IT鈥橲 the one equation that everybody knows, but it鈥檚 still just part of a theory. How do you go about proving E really does equal mc2?
The short answer is, with a great deal of care. A multinational team has just published the most accurate ever test of Einstein鈥檚 equation. It involved measuring how the mass of an ion changes when it gives off a photon, and as you can probably imagine, that鈥檚 not a huge change: detecting the difference is equivalent to detecting a hair鈥檚 breadth change in the distance from New York to Los Angeles. Weighing an ion to that accuracy requires more than your standard set of kitchen scales. In fact, it requires quantum scales.
David Pritchard started building his quantum scales at the Massachusetts Institute of Technology in 1985. Back then he wasn鈥檛 interested in verifying Einstein鈥檚 equation; the plan was to weigh subatomic particles called neutrinos and discover whether they could account for the unseen mass that the universe appears to hold. Astronomers had noticed that many galaxies spin faster than their internal gravity should permit 鈥� centrifugal forces should tear them apart. The only explanation was that extra gravity from invisible 鈥渄ark matter鈥� was holding the galaxies together. Pritchard鈥檚 group aimed to find out exactly what neutrinos 鈥� the leading candidate for dark matter 鈥� weighed.
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鈥淚t was such a great story. Working in a little lab with just two or three people, we could discover the missing mass of the universe,鈥� says Eric Cornell. 鈥淭hat was what sucked me into the project.鈥� Cornell is now a Nobel prize-winning physicist based at the University of Colorado. But in 1985 he was a young graduate student sniffing around MIT for a PhD project. He signed up with Pritchard, who was building what is called a Penning trap. Cornell didn鈥檛 know what he was letting himself in for.
Invented in 1936, the Penning trap is the definitive gadget for precision mass measurement. It is a cage of strong magnetic and weak electric fields that work together to keep a charged particle trapped inside (see Diagram). The combination of fields keeps the ion moving in a complex spiral: if the particle left a visible trace it would look like a wiggling Slinky spring toy looped within the trap. Measure the frequency of that wiggle and you can deduce the mass of the particle.
Once you have the trap working properly, that is. Penning traps are notoriously temperamental, and the one in Pritchard鈥檚 lab was more so than most. Any disturbance 鈥� street traffic, a train passing by half a kilometre away, the janitor riding the freight elevator 鈥� could perturb the lone ion鈥檚 tiny dance and disrupt the femtoamp (10-15 amp) signal from its oscillations.
Even when Pritchard鈥檚 group had a trap up and running, they spent most of their time battling electrical interference. 鈥淚n 1995 and 1996 we were banging our heads against the wall from noise problems,鈥� says Michael Bradley, a physicist at the University of Saskatchewan in Canada who joined Pritchard鈥檚 group as a graduate student in 1992. Disaster could strike from anywhere: something as innocuous as a new air conditioner could doom their data to uninterpretable fuzz. Random thermal jostling of electrons in the detector was another source of frustration; the jiggle of a few electrons could swamp the faint signal.
The trap took its toll. Bradley鈥檚 PhD, a quest to improve the caesium mass measurement, spanned seven years. Nor was he the only one sorely tested by the trap鈥檚 capricious behaviour. 鈥淚鈥檓 a pretty cheerful person,鈥� Cornell says. 鈥淏ut it strained my cheerfulness.鈥�
However, in 1999, working with an undergrad named Debbie Fygenson, Cornell made a significant leap forward. The pair altered the way they used the Penning trap so that it confined two different ions at the same time. In this configuration, the ions move in a kind of waltz, keeping a fixed distance apart and circling in step. This created the equivalent of a double-pan kitchen balance: by considering the ratio of the two ions鈥� wiggle frequencies, rather than their absolute values, you can weigh the ions against each other and cancel out the effects of external disturbances.
This revolution wasn鈥檛 put to use immediately. Most of the group鈥檚 work carried on using refinements of the single-ion Penning trap, until in 2003 they reached a point where instabilities in the trap鈥檚 magnetic field were compromising results. Moving to two ions eliminated the magnetic field fluctuations (Science, vol 303, p 334).
After nearly 20 years of work, Pritchard and his colleagues had reached the point where they could operate Penning traps with a sensitivity that could measure mass to 5 parts in a trillion. 鈥淲e鈥檝e made one-third of all the progress that鈥檚 ever been made in mass measurement,鈥� Pritchard says.
Meanwhile, researchers at the US National Institute of Standards and Technology (NIST) in Gaithersburg, Maryland, and the Institute Laue-Langevin in Grenoble, France, had been working on the other side of the equation 鈥� measuring the energy of a gamma-ray photon. They had honed the accuracy of their measurements down to just below 1 part in a million. With these developments in place, the teams were in a position to beat the most accurate tests of Einstein鈥檚 famous equation, which had compared the masses of an electron and a positron with the energy released when they annihilate. This test, which was carried out by a team including some of the NIST researchers, had verified E = mc2 to an accuracy of 1 in 50,000.
鈥淚t was a nerve-racking Friday afternoon waiting for the fax鈥�
The MIT and NIST groups carried out their experiments without sharing results. They each studied radioactive sulphur and silicon ions that emit gamma rays; the MIT group used the Penning trap to measure the mass before and after emission, while the NIST team used their high-precision spectrometer to measure the wavelength of each emitted gamma ray, and thus determine their energy. When each group was completely confident in the accuracy of their results, they faxed them to each other: the MIT group received a value of E, and the NIST group got mc2.
It was a nerve-racking Friday afternoon waiting for that paper to come off the fax machine, Pritchard says. 鈥淵ou ask yourself: what if we have a discrepancy? Though it鈥檚 likely to be something you鈥檝e overlooked, you like to think you鈥檙e going to bring down one of the pillars of 20th-century physics.鈥�
No pillars came crashing down, however: the match was near perfect. We now know that E does indeed equal mc2 to better than 5 parts in 10 million (Nature, vol 438, p 1096).
That鈥檚 it for Pritchard now: he is not planning further tests of Einstein鈥檚 equation. 鈥淚f we pushed it, we might get another three times better, but that鈥檚 not really worth it,鈥� he says. In fact, he has given away his Penning trap to another research group. Which seems rather disappointing when the missing mass of the universe is still missing.
