## Physics for the 21st Century

# Gravity

Although by far the weakest of the known forces in nature, gravity pervades the universe and played an essential role in the evolution of the universe to its current state. Newton’s law of universal gravitation and its elegant successor, Einstein’s theory of general relativity, represent milestones in the history of science and provide the best descriptions we have of gravity. General relativity is founded on the principle of equivalence of gravity and acceleration; an inescapable consequence is that gravity governs the very geometry of space and time. This property of gravity distinguishes it from the other forces and makes attempts to unify all of the forces into a “theory of everything” exceedingly difficult. How well do we really understand gravity? Do the same laws of gravity apply to objects on the opposite sides of the universe as to particles in the microscopic quantum world? Current research is attempting to improve the precision to which the laws of gravity have been tested and to expand the realm over which tests of gravity have been made. Gravitational waves, predicted by general relativity, are expected to be observed in the near future. This unit will review what we know about gravity and describe many of the directions that research in gravitation is following.

### Unit Glossary

**black hole**

A black hole is a region of space where gravity is so strong that nothing can escape its pull. Black holes have been detected through their gravitational influence on nearby stars and through observations of hot gas from surrounding regions accelerating toward them. These black holes are thought to have formed when massive stars reached the end of their cycle of evolution and collapsed under the influence of gravity. If a small volume of space contains enough mass, general relativity predicts that spacetime will become so highly curved that a black hole will form.

**cosmic microwave background**

The cosmic microwave background (CMB) radiation is electromagnetic radiation left over from when atoms first formed in the early universe, according to our standard model of cosmology. Prior to that time, photons and the fundamental building blocks of matter formed a hot, dense soup, constantly interacting with one another. As the universe expanded and cooled, protons and neutrons formed atomic nuclei, which then combined with electrons to form neutral atoms. At this point, the photons effectively stopped interacting with them. These photons, which have stretched as the universe expanded, form the CMB. First observed by Penzias and Wilson in 1965, the CMB remains the focus of increasingly precise observations intended to provide insight into the composition and evolution of the universe.

**Coulomb’s Law**

Coulomb’s Law states that the electric force between two charged particles is proportional to the product of the two charges divided by the square of the distance between the particles.

**Doppler shift (Doppler effect)**

The Doppler shift is a shift in the wavelength of light or sound that depends on the relative motion of the source and the observer. A familiar example of a Doppler shift is the apparent change in pitch of an ambulance siren as it passes a stationary observer. When the ambulance is moving toward the observer, the observer hears a higher pitch because the wavelength of the sound waves is shortened. As the ambulance moves away from the observer, the wavelength is lengthened and the observer hears a lower pitch. Likewise, the wavelength of light emitted by an object moving toward an observer is shortened, and the observer will see a shift to blue. If the light-emitting object is moving away from the observer, the light will have a longer wavelength and the observer will see a shift to red. By observing this shift to red or blue, astronomers can determine the velocity of distant stars and galaxies relative to the Earth. Atoms moving relative to a laser also experience a Doppler shift, which must be taken into account in atomic physics experiments that make use of laser cooling and trapping.

**ether**

In the late nineteenth century, physicists were putting what they thought were the finishing touches on their theoretical description of electricity and magnetism. In the theory, electromagnetic waves traveled through a medium called “luminiferous ether” just as sound waves travel through the air, or the seismic waves that we experience as earthquakes travel through the Earth. The last remaining detail was to detect the ether and understand its properties. In 1887, Albert Michelson and Edward Morley performed an experiment, verified by many others, that demonstrated that light does not travel through ether. The lack of ether was one of many factors leading Einstein to develop special relativity.

**event horizon**

A black hole’s event horizon is the point of no return for matter falling toward the black hole. Once matter enters the event horizon, it is gravitationally bound to the black hole and cannot escape. However, an external observer will not see the matter enter the black hole. Instead, the gravitational redshift due to the black hole’s strong gravitational field causes the object to appear to approach the horizon increasingly slowly without ever going beyond it. Within the event horizon, the black hole’s gravitational field warps spacetime so much that even light cannot escape.

**general relativity**

General relativity is the theory Einstein developed to reconcile gravity with special relativity. While special relativity accurately describes the laws of physics in inertial reference frames, it does not describe what happens in an accelerated reference frame or gravitational field. Since acceleration and gravity are important parts of our physical world, Einstein recognized that special relativity was an incomplete description and spent the years between 1905 and 1915 developing general relativity. In general relativity, we inhabit a four-dimensional spacetime with a curvature determined by the distribution of matter and energy in space. General relativity makes unique, testable predictions that have been upheld by experimental measurements, including the precession of Mercury’s orbit, gravitational lensing, and gravitational time dilation. Other predictions of general relativity, including gravitational waves, have not yet been verified. While there is no direct experimental evidence that conflicts with general relativity, the accepted view is that general relativity is an approximation to a more fundamental theory of gravity that will unify it with the Standard Model. See: gravitational lensing. gravitational time dilation, gravitational wave, precession, spacetime, special relativity, Standard Model.

**gravitational lensing**

Gravitational lensing occurs when light travels past a very massive object. According to Einstein’s theory of general relativity, mass shapes spacetime and space is curved by massive objects. Light traveling past a massive object follows a “straight” path in the curved space, and is deflected as if it had passed through a lens. Strong gravitational lensing can cause stars to appear as rings as their light travels in a curved path past a massive object along the line of sight. We observe microlensing when an object such as a MACHO moves between the Earth and a star. The gravitational lens associated with the MACHO focuses the star’ light, so we observe the star grow brighter then dimmer as the MACHO moves across our line of sight to the star.

**gravitational mass**

The gravitational mass of a particle is the gravitational equivalent of electric charge: the physical property of an object that causes it to interact with other objects through the gravitational force. According to the equivalence principle, gravitational mass is equivalent to inertial mass. See: equivalence principle, inertial mass.

**gravitational time dilation**

Clocks in a strong gravitational field run slower than clocks in a weaker gravitational field. This effect, predicted by Einstein’s theory of general relativity and confirmed by precision experiments both on Earth and in space, is called “gravitational time dilation.”

**gravitational waves**

Gravitational waves are oscillations of a gravitational field, just as light waves are oscillations of an electromagnetic field. Predicted by general relativity, gravitational waves travel at the speed of light and have transverse polarization. It is difficult to detect gravitational waves directly because their amplitude is so small, but their effect on the binary pulsar system discovered by Hulse and Taylor provides indirect evidence of their existence.

**Hertz**

Hertz (Hz) is a unit of frequency, defined as the number of complete cycles of a periodic signal that take place in one second. For example, the frequency of sound waves is usually reported in units of Hertz. The normal range of human hearing is roughly 20–20,000 Hz. Radio waves have frequencies of thousands of Hz, and light waves in the visible part of the spectrum have frequencies of over 1014 Hz.

**inertial mass**

Inertia is the measure of an object’s reluctance to accelerate under an applied force. The inertial mass of an object is the mass that appears in Newton’s second law: the acceleration of an object is equal to the applied force divided by its inertial mass. The more inertial mass an object has, the less it accelerates under a fixed applied force. See: equivalence principle, gravitational mass.

**MOND**

MOND, or Modified Newtonian Dynamics, is a theory that attempts to explain the evidence for dark matter as a modification to Newtonian gravity. There are many versions of the theory, all based on the premise that Newton’s laws are slightly different at very small accelerations. A ball dropped above the surface of the Earth would not deviate noticeably from the path predicted by Newtonian physics, but the stars at the very edges of our galaxy would clearly demonstrate modified dynamics if MOND were correct.

**Newton’s law of universal gravitation**

Newton’s law of universal gravitation states that the gravitational force between two massive particles is proportional to the product of the two masses divided by the square of the distance between them. The law of universal gravitation is sometimes called the “inverse square law.” See: universal gravitational constant.

**polarization**

The polarization of a wave is the direction in which it is oscillating. The simplest type of polarization is linear, transverse polarization. Linear means that the wave oscillation is confined along a single axis, and transverse means that the wave is oscillating in a direction perpendicular to its direction of travel. Laser light is most commonly a wave with linear, transverse polarization. If the laser beam travels along the x-axis, its electric field will oscillate either in the y-direction or in the z-direction. Gravitational waves also have transverse polarization, but have a more complicated oscillation pattern than laser light.

**precession**

Precession is a systematic change in the orientation of a rotation axis. For example, the orbits of planets in our solar system precess. Each planet follows an elliptical path around the Sun, with the Sun at one of the focal points of the ellipse. The long axis of the ellipse slowly rotates in the plane of the orbit with the Sun as a pivot point, so the planet never follows exactly the same path through space as it continues to orbit in its elliptical path. The precession measured in Mercury’s orbit was found to be different from the prediction of Newtonian gravity but matched the prediction of general relativity, providing some of the first concrete evidence that Einstein’s version of gravity is correct.

**pulsar**

A pulsar is a spinning neutron star with a strong magnetic field that emits electromagnetic radiation along its magnetic axis. Because the star’s rotation axis is not aligned with its magnetic axis, we observe pulses of radiation as the star’s magnetic axis passes through our line of sight. The time between pulses ranges from a few milliseconds to a few seconds, and tends to slow down over time.

**spacetime**

In classical physics, space and time are considered separate things. Space is three-dimensional, and can be divided into a three-dimensional grid of cubes that describes the Euclidean geometry familiar from high-school math class. Time is one-dimensional in classical physics. Einstein’s theory of special relativity combines the three dimensions of space and one dimension of time into a four-dimensional grid called “spacetime.” Spacetime may be flat, in which case Euclidean geometry describes the three space dimensions, or curved. In Einstein’s theory of general relativity, the distribution of matter and energy in the universe determines the curvature of spacetime.

**special relativity**

Einstein developed his theory of special relativity in 1905, 10 years before general relativity. Special relativity is predicated on two postulates. First, the speed of light is assumed to be constant in all inertial frames. Second, the laws of physics are assumed to be the same in all inertial frames. An inertial frame, in this context, is defined as a reference frame that is not accelerating or in a gravitational field. Starting from these two postulates, Einstein derived a number of counterintuitive consequences that were later verified by experiment. Among them are time dilation (a moving clock will run slower than a stationary clock), length contraction (a moving ruler will be shorter than a stationary ruler), the equivalence of mass and energy, and that nothing can move faster than the speed of light. See: general relativity, spacetime.

**standard model of cosmology**

Our best model for how the universe began and evolved into what we observe now is called the “standard model of cosmology.” It contends that the universe began in a Big Bang around 14 billion years ago, which was followed by a short period of exponential inflation. At the end of inflation, quarks, photons, and other fundamental particles formed a hot, dense soup that cooled as the universe continued to expand. Roughly 390,000 years after the end of inflation, the first atoms formed and the cosmic microwave background photons decoupled. Over the course of billions of years, the large structures and astronomical objects we observe throughout the cosmos formed as the universe continued to expand. Eventually the expansion rate of the universe started to increase under the influence of dark energy.

**torsion pendulum**

A conventional pendulum is a mass suspended on a string that swings periodically. A torsion pendulum is a mass suspended on a string (or torsion fiber) that rotates periodically. When the mass of a torsion pendulum is rotated from its equilibrium position, the fiber resists the rotation and provides a restoring force that causes the mass to rotate back to its original equilibrium position. When the mass reaches its equilibrium position, it is moving quickly and overshoots. The fiber’s restoring force, which is proportional to the rotation angle of the mass, eventually causes the mass to slow down and rotate back the other way. Because the restoring force of the torsion fiber is very small, a torsion pendulum can be used to measure extremely small forces affecting the test mass.

**universal gravitational constant**

The universal gravitational constant, denoted by G, is the proportionality constant in Newton’s law of universal gravitation. The currently accepted value for G is 6.67428±0.00067 x 10-11 N-m2/kg2.

**universality of free fall**

The universality of free fall, sometimes abbreviated UFF, is the idea that all materials fall at the same rate in a uniform gravitational field. This is equivalent to stating that inertial and gravitational mass are the same. See: equivalence principle, gravitational mass, inertial mass.

### Content Developer: Blayne Heckel

Blayne Heckel is professor of physics and chair of the Department of Physics at the University of Washington. His research interests focus on tests of fundamental symmetries: torsion balance tests of spatial isotropy, the equivalence principle, and the gravitational inverse square law, and searching for time reversal symmetry violation in the electric dipole moments of atoms.

### Featured Scientist: Eric Adelberger

Eric Adelberger is emeritus professor of physics at the University of Washington. His research interests lie in the area of high-precision experimental physics: gravitation, nuclear astrophysics, and fundamental symmetries. He has recently tested speculative ideas that would produce violations of the Einstein Equivalence Principle, short-distance deviations from the Gravitational Inverse-Square Law, Planck-Scale breakdown of Lorentz symmetry, and time variations of Newton’s constant.

### Featured Scientist: Nergis Mavalvala

Nergis Mavalvala has been on the physics faculty at MIT since 2002. Her research focuses on detection of gravitational waves using laser interferometry. She has been involved with the Laser Interferometer Gravitational-Wave Observatory (LIGO) since her early years in graduate school at MIT and she has also been working on instrument development for interferometric gravitational-wave detectors. Her recent research interests address fundamental limits to measurement imposed by quantum mechanics, an important issue facing the next generation of gravitational wave detectors currently being developed for LIGO and other international gravitational wave observatories. Professor Mavalvala received a B.A. in physics and astronomy from Wellesley College in 1990, a Ph.D. in physics from MIT in 1997, and was a postdoctoral fellow at the California Institute of Technology before joining the faculty at MIT.