A team of researchers from the University of Glasgow found what appeared to be a basic contradiction in Einsteins physics, so they went on trying to fix it. The contradiction or rule that confused these researchers was that when they observed atoms in motion, they were emitting small bursts of light, that sometimes generated a new friction-esque force. Identical, but stationary atoms were induced to spit out light beams, which had no corresponding force. So they set out to find what happened.
The researchers set out to identify where the extra bursts of light and energy was coming from and they found out that the photons that go flying off these atoms act both as particles and as waves, and as waves they are subject to the Doppler effect. Furthermore, they found that the energy of the photons spat out in a forward-moving direction, would be higher, than the energy of the photons that spat out in a backward-moving direction. Also, these two types of energy coming from photons, both moving in a forward and backward direction, still leave the universe with some excess energy that didn’t seem to come from anywhere. The researchers had a solution to this.
The solution was found in a standard equation in classical physics, (p=mv), (p) being Momentum, (m) being mass and (v) being velocity. Usually running this equation involves keeping the mass static while the velocity changes, since for the most part the mass isn’t going to change enough to have a meaningful effect, in this case of the tiny atoms, allowing for the mass to change accounted for the excess energy. In other words, what the researchers found was another way to arrive at the conclusion that mass and energy are interchangeable.
These researchers found at the solution to this problem by using one classical equation, (p = mv), and that the excess energy was the change in mass of tiny atoms.
Source: http://www.thespaceacademy.org/2017/11/a-mystery-of-einsteins-relativity-has.html