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E=mc2 passes tough MIT test

MIT physics Professor David E. Pritchard, left, and James K. Thompson display the key part of the apparatus they used to check Einstein's most famous equation. Their test was 55 times more accurate than previous tests.
MIT physics Professor David E. Pritchard, left, and James K. Thompson display the key part of the apparatus they used to check Einstein's most famous equation. Their test was 55 times more accurate than previous tests.
Photo / Donna Coveney

In a fitting cap to the World Year of Physics 2005, MIT physicists and colleagues report the most precise direct test yet of Einstein's most famous equation, E=mc2.

And, yes, Einstein still rules.

The team found that the formula predicting that energy and mass are equivalent is correct to an incredible accuracy of better than one part in a million. That's 55 times more precise than the best previous test.

Why undertake the exercise? "In spite of widespread acceptance of this equation as gospel, we should remember that it is a theory. It can be trusted only to the extent that it is tested with experiments," said team member David E. Pritchard, the Cecil and Ida Green Professor of Physics at MIT, associate director of MIT's Research Laboratory for Electronics (RLE) and a principal investigator in the MIT-Harvard Center for Ultracold Atoms.

Pritchard and colleagues from the National Institute of Standards and Technology (NIST), the Institut Laue Langevin (ILL), Florida State and the University of Oxford report their results in the Dec. 22 issue of Nature. They write: "If this equation were found to be even slightly incorrect, the impact would be enormous -- given the degree to which [it] is woven into the theoretical fabric of modern physics and everyday applications such as global positioning systems."

In the famous equation, E stands for energy, m for mass, and c for the speed of light. "In the test, we at MIT measured m, or rather the change in m associated with the energy released by a nucleus when it captures a neutron," said former MIT graduate student Simon Rainville.

The NIST/ILL scientists, led by Hans B̦rner of ILL and the late Richard Deslattes��of NIST, measured E. (The speed of light is a defined and therefore exactly known quantity, so it was simply plugged into the equation.)

Specifically, the ILL/NIST team determined the energy of the particles of light, or gamma rays, emitted by the nucleus when it captures a neutron. They did so using a special spectrometer to detect the small deflection of the gamma rays after they passed through a very pure crystal of silicon.

The mass loss was obtained at MIT by measuring the difference between the mass of the nucleus before the emission of a gamma ray and after. The mass difference was measured by comparing the cyclotron orbit frequencies of two single molecules trapped in a strong magnetic field for several weeks.

Pritchard notes that the mass of the nucleus is about 4,000 times larger than the much smaller mass difference. As a result, "determining the mass difference requires the individual masses to be measured with the incredible accuracy of one part in 100 billion -- equivalent to measuring the distance from Boston to Los Angeles to within the width of a human hair!"

Despite the results of the current test of E=mc2, Pritchard said, "This doesn't mean it has been proven to be completely correct. Future physicists will undoubtedly subject it to even more precise tests because more accurate checks imply that our theory of the world is in fact more and more complete."

Pritchard's MIT colleagues are Rainville (now at Universit̩ Laval, Quebec) and James K. Thompson (now an RLE postdoctoral associate in the MIT-Harvard Center for Ultracold Atoms). Rainville and Thompson are co-lead authors of the Nature paper.

This work was funded by the National Science Foundation and by a Precision Measurement Grant from NIST.

Einstein on E=mc2

"It followed from the special theory of relativity that mass and energy are both but different manifestations of the same thing -- a somewhat unfamiliar conception for the average mind. Furthermore, the equation E is equal to m c-squared, in which energy is put equal to mass, multiplied by the square of the velocity of light, showed that very small amounts of mass may be converted into a very large amount of energy and vice versa. The mass and energy were in fact equivalent, according to the formula mentioned above. This was demonstrated by Cockcroft and Walton in 1932, experimentally."

To hear an audio clip of Einstein explaining this, go to

A version of this article appeared in MIT Tech Talk on January 25, 2006 (download PDF).

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