Physics

# An Overview of the Theory of Relativity

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When asked to list the individuals they believe have had the greatest impact on modern science, most people will undoubtedly list Albert Einstein.  He was, without a doubt, one of the most profound thinkers of the 20th century.  "Time" magazine even bestowed upon him the title “Person of the Century” in their December 31, 1999, issue.  Einstein made many contributions to 20th-century science during his lifetime, including a discovery and explanation of the photoelectric effect, as well as an energy-saving refrigerator.  He is best known, however, for his theory of relativity.  Einstein actually published two separate papers on relativity.  The first is called the Special Theory of Relativity.  The second paper is called the General Theory of Relativity.

The Special Theory of Relativity is called special because it claims that each frame of reference, each state of motion, is unique with respect to all other states of motion.  Any action or event which takes place within a specific, or special, frame of reference will follow a unique set of laws and, when observed from a differently moving frame of reference, will appear to follow a different set of laws.  Furthermore, observers from each frame of reference will disagree about what actually happened and the time that it took.  Yet there is one frame of reference which has a velocity that remains constant regardless of the motion of the frame from which it is observed.  That one special frame is light.  In other words, the speed of light in the vacuum of space will look the same to any observer, regardless of the motion of that observer.  Even if two differently moving observers attempt to measure the speed of light, they will get the same result.  The reason for this is called a Lorentz transformation

The Lorentz transformation shows that a particle accelerating at the speed of light actually becomes distorted in the direction of travel relative to the speed of a slower moving particle.  This is not a spatial distortion; rather, it is a distortion of time.  The particle accelerating at the speed of light will always appear, to the slower moving particle, to be accelerating at the speed of light.  The reason is that the rate of time is slowed for fast moving objects.

This last point that the Special Theory of Relativity makes is that time is slowed for fast-moving objects, which gives rise to what is known as the space-time paradox, more commonly called the twins paradox.  The paradox states that when two twin particles are separated by acceleration there will be a difference in the rates at which the particles age.  It is illustrated by the thought-experiment that a twin who has returned from a trip around the solar system will be slightly younger than the other twin, who had remained on the surface of the Earth.  The difference in age is due to the effect of acceleration.

In other words, acceleration slows down time relative to non-accelerating frames of reference.  This is even evidenced by the fact that muons, particles that have been observed in laboratories to have very short lives, are able to travel thousands of miles through space.  Einstein did not know about muons because they had not been discovered during his lifetime.  He used mathematics to draw his conclusion about the rates of time in different frames of reference.

There is a great deal of confusion surrounding one of the equations in the Special Theory of Relativity.  The misunderstanding is that Einstein formulated E=mc2, a mass-energy conversion formula that led to the creation of the atomic bomb.  In fact, the actual formula is far more complicated, and E=mc2 is only a very rough approximation of it.  Furthermore, Einstein had nothing to do with the creation of the atomic bomb.  The principles used were already well-known before Einstein published his theory, and efforts to create it were already underway.  Einstein’s formula simply shows that, at high energies, the energy of a moving body is not conserved but transformed into mass.  This formula also shows that the speed of light is the fastest possible speed since all of a body’s rest mass would be converted to energy at the speed of light, leaving a rest mass of zero.

The General Theory of Relativity unites the field equations of Maxwell, which describe the physical behavior of electricity, with those of Carl Gauss, who is known for his work in differential geometry.  The General Theory of Relativity combines space and time into a single manifold which is distorted by massive objects, such as planets and stars.  This is roughly illustrated as a bowling ball on a trampoline.  The bowling ball creates a huge indentation in the trampoline that would not otherwise be there.  If marbles are then rolled across the trampoline’s surface, the ones that pass near the bowling ball will experience a slight curve in trajectory.

Einstein said that light behaves the same way.  He might not have known that light was composed of particles at the time he wrote the paper, but he proposed that the path of light curves around massive objects.  It is important to understand, at this point, that mass does not necessarily equate to size.  Two equal-sized objects can have differing masses, and light waves will curve differently around each one.  The behavior of light waves passing near massive bodies explains a phenomenon known as gravitational lensing, in which an object will appear to have a different concentration of mass than it actually has.  Gravitational lensing is like looking at a fun house mirror.  The image displayed by the mirror is distorted by the shape of the mirror, thus the observer sees the distorted image.  Gravitational lensing can even cause scientists to observe “ghost images” of objects.  For example, a quick glance at a certain section of space might show two stars, or even a cluster of objects, where there is really only one.

The distortion of the path of light in the vicinity of massive bodies leads to the conclusion that the velocity of light is altered by mass.  The acceleration is still the same, but velocity includes both speed and direction.  Thus, a change in direction means a change in velocity.  The velocity of light is the ultimate measure of the passage of time.  This leads to a second remarkable prediction of the Theory of General Relativity; that the rate at which time passes is slowed down by massive bodies.  In other words, a clock on the surface of the sun will tick slower than one on the surface of the Earth.  This phenomenon is called gravitational time dilation.  The prediction that time is dilated due to gravity has been tested and confirmed

There is one more part to the General Theory of Relativity.  It is known as the equivalence principle.  This principle states that being inside a gravitational field, or near a massive body that distorts space-time by a certain, measurable amount is the equivalent of being in an accelerated frame of reference that also provides the same amount of distortion and is accelerating in the reverse direction.  In other words, being pulled down at five feet per second within a stationary frame of reference is the same as being stationary inside a frame of reference that is being pushed upward at five feet per second.  There is no test one can perform, from inside the frame of reference, that will determine the true direction of motion.  This may seem obvious, but the fact is that the equivalence principle shows that a frame of reference that is thought to be stationary may actually be moving.  The principle provides a way to test for relative motion.

Einstein’s relativity theory has helped scientists to understand the behavior of subatomic particles at various energy levels.  It was truly a revolution in 20th- century physics.  The theory may even still be useful in the 21st century as new discoveries are made.  Starting at the end of the last century, astronomers began to discover black holes.  Black holes are one more startling prediction made by the Theory of General Relativity.  A black hole is a region of space where the classical laws of physics break down and relative physics takes over.  Now astronomers have begun to discover black holes at the center of every galaxy.  Einstein’s relativity may be useful in predicting what happens to the energy that gets swallowed up by black holes.  Furthermore, the mass-energy conversion formulas of Einstein can help physicists predict what will happen as particles are continually accelerated in particle accelerators such as the Large Hadron Collider, at CERN in Switzerland.

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## From Around the Web

ARTICLE SOURCES AND CITATIONS
• http://www.nobelprize.org/nobel_prizes/physics/laureates/1921/einstein-bio.html
• http://science.howstuffworks.com/innovation/famous-inventors/what-did-albert-einstein-invent.htm
• http://galileo.phys.virginia.edu/classes/252/lorentztrans.html