One of the predictions of special relativity is that the speed of light in a vacuum is a universal constant. This prediction has held up so well that we now use the speed of light to define part of the metric system. The first verification of special relativity is typically seen as the Michelson-Morley experiment, which demonstrated there wasn’t a luminiferous aether. But this experiment was actually done before Einstein proposed relativity, and so it wasn’t technically a prediction. It took two other experiments to completely verify Einstein’s model.

The Michelson-Morley experiment focused on determining the speed of the Earth through the aether. It wasn’t designed as a test of special relativity, and so it only tested that the speed of light was the same with different orientations. No matter which way you orient your device, the travel time back and forth along your experiment is the same. That’s certainly a prediction of relativity, but the theory goes further to claim that light speed is the same even if you’re moving at different speeds.

It took two other experiments to fully pin down the veracity of relativity. One, known as the Ives-Stilwell experiment looked at the time dilation effects of the model. In order for the speed of light to be the same in every reference frame, the clock of an experiment moving relative to you must appear to tick more slowly than that of an experiment sitting next to you. This effect is known as time dilation, and is one of the stranger aspects of relativity.

The Ives-Stilwell experiment looks at the light emitted or absorbed by fast moving particles and compares them with the transverse Doppler effect. If an object speeds past you from left to right, when it is directly in front of you would you see any Doppler shift of its light? Since the relative motion along your line of sight at that moment is zero, you might think there would be no shift. But since the object is speeding past you, its time should be dilated. As a result there should be a Doppler shift. The experiment confirmed the Doppler shift just as relativity predicts.

But relativity also predicts that space and time are connected, so a time dilation must also create a change of apparent length (known as length contraction). In other words not only must the clock of a moving experiment appear slower, then length of the experiment must appear shorter. Ives-Stilwell confirmed the first part, but not the second. To do that took a different test known as the Kennedy-Thorndike experiment.

Schematic of the Kennedy-Thorndike experiment.

The Kennedy-Thorndike experiment is similar to the Michelson-Morley. A beam of light is split to travel along two different paths. The separate beams of light are then recombined to create an interference pattern. The main difference is that the path length of the two beams is radically different. Since (according to Michelson-Morley) the speed of light is independent of orientation, the travel time of each path is different. Since Ives-Stilwell verified time dilation, as the apparatus moves with Earth, the amount of time dilation along one path is different from the other. This would produce a shift in the resulting interference pattern unless the lengths of the two paths also contract as relativity predicts.

The Kennedy-Thorndike experiment found no apparent shift in the interference pattern. Combined with the results of Michelson-Morley and Ives-Stilwell, this confirms that the speed of light is constant, and time dilation and length contraction both occur in agreement with special relativity.

And that’s why relativity is the strangest theory we know is true.

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In introductory physics courses we often assume the force of gravity near the Earth is constant. That isn’t really true, since the farther you get from the Earth’s surface, the weaker its gravitational force becomes, but this change is very small. If you could stand on a platform 5 kilometers above the Earth, the gravitational force you feel would only be about 0.2% less than on the surface.

The rate at which the gravitational force varies with height is known as the gradient. By measuring the force of gravity at two different heights, we can determine the variation of the gravitational field. It is similar to the way you can measure the speed of a car by measuring its position at two different times. We’ve been able to measure gravitational gradients for some time, but a bigger challenge is measuring how the gradient changes with height, which is known as the curvature. Despite its name, “curvature” in this sense is not the same as the relativistic curvature of space. Now a team has successfully measured this curvature, and the results are published in Physical Review Letters.

To achieve this, the team used very cold clouds of atoms and tossed them in a vertical chamber. They then flashed the clouds with laser light from above and below. The first flash from above caused some of the atoms to absorb the light and become excited. These excited atoms also get a slight push from the laser pulse, so they shift relative to unexcited atoms in the cloud. The second pulse from below remixes the excited and unexcited atoms, which then interfere with each other quantum mechanically. The amount of interference depends upon how widely the two groups were separated, which depends upon the strength of the gravitational field around them. So by measuring the interference, the team could measure the acceleration of gravity to within a few millionths of a percent. The team did this measurement at three different heights, from which they could determine not only the gradient of gravity in this region, but also the curvature.

You might wonder why this is a big deal. After all, we know that gravity is an inverse square force, so a bit of math should tell us what the gradient and curvature is. While that’s true, it’s only true for “point” masses, or spherical masses of uniform density. The Earth is neither, so there are fluctuations of gravitational strength, gradient and curvature depending on where you are on Earth. Since these fluctuations depend upon the shape and density of Earth at different regions, this type of measurement useful for determine what lies underneath the Earth’s surface. The experiment could also be useful in better determining the universal constant of gravity.

In this particular work the team really performed a proof of concept. Rather than measuring the curvature of Earth’s gravity directly, they placed large weights around their device in order to give the region a stronger gravitational curvature. But with this experiment under their belt, the team can now work to increase the sensitivity to be useful for real-world applications.

Paper: G. Rosi, L. et al. Measurement of the Gravity-Field Curvature by Atom Interferometry. Phys. Rev. Lett. 114, 013001 (2015)

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We all know the Earth moves, but how can we tell?  It certainly doesn’t feel like we’re spinning around the Earth.  But there is a simple experiment that can show the motion of the Earth, known as a Foucault pendulum.  It’s an experiment you can do at home with a baseball, a hook screw and some string.

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