SAT Physics Subject Test

Chapter 16 Modern Physics


While 1915 may seem like a long time ago, virtually all physics that has been done since then (with the exception of atomic and nuclear physics) is beyond the scope of most introductory physics classes and can be called “contemporary physics.” While you do not need to know the details of any of the theories in this section, knowing some of the major results may be useful in answering a few questions on the test, which may focus either on the major results themselves or the people who worked on the theories.

The dates in the
discussion that follow
are just for context, not
to be memorized.

In 1915, a decade after he published on special relativity, Einstein published the theory of general relativity, which (as the name suggests) was more general than the first theory because it could account for accelerated motion and for motion in the strong gravitational fields near large masses. Indeed, the guiding principle of general relativity, called the Equivalence Principle, is that it is impossible to differentiate between an accelerating reference frame and a reference frame in a gravitational field; such frames are equivalent.

For example, consider an elevator in space (far from Earth) that is accelerating upward. A person standing in that elevator will feel pressed against the floor as if pulled down by gravity, even though there is no gravitational field nearby. Likewise, a person in a stationary elevator on Earth feels pressed against the floor because of Earth’s gravitational field. Next, consider what the person would see if the elevator were accelerating very quickly and the person shined a flashlight at the opposite wall. The light would appear to bend down, since it is going straight as the person accelerates up. The Equivalence Principle dictates that the same bending must occur in a strong gravitational field as well. That is, gravity makes light bend. Einstein went on to point out that this is not simply a property of light. Light bends because space itself bends. The space near large amounts of mass is bent, and it is this bending that causes all the gravitational effects that we see. Furthermore, it is not simply space that bends. Four-dimensional spacetime bends, with the result that time dilates in a gravitational field just as it does for an object moving at very high speed.

If the elevator were simply
moving up at constant
speed, special relativity
says that the light would
go straight instead; it is
impossible to distinguish
between a reference
frame that is moving at
constant velocity and one
that is not moving, and
clearly in a motionless
elevator would not make
the light bend.

In almost all circumstances, both Newton’s and Einstein’s description of gravity give similar results. However, very precise measurements, especially in close proximity to a very massive object, show deviations and agree with Einstein’s general relativity exactly. One field in which general relativity has had particularly special importance is astrophysics. Since stars, galaxies, and other astronomical objects often have very large amounts of mass, the bending of spacetime is significant in the vicinity of these objects. For example, the orbit of Mercury, the closest planet to the Sun, deviates measurably (if slightly) from the ellipse predicted by Newtonian gravitation. The orbit precesses, supporting Einstein’s theory. Light passing near the Sun bends measurably, as predicted by Einstein and measured originally by Arthur Eddington in 1919. Very precise clocks have measured gravitational time dilation by detecting differences in time near the surface of Earth and far above it.

Furthermore, very massive objects may have so much gravitational pull that the velocity required to escape from their attraction is greater than the speed of light. In general relativity, because light is subject to the curvature of space that affects matter as well, light cannot escape from these objects either, and as a result, they are called black holes. They are black because they emit no light, nor can they even reflect light. They cannot be seen directly, but their gravitational effects on nearby objects can be quite dramatic and they can be detected thereby. For example, quasars are extremely bright but extremely distant objects that were unexplained in astronomy for a very long time, but the best explanation now is that they are caused by black holes that are pulling matter in at extremely high speeds. The matter rubs against other falling in matter, and the frictional effects generate light. They eventually attract all the nearby matter and run out of fuel, in effect, so that they stop generating light, and this is the reason that the only ones that we can see are very distant: Very distant in astronomy means that it takes the light a very long time to reach the Earth, so astronomers are seeing light emitted a long time ago, and therefore they have a picture of the quasar in the very distant past. By now, quasars have likely stopped emitting light, but they won’t wink out in our sky until many years from now, because light they emitted long ago is still traveling to us.

Another landmark discovery in astronomy in the 20th century, made by Edwin Hubble, was that galaxies outside our own send light to us that appears redshifted; that is, by the Doppler Effect for light, they must be moving away from us. This is evidence that the universe is expanding, because within an expanding universe, all galaxies would appear to moving away from each other. Astrophysicists have attempted to use the equations of general relativity to explain this. Larger and larger telescopes, which work by collecting more and more light in order to see distant objects better, among other advances in telescope technology, have allowed for more precise measurements that have continued to refine the science of astronomy.

After the development of general relativity, which described the very large, the quantum mechanics of the 1920s came to describe the very small. Niels Bohr, after working on the Bohr model of the atom, which accurately describes the emission spectra of the hydrogen atom but seemed to be based on arbitrary postulates, continued to develop models of the atom. Louis de Broglie proposed that, since light could be treated both as a stream of particles and as a wave, perhaps matter could as well, so electrons might be able to be described by wave theory, and he gave the equation for the wavelength of such waves. One practical application of this is the electron microscope. Electron microscopes bombard very tiny objects with magnetically-focused electrons (instead of the usual photons by which we normally see things) and can get extremely high resolution because of the very small wavelengths of such electrons. Erwin Schrödinger introduced the equation that described the way the waves propagated in space and time. Werner Heisenberg, who also developed an equivalent formulation of quantum mechanics using matrix algebra, showed that the new quantum mechanics predicted that the degree to which one knew the position of a particle was inversely proportional to the degree to which one could, even in principle, know the momentum of a particle. In other words, Heisenberg’s principle, called the Uncertainty Principle, says that one cannot simultaneously know both where a particle is and where it is going to arbitrary accuracy. Many others worked on quantum mechanics, including Wolfgang Pauli, who stated the Pauli Exclusion Principle, that certain types of particles, such as electrons, cannot be in the same quantum states.

One great success of quantum mechanics was in explaining superconductivity. The resistivity of a material is slightly temperature dependent: An object will conduct better at lower temperatures, and at very low temperatures (often only 20 or 30 degrees above absolute zero), the resistivity of some substances will drop to zero. A material with zero resistivity and therefore zero resistance to electric current is a superconductor. With quantum mechanics (and, frankly, a great deal of math), superconductivity can be explained, a feat that classical electromagnetic theory cannot duplicate.

Despite the tremendous successes of general relativity and quantum mechanics, the history of physics is not over, since these two theories have not been successfully united. Almost immediately after quantum mechanics was proposed, attempts began to unite it with relativity. Special relativity was successfully united with quantum mechanics in quantum field theory and the Standard Model of Particle Physics. Quantum field theory adequately describes three of the four fundamental forces of nature: the electromagnetic force, the strong nuclear force, and the weak nuclear force. The electromagnetic force is responsible for almost all of the forces that we see in daily life, including friction, the normal force, and many others. The strong nuclear force, as mentioned earlier, is what holds the nucleus of an atom together, since protons, which are positively charged, repel each other electrically but are bunched together in the nucleus of an atom. The weak nuclear force mediates radioactive decay.

However, general relativity and the force of gravity have remained difficult to relate to quantum mechanical effects. This only matters when examining objects that are so dense that they can, on the one hand, have enough mass that general relativity is significant (remember that general relativity has only tiny effects even in the near vicinity of the Sun, so a very great deal of mass is necessary), and on the other hand, are small enough that quantum mechanical effects are important (remember that quantum mechanics most regularly describes atomic structure and atomic interactions). What has the mass of the Sun or more but is the size of an atom or smaller? In the present universe, only a black hole has such densities. As a result, physicists are investigating black holes and what can be learned about them without seeing them.

The very early universe, before it had expanded very much, also involved extraordinarily high densities, and light emitted extremely long ago that is just now reaching us (because it was emitted very far away) can help in investigating current problems in physics. One major source of information is the Cosmic Microwave Background (CMB). In the early universe, a great deal of matter and a great deal of energy (including light) were in a very small space, and as a result, photons that were emitted from one source just hit particles of matter and were absorbed. As the universe expanded, the density of the universe decreased, or, equivalently, the space between particles increased, such that light could travel farther and farther before hitting matter and being absorbed. Eventually, at a certain point, light became able to travel almost freely without bumping into matter anymore, and that light, which happened to be in the microwave area of the electromagnetic spectrum because of the prevailing temperature of the universe at the time, is still moving through the universe today. Since this light was everywhere in the universe at the time, it is everywhere today as well, so it forms a background to everything in the cosmos (hence the name Cosmic Microwave Background). Measurements of the CMB are also evidence of the expanding universe, since the explanation for the CMB is that the universe was once much smaller than it presently is and has been expanding ever since, and it is hoped that more and more precise measurements of the CMB will yield answers to questions about how the universe came to be in its present state.

Several other major puzzles remain in physics. One is that current theories of gravity (both Newtonian and Einsteinian) predict that a particular graph should describe the rotation of stars in a galaxy—stars orbit the center of galaxies in much the same way that planets orbit the centers of solar systems—but when one actually observes the rotation of stars, the graph one draws is substantially different. It appears that a great deal of mass should be in each galaxy, but none can be seen. This missing mass is called dark matter, because it is matter that cannot be seen (i.e. is dark). There are many guesses about the nature of dark matter, but no definitive explanation has been found.

Similarly, when one uses general relativity to describe the expansion of the universe and inputs what we know about the current state of the universe, it appears that the expansion of the universe should be decreasing (distant galaxies should be redshifted by smaller and smaller amounts). However, observing the actual expansion of the universe reveals that it is in fact increasing. The source of the energy that could cause this, called dark energy (by analogy with dark matter), is unknown. Investigations of black holes, dark matter, and dark energy are ongoing in physics, along with many other studies of many other phenomena, and the search for a more complete picture of the universe continues.