Farewell to Reality (17 page)

Experimental tests of general relativity

Einstein estimated that the curvature of spacetime in the vicinity of the sun should make a further contribution to the bending of starlight, giving a total shift of 1.7 arc seconds.

This prediction was famously borne out by a team led by British astrophysicist Arthur Eddington in May 1919. The team carried out observations of the light from a number of stars that grazed the sun on its way to earth. Obviously such starlight is usually obscured by the scattering of bright sunlight by the earth's atmosphere, and can therefore only be observed during a total solar eclipse. Eddington's team recorded simultaneous observations in the cities of Sobral in Brazil and in São Tomé and Príncipe on the west coast of Africa. The apparent positions of the stars were then compared with similar observations made in a clear night sky.

Eddington was rather selective with his data, but his conclusions have since been vindicated by further observations. The shift is correctly predicted by general relativity.

Newton's theory of universal gravitation provided a powerful physical and mathematical underpinning of Kepler's three laws of
planetary motion. Newton predicted that planets should describe elliptical orbits around the sun, each with a fixed perihelion — the point of closest approach of the planet to the sun. However, these points are not observed to be fixed — over time they
precess,
or rotate around the sun.

Much of the observed precession is caused by the cumulative gravitational pull of all the other planets in the solar system, and this can be predicted by Newton's theory. Collectively, it accounts for a precession in the perihelion of the planet Mercury of about 5,557 arc seconds per century. However, the observed precession is rather more, about 5,600 arc seconds per century, a difference of 43 arc seconds or 0.8 per cent.

Newton's gravity could not account for this difference, and other explanations — such as the existence of another planet, closer to the sun than Mercury — were suggested. General relativity predicts a contribution due to the curvature of spacetime of precisely 43 arc seconds per century.
^*

There is one further effect predicted by general relativity. This is the redshift in the frequency of light caused by gravity.

Once again, imagine for a moment that light consists of tiny corpuscles. Such corpuscles emitted from an object should be affected by the object's gravity — if the object were large enough, they could even be slowed down completely and pulled back. This seems all very reasonable, but we know that light doesn't consist of corpuscles (or, at least, ones with conventional mass). Reaching for a wave theory of light makes it difficult to understand the precise nature of the relationship that might exist between light and gravity. In classical wave theory, light is characterized by its frequency or wavelength, and once emitted, these properties are fixed. It simply wasn't obvious how gravity could exert an effect on the frequency of light waves.

Einstein figured out the solution in 1911. Gravity does not exert a direct effect on the frequency of a light wave, but it does have an effect on the spacetime in which the frequency is observed or measured. If, from an observer's perspective, time itself changes, then the frequency
of the wave (the number of up-and-down cycles per unit time) will change if measured against some standard external clock.

Einstein concluded that time should be perceived to slow down close to a gravitating object. A standard clock on earth will run more slowly than a clock placed in orbit around the earth. There are now two relativistic effects to be considered in relation to time. The atomic clock on board the plane from London to Washington DC loses 16 billionths of a second relative to the clock at the UK's National Physical Laboratory due to time dilation associated with the speed of the aircraft. But the clock
gains
53 billionths of a second due to the fact that gravity is weaker at a height of 10 kilometres above sea level. In this experiment, the net gain is therefore predicted to be about 40 billionths of a second. The measured gain was reported to be 39±2 billionths of a second.

What does this mean for light? As a light wave (or a photon) is emitted and travels away from a gravitating object, time speeds up as the effects of gravity reduce. There are now fewer up-and-down cycles per unit time. Seen from the reference frame of the source and a standard clock, those fewer up-and-down cycles per unit time are perceived as a shift to lower frequencies (longer wavelengths).

The effect is called the
gravitational redshift.
The light emitted from a gravitating object is shifted towards the red end of the electromagnetic spectrum as the effects of gravity weaken.

The opposite effect is possible. Light travelling towards a gravitating object will be blueshifted as the effects of gravity grow stronger. American physicists Robert Pound and Glen Rebka were the first to provide a practical earthbound test, at Harvard University in 1959. Gamma-ray photons emitted in the decay of radioactive iron atoms at the top of the Jefferson Physical Laboratory tower were found to be blueshifted by the time they reached the bottom, 22.5 metres below. The extent of the blueshift was found to be that predicted by general relativity, to within an accuracy of about 10 per cent (later reduced to 1 per cent in experiments conducted five years later).

Newton's bucket revisited: Gravity Probe B

Einstein pulled our understanding of space and time inside out. He had dismissed the notion of absolute space and time in his special theory of relativity. But the notion of an absolute spacetime persisted, as did the
question posed by Newton's bucket, which suggested that absolute motion is possible.

When Einstein delivered the last of a series of four lectures on general relativity at the Prussian Academy of Sciences on 25 November 1915, he believed he had finally settled the matter. In the paper he wrote summarizing the theory, he claimed that its general relativistic principle ‘takes away from space and time the last remnant of physical objectivity'.
¹⁹
In other words, he declared the defeat of the absolute and the triumph of the relative.

So, if the motion of the water in Newton's bucket is not absolute, to what, then, is it relative? We have established that it cannot be relative to the bucket itself. So it must be relative to the rest of the universe. And this means that if the bucket and the water in it were perfectly still, and we could somehow spin the entire universe around it, we would expect that the surface of the water would become concave. How can this be?

The answer is simply stunning. We could expect that the stationary water would be affected by the universe spinning around it because all the mass-energy in the universe collectively drags spacetime around with it as it spins. This was an effect first deduced from general relativity by Austrian physicists Josef Lense and Hans Thirring, known variously as
frame-dragging
or the Lense—Thirring effect. Frame-dragging means that there is no measurement we can make that would tell us if it is the water that is rotating in a stationary universe or the universe that is rotating around a stationary bucket of water. The motion of the water is relative.

So, is frame-dragging a real phenomenon? The answer is yes. On 24 April 2004, an exquisitely delicate instrument called Gravity Probe B was launched into polar orbit, 642 kilometres above the earth's surface. The satellite housed four gyroscopes, each with a 38-millimetre-diameter spherical rotor of fused quartz coated with superconducting niobium, cooled to -271
⁰
C. SQUIDs were used to monitor continually the orientations of the gyroscopes as the satellite orbited the earth. To eliminate unwanted torque on the gyroscopes, the satellite was rotated once every 78 seconds and thrusters kept it pointing towards the star IM Pegasi in the constellation of Pegasus.

Two effects were being measured. The fact that the earth curves the spacetime in its vicinity, and this causes the rotation axis of the gyroscopes to tilt (or precess) by a predicted 6,606 milliarc seconds per
year (about 1.8 thousandths of a degree per year) in the plane of the satellite's orbit (that is, in a north-south direction). This precession is called
geodetic drift
, a phenomenon first identified by Dutch physicist Willem de Sitter in 1916.

The second effect is frame-dragging. As the earth rotates on its axis, it drags spacetime around with it in the plane perpendicular to the plane of the satellite orbit (in a west-east direction). This gives rise to a second precession of the gyroscopes, predicted to be 39.2 milliarc seconds per year.

The idea of an experimental test of general relativity based on satellite-borne gyroscopes had first been conceived in 1959. Over forty years elapsed from initial conception to launch, at a cost of $750 million. Data collection began in August 2004 and concluded about a year later. The project suffered a major disappointment when it was discovered that the gyroscopes were experiencing a substantial and unexpected wobble. Small patches of electrostatic charge on the rotors interacted with electrostatic charge on the inside of their housing, caused unexpected torque. These effects could be accounted for using an elaborate mathematical model, but at the cost of increased uncertainty in the final experimental results.

Consequently, analysis of the data took a further five years. The results were announced at a press conference on 4 May 2011. The geodetic drift, measured as a north—south drift in the orbital plane of the satellite, was reported to be 6,602±18 milliarc seconds per year. The west—east drift caused by frame-dragging was reported to be 37.2±7.2 milliarc seconds per year. The high (19 per cent) uncertainty in this last result was caused by the need to model the unexpected wobble.

Despite the uncertainty, this is still a very powerful experimental vindication of general relativity.

Einstein had argued that spacetime is relative. It owes its existence to matter and energy. Take all the matter and energy out of the universe and there would be no empty container. There would be nothing at all.

Interestingly, the debate did not end in 1916. There are further arguments to suggest that Einstein may have misinterpreted his own equations of general relativity. Today, many contemporary physicists and philosophers argue that Einstein was mistaken: spacetime may exist absolutely. It nevertheless
behaves
relatively, as the phenomenon of frame-dragging demonstrates. The debate is likely to run and run.

^*
Readers interested in exploring the nature of this synthesis should consult Michael Morgan's
The Spate Between Our Ears: How the Brairt Represents Visual Space
, published by Weidenfeld $ Nicolson in 2003.

^*
It'll have to be your garden. I live in a fourth-floor apartment.

^*
The speed of light in a vacuum is about 299.792 million metres per second, or 186,282 miles per second.

^*
Kinetic energy is energy associated with the motions of objects.

^*
No pun intended.

^*
The perihelia of other planets are also susceptible to precession caused by the curvature of spacetime, but the contributions are much less pronounced.

5

The (Mostly) Missing Universe

The Universe According to the
Standard Model of Big Bang Cosmology

We admittedly had to introduce an extension to the field equations that is not
justified by our actual knowledge of gravitation.

Albert Einstein
¹

One of the most remarkable aspects of contemporary theoretical physics is its relatively new-found capacity to address questions that might be considered the preserve of high priests. Human beings possess a deep-rooted desire to understand their place in the universe. We have an innate need to fathom the seemingly unfathomable. Typically, what we are unable to fathom using observation, experiment and simple logic, the high priests attempt to explain through invention and the spinning of elaborate religious mythologies.

Today, the two principal building blocks that underpin our contemporary understanding of the physical world — relativity and quantum theory — are combined to tell the truly fascinating story of the origin and evolution of our universe. It is a story that is certainly no less remarkable than the creation myths of religious doctrine, and all the more remarkable because it happens to be ‘true', at least for now, in the sense of the Veracity Principle.

Most readers will be already familiar with aspects of this modern creation story.

We now know that, insofar as the word ‘began' is deemed appropriate, the universe began some 13.7 billion years ago in a ‘big bang', a primeval quantum fluctuation of some kind that led to the creation of space, time and energy. What we now recognize as the four fundamental forces of nature disentangled themselves from the first,
primeval force, in a series of what we might think of as phase transitions, much as steam condenses to water which freezes to ice.

Gravity was the first to be spun off, followed by the strong nuclear force, whose splitting triggered a short burst of exponential expansion of spacetime called
inflation.
Quantum fluctuations from this beginning of all things became imprinted by inflation on the large-scale structure of the universe we see today: a telltale thumbprint left at a cosmic crime scene. A subsequent phase transition separated the weak nuclear force from electromagnetism.

About 380,000 years after the big bang, primordial electrons latched themselves on to primordial atomic nuclei in a process called ‘recombination'. The first neutral hydrogen and helium atoms were formed, releasing a flood of hot electromagnetic radiation to fill all of space.

The universe continued to evolve and expand, a fact belied by the simple observation that the night sky is largely dark.
²
The hot radiation released during recombination cooled as the universe expanded, and appears today in the form of microwaves with an average temperature of around -270.5°C, or 2.7 kelvin, almost three degrees above absolute zero. It is a cold remnant, an ‘afterglow' of a tumultuous time in the history of the universe.