A foundational thought experiment in Einstein’s theory of general relativity just got its most precise confirmation ever by turning the entire Earth into a laboratory.
Monday, physicists from the National Institute of Standards and Technology published the results of a 14-year experiment that used some of the most accurate atomic clocks in the world to test a fundamental principle in the theory of general relativity. The results, published in Nature Physics, offer the most precise confirmation of one of the core concepts of Einstein’s unified theory of spacetime and gravity, the equivalence principle.
The experiment involved tracking the measurements of 12 atomic clocks located in the United States, Germany, France, Italy, and the United Kingdom from 1999 to 2014. Based on Einstein’s theory of general relativity, the relationship between the measurements of these clocks shouldn’t change as the Earth orbits the Sun. This is exactly what the physicists found, confirming several similar experiments that occurred over the years.
At the heart of Albert Einstein’s unified framework of spacetime and gravity is the equivalence principle, which states that in small reference frames the force of gravity is almost entirely absent. This realization allowed Einstein to reconcile his theory of special relativity, which only makes sense when gravity is taken out of the picture, with Newton’s law of gravity. The result was a new theory known as general relativity.
To help explain the equivalency principle, Einstein came up with a thought experiment that went something like this. Imagine you’re standing in a windowless box that looks like an elevator and you drop your phone, which falls to the floor just as you’d expect. From this mundane event can you deduce that you are in fact in an elevator on Earth? Not necessarily—you could also be in an elevator-shaped box inside a rocket deep in space, far from the gravitational influence of any planet. In this case, you would be able to tell that the rocket was accelerating at a rate of 9.81 meters per second squared—the gravitational acceleration rate near the Earth’s surface— because the floor of the elevator accelerated toward your phone at the same rate. From your perspective in your windowless box, it’s impossible to tell the difference.
Now imagine that you’re in the same windowless box, but you’re floating in the air. You’ve got to be in space, right? Again, not necessarily. You could also be in an elevator shaft on Earth where the elevator’s cables have just been cut. You’re technically in free fall, but it’s impossible to distinguish this from microgravity from your limited frame of reference.
This is why astronauts on the International Space Station float, even though the strength of Earth’s gravity at 300 miles up is about 90 percent as strong as it is on Earth’s surface. The ISS is technically in constant free fall, but if you blindfolded an astronaut when they got on a rocket to the ISS and shut all the windows when they got there, they wouldn’t be able to tell whether they were just above Earth or well on their way to Mars based on the way they floated in the station.
Another aspect of Einstein’s theory of general relativity called the principle of local position invariance (LPI) says that the properties of objects relative to one another in a free-falling elevator will remain the same. A way to envision this is that if you were to drop your phone and your wallet right as the elevator cable is cut and the elevator goes into free fall, those two objects will stay the same distance from each other during the fall. Their location in the elevator doesn’t affect their properties.
Okay, But What Does This Have to Do With Atomic Clocks?
In NIST’s recent experiment they basically considered the entire Earth as the free falling elevator and a bunch of atomic clocks spread around the world as the equivalent of the dropped phone and wallet. On this view, the Earth is in free fall around the Sun and if the entire planet is considered the local frame of reference then the relationship between the ‘ticks’ of the atomic clock—that is, an electron’s transition between energy levels—should remain the same during the Earth’s orbit.
Atomic clocks measure time by measuring the frequency at which electrons transition between discrete energy levels. Electrons “orbit” the nucleus of an atom at certain stable energy levels that depend on the electrical properties of the nucleus itself. These orbits can be changed by adding energy to the system, which causes the electrons to temporarily get bumped up to a higher energy level and emit electromagnetic radiation during the transition. Different types of atoms are able to absorb energy at different wavelengths.
Some of NIST’s most accurate atomic clocks are called cesium fountain atomic clocks because they use a cesium-133 isotope to keep time. Cesium-133 naturally absorbs energy at a 3.2 centimeter wavelength, so when it is hit with 3.2 cm microwaves it causes the atom’s single outermost electron to transition between energy states at a rate of 9,192,631,770 times per second. In this sense, the transition between the energy levels is like a pendulum that swings over 9 billion times for every second marked on the clock face.
Although Einstein’s principle of local position invariance predicts zero deviation between the properties of objects in a free falling elevator, the actual number is not zero, but it is miniscule. So small, in fact, that as far as general relativity is concerned it may as well be zero. Over the course of 14 years, NIST researchers found that violation of the local position invariance principle was about 0.00000022.
This confirmation of Einstein’s theory of general relativity is the most precise measurement of LPI violation yet—about five times more precise than a previous measurement conducted in 2007 after seven years of observation. According to the physicists, the better results were due to improvements in the accuracy of cesium fountain atomic clocks as well as improved measurements of Earth’s position and velocity in space. The researchers hope that in the future, still more accurate atomic clocks will improve the precision of this test of general relativity even more.