Solving Apparent Violation Of Relativity Leads To New Way To Derive Einstein's Famous Equation

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Earlier this year, researchers discovered that photon-emitting atoms moving through a vacuum experienced a friction-like force never detected before. This was not just unexpected but it also challenged one of the crucial principles of Einstein’s special relativity.

The team looked at the whole setup again trying to understand if the effect was real, what could its cause be, and if it was a violation of relativity. As reported in their new paper published in the Journal of Modern Optics, the effect is very real but it was not a violation. However, the new approach has led them to a new way to derive E=mc2 in physics.

The principle of relativity simply states that if there are no external forces a stationary object stays stationary, and objects in motion will continue to move with a constant velocity. This principle was first written out by Galileo in 1632 and became a cornerstone of mechanics and eventually of Einstein’s theory.

The team had studied this in an excited two-level atom. Such an atom would emit a photon to go from an excited state to the ground state. If the atom was stationary, once it emits the photon it would recoil, just as expected. But in the moving atom, depending on which direction the photon has been emitted (either backward or forward) the momentum was not conserved anymore. This was caused by the Doppler effect and it created quite a problem with the theory.

“In short, we have a friction force associated with the spontaneous emission event. Yet the existence of a force in one frame that does not exist in another seems to be at odds with both the Galilean and Einsteinian principles of relativity. Hence we have a paradox,” the researchers Stephen Barnett and Matthias Sonnleitner, from the University of Glasgow, explain in the paper.

So, how did they solve the paradox? The team actually used high school physics, but with a twist. Usually, in conservation of momentum problems, you vary the velocity of your billiard balls or ice skaters, or whatever you're using, but the mass stays the same. The researchers instead allowed for both the mass and the velocity to change. Not only did it solved the paradox, it also delivered to the researchers a familiar equation.

By allowing the mass to change, they proved that the mass loss by the atom abandoning its excited state is equivalent to the energy of the photon escaping. Their work found the mass-energy equivalence that made Einstein famous, and surprisingly they found it without having to use any relativistic ideas.

[H/T: Gizmodo]

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