“The distinction between past, present, and future is only a stubbornly persistent illusion.” – Albert Einstein
A comprehensive overview of the theory of relativity and its applications in astronomy would require a course in itself. The purpose of this post will be to give a brief overview of the subject and in particular, the history of its development as a theory. What I would like to stress that despite its fearsome reputation as being difficult to understand, the major concepts of the theory can be understood by the public. In its most advance form, the mathematics of relativity can provide a challenge to any student of physics. However, this is true of any area of physics. You will not find many physics students tell you that a graduate level electricity & magnetism course is a breeze. However, the subject of electricity & magnetism can be presented in a manner that the public can understand. The difficulties of relativity lie in that it deals with phenomena we do not ordinarily observe in our lives. Relativity provides accurate predictions in two areas where Newton’s Laws do not. These are when matter has velocity near the speed of light and/or is located near a large gravity well (such as a star or a black hole). However, I do want to stress that outside of these two situations, Newton’s Laws and Einstein’s Theory of Relativity give essentially the same results.
Beginnings
In the latter part of the 1800’s, physics was thought by many to be a dead science. Newton’s Laws were considered the final say in predicting the behavior of matter in motion. James Clerk Maxwell, using four equations, successfully provided a comprehensive explanation of the properties of electricity and magnetism. The major problems in physics and astronomy seemed to be solved. However, as the century came to a close, cracks were appearing in this assumption. One was the failure of Newton’s Laws to accurately predict the orbit of Mercury around the Sun. The perihelion (closest approach to the Sun) advanced 574″ (about 1/6 of a degree) per century, which is 43″ more than the 531″ advance predicted by Newton’s Laws. This advance is caused by the presence of the other planets in the solar system. For a time, scientists thought the extra advance in Mercury’s orbit was due to the presence of an undiscovered planet. As none was found, a new explanation was required. An image of the advance is depicted below. It is exaggerated to demonstrate the effect.
Einstein’s Papers
In 1905, Albert Einstein, who was working as a technical expert in a Swiss patent office, published four landmark papers (in addition to his doctoral dissertation) revolutionizing physics. This year is often called “annus mirabilis” or miracle year. The topics of these four papers are the following:
1. The photoelectric effect demonstrating light behaves as a stream of particles as well as waves. It was known at the time that a beam of light would knock electrons off a metal surface. This is similar to a baseball thrown on a beach. The impact of the ball will knock sand in the air. The accepted theory at the time was light consisted as a series of waves and this could not explain the photoelectric effect. Einstein showed that light behaves as a stream of discrete particles as well. Thus, light has a duality in that it behaves as a stream of particles as well as waves. This discovery is the foundation of quantum physics.
2. The second paper concerned the nature of Brownian motion explaining that heat is created by the motion of atoms and molecules. It was this paper that put the rest the ongoing debate if atoms existed as the constituent particles of matter.
3. The Special Theory of Relativity. This paper was concerned with the motion of objects in non-accelerating frames of reference. This means gravity is not a factor in the Special Theory as opposed to the later developed General Theory of Relativity.
4. The mass-energy equivalence principle. This paper gave us that famous equation E = mc2.
The last two papers will be discussed below.
The Special Theory of Relativity
As mentioned earlier, James Clerk Maxwell, in the mid-1800’s, formulated four basic equations outlining the properties of electricity and magnetism. One outcome of these equations is electromagnetic radiation travels at a rate of 3.0 x 108 m/s (186,282 miles per second). This rate of speed is constant regardless of the observer’s velocity relative to the radiation. What exactly does this mean? Think of yourself on a highway and your speed is 55 mph. The car in the lane next to you is moving at 60 mph. That car will pass you at a rate of 5 mph, as their velocity is that much faster than your velocity. Now, let’s ramp up the speed of your car to 186,277 miles per second. This is exactly five miles per second slower than the speed of light. Remember, light is just a form of electromagnetic radiation. Imagine a beam of light traveling in the lane next to your car. At what rate of speed would it pass you? All your life’s experience would lead you to answer five miles per second. But that would be the incorrect answer! The light beam would pass you at a rate of 186,282 miles per second as if you were standing still. This is true regardless of your velocity relative to the beam of light. The genius of Einstein was to realize that contrary to what we perceive, the speed of light is constant for all observers and time is variable as a function of your velocity. The Special Theory of Relativity leads to the following conclusions:
1. As an object (or person) approaches the speed of light, their clock slows down compared to a stationary observer. If you were to take a round-trip voyage 100 light years away and travel at 99.995 percent of the speed of light, you would only age two years but arrive back on Earth 200 years later. In popular entertainment, the original 1968 movie Planet of the Apes gives a reasonably accurate portrayal of this effect.
2. Mass of an object increases as it approaches the speed of light. In fact, the mass of an object approaches infinity as it approaches the speed of light. This is why the speed of light is the maximum speed obtainable in our universe. As its mass approaches infinity, the force required to accelerate it approaches infinity.
3. The length of an object appears to decrease to a stationary observer as it approaches the speed of light.
4. E = mc2. This is the equation that gives us the understanding of nuclear fusion that occurs in the Sun. As hydrogen fuses to form helium, the mass of the helium atoms is less than the mass of the original hydrogen atoms. The difference is converted to energy. The Sun converts 4.3 million tons of mass into energy each second. A fraction of which reaches the Earth providing the energy to sustain life.
General Theory of Relativity
After publishing his Special Theory of Relativity, Einstein spent the next ten years working out the General Theory of Relativity. It is general in that it applies to all reference frames, accelerating and non-accelerating. This theory was published in 1916 and provided a dramatically different way of looking at gravity. Unlike Newton, who postulated gravity was a force between two bodies, Einstein postulated that gravity represents a curvature in space-time itself. Lets look at an analogy. Think of a trampoline with nothing on it. This represents a universe with no mass in it. If you rolled a golf ball across it, the ball would move in a straight line. Now place a baseball (which could represent a planet) on the trampoline. The ball would depress the trampoline slightly. Now roll the golf ball again. As it approached the baseball, the depression in the trampoline would cause the golf ball to move in a curved motion. Now place a bowling ball (this could represent a star) on the trampoline. The depression becomes more pronounced and the path of the golf ball as it moves towards the bowling ball becomes more curved. In fact, if the golf ball got too close to the bowling ball, its path would curve into the bowling ball much like a meteor would fall to the Earth’s surface if captured by Earth’s gravity well. The video below describes the difference between Newton & Einstein’s theories on gravity.
Experimental Proof
Einstein’s General Theory of Relativity predicted the advance of Mercury’s perihelion accurately. Remember, the predictions of relativity and Newton’s Laws diverge in two circumstances. When an object travels near the speed of light and when it is located near a large gravity well. Mercury is the closest planet to the Sun. This closeness is enough for predictions of its motion using the theory of relativity to vary slightly than Newton’s Laws. While this created a buzz in the physics community, relativity did not gain general acceptance until it passed an experimental test in 1919. Relativity predicts that light would be deflected by the Sun’s gravity. A beam of light would follow the path of space-time. If space-time is curved, then the path of light is curved as well. On May 29, 1919, British astronomer Arthur Eddington led an expedition to measure a star’s position near the Sun during a solar eclipse. Einstein’s theory predicted a deflection of 1.75 seconds of arc as opposed to Newton’s Law predicting the deflection at 0.875 seconds of arc. The measurements came in at 1.98 and 1.61 seconds of arc. These measurements are within the range of 30 seconds of arc error allowed for observational uncertainties and proved light was deflected by the Sun’s gravity well. Both the London Times and the New York Times reported the story and Einstein quickly became, by far, the most famous scientist of the era.
The Cosmological Constant
The General Theory of Relativity yields a field equation which takes the following form: (Ruv)-1/2 (guv) R = (8)(π)Tuv – Λ(guv)
The subscripts in the equation are indications of what are called stress tensors. This enables mathematicians to express a complex set of equations in a compact form. You can think of this as a mathematical version of a zip file. This equation explains how matter and energy ( Tuv) curves space-time [(Ruv)-1/2 (guv)]. Now, I won’t go into the gory details of this equation. In fact, Einstein himself needed help with the complexities of the mathematics when he derived it. What is important about this equation is it predicts the universe must be either contracting or expanding as matter will deform space-time.
Einstein was not satisfied with this result. At the time, the universe was considered to be a permanent unchanging entity. What Einstein did to correct this was to add the constant Λ in the right side of the equation. This constant changes the equation providing a stable universe offsetting the effects of gravity on space-time. During the 1920’s, Georges Lemaitre argued the cosmological constant was not required and the universe could expand after originating from a primeval atom. Lemaitre used relativity to formulate what would later be called the Big Bang theory. Edwin Hubble (whom the Hubble Space Telescope was named after) discovered that all the galaxies in the universe were receding from each other. The universe was expanding! Relativity, in its original form, had predicted this result. Einstein would later admit his addition of the cosmological constant was an error.
New knowledge contradictory to our preconceived ideas can form a disequilibrium in our minds that can take time to sort out . Even Albert Einstein, who did as much as anybody to revolutionize physics, suffered once from an inability to overcome a preconceived idea. In this case, he believed the universe was static. It is something we all must guard against. In science, we must let the evidence point us to a conclusion and not allow a preconceived conclusion allow us to define the evidence. It should be noted that once the evidence of the Big Bang arrived, Einstein came around as a supporter of the theory rather than sticking with an outdated idea of the universe. As I speak of preconceived ideas, most would assume when Einstein was awarded the Nobel Prize in 1921, it would have been for relativity. However, he won the Nobel Prize for his explanation of the photoelectric effect.
If you want to read more about Einstein and Relativity
The following sources I highly recommend for anybody who desires a greater understanding of the theory of relativity.
Issacson, W., (2007) Einstein. New York, Simon and Schuster.
A very readable biography of Einstein includes non-mathematical overviews of Einstein’s work. I found this book very enlightening describing the educational and life experiences that enabled Einstein to make breakthroughs where others failed.
Guttfreund, H. & Renn, J., (2015). The Road to Relativity. Princeton, Princeton University Press.
This book contains Einstein’s original manuscript for the theory of general relativity with a page by page interpretation for the public. It also has an excellent historical background on how Einstein developed the theory.
Einstein, A., Relativity: The General and Special Theory.
Want to learn about relativity directly from the source? This is Albert Einstein’s attempt to describe the theory to the public. The book can be purchased in the usual online outlets but is also in the public domain and can be read online for free, for example, here.
Lambourne, R., (2010). Relativity, Gravitation, and Cosmology. Cambridge University Press.
If you are seeking a textbook to get started on relativity, this is the best treatment I have seen. It will walk you through the algebra of special relativity to the tensors of general relativity. The text has many problems to work through to obtain a solid understanding of the subject. Lambourne has in the past taught a short course in relativity at Oxford’s Department for Continuing Education open to the public. Sounds like a good way to spend a week in the summer.
*Image atop post is the gravitational lensing of a galaxy by another galaxy in front. Typically, such lensing can result in two or more images of an object but if the alignment is just right, it will form a ring structure. Gravitational lensing was predicted by Einstein in 1915. Credit: ESA/NASA/Hubble