Speed of Gravity

Einstein and Relativity

What is the speed of gravity? It’s 299,792,458 m/s. Seem familiar? Yep, it’s the speed of light (in a vacuum)!

How do we know that that’s the speed of gravity? Not by direct measurement, yet, but by the great success of Einstein’s theory of general relativity (GR).

In general, because it is so successful, and because the speed of gravity in GR is the same as the speed of light, we can say we know how fast gravity propagates.

In particular, observations of the Hulse-Taylor binary pulsar (and other binary pulsars) show the mutual orbit is decaying (the stars are slowly spiraling in, and will one day collide). The rate of decay is exactly as predicted by GR, and is due to the system radiating gravitational waves. The rate at which the system is losing energy tells us how fast that gravitational wave radiation is travelling … and it’s c, the speed of light, to within 1%!

Working out how gravity, as geometry in GR, makes planets in our solar system orbit the Sun is somewhat tricky, and misunderstanding of the details is what’s behind an erroneous claim you might come across on many websites (that the speed of gravity is many millions of times c, or even infinite).

A very long baseline radio interferometric observation of a quasar as it passed near Jupiter, in 2002, lead two researchers to claim to have directly measured the speed of gravity (they found it to be c, plus or minus about 20%). However, this claim is controversial, with several GR experts claiming the analysis contains subtle flaws, and that what was actually measured is the speed of light. The method Fomalont and Kopeikin used might allow a direct estimate of the speed of gravity to be made in future, in the view of their critics, with big improvements in precision.

More to explore: Speed of Gravity (NASA), What is the speed of gravity? (Cornell University), and Does Gravity Travel at the Speed of Light? (University of California Riverside).

Gravity Moves at the Speed of Light is an interesting Universe Today story on the speed of gravity; Warp Drives Probably Impossible After All is a very different take!

And check out the Astronomy Cast September 18th, 2008 Questions Show episode for more on the speed of gravity.

Nobel Prize Press Release
Living Reviews in Relativity
Cornell Astronomy

This is Getting Boring: General Relativity Passes Yet another Big Test!

Published in 1915, Einstein’s theory of general relativity (GR) passed its first big test just a few years later, when the predicted gravitational deflection of light passing near the Sun was observed during the 1919 solar eclipse.

In 1960, GR passed its first big test in a lab, here on Earth; the Pound-Rebka experiment. And over the nine decades since its publication, GR has passed test after test after test, always with flying colors (check out this review for an excellent summary).

But the tests have always been within the solar system, or otherwise indirect.

Now a team led by Princeton University scientists has tested GR to see if it holds true at cosmic scales. And, after two years of analyzing astronomical data, the scientists have concluded that Einstein’s theory works as well in vast distances as in more local regions of space.

A partial map of the distribution of galaxies in the SDSS, going out to a distance of 7 billion light years. The amount of galaxy clustering that we observe today is a signature of how gravity acted over cosmic time, and allows as to test whether general relativity holds over these scales. (M. Blanton, SDSS)

The scientists’ analysis of more than 70,000 galaxies demonstrates that the universe – at least up to a distance of 3.5 billion light years from Earth – plays by the rules set out by Einstein in his famous theory. While GR has been accepted by the scientific community for over nine decades, until now no one had tested the theory so thoroughly and robustly at distances and scales that go way beyond the solar system.

Reinabelle Reyes, a Princeton graduate student in the Department of Astrophysical Sciences, along with co-authors Rachel Mandelbaum, an associate research scholar, and James Gunn, the Eugene Higgins Professor of Astronomy, outlined their assessment in the March 11 edition of Nature.

Other scientists collaborating on the paper include Tobias Baldauf, Lucas Lombriser and Robert Smith of the University of Zurich and Uros Seljak of the University of California-Berkeley.

The results are important, they said, because they shore up current theories explaining the shape and direction of the universe, including ideas about dark energy, and dispel some hints from other recent experiments that general relativity may be wrong.

“All of our ideas in astronomy are based on this really enormous extrapolation, so anything we can do to see whether this is right or not on these scales is just enormously important,” Gunn said. “It adds another brick to the foundation that underlies what we do.”

GR is one, of two, core theories underlying all of contemporary astrophysics and cosmology (the other is the Standard Model of particle physics, a quantum theory); it explains everything from black holes to the Big Bang.

In recent years, several alternatives to general relativity have been proposed. These modified theories of gravity depart from general relativity on large scales to circumvent the need for dark energy, dark matter, or both. But because these theories were designed to match the predictions of general relativity about the expansion history of the universe, a factor that is central to current cosmological work, it has become crucial to know which theory is correct, or at least represents reality as best as can be approximated.

“We knew we needed to look at the large-scale structure of the universe and the growth of smaller structures composing it over time to find out,” Reyes said. The team used data from the Sloan Digital Sky Survey (SDSS), a long-term, multi-institution telescope project mapping the sky to determine the position and brightness of several hundred million galaxies and quasars.

By calculating the clustering of these galaxies, which stretch nearly one-third of the way to the edge of the universe, and analyzing their velocities and distortion from intervening material – due to weak lensing, primarily by dark matter – the researchers have shown that Einstein’s theory explains the nearby universe better than alternative theories of gravity.

Some of the 70,000 luminous galaxies in SDSS analyzed (Image: SDSS Collaboration)

The Princeton scientists studied the effects of gravity on the SDSS galaxies and clusters of galaxies over long periods of time. They observed how this fundamental force drives galaxies to clump into larger collections of galaxies and how it shapes the expansion of the universe.

Critically, because relativity calls for the curvature of space to be equal to the curvature of time, the researchers could calculate whether light was influenced in equal amounts by both, as it should be if general relativity holds true.

“This is the first time this test was carried out at all, so it’s a proof of concept,” Mandelbaum said. “There are other astronomical surveys planned for the next few years. Now that we know this test works, we will be able to use it with better data that will be available soon to more tightly constrain the theory of gravity.”

Firming up the predictive powers of GR can help scientists better understand whether current models of the universe make sense, the scientists said.

“Any test we can do in building our confidence in applying these very beautiful theoretical things but which have not been tested on these scales is very important,” Gunn said. “It certainly helps when you are trying to do complicated things to understand fundamentals. And this is a very, very, very fundamental thing.”

“The nice thing about going to the cosmological scale is that we can test any full, alternative theory of gravity, because it should predict the things we observe,” said co-author Uros Seljak, a professor of physics and of astronomy at UC Berkeley and a faculty scientist at Lawrence Berkeley National Laboratory who is currently on leave at the Institute of Theoretical Physics at the University of Zurich. “Those alternative theories that do not require dark matter fail these tests.”

Sources: “Princeton scientists say Einstein’s theory applies beyond the solar system” (Princeton University), “Study validates general relativity on cosmic scale, existence of dark matter” (University of California Berkeley), “Confirmation of general relativity on large scales from weak lensing and galaxy velocities” (Nature, arXiv preprint)

Einstein’s General Relativity Tested Again, Much More Stringently

Einstein and Relativity

This time it was the gravitational redshift part of General Relativity; and the stringency? An astonishing better-than-one-part-in-100-million!

How did Steven Chu (US Secretary of Energy, though this work was done while he was at the University of California Berkeley), Holger Müler (Berkeley), and Achim Peters (Humboldt University in Berlin) beat the previous best gravitational redshift test (in 1976, using two atomic clocks – one on the surface of the Earth and the other sent up to an altitude of 10,000 km in a rocket) by a staggering 10,000 times?

By exploited wave-particle duality and superposition within an atom interferometer!

Cesium atom interferometer test of gravitational redshift (Courtesy Nature)

About this figure: Schematic of how the atom interferometer operates. The trajectories of the two atoms are plotted as functions of time. The atoms are accelerating due to gravity and the oscillatory lines depict the phase accumulation of the matter waves. Arrows indicate the times of the three laser pulses. (Courtesy: Nature).

Gravitational redshift is an inevitable consequence of the equivalence principle that underlies general relativity. The equivalence principle states that the local effects of gravity are the same as those of being in an accelerated frame of reference. So the downward force felt by someone in a lift could be equally due to an upward acceleration of the lift or to gravity. Pulses of light sent upwards from a clock on the lift floor will be redshifted when the lift is accelerating upwards, meaning that this clock will appear to tick more slowly when its flashes are compared at the ceiling of the lift to another clock. Because there is no way to tell gravity and acceleration apart, the same will hold true in a gravitational field; in other words the greater the gravitational pull experienced by a clock, or the closer it is to a massive body, the more slowly it will tick.

Confirmation of this effect supports the idea that gravity is geometry – a manifestation of spacetime curvature – because the flow of time is no longer constant throughout the universe but varies according to the distribution of massive bodies. Exploring the idea of spacetime curvature is important when distinguishing between different theories of quantum gravity because there are some versions of string theory in which matter can respond to something other than the geometry of spacetime.

Gravitational redshift, however, as a manifestation of local position invariance (the idea that the outcome of any non-gravitational experiment is independent of where and when in the universe it is carried out) is the least well confirmed of the three types of experiment that support the equivalence principle. The other two – the universality of freefall and local Lorentz invariance – have been verified with precisions of 10-13 or better, whereas gravitational redshift had previously been confirmed only to a precision of 7×10-5.

In 1997 Peters used laser trapping techniques developed by Chu to capture cesium atoms and cool them to a few millionths of a degree K (in order to reduce their velocity as much as possible), and then used a vertical laser beam to impart an upward kick to the atoms in order to measure gravitational freefall.

Now, Chu and Müller have re-interpreted the results of that experiment to give a measurement of the gravitational redshift.

In the experiment each of the atoms was exposed to three laser pulses. The first pulse placed the atom into a superposition of two equally probable states – either leaving it alone to decelerate and then fall back down to Earth under gravity’s pull, or giving it an extra kick so that it reached a greater height before descending. A second pulse was then applied at just the right moment so as to push the atom in the second state back faster toward Earth, causing the two superposition states to meet on the way down. At this point the third pulse measured the interference between these two states brought about by the atom’s existence as a wave, the idea being that any difference in gravitational redshift as experienced by the two states existing at difference heights above the Earth’s surface would be manifest as a change in the relative phase of the two states.

The virtue of this approach is the extremely high frequency of a cesium atom’s de Broglie wave – some 3×1025Hz. Although during the 0.3 s of freefall the matter waves on the higher trajectory experienced an elapsed time of just 2×10-20s more than the waves on the lower trajectory did, the enormous frequency of their oscillation, combined with the ability to measure amplitude differences of just one part in 1000, meant that the researchers were able to confirm gravitational redshift to a precision of 7×10-9.

As Müller puts it, “If the time of freefall was extended to the age of the universe – 14 billion years – the time difference between the upper and lower routes would be a mere one thousandth of a second, and the accuracy of the measurement would be 60 ps, the time it takes for light to travel about a centimetre.”

Müller hopes to further improve the precision of the redshift measurements by increasing the distance between the two superposition states of the cesium atoms. The distance achieved in the current research was a mere 0.1 mm, but, he says, by increasing this to 1 m it should be possible to detect gravitational waves, predicted by general relativity but not yet directly observed.

Sources: Physics World; the paper is in the 18 February, 2010 issue of Nature

Sirius B

Sirius B is the name of the fainter, smaller, less massive star in the Sirius binary system (the brighter, larger, more massive one is Sirius A, or just Sirius). It was hypothesized to exist almost eighteen years before it was actually observed!

Details: Bessel – yep, the guy who Bessel functions are named after – analyzed data on the position of Sirius (Bessel was the one who first observed stellar parallax), in particular its proper motion, and concluded – in 1844 – that there was an unseen companion star (the same principle used to infer the existence of Neptune, around the same time). In 1862 Alvan Clark saw this companion, using the 18.5″ refracting telescope he’d just built (quite a feat; Sirius B is ~10 magnitudes fainter than Sirius A, and separated by only a few arcseconds).

Sirius B is a white dwarf, one of the three “classics”, discovered to be white dwarf stars in the early years of the 20th century (Sirius B was the second to be discovered – 40 Eridani B had been found much earlier, and Procyon B was also hypothesized by Bessel (in 1844) though not observed until much later (in 1896)). It is one of the most massive white dwarfs so far discovered; its mass is the same as that of the Sun (approximately). Like all white dwarfs, it is small (it has a radius of only 0.008, compared with the Sun’s, which makes it smaller than the Earth!); like most seen so far, it is hot (approx 25,000 K).

Sirius B was likely a five sol B star as recently as 60 million years ago (when it was, coincidentally, approximately 60 million years old!), when it entered first a hydrogen shell burning, then a helium shell burning, stage, shed most of its mass (and enriching its companion with lots of ‘metals’ in the process), and shrank to become a white dwarf. There is no fusion taking place in Sirius B’s degenerate carbon/oxygen core (which makes up almost all of the star; there is a thin, non-degenerate, hydrogen atmosphere … this is what we see), so it is slowly cooling (it cools so slowly because it has such a small surface area).

Packing such a large mass into such a small volume means that Sirius B’s surface gravity is huge … so great in fact that it serves as an excellent test of one of the predictions of Einstein’s theory of General Relativity: gravitational redshift (this was first observed in the lab in 1959, by Pound and Rebka). The most recent observation of this gravitational redshift was by the Hubble, in 2005, as described in the Universe Today article Sirius’ White Dwarf Companion Weighed by Hubble.

Other Universe Today stories about Sirius B include White Dwarf Theories Get More Proof, and this 2005 What’s Up This Week one.

Astronomy Cast has two episodes related to Sirius B, Dwarf Stars, and Binary Stars.


What is an Event Horizon?

The event horizon of a black hole is the boundary (‘horizon’) between its ‘outside’ and its ‘inside’; those outside cannot know anything about things (‘events’) which happen inside.

What an event horizon is – its behavior – is described by applying the equations of Einstein’s theory of General Relativity (GR); as of today, the theoretical predictions concerning event horizons can be tested in only very limited ways. Why? Because we don’t have any black holes we can study up close and personal (so to speak) … which is perhaps a very good thing!

If the black hole is not rotating, its event horizon has the shape of a sphere; it’s like a 2D surface over a 3D ball. Except, not quite; GR is a theory about spacetime, and contains many counter-intuitive aspects. For example, if you fall freely into a black hole (one sufficiently massive that tidal forces don’t rip you to pieces and smear you into a plastic-wrap thin layer of goo, a supermassive black hole for example), you won’t notice a thing as you pass through the event horizon … and that’s because it’s not the event horizon to you! In other words, the location of the event horizon of a black hole depends upon who is doing the observing (that word ‘relativity’ really does some heavy lifting, if you’ll excuse the pun), and as you fall (freely) into a black hole, the event horizon is always ahead of you.

You’ll often read that the event horizon is where the escape velocity is c, the speed of light; that’s a not-too-bad description, but it’s better to say that the path of any ray of light, inside the event horizon, can never make it beyond that horizon.

If you watch – from afar! – something fall into a black hole, you’ll see that it gets closer and closer, and light from it gets redder and redder (increasingly redshifted), but it never actually reaches the event horizon. And that’s the closest we’ve come to testing the theoretical predictions of event horizons; we see stuff – mass ripped from the normal star in a binary, say – heading down into its massive companion, but we never see any sign of it hitting anything (like a solid surface). In the next decade or so it might be possible to study event horizons much more closely, by imaging SgrA* (the supermassive black hole – SMBH – at the center of our galaxy), or the SMBH in M87, with extremely high resolution.

The Universe Today article Black Hole Event Horizon Measured is about just this kind of black hole-normal star binary, Black Hole Flares as it Gobbles Matter is about observations of matter falling into a SMBH, and Maximizing Survival Time Inside the Event Horizon of a Black Hole describes some of the weird things about event horizons.

There’s more on event horizons in the Astronomy Cast Relativity, Relativity and More Relativity episode, and the Black Hole Surfaces one.

Sources: NASA Science, NASA Imagine the Universe