Einstein’s Theory of Relativity

So what’s the big deal? What did Einstein do which was so… different? And what does it mean to say that it is “relative” anyway?

Calvin and Hobbes

The 19 th century ushered in Wave Theory In 1864 Christian Huygen explained some phenomena in terms of wave dynamics and was able to graphically explain how sound and water waves behaved. Simultaneously James Clerk Maxwell verified Faraday’s discovery that a changing magnetic field would induce an electric field and subsequent current flow through a wire. It was soon discovered that a changing electric field would induce a magnetic field as well. Electric and magnetic fields were clearly interrelated. This verified Michael Faraday’s work from earlier in the century. A few years later Maxwell introduced a sophisticated and amazing set of equations to mathematically explain what he had observed. He applied them to electric and magnet field theory (1873). This revolutionized wave theory. It also revolutionized light theory. Light had previously been considered to be particles, called corpuscles. That was replaced by the latest-greatest: wave theory.

Electric and Magnetic Fields Before James Clerk Maxwell’s equations people had ways of describing mathematically either electric or magnetic fields. Maxwell’s equations combined them into one mathematical phenomena. (Equations published in BTW, you should memorize this date.) 30 years later a young Jewish German recent graduate, working in a patent office because he could find no work in physics took note and was duly impressed.

6 Historical Perspective Light is a wave. Waves require a medium through which to propagate. Medium was called the “aether.” (from the Greek aither, meaning upper air) Maxwell’s equations assumed that light obeys the Newtonian-Galilean transformation.

Albert Michelson Albert Michelson Actual attempts at the measurement of the speed of light began in 1629 with Isaac Beeckman, who observed the flash from a cannon reflecting off a mile away. The experiment was an utter failure due to the lack of precision equipment. In 1638, Galilee Galileo conducted an experiment using covered lanterns separated by one mile, attempting to see the time the light took to reach the observer one mile away from the lantern. Again no delay between uncovering the lantern to reaching the observer existed. The first real breakthrough about this concept was done by Ole Roemer in 1676, which was completely accidental. While he was studying the time for Jupiter’s moon, Io, to complete an eclipse, he noticed that his measurements varied considerably, becoming inaccurate, and then strangely becoming accurate again. More specifically, at some times, Io’s exit from the shadow would begin later than predicted, and vice versa. Many still said that the speed of light (c) was infinite. In 1878, Albert Michelson conducted an experiment on Mt. Wilson in California to precisely determine c. A mirror on Mt. San Antonio 22.5 miles away was used with a high-speed rotating octagon of mirrors. Which increased the accuracy 20 times over previous measurements.

Michelson- Morley Michelson- Morley In 1887, Albert Michelson conducted an experiment which proved that c does not change. With the help of an apparatus that allowed measuring minute differences in the speed of light by changes in the resulting interference patterns, Michelson observed that the speed of light is always the same. (He was actually trying to prove the ether theory.) Numerous attempts were made at reconciling these discrepancies, yet they were all unsuccessful, until Lorentz solved the dilemma and received the 1902 Nobel Prize for his work. Einstein took hid work and re- applied it in his famous paper On the Electrodynamics of Moving Bodies in 1905, in which he developed his Special Relativity Theory. Flash demo

So what was the big deal anyway?

Captain Kirk, pull over! SPEED LIMIT – STRICTLY ENFORCED

Effects of light speed limit on Views of Fixed and Moving Observers Stationary observer at position A sends flash of light to observer and mirror at position B, moving at velocity v. Time to send and receive is 2a/c. Moving observer at B sees A moving to the left between A’s sending and receiving the (reflected) light, and so finds a longer path length of travel. If the speed of light is still c, then the time also has to be longer.

kinks in Wave Theory Appear Max Karl Ernst Ludwig Planck was a genius who did much research in thermodynamics (heat transfer theory). In 1900 he discovered that light energy could not be released in just any amount, but only in discrete “packets” he referred to as “quanta.” (The beginning of quantum mechanics theory.) The young German working in the patent office took notice.

Before Einstein’s “Big Idea” James C. Maxwell had shown that light always travels at the same speed. Albert Michelson developed an experiment to show that the speed of light actually does change, contrary to what Maxwell had hypothesized. Ether theory. (The ether is the dotted-line vectors.) Ether theory was an attempt to explain Michelson’s results, who had expected to show that “c” does actually change in his precise measurements. His experiment actually proved just the opposite!

Problem: Some aspects of electromagnetism don’t work right unless there is a preferred frame of reference - i.e. of motion Is there? Is there a “material” that light propagates in - the “aether”? 1887 – Michelson & Morley Experiment – speed of light in a “ vacuum ” is independent of the motion of the source! Results: all observers measure the same speed of light, regardless of their motion w.r.t. the light source!!!!

A Theoretical Physicist… what’s that?! The young German scientist began to run “thought experiments,” as he called them. He attempted to explain these controversies by thinking of possibilities that no one had considered before. He did no experimentation. Some said he had his head in the clouds. The man… Albert Einstein.

Einstein’s miracle year Einstein had his big year in 1905 – he received his doctorate later that year, after publishing 4 very significant articles. He was still working in the patent office. In that one year, Einstein uncovered the nature of light (the photoelectric effect), created the framework for experiments that would prove matter is composed of atoms (Brownian motion), and also developed a theory of relativity, which forced us to radically change our view of mass, energy and time… Oh, he later received his Nobel Prize for his explanation of the photoelectric effect… much later. Not a bad year.

E = mc 2 … Bah Humbug!! E = mc 2 … Bah Humbug!! Einstein was quickly acclaimed as a genius… in another 14 years or so, that is! At the time, his work was generally discredited and ignored. Partially because he was Jewish and also because he had offended most of his professors, and his ideas were unbelievable. Also, no one knew who he was. Scientists were also troubled that he did not actually perform experiments to support his amazing claims. He just… sat and thought. And of course he had this day job to pay the bills!

Relativity—an overview Relativity—an overview Einstein published two theories of relativity: In 1905 he published his “Special Theory of Relativity.” Actually, that became its name later. He titled it, “The Electrodynamics of Moving Bodies.” This paper tried to explain some discrepancies in uniform motion and reconcile light motion with other things. It became known as the “Lorentz-Einstein theory” because the math was taken from the Dutch physicist, Hendrik Lorentz, as well as 85% of the concepts. In 1916 he published his General Theory of Relativity, which incorporated accelerating systems and gravity, based on 10 differential equations (advanced calculus) which he developed.

Calvin and Hobbes

Relativity Before Einstein, people thought time to be absolute, which is to say that one clock can be used to measure the time for the entire universe. So then one hour on Earth would be one hour on Mars, or one hour in another galaxy or on a high- speed space ship. However, there was a problem with this concept. In such a framework the speed of light cannot be constant. However evidence indicated that the speed of light is finite and has a certain, quantifiable velocity (usually abbreviated with “c.”)

Lorentz Lorentz In 1895, Hendrik Lorentz developed a conceptual description involving time dilation and length contraction and mass increase to explain Michelson’s results. In 1904 he derived a mathematical expression which accounted for his concepts. This is referred to as the “Lorentz transformation.” His transformation equations proved to be the mathematical heart of Einstein’s special theory of relativity. 85% of special relativity concepts and mathematics came from Lorentz, though Einstein applied them in a cdifferent manner than Lorentz... E = mc 2 was all Einstein’s. So the breakthrough concepts were all Einstein’s, and were so original, that no one had seriously considered them before.

Special Theory of Relativity Einstein described space-time as curved. Just as the path an airline would take from NYC to France which is the shortest distance is actually not a straight line, but curved, so Einstein reasoned that gravity is just the result of the curvature of space-time. It was the first time someone had come up with an explanation of the why of gravity, not just an explanation of how gravity worked. Einstein followed Bernhard Riemann’s explanation of space as being comprised of an arbitrary number of dimensions, and non-Euclidean geometry. This curved line light travels is called a geodesic. Flash demo

Einstein’s Day-dreaming Einstein imagined a person on a motorcycle traveling alongside a light beam, if that were possible, and asked himself, “What would he observe?” He concluded that he would see light as standing still, which had been shown to never happen by Maxwell. Hence, he developed a theory which allowed for matter and time to be distorted so that this light would still travel at “c” and also that Newton’s relativity ideas would apply at speeds close to that of light as well.

Special Theory of Relativity As a result, two postulates of Special Relativity: All the laws of nature are the same in all uniformly moving frames of reference. The speed of light is always the same from all inertial frames (You will measure “c” the same regardless how fast either you or the light source is moving.)

Ramification: Although relative velocities add/subtract for most common objects, THIS IS NOT TRUE FOR LIGHT! The speed of a light source coming toward you is the same as one going away from you.

Consequences of Special Relativity Some consequences of the Special Theory: Since light does not have “rest mass” and the speed of light is a physical speed barrier... Time dilation – each sees the other’s clock as running slower. Length contraction – from the stationary observer’s perspective, the length of the traveler is contracted (shortened). mass expansion. – from the stationary observer’s perspective, the mass of the traveler is larger than when he was at rest. But – it’s all relative.

Time Dilation

Significance of Special Relativity fundamental featureSpecial relativity reveals that c is not just the velocity of electromagnetic radiation (light)—how fast light travels—but rather a fundamental feature of the way space and time are unified as space-time. It’s a radically new way of looking at creation. A consequence of this is that it is impossible for any particle that has rest mass to be accelerated to the speed of light.

Consequences of the Special Theory of Relativity According to the principle of relativity, there is no preferred location in the Universe, and hence no absolute reference point for a coordinate system (such as the Sun provides for our solar system, or the center of our Galaxy provides for the stars within it). The speed of light, as witnessed by an observer, is the same regardless of position in space, or velocity relative to the observed object. The concept of spacetime is a 4-dimensional coordinate system, consisting of three spatial dimensions and time. An observer can only detect “events” that occur within his or her “light cone”, whose boundaries correspond to velocities equal to the speed of light. Time can change only in one direction (forward, in the light cone diagram). Distance (3 dimensions) Time Observer Velocity = Speed of Light

An expanding universe The universe is expanding. No matter where we are located in the Universe, it will appear that we are at the center of the expansion, with generally uniform distributions (in direction and distance) of galaxies as seen from our location (there is no “preferred” location in the Universe). A two-dimensional analog to the three-dimensional expansion of the Universe is given by placing adhesive paper dots on the surface of a partially-inflated balloon. As the balloon is further inflated, the dots will appear (to an observer, such as an ant, on any one of the dots) to move outward, in all directions (in the 2-dimensional space of the balloon’s surface), at a velocity proportional to distance. Therefore, no matter where on the balloon the observing ant is located, it will have the impression that it is at the center of the expansion. Likewise, no matter where we are located in the Universe, we will see uniform expansion away from our apparently central location; in the (apparently) three-dimensional Universe, time serves as a fourth dimension for the general expansion.

THE “BIG BANG” AND THE ORIGIN OF ELEMENTS An hypothesis developed shortly after Einstein’s General Theory of Relativity was published, concerning the origin of the universe, was that it started out from a point (or very compact) object, composed of pure energy, which exploded outward in a “big bang” at the speed of light, and has continued to expand outward at this speed ever since. Currently, the Universe consists of matter, as well as energy in the form of heat, kinetic energy, and electromagnetic radiation, and (hypothetically) “dark energy”. Energy and matter can be interchanged, according to Einstein’s equation E = mc 2, where E is energy, m is mass, and c is the speed of light (300,000 km/sec). Currently, in our Universe, the matter which it contains far exceeds (in energy equivalence) the electromagnetic radiation (in the form of starlight and the cosmic microwave background radiation) and so is considered to be matter-dominated.

Has the rate of expansion slowed? The Hubble Space Telescope (HST) and new large ground-based telescopes have allowed imaging and red-shift measurements of galaxies at much greater distances from Earth than previously possible. Observations of very distant galaxies are required to determine the time /distance variation of the expansion rate, and whether the total mass of the Universe is less than, equal to, or greater than the critical mass. However, recent observations appear to indicate a less than perfectly linear increase in velocity with distance, which would indicate that the rate of expansion may actually have increased with time since the “big bang”. The planned Next Generation Space Telescope (NGST), recently re- named the James Webb Space Telescope (JWST), will extend our observations of galaxies to much greater distances than currently possible, by the use of a much larger aperture than HST, and by observing farther into the infrared (corresponding to larger red-shifts).