Last year, three physicists shared the Nobel Prize for their detection of gravitational waves produced by colliding black holes. Just two weeks after the prize was announced, physicists from the same lab—the Laser Interferometer Gravitational-Wave Observatory (LIGO)—announced they had detected a gravitational wave produced by the collision of two ultra-dense neutron stars.
Unlike the black holes, which were only detected by tiny perturbations in a giant laser system, the neutron star collision also produced light that could be detected with an optical receiver. Thus the LIGO physicists had two measurements of the same event: One that measured gravitational waves and another that measured light particles. In extra-dimensional theories of gravity, the propagation of light through space isn’t affected by these extra dimensions, but gravitational waves are. Thus, by comparing measurements of gravitational waves and light as it propagated through space, physicists at LIGO were able to determine whether these two different waveforms were experiencing the same number of dimensions of spacetime.
According to their research recently published in the Journal of Cosmology and Astroparticle Physics, the measurements of the neutron star collision suggest that both gravitational waves and particles of light experience four dimensions (three spatial dimensions plus time). In other words, this astrophysical event didn’t provide any evidence for the existence of higher dimensions of spacetime predicted by several theories of gravity. This is a big deal insofar as this constraint limits the admissible theories of the nature of gravity and its relationship to dark matter and dark energy, two of the biggest mysteries in the physics.
"We have lots of indirect evidence that dark matter and dark energy exist, but we don't know what they are," Daniel Holz, an associate professor of physics at the University of Chicago, told me in an email. "One of the creative ways theorists have explained these phenomena is by modifying the way gravity works at large distances, and in particular, by adding extra dimensions to the theory."
According to Einstein’s theory of general relativity, the strength of a gravitational wave “decreases inversely with luminosity distance.” In other words, after taking into account how things like the curvature of spacetime and the expansion of the universe affect the source of gravitational waves, an increase in the distance to the source corresponds to a decrease in the strength of the gravitational wave. As soon as you start adding extra dimensions into theories of gravity, however, this relationship starts to change. For “non-compact” extra-dimensional theories of gravity—basically those that aren’t string theory, where the extra dimensions coil in on themselves—gravitational waves “leak” into these extra dimensions as they propagate through space and time. This should lead to a reduction in their strength when detected by a receiver compared to what is predicted by general relativity.
This would be impossible to test using data from gravitational waves alone, since it depends on knowing the distance to the source of the gravitational wave. A detected wave with a strength that is smaller than expected could be due to an error in the inferred distance to the source of the wave or it could be due to leakage into higher dimensions. There’s no way to tell one way or the other without a different way of measuring the same event that isn’t affected by extra dimensions.
In extra-dimensional theories of gravity, leakage into other dimensions only occurs for extremely low frequency gravitational waves. Some theories even posit that this only happens at wavelengths on the scale of the cosmic horizon (i.e., several billion light years). Thus, an event that produces gravitational waves and electromagnetic radiation—such as the collision of two neutron stars—provides its own baseline for measuring the effects of extra dimensions on gravitational waves since electromagnetic radiation isn't affected in these theories.
"It's kind of amazing that we can directly measure the number of spacetime dimensions across a huge swath of the universe."
According to the new results from LIGO, however, there was no apparent leakage of gravitational waves into another dimension of spacetime. Their strength at the LIGO receiver was exactly what was expected. This implies that both gravitational waves and electromagnetic waves only experience four dimensions (three spatial dimensions plus time), even on scales of hundreds of millions of light years.
“We can directly test that gravitational waves and light travel through identical universes, and we find that they both see the usual 3 + 1 dimensions," Holz said. "This is the first time we've been able to test this directly, and it's kind of amazing that we can directly measure the number of spacetime dimensions across a huge swath of the universe."