Testing Einstein?

There has recently been a flurry of media stories about experiments searching for gravitational radiation, usually with headlines about “testing Einstein’s theory”.  In fact, these experiments are testing our ability to measure gravitational radiation, because there is already compelling proof that this prediction of the general theory of relativity (which is itself exactly 100 years old as I write) is correct.  This extract from my book Einstein’s Masterwork (http://www.iconbooks.com/blog/title/einsteins-masterwork/) should make everything clear.  But the experiments are still hugely important.  If we can detect gravitational radiation directly, we will have a new way to study things like black holes, supernovas — and binary pulsars.


Massive objects, such as the Earth or a star, drag spacetime around with them as they rotate.  If they move back and forth, they can also generate waves in the fabric of spacetime, known as gravitational waves, or gravitational radiation, like the ripples you can make in a bowl of water by wiggling your finger about in it.  The resulting ripples in the fabric of space are very weak, unless a very large mass is involved in fairly rapid motion.  But the waves were predicted by Einstein in a paper published in 1916, where he showed that they should move at the speed of light.  Physicists have been trying for decades (as yet unsuccessfully) to detect gravitational radiation using very sensitive detectors here on Earth, and plan to put even more sensitive detectors into space.  But meanwhile absolute proof of the accuracy of his prediction has come from observations of compact objects far away in space — the latest, and most precise, of these observations being reported in 2013.  The objects involved are compact binary stars, systems in which one star orbits closely around another — or rather, where both stars orbit around their common centre of mass, like a whirling dumbbell or the twirling mace of a drum majorette.  The first of these systems extreme enough to test Einstein’s prediction was a “binary pulsar”, studied in the mid-1970s.
A binary pulsar exists when two neutron stars, one of which is a pulsar, are in orbit around one another, forming a binary star system.  The term is also used to refer to a pulsar in orbit about any other star, for example, a white dwarf.  More than twenty binary pulsars are now known, but astronomers reserve the term “the binary pulsar” for the first one to be discovered, which is also known by its catalog number, as PSR 1913+16.
The binary pulsar was discovered in 1974 by Russell Hulse and Joseph Taylor, of the University of Massachusetts, working with the Arecibo radio telescope in Puerto Rico.   This pulsar was at the time the most accurate clock yet discovered.  What they found that summer was so important that in 1993 the pair received the Nobel Prize for their work on the binary pulsar.
The first hint of the existence of the binary pulsar came on 2 July, when the instruments recorded a very weak signal.  Had it been just 4 per cent weaker still, it would have been below the automatic cutoff level built in to the computer program running the search, and would not have been recorded.  The source was especially interesting because it had a very short period, only 0.059 seconds, making it the second fastest pulsar known at the time.  But it wasn’t until 25 August that Hulse was able to use the Arecibo telescope to take a more detailed look at the object.
Over several days following 25 August, Hulse made a series of observations of the pulsar and found that it varied in a peculiar way.  Most pulsars are superbly accurate clocks, beating time with a precise period measured to six or seven decimal places; but this one seemed to have an erratic period which changed by as much as 30 microseconds (a huge “error” for a pulsar) from one day to the next.  Early in September 1974, Hulse realised that these variations themselves follow a periodic pattern, and could be explained by the Doppler effect caused by the motion of the pulsar in a tight orbit around a companion star.  Taylor flew down to Arecibo to join the investigation, and together he and Hulse found that the orbital period of the pulsar around its companion (its “year”) is 7 hours and 45 minutes, with the pulsar moving at a maximum speed (revealed by the Doppler effect) of 300 kilometers per second, one tenth of the speed of light, and an average speed of about 200 km/sec, as it zipped around its companion.  The size of the orbit traced out at this astonishing speed in just under 8 hours is about 6 million km, roughly the circumference of the Sun.  In other words, the average separation between the pulsar and its companion is about the radius of the Sun, and the entire binary pulsar system would neatly fit inside the Sun.
All pulsars are neutron stars; the orbital parameters showed that in this case the companion star must also be a neutron star.  The system was immediately recognised as an almost perfect test bed for the General Theory — and, indeed, for the Special Theory, as well.  As I have explained, one of the key tests of the General Theory is the advance of the perihelion of Mercury.  The equivalent effect in the binary pulsar (the shift in the “periastron”) would be about a hundred times stronger than for Mercury, and whereas Mercury only orbits the Sun four times a year, the binary pulsar orbits its companion a thousand times a year, giving that much more opportunity to study the effect.  It was duly measured,and found to conform exactly with the predictions of Einstein’s theory —  the first direct test of the General Theory made using an object outside the Solar System.  By feeding back the measurements of the shift into the orbital data for the system, the total mass of the two stars in the system put together was eventually determined to unprecedented accuracy, as 2.8275 times the mass of our Sun.
But this was only the beginning of the use of the binary pulsar as a gravitational laboratory in which to test and use Einstein’s theory.  Extended observations over many months showed that, once allowances were made for the regular changes caused by its orbital motion, the pulsar actually kept time very precisely.  Its period of 0.05903 seconds increased by only a quarter of a nanosecond (a quarter of a billionth of a second) in a year, equivalent to a clock that lost time at a rate of only 4 per cent in a million years.
The numbers became more precise as the observations mounted up.  For 1 September, 1974, the data were: Period, 0.059029995271 sec; rate of increase, 0.253 nanoseconds per year; orbital period 27906.98163 seconds; rate of change of periastron, 4.2263 degrees of arc per year.
The accuracy of the observations soon made it possible to carry out more tests and applications of the theory of relativity.  One involves the time dilation predicted by the Special Theory of relativity.  Because the speed of the pulsar around its companion is a sizeable fraction of the speed of light, the pulsar “clock” is slowed down, according to our observations, by an amount which depends on its speed.  Since the speed varies over the course of one orbit (from a maximum of 300 km/sec down to “only” 75 km/sec), this will show up as a regular variation of the pulsar’s period over each orbit. And because the pulsar is moving in an elliptical orbit around its companion, its distance from the second neutron star varies.  This means that it moves from regions of relatively high gravitational field to regions of relatively low gravitational field, and that its timekeeping mechanism should be subject to a regularly varying gravitational redshift.
The combination of these two effects produces a maximum measured variation in the pulsar period of 58 nanoseconds over one orbit, and this information can be fed back in to the orbital calculations to determine the ratio of the masses of the two stars.  Since the periastron shift tells us that the combined mass is 2.8275 solar masses, the addition of these data reveals that the pulsar itself has 1.42 times the mass of our Sun, while its companion has 1.40 solar masses.  These were the first precise measurements of the masses of neutron stars.
But the greatest triumph of the investigation of the binary pulsar was still to come.  Almost as soon as the discovery of the system had been announced, several relativists pointed out that in theory the binary pulsar should be losing energy as a result of gravitational radiation, generating ripples in the fabric of spacetime that would carry energy away and make the orbital period speed up as the binary pulsar and its companion spiraled closer together as a result.
Even in a system as extreme as the binary pulsar, the effect is very small.  It would cause the orbital period (about 27,000 seconds) to increase by only a few tens of a millionth of a second(about 0.0000003 per cent) per year.  The theory was straightforward, but the observations would require unprecedented accuracy.  In December 1978, after four years of work, Taylor announced that the effect had been measured, and that it exactly matched he predictions of Einstein’s theory.  The precise prediction of that theory was that the orbital period should decrease by 75 millionths of a second per year; by 1983, nine years after the discovery of the binary pulsar, Taylor and his colleagues had measured the change to a precision of 2 millionths of a second per year, quoting the observed value as 76+2 millionths of a second per year.  Since then, the observations have been improved further, and show an agreement with Einstein’s theory that has an error less than 1 per cent.  This was a spectacular and comprehensive test of the General Theory, and effectively ruled out any other theory as a good description of the way the Universe works.
But astronomers were not prepared to rest on their laurels, and kept searching for other objects which might be used to test the General Theory.  Their latest success involves a neutron star and a white dwarf star orbiting around each other some 7,000 light years from Earth.  The neutron star — another pulsar, dubbed PSR J0348+0432 — was discovered by radio astronomers using the Green Bank Telescope, and its companion was soon detected in optical light, with the system being studied using both optical and radio telescopes around the world from late 2011.  The two stars orbit around each other once every 2.46 hours, with the pulsar spinning on its axis once every 39 milliseconds — that is, roughy 25 times per second. The same kind of analysis as that used for the binary pulsar reveals that in this case the neutron star has a mass just over twice that of the Sun, with a diameter of about 20 km, while the white dwarf has a mass a bit less than 20 per cent of the mass of the Sun.  The distance between the two stars is about 1.2 times the radius of the Sun, just over half the Sun’s diameter, so once again the whole system would fit inside the Sun.  With the measured orbital properties, this implies that gravitational radiation should make the orbit “decay” at a rate of 2.6 x 10-13 seconds per second; the measured rate is 2.7 x 10-13 seconds per second, with an uncertainty of + 0.5.  Over a whole year, this amounts to just 8 millionths of a second.  This is an even better test of the General Theory, partly because of the larger mass of the pulsar (the most massive neutron star yet discovered) compared with the neutron stars in the original binary pulsar system.
Over the years ahead, continuing observations will provide even more precise tests of the General Theory.  But the accuracy of the test is already so precise, and the agreement with the predictions of Einstein’s theory are so good, that the General Theory of relativity can now be regarded as one of the two most securely founded theories in the whole of science, alongside quantum electrodynamics.

One comment on “Testing Einstein?

  1. RhEvans says:

    Reblogged this on thecuriousastronomer and commented:
    A very clear and timely explanation of one test of Einstein’s general theory of relativity – the search for gravitational waves. Cardiff University has a very active research group in this area.

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