Taken from the October 2016 issue of Physics World

The simultaneous drop of two dissimilar masses is one of the oldest experimental results. But as Jon Cartwright reports, new techniques may show that not everything falls the same way

What goes up must come down. But does everything come back down at the same time? Galileo said yes. Newton said yes. Einstein said yes. Still, many physicists today secretly believe the answer might be no.

That belief might seem strange. Countless experiments over the years have concluded that two objects dropped from a height will – regardless of their composition – fall to the ground at precisely the same moment, provided they do not suffer disparities in air resistance. Schoolchildren are routinely taught about this “universality of free fall”, often with reference to the famous 1971 video of the US astronaut David Scott standing on the Moon and demonstrating that, in the absence of any air, even a feather and a hammer fall in unison. If the universality is not clear from everyday experience, it is at least implied by Newton’s laws of motion and gravitation, which combine to suggest that the acceleration of a body due to gravity is proportional only to the mass of the planetary object it is being attracted to, not to its own mass. The conclusion would appear irrefutable.

Yet, some violation of the universality of free fall could come in very useful. One of the greatest obstacles to progress in physics is the gaping chasm between the classical world of Einstein’s general theory of relativity, our current best theory of gravity, and the fuzzy, largely microscopic world of quantum mechanics, which accurately describes the other three known forces of nature: electromagnetism; and the strong and weak nuclear forces. A bridge between the two worlds – a quantum theory of gravity – is the neatest theoretical solution, but it has been elusive. Some candidate theories would seem to entail additional forces that, at very fine timescales, create an imbalance in the pull of gravity for different objects. Indeed, the observation of a tiny and hitherto imperceptible difference in acceleration for two falling objects could be the first evidence that general relativity is flawed, ushering in a new paradigm in modern physics.

Before the turn of this century, the best tests of gravitational free fall could find no deviation in the acceleration of two masses to within one part in 10 trillion. But a new host of lab- and space-based experiments promises up to a 10,000-fold increase in this precision, potentially offering the first chance of testing quantum gravity theories. What is more, some experimentalists are presenting new ways to approach tests of free fall – for example, by employing purely quantum systems, or antimatter. The question “Does everything fall back to Earth at the same speed?” may soon have an answer far more accurate than ever before.

An old story

To Galileo, the answer was certainly obvious. Even as a young medical student at the University of Pisa in Italy, in the late 16th century, he argued that all bodies must fall to the ground at the same speed, because otherwise, in a shower of hailstones, large stones would reach the ground before small stones – assuming they all start their fall at the same altitude. This post-Aristotelian logic was famously tested in the (almost certainly apocryphal) story of Galileo dropping two different weights from the top of the Leaning Tower of Pisa.

But it was only the better part of a century later with the Newtonian revolution that a mathematical basis for the universality of free fall was established. Combine Newton’s second law of motion (the force on an object is equal to its mass multiplied by its acceleration in the direction of the force) and his law of universal gravitation (gravitational attraction is directly proportional to the product of two gravitating masses and inversely proportional to the square of the distance between them), and you naively find that the acceleration of a gravitating object is proportional to the mass of the object it is being attracted to, not to its own mass. Naively, that is, because the combination of these laws implicitly assumes an equivalence between two types of mass. On the one hand there is inertial mass, which we feel in situations describable by the second law of motion – turning a corner in a car, say – and on the other hand there is gravitational mass, which we feel all the time, being attracted to the surface of the Earth.

This implicit assumption of an equivalence between inertial and gravitational mass was pointed out by the German physicist Heinrich Hertz in the late 19th century. “[The properties] must be thought of as being completely independent of each other,” he wrote, “but in our experience, and only in our experience, appear to be exactly equal. This correspondence must mean much more than being just a miracle”: there must be “a deeper explanation”.

In 1915, within his general theory of relativity, Einstein established what has since become the agreed explanation: space–time. Like Galileo and Newton before him, Einstein accepted that objects travel in a straight line unless a force drives them otherwise. Unlike his predecessors, however, he established that this straight line exists on the fabric of 4D space–time, which is warped by mass. In the vicinity of very massive objects such as our planet, there is a pronounced depression in space–time. Roughly speaking, that means that a straight line in our everyday, 3D Euclidean geometry is bent inwards, towards the centre of the Earth, in much the same way that a straight flight path from London to New York appears on a 2D map to be an arc.

In this description, we feel gravity pulling us towards Earth simply because the ground under our feet – or the chair under our bottom – is diverting us from this straight line in distorted space–time. Likewise, we experience inertia when we are pushed from our existing straight line by another force – the grip of car tyres, the blast of a rocket or the sobering contact of an easy-to-miss lamppost.

In short, Einstein showed that inertia and gravity are locally two sides of the same coin: that they are the same is embodied in his “equivalence principle”.

Today, physicists describe three versions of the equivalence principle, of which one is the universality of free fall, or the so-called weak equivalence principle. Another version, known for historical reasons as the Einstein equivalence principle, states that this weak equivalence principle holds whenever and wherever an experiment is carried out. The third version, the so-called strong equivalence principle, states that the Einstein equivalence principle holds even if a mass is large and has substantial internal gravitational interactions.

In general, the equivalence principle can be seen to form the basis for general relativity, which is defined as a “metric” theory – that is, one in which matter behaves according to functions of distance on the fabric of space–time. Quantum mechanics is not a metric theory, and it is therefore widely assumed that any future theory bridging quantum mechanics with general relativity will have to ditch one or more aspects of the equivalence principle. “If you’re looking for a unified theory, you may have to abandon this concept of a metric space–time theory,” says experimental physicist Sven Herrmann of ZARM at the University of Bremen, Germany. “That would mean the equivalence principle was violated.”

Weak principle

One well-established method to test the strong equivalence principle is lunar laser-ranging, which takes advantage of retroreflectors – devices like cat’s eyes that reflect light back to its source – placed on the Moon during the US and Soviet Moon landings. The best results using this technique were reported in the mid-1970s by physicists Irwin Shapiro and Charles Counselman at the Massachusetts Institute of Technology in Cambridge, US, together with Robert King of the US Air Force Cambridge Research Laboratories. They analysed nearly 1400 measurements of the time required for laser light to go from a telescope on Earth to a retroreflector on the Moon and back, and found that the Earth and Moon must be “falling” towards the Sun with exactly the same acceleration, give or take one part in a trillion (1976 Phys. Rev. Lett. 36 555). That precision is expected to be bettered soon with new data taken as part of the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) in New Mexico, US.

Indeed, it has been bettered already by another tool: the torsion pendulum, which consists of two different masses suspended on a wire. If the Sun’s gravity pulls on the masses differently due to a violation of the universality of free fall, there should be a twist of the pendulum. In 1999 Eric Adelberger and others in the Eöt-Wash group at the University of Washington in Seattle, US, found no such twist to a precision of one part in 10 trillion (1013), setting the current record for tests of the weak equivalence principle (Phys. Rev. Lett. 83 3585).

In more than 15 years since this result, the Eöt-Wash group has struggled to improve its experimental precision, though it still hopes to do so by an order of magnitude by cooling its apparatus to near absolute zero. But many experimentalists believe it will prove too difficult to surpass it here on Earth. “It seems to me that a significant improvement in accuracy will only take place in space-based experiments in the future,” says Herrmann. “It’s hard for me to see that a 10–15 experiment will be done on the ground. But, with some clever new ideas, maybe!”

As it happens, this year brings the first possibility of a 10–15 precision from a space-based experiment, namely Microscope, or the Micro-Satellite à traînée Compensée pour l’Observation du Principe d’Equivalence (the drag-compensated micro-satellite for the observation of the equivalence principle), which was launched in April. Developed by the French National Centre for Space Studies (CNES), Microscope contains two cylindrical test masses – one made of the light metal titanium and the other of an alloy of the two heavy metals platinum and rhodium. The cylinders sit concentrically (to have coincident centres of mass) on separate accelerometers, undisturbed by terrestrial sources of noise, such as seismic perturbations.

Being in orbit, the satellite and its contents are in free fall towards Earth, and if general relativity is correct, the two test masses should remain motionless relative to each other. If there is a violation of the weak equivalence principle, however, one of the test masses will experience slightly more free-fall acceleration than the other, and this will be recorded by its accelerometer. Prior to launch, scientists from the French national aerospace centre ONERA, who are responsible for interpreting the Microscope data, claimed that the first results could come in as little as a few months, but so far none have been announced. The CNES is not the only institution hoping to exploit the calmer benefits of space, however. For several years physicists Robert Reasenberg and James Phillips, formerly of the Harvard–Smithsonian Center for Astrophysics in Massachusetts, US, have been developing an experiment designed to fly on a sounding rocket that briefly enters space in free fall. Unlike Microscope, SR-POEM (Sounding-Rocket based Principle Of Equivalence Measurement) has a pair of test masses that are interleaved with each other in order to keep their centres of mass coincident; one of the masses is made of solid aluminium, while the other contains hollow lead inserts. Moreover, SR-POEM has a markedly different system to determine acceleration. Each of the masses forms one end of a triplet of optical cavities, and if either mass moves, its cavities lengthen or shorten. Using a “laser gauge” based on a technique known as Pound–Drever–Hall locking, Reasenberg and Phillips lock the frequency of a separate laser to each cavity, so that if the cavity lengths change due to the acceleration of the test mass, so do the laser frequencies – and frequency can be measured to very high precision.

The physicists plan to measure the acceleration of the test masses towards Earth, with the apparatus pointed up and then – rotating the entire payload – with the apparatus pointed down. “We move the Earth to the other side of the experiment, then do it again,” jokes Reasenberg, who is now based at the University of California, San Diego, in the US. In this way, any spurious accelerations should perfectly cancel out, yielding a signal only if one of the test masses experiences more gravity than the other (2012 Class. Quantum Grav.29 184013). “If it’s not zero, either you’ve got a systematic error, or you’ve discovered a violation of the equivalence principle,” Reasenberg says.

SR-POEM should have an accuracy 100 times greater than Microscope, due to the isolation of the test masses and the acuity of the laser gauges. Reasenberg also reckons it could be done at 10% of the cost, and in as little time as half an hour. But currently there is no funding to realize the experiment as, according to Reasenberg, NASA funds are devoted to the forthcoming James Webb Space Tele­scope, which is scheduled for launch in late 2018. “I don’t think there’s a good chance of getting funding until the James Webb is launched,” he says.

What goes up, keeps going up?

The good news for Reasenberg and Phillips is that their highly precise system for distance measurement has found its way onto an altogether different test of the equivalence principle – one that investigates antimatter. Believe general relativity, and antimatter should fall to the Earth exactly like matter; but some alternative gravity theories predict it should do the opposite, and “fall” upwards. This kind of antigravity effect could explain why we don’t observe equal quantities of matter and antimatter in our local universe, even though the two types are predicted to have been generated in equal quantities after the Big Bang. Simply put, the two types of matter might have repelled each other, driving all the antimatter into distant regions of the universe. “Maybe clusters of galaxies, or even portions of the universe as big as we can see, are made of antimatter,” says Reasenberg.

The antimatter “free fall” test to which Reasenberg and Phillips are contributing is being led by Daniel Kaplan at the Illinois Institute of Technology in Chicago, US. It involves sending a beam of muonium – a hydrogen-like atom, consisting of an electron orbiting an antimuon – into an atom interferometer, horizontally. The muonium beam is split at a diffraction grating, with each new beam taking a slightly different path before being diffracted again at a second diffraction grating, generating an interference pattern at a third diffraction grating. From the position of this pattern, which can be measured with the help of the third grating, it is possible to work out whether the muonium atoms fall down or up (EPJ Web Conf. 95 05008).

One difficulty with this type of experiment comes down to the lifetime of muonium: with a half life of just a couple of microseconds, the window for observing any up or down movement is very small, even if large numbers of particles are employed. The challenge, therefore, is incredibly high precision in the interferometer’s alignment to observe tiny changes in the position of the interference pattern. Kaplan’s group plans to use Reasenberg and Phillips’s laser gauge to ensure that the motion of the third grating is known to within 10 picometres (10–11 m) or so, and calibrate zero acceleration through use of an X-ray beam that has roughly the same wavelength as muonium. “If you found antimatter was falling up, that would be a major discovery,” says Reasenberg. “It changes physics. It changes cosmology.”

The benefit of investigating antimatter is that it provides an alternative way to tackle the equivalence principle, one for which no precise precedent has yet been set. That is also the case with PRIMUS, the Präzisionsinterferometrie mit Materiewellen unter Schwerelosigkeit (precision interferometry with matter waves in zero gravity), which is being funded by the German space agency DLR and is being performed at the 146 m-high drop tower at the University of Bremen by Herrmann as well as Dennis Schlippert and others at the University of Hannover in Germany. It also involves sending atom-waves into an interferometer, but these atoms are in a Bose–Einstein condensate (BEC): they are in the same, lowest quantum state, and behave as a single quantum entity. The speculation is that such a decidedly quantum system could, like antimatter, behave differently when it comes to the universality of free fall. “It might be more sensitive to violation,” says Herr­mann, “because it is closer to the boundary between quantum theory and gravity.”

As a matter-wave in an interferometer, a BEC has a phase, although this phase can be altered with exposure to a laser of the right wavelength. In PRIMUS, a BEC is allowed to free fall in the drop tower before being hit by such a laser pulse, which simultaneously splits the quantum entity into two paths (like a diffraction grating) and changes its phase, with the new phase dependent on when and where the laser struck. Farther down the drop tower the BEC is struck by another laser, which recombines the two halves to create an interference pattern. By examining the periodicity of this pattern, it is possible to work out the initial phase change, where it took place, and therefore the acceleration on the BEC due to gravity.

Last year, as a precursor to PRIMUS, Schlippert and colleagues performed a similar free-fall test for two BECs, one made of potassium and one of rubidium, to a precision of one in 10–7 (Phys. Rev. Lett. 112 203002). No violation yet, but the experiments are breaking ground for a different type of test of the equivalence principle. Indeed, Herrmann says that a future version of the PRIMUS experiment may one day find its way into space.

And what if a violation is found? That could well be the first evidence for a theory of quantum gravity – perhaps string theory, in which all fundamental particles are in fact twisted loops that, when expanded, spread into 10 or more dimensions. There are currently no firm predictions of where experimentalists should expect violations of the equivalence principle according to string theory, but some theorists expect them to become visible at precisions greater than 10–13.

Even then, there is the natural caution with which one interprets a single experimental result, particularly when it affects a theory that has proved unshakeable for 100 years. “You don’t topple a major piece of physics like general relativity based on one experiment,” says Reasenberg. “There’s always the possibility that there’s some systematic error nobody thought of, and there’s no physics in it at all.”

Enjoy the rest of the October 2016 issue of Physics World in our digital magazine or via the Physics World app for any iOS or Android smartphone or tablet. Membership of the Institute of Physics required