory of special relativity, the researchers solved their paradox and simultaneously found that a core idea of relativity, that energy and mass are equivalent, pops out regardless.

Forgive me, but is their method significantly different from Einstein's own method of finding the relationship between mass and energy as published in his 1905 paper? They look remarkably similar to my naive eyes.

 

[DrStupid]

I don't see any paradox. The mentioned force is equal to the change of momentum of the atom. That's exactly what the second law says and in full agreement with Galilean relativity.