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Free Fallin’: Equivalence Holds Even At Atomic Level

The views expressed are those of the author and are not necessarily those of Scientific American.


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One of the first things we learn in school about physics — along with Newton’s laws of motion — is that all objects fall at the same rate, regardless of their mass. It’s now known as the equivalence principle — more precisely, the weak equivalence principle — and it is a central tenet of Einstein’s general theory of relativity. And now a team of German physicists has demonstrated that even matter waves adhere to Einstein when it comes to free fall.

There’s a long, proud (and often colorful) tradition of experimentally testing the weak equivalence principle. Remember that scene in Addams Family Values, where Wednesday and Pugsly take their newborn baby brother and a hefty cannonball to the roof of the family’s decrepit gothic mansion? The perpetually poker-faced Wednesday poses a scientific hypothesis to her brother:

Wednesday: Pugsly, the baby weighs ten pounds, the cannonball weighs twenty pounds. Which will hit the stone walkway first?
Pugsly: I’m still on fractions.
Wednesday: Which do you think?
Pugsly: The cannonball?
Wednesday: Very good. But which one will bounce?
Pugsly: The baby?
Wednesday: There’s only one way to find out. Ready? One… two… three.

And she and Pugsly unceremoniously drop both baby and cannonball from the roof. That’s pretty much how scientists have been testing the weak equivalence principle since John Philoponus, the 6th century philosopher, dropped balls of different masses and observed no detectable difference in the rate in which they fell. He was the first to contend that the velocity at which an object will fall has nothing to do with its weight (mass), and later became a major influence on Galileo Galilei some 900 years later.

Galileo supposedly dropped cannonballs of varying masses off Italy’s famed Leaning Tower of Pisa but the story is probably apocryphal. Maybe somewhere along the line folks started confusing him with Flemish mathematician Simon Stevin, who dropped lead balls of varying masses off the church tower in Delft around 1586.

Galileo's inclined plane experiment. Fresco by G. Bezzuoli, 1841.

Galileo did roll balls down inclined planes circa 1610 (some peg the date as 1604). That incline insured the balls rolled at much lower speeds, making their acceleration easier to measure. The balls were similar in size, but some were made of iron, others of wood, making their masses different. Lacking an accurate clock, Galileo reportedly timed the balls’ travel with his pulse. And like Philoponus (and Stevin), he found that no matter what the incline, the balls would travel at the same rate of acceleration.

Still, the Addams children actually guessed right, just for the wrong reason. Their experiment is interrupted when Papa Gomez serendipitously leans out a window just at the right moment to catch baby Pubert mid-fall. Had the baby continued on course, the cannonball would indeed have hit the ground first. But its earlier arrival would have had nothing to do with its relative weight. (That’s actually the first nitpick right there: Wednesday confuses mass with weight. Weight fluctuates with gravity while mass is constant.)

The key variable is the friction caused by the presence of air. The air exerts more friction on Pubert than on the cannonball because the baby has more surface area. This slows Pubert’s fall, and the cannonball hits the ground first. Had the Addams siblings conducted their experiment in a vacuum, there would have been no air resistance and both baby and cannonball would have hit the ground at the same time, despite the ten-pound difference in weight.

That’s the basic principle behind the classic coin and feather experiment. Galileo and his free falling cohorts weren’t making the most rigorously precise of measurements (Galileo’s were accurate to about 1%); they did a great job considering the tools available to them at the time. But then scientists figured out how to create a vacuum chamber, and used it to study the effects of a vacuum on experimental tests of the equivalence principle. You can watch the result in any number of YouTube videos, and it is freakishly counter-intuitive. We’re so accustomed to watching a coin fall straight down while a feather wafts gently to the ground at a more leisurely pace, but that’s not what happens in a vacuum. They really do fall at the same rate.

The same thing can be observed in a low-gravity environment like the moon, which also has little to no air resistance. NASA Apollo 15 astronaut David Scott performed his own version of the experiment during his 1971 moon walk. He dropped a falcon feather and a hammer at the same time via a live television feed, and when the two objects hit the dirt simultaneously, he enthused, “What do you know? Mr. Galileo was right.”

There’s more than one way to test the equivalence principle. Galileo later refined his approach using a pendulum apparatus, which involved measuring the oscillation period of pendulums of different mass but identical length. This was also the method favored by Isaac Newton circa 1680, and later, in 1832, by Friedrich Bessen, both of whom vastly improved the accuracy of the measurements compared to Galileo. Newton also realized that the principle extended to celestial bodies, calculating that the earth and moon, as well as Jupiter and its satellites, fall toward the sun at the same rate.

Newton didn’t have any way to test this experimentally at the scale of the solar system, but a few centuries later NASA obliged, thanks to the reflector arrays placed on the Moon by Apollo astronaut. This enabled lunar laser ranging: we can send a laser beam through a telescope to the moon, and when it hits a reflector, we can detect the return signal. Okay, not just anyone can detect it, since it amounts to about one photon received every few seconds, but with the right equipment, it’s possible.

Here, I’ll let Leonard of The Big Bang Theory explain the specifics in this most excellent scene:

(Remember kids, don’t try this at home — but if you do, be sure to set your laser to stun.)

The Earth has a core of iron, while the Moon’s core is mostly made of silicates, and their masses are quite different. Yet laser lunar ranging experiments have confirmed Newton’s calculations: they do indeed fall around the sun at the same rate. So once again we see that neither mass nor the material from which an object is made has any affect on the rate at which it falls.

Towards the end of the 19th century, Hungarian physicist Baron Lorand Eotvos de Vasarosnameny combined the pendulum approach with a torsion balance to create a torsion pendulum, and used it to conduct an even more accurate test of the equivalence principle (it also became a workhorse tool in geophysics, especially useful for locating oil fields). In the baron’s own words:

Schematic for Eotvos' torsion experiment to test equivalence principle.

“It was just a simple, straight stick that I used as instrument, specially loaded at both ends, enclosed into a metal sheath to protect it from the wind and temperature changes. Upon this stick every single mass, be it near or far, exerts a directing force; but the wire upon which it hangs resists, and whist resisting it twists, wit the degree of this twist showing us the exact magnitude of the forces acting upon the stick….”

“It is simple, like the flute of Hamlet, you only have to know how to play on it, and just like the musician who can delight you with splendid variations, the physicist can, on this balance, with no less delight determine the finest variations of gravity. This way we can peer into such depth of the crust of the Earth, that neither our eyes nor our longest drills could read.”

That simple straight stick proved accurate enough to test the equivalence principle much more precisely — some 400 times better than Bessen’s pendulum experiments. Albert Einstein cited the Eotvos experiment in his 1916 paper laying out the foundation for his general theory of relativity. (Side note: A torsion balance is also frequently used to make precise measurements of the gravitational constant, a.k.a. “Big G.”)

Torsion balances were also employed in subsequent experiments of the weak equivalence principle, for example, one in 1964 that used chunks of aluminum and gold as the test masses, and another in 1987 that used it to measure the acceleration of various masses as they fell toward Earth, the Sun, and the galactic center for good measure.

All told, the current best measurements (from lunar laser ranging data) indicate that equivalence holds within a few parts in a trillion.

That’s pretty darn good, but physicists are never satisfied. It would be nice to conduct further tests of equivalence in space. Sure, it’s fun to drop objects off clock towers but it happens so quickly that it’s hard to make precision measurements on the scale where such violations are likely to occur. Orbiting bodies are literally free falling continuously, making them an ideal laboratory.

There were a couple of proposed satellite experiments designed to do just that. One was called STEP (Satellite Test of the Equivalence Principle), using technology developed for Gravity Probe B, which to tested other key aspects of relativity (i.e., frame-dragging). But there hasn’t been much in the way of updated information on STEP since 2009, and given the current funding squeeze, I’m not holding my breath on STEP ever launching. (It may have been cancelled but I couldn’t find any official notice in a quick Google search.) The French had a similar project called MICROSCOPE (MICROSatellite pour l’Observation de Principe d’Equivalence), originally pegged to a 2015 launch date, but it seems it was cancelled in December 2011.

Since further space-based tests seem to be off the table for now, why not test equivalence at much smaller scales, too? I mean, maybe there are some special circumstances under which equivalence can be violated. That would be hugely significant — possible evidence of, say, a new, ultra-weak force (ten million million times weaker than gravity, even) that cumulatively, over time, could give rise to tiny differences in gravity’s pull.

Path of light in a Michaelson interferometer. Source: Wikimedia. Credit: Jbeam.scholar.

And that brings us back to the latest PRL paper.  Another way to test equivalence at the quantum scale is to use matter-wave interferometry. It’s related to the classic Michaelson-Morley experiment attempting to detect the movement of the Earth through a medium called the luminiferous aether, which physicists at the time believed permeated space. Per Wikipedia, a Michaelson interferometer works like this:

“Using a beamsplitter, a light source is split into two arms. Each of those is reflected back toward the beamsplitter which then combines their amplitudes interferometrically. The resulting interference pattern which is not directed back toward the source is typically directed to some type of photoelectric detector or camera. Depending on the interferometer’s particular application, the two paths may be of different lengths or include optical materials or components under test.

There are actually many different types of interferometers.  In the late 19th century, Thomas Young used such an instrument for his famous double-slit experiment to test whether light was a particle or a wave — and as we now know, light is both. The Time Lord would clarify further and insist that technically it is a wave until we look at it, at which point we see a particle. Duly noted. (For a detailed description of Young’s double-slit experiment, see my 2007 (reposted in 2012) post on the topic.) Louis de Broglie later showed that the same holds true for matter. Yes, there are matter waves, and that’s what makes matter-wave interferometers possible.

Anyway, atoms are really sensitive to gravity, so they make great test subjects to study weak equivalence at the atomic scale. It should be possible, for instance, to determine whether (or how) gravity may depend on certain quantum properties, like spin. Prior experiments using matter-wave interferometry measured the free fall of two isotopes of the same atomic element, hoping to detect minute differences. No dice.

But a team of physicists hailing from Leibniz University in Hannover and the University of Ulm thought that perhaps there was not sufficient difference between their composition to achieve the utmost sensitivity. So they used isotopes of different elements, namely rubidium and potassium atoms. Using a magneto-optical trap — the same basic technique used to achieve Efimov states, as discussed in yesterday’s post – they cooled the atoms down to just a few microkelvins. Then they released the atoms. Laser pulses ensured the atoms fell along two separate paths before recombining. Basically, if the researchers observed an interference pattern, equivalence held; if not, perhaps they were onto something revolutionary. Lo and behold, there was that telltale interference pattern. Equivalence still holds! At least to within 1 part in 10 million.

“Whoop-de-doo!” I can hear you snarking. “Einstein is still right. How is this even news?” Just because there’s a null result doesn’t mean it’s insignificant. Among other things, this could help rule out a few competing versions of string theory, some of which predict tiny variations in the pull of gravity for different materials. So if equivalence continues to stand, even at the atomic level, those versions could be discarded, clearing a bit of much-needed space in the cluttered playing field of alternate theories of gravity.

And if not? Any physicist would tell you that would be incredibly exciting. Why do you think they’re still hunting for violations? For now, at least, Einstein remains right.

References:

Adelberger, Eric G. et al. (1990) “Testing the equivalence principle in the field of the Earth: Particle physics at masses below 1 μeV?” Physical Review D 42: 3267–3292.

Baeßler, Stefan, et al. (1999) “Improved Test of the Equivalence Principle for Gravitational Self-Energy,” Physical Review Letters 83(18): 3585.

Bessel, Friedrich W. (1832) “Versuche Uber die Kraft, mit welcher die Erde Körper von verschiedner Beschaffenhelt anzieht,” Annalen der Physik und Chemie 25:401–408.

Bod, L. et al. (1991) “One hundred years of the Eotvos experiment,” Acta Physica Hungarica 69(3-4): 335-355.

de Broglie, Louis. (1925) “Researches on the quantum theory,” Ann. Phys. 3: 22.

Cronin, A.D.; Schmiedmayer, J.; Pritchard, D.E. (2009) “Optics and interferometry with atoms and molecules,” Reviews of Modern Physics 81.

Dicke, Robert H. (1959) “New Research on Old Gravitation,” Science 129, 3349.

Dicke, Robert H. “Mach’s Principle and Equivalence,” Evidence for Gravitational Theories: Proceedings of Course 20 of the International School of Physics Enrico Fermi, ed. C. Møller. New York: Academic Press, 1962.

Eötvös, Loránd. Mathematische and naturnissenschaftliche Berichte aus Ungarn 8: 65 (1889); Annalen der Physik (Leipzig) 68: 11 (1922).

Hadley, Mark J. (1997) “The Logic of Quantum Mechanics Derived from Classical General Relativity,” Foundations of Physics Letters 10: 43–60.

Michelson, Albert, and Morley, Edward. (1887) “On the Relative Motion of the Earth and the Luminiferous Ether,” American Journal of Science 34 (203): 333–345.

Roll, Peter G.; Krotkov, Robert; Dicke, Robert H. (1964) “The equivalence of inertial and passive gravitational mass,” Annals of Physics,  26(3): 442-517.

Schlamminger, Stephan, et al. (2008) “Test of the Equivalence Principle Using a Rotating Torsion Balance,” Physical Review Letters 100 (4).

Schlippert, D. et al. (2014) “Quantum Test of the Universality of Free Fall,” Physical Review Letters 112: 203002.

Stubbs, Christopher W. et al. (1989) “Limits on Composition-Dependent Interactions Using a Laboratory Source: Is There a Fifth Force Coupled to Isospin?” Physical Review Letters 62: 609.

Wagner, Todd A. et al. (2012) “Torsion-balance tests of the weak equivalence principle,” Classical Quantum Gravity 29: 184002.

Jennifer Ouellette About the Author: Jennifer Ouellette is a science writer who loves to indulge her inner geek by finding quirky connections between physics, popular culture, and the world at large. Follow on Twitter @JenLucPiquant.

The views expressed are those of the author and are not necessarily those of Scientific American.





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  1. 1. jtdwyer 11:20 am 05/28/2014

    There’s an exceedingly simple explanation for this phenomenon – objects of different weight or mass fall at the same rate in the Earth’s gravitational field (controlling for aerodynamic effects) because the gravitational ‘force’ (in classical terms) imparted is determined almost exclusively by the overwhelming mass of the Earth. Whether a pea or a cannonball is falling within the gravitational field of the Earth, the accelerating force imparted is effectively determined entirely by the mass of the Earth. Small objects contribute almost nothing to the net gravitational force.
    … The same goes for the Earth and Moon’s, and other planets, motions in relation to the Sun, since even Jupiter’s mass is insignificant in relation to the Sun’s. The Sun contains an estimated 99.86% of the total mass of the entire Solar system!
    … Of course, the same applies to atoms and other particles within the Earth’s gravitational field. There are variations in the gravitational force imparted at various locations (due to local mass density) and elevations on the Earth (and other bodies).
    … As pointed out, objects weigh less on the Moon than they do on the Earth, while their mass is essentially invariant. Weight is the product of the mass of an object and the magnitude of the local gravitational acceleration. Objects also weigh differently at various elevations within the Earth’s gravitational field and, at sufficient distance from all gravitating bodies, achieve an effective state of ‘weightlessness’. Objects’ weights also vary as a function of the Earth, Moon and Sun’s combined gravitation – which can be most clearly observed in the tidal variations of large bodies of water.
    … In contrast, if one were to drop the Moon and a cannonball from a distance of 1 km from the Earth’s surface, one could likely be able to measure significant difference in the rate of their fall – but then the total gravitational force imparted would be changed, and the direction of fall for all three objects would be the combined center of mass…

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  2. 2. Ooloom 3:03 pm 05/30/2014

    The things you’re saying are true, but the point of the article, and the reason why these types of experiments are relevant and necessary, is because they are taking these simple fundamental rules and testing them under quantum mechanical conditions, in which we all know there have been surprising and inconsistent findings.

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