Image: Robert Couse-Baker/Flickr

Even if you don’t know much physics, you probably know one of its core tenets: an object at rest stays at rest, and an object in motion stays in motion. In fact, in a vacuum where there’s literally nothing to slow things down, things don’t prefer being at rest or in motion. This plays out in real life all the time—when you’re sitting in the bathroom on a plane, for instance, you can’t feel that you’re moving 500 miles an hour. You only feel the changes in your velocity via the bumps.

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?

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“Either we missed something subtle or there was something wrong with the techniques the entire community was using to analyze light-matter interactions,” Stephen Barnett, a theoretical physicist at the University of Glasgow told Gizmodo. It turns out that their paradox came from leaving out tiny effects of mass and energy in the atom. And, they say, using only the classical, pre-Einstein laws of physics, they simultaneously killed that frictional force and came up with a new way to derive Einstein’s laws.

The paradox that arose in Barnett’s earlier paper comes from combining two crucial points. First of all, atoms (moving or not) that have gotten excited by a jolt of energy in the past can spontaneously release packets of light energy called photons. Secondly, photons act as particles and waves simultaneously, and anything that acts like a wave experiences the Doppler effect. You’ve experienced a kind of Doppler effect when a train blasting its whistle whizzes by—the sound waves are squished as the train move towards you and stretched as the train moves past, making the pitch change. With light, this same effect changes its wavelength, or color, making it look bluer and redder, and therefore changes its momentum.

Combining these facts, the researchers realized that if a moving atom spat out a forward-moving photon, an observer would see the atom losing more momentum than if it spat out a backward-moving photon, thanks to the Doppler effect. The momentum changes on the stationary atom—where there’s no Doppler effect—average out to zero, as it recoils to make up for the lost photon. Those changes do not average out to zero when the atom is moving. That creates a leftover force. “In short, we have a friction force associated with the spontaneous emission event,” the researchers wrote. “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.”

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They thought they found a force that only exists when the atom is moving, and that’s bad.

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.

Physicist John Baez from the University of California, Riverside emphasized one of the lines from the paper: “We may ponder the point at which relativity sneaked into our analysis or simply marvel at the way in which in physics seems to take care of itself.” Another outside researcher I sent the paper to, Martin Bojowald at Penn State, felt the paper was an interesting teaching moment and “provides a new and perhaps elegant derivation of E=mc^2,” according to an email. He did take some issue with the author’s claim that they employed an entirely non-relativistic analysis, since he thought the speed of light remained constant in the analysis (and this is a core principle of special relativity). Barnett disagreed with Bojowald, and said the effect would have appeared regardless.

Ultimately, the central point of the paper is that physics is weird and words like “classical,” “quantum,” and “relativistic” are things humans made up to categorize a universe that can really behave however it would like. It concludes that “[Physics] has no regard for our attempts to classify parts of it as classical or quantum, or as relativistic or non-relativistic.”

[Journal of Modern Optics]