Continuing this week’s theme, today’s post is an essay about Nigel Calder’s book entitled “Einstein’s Universe.” Enjoy!
In his book entitled Einstein’s Universe, Nigel Calder explores the world described by Albert Einstein’s Theory of Relativity—a world that seems to be remarkably similar to the observed universe. As far as formal technique is concerned, Calder often writes with irreverence of the rules of basic syntactical control, and his style is inundated with nouns where verbs would suffice, hyperbolic language, and convoluted sentence structure. Yet as the pages flew by, I found that his idiosyncratic style grew more enjoyable because of the skill with which he could convey the ideas of Einstein’s Relativity. Although I found Calder’s chapters on General Relativity to be fascinating, I did not care for his later chapters on Special Relativity. He did well enough explaining Special Relativity, but I cannot help but compare any discussion of Special Relativity to Brian Greene’s second chapter of his book entitled The Elegant Universe. Brian Greene offers the clearest and most concise explanation of Special Relativity that I have read. I did not read Greene’s later chapters on General Relativity from that same book, so I cannot yet do a direct comparison between his explanation and Calder’s. There were three aspects of Calder’s book that I especially appreciated: First, Calder provides a short list of ideas under each chapter heading, making it easier to find explanations of topics quickly and easily; Second, the author makes the effort to describe topical experiments and associated error margins; And last, he provides a relatively recent afterword from 2005 that clears up some lingering questions.
Einstein’s Theory of General Relativity seeks to describe the phenomenon of “gravitational attraction” that occurs between objects with inertia in the universe. One might ask why Relativity is necessary when Newton’s model for gravity is so accurate in every-day measurements. Einstein saw it necessary to revise Newtonian gravity because he saw a stark contradiction between the proclamation of Special Relativity that says that no means of communication can be faster than light in vacuum and the property of Newtonian gravity that says gravity is communicated instantaneously. Einstein had to re-imagine the inner workings of the universe in order to explain gravity in a way that is consistent with Special Relativity. In particular, the properties of mass in General Relativity are surprisingly exotic when compared to Newtonian mass. Three features of mass in Relativity that are distinct from features of mass in Newtonian Gravity are the effect of mass on space and time, the equivalence of mass and energy, and the existence of gravity waves.
One of the most fascinating and counterintuitive effects of mass is its ability to distort space and time. Newton’s formulation of the force of gravity violates Einstein’s mandate that communication cannot exceed the speed of light, and moreover, does not explain the curious fact that someone in gravitational free fall feels no force acting on her. If one feels no force in free fall, then it seems that gravity cannot be a force. Newton’s First Law of Motion says that an object will maintain its energy and direction of motion unless acted upon by a net external force. This law suggests that gravity is a force, since it tends to affect an object’s energy and path of motion. In order to reconcile the claim that gravity is not a force with the fact that the energy and direction of objects seem to change in the presence of gravity, Einstein had to rethink the very nature of time and space. Einstein proposed that since gravity is not a force, then a falling object actually is obeying Newton’s First Law. The falling object only seems to have a curved path because its straight path happens to be moving through curved space. The falling object’s energy seems to be increasing, but that is only because it is compensating for the fact that time itself is slowing down as it falls closer to the massive body. This last detail will be further explored in the mass-energy equivalence section. Under Einstein’s theory, the presence of mass distorts time and curves space. Mass in Einstein’s universe further removes itself from Newtonian mass with the prediction that a rotating mass should not only bend space, but twist it as well. Even more amazingly, this bending, dragging and twisting of space has been clearly observed by Stanford’s Gravity Probe B, an ultrasensitive gyroscope in orbit around Earth. The peculiar bending of space around massive bodies is also clearly observed in the precession of the perihelion of Mercury as well as binary pulsar systems. According to Newton, orbits should be elliptical and static, whereas Einstein’s notion of curved space should cause ever-so-slight disturbances to the elliptical orbits. While experiments have verified that mass curves space, it would seem almost too bizarre for the universe to play by Einstein’s rules for time as well. Relativity requires that an object experience time more slowly when it is closer to a source of gravity. Surely enough, matter does indeed seem to slow the rate of time. Wallops Island, Virginia in 1976 was the launch pad for a scout rocket that carried an atomic clock 6000 miles above Earth. After corrections for special relativity, the atomic clock ran a billionth of a second per second faster than clocks on the ground due to the reduced effect of gravity at high altitude. In addition, the fact that time slows down near a source of gravity can explain gravitational redshift without appealing to gravity as a force doing negative work on outgoing light. A far-away observer will observe light from a gravity source as being redshifted not because it has lost energy due to a force of gravity, but rather because time itself has sped up as the light travels away from the gravity source. In this way, a blue light near the surface of a strong gravity source with a frequency of x oscillations per slow second would appear to have a frequency of (1/2)x oscillations per fast second to a far-away observer with a faster clock (in this case, one slow second near the surface is two fast seconds to a distant observer). So, what appears blue near the surface will appear red to a distant observer because of her faster clock. Mass in Einstein’s universe curves space and stretches time in ways that are well documented and completely removed from a Newtonian understanding of gravity.
Perhaps the most well known equation in the public domain, Einstein’s equation E=mc2 contains the powerful idea that mass is a condensed form of energy. This equation opens the awesome and terrifying possibility of unleashing the vast amounts of energy that is locked away in the form of mass. Einstein first conceived the idea of mass a measure of energy content to explain the following Gedankenexperiment: Suppose an astronaut zooms by a star at a constant velocity. As the astronaut flies by, he sees the light emitted by the star on the nearside as blueshifted and the light on the far side as redshifted. Since the energy gained in a blueshift is always greater than the energy lost in redshift, the astronaut sees the star outputting more light energy than the star outputs in its own inertial reference frame. Einstein suggested that the extra light energy comes from the star’s extra relativistic mass in the astronaut’s frame. Going further, a star liberates the energy in its mass in order to emit light in the first place. One can also use the equivalence of mass and energy to clarify the simple act of an object falling to the earth under Einstein’s model of General Relativity. A falling object seems to gain energy of motion as it falls. In order for an object to gain energy, a force must do work on it. So, in order to say that gravity is not a force, Einstein has to claim that a falling object does not gain energy. Instead, one observes that as the object falls, it enters regions of slower time. Compared to the perspective of a far-away observer, the speed of light seems to slow down. If the speed of light is slower, then E=mc2 suggests that the falling object’s rest mass-energy is decreasing. Since, however, the object feels no force, its energy must remain the same. In order to compensate for the decreasing rest mass-energy, the object must gain energy of motion. A similar argument must be made not only from the perspective of distant observers, but other observers as well. Calder mentions this idea, but does not elaborate. So, Einstein is able to explain the simple and natural act of falling down with the elementary combination of curved space, stretched time, and the concept of mass as condensed energy.
A third revolutionary feature of Einstein’s gravity is the existence of so-called “gravity waves.” General Relativity serves as a field theory, and as such, predicts that gravity causes slight ripples through space and time called “gravity waves.” These waves are predicted from General Relativity in much the same way that light waves are predicted from Maxwell’s electromagnetism. It is also interesting to note that just as light was discovered to have an associated particle called the photon, gravity waves are predicted to have an associated particle called the graviton. Also like light, the gravity waves and the graviton are expected to travel at the speed of light. That means that if the sun were removed from the center of the solar system, it would take eight minutes for earthlings to notice the absence of its light as well as its gravity. The comparison with light continues as gravity waves are supposed to carry a certain energy (although a small amount), meaning that an object in orbit around a gravity source will eventually shed enough energy in the form of gravity waves until it crashes inward. The graviton has not been observed in either particle or wave structure. The experimental difficulty comes from the fact that gravity waves are predicted to be incredibly feeble. Careful experiments have been done in order to detect gravity waves, but none have been conclusive thus far.
Einstein re-envisioned the mechanics of gravity, and in doing so was able to peer into the awesome and humbling nature of the universe itself. Even if one prefers Newton’s simple and beautiful universe, the fact is that his is not the universe in which we live. This is, at least to some great extent, Einstein’s universe.
Appendix: Twin Paradox
Einstein’s Special Relativity says that when an object travels at high speed relative to a stationary frame of reference, observers in the stationary frame see the clocks of the moving object as running more slowly then their own clocks. Using reasoning purely from Special Relativity, this means that if one member of a pair of twins were to take off in a spaceship and fly away from earth at speeds close to the speed of light and return, she would find her twin to have aged considerably in her absence. In fact, she could return to find that her twin had been dead for thousands of years! The reasoning is as follows: Imagine that the moving twin flies to a distant planet, swings around the planet and immediately returns to Earth always moving at constant speed. On the journey away from earth, the stationary twin sees the clock of the moving twin as ticking slowly, and since the moving twin is moving at constant speed relative to Earth, it will take just as much time for the moving twin to return from the distant planet as it did to get there. For simplicity, say it takes the moving twin one year to reach her destination and one year to return. The stationary twin will see the moving twin’s clocks as very slow, since the moving twin is travelling close to the speed of light. So, what seems like a year to the moving twin seems like 20 years to the stationary twin. That means that the moving twin will feel like the round-trip took only two years, whereas the stationary twin clocks the journey at 40 years. So the moving twin will return home to find her sister 38 years older than she is.
One might reasonably object that from the reference from of the moving twin, it was the Earth that flew away and came back, so the stationary twin should also be 38 years older than the moving twin. However, this only serves to highlight the shortcomings of Special Relativity when acceleration is involved. One cannot argue that the perspective of the moving twin is equally valid with the stationary twin as Special Relativity might suggest, since the entire Earth did not feel acceleration as it changed directions in order to return to the moving twin. The moving twin, however, DID feel acceleration as she changed directions in order to return home. The acceleration required in order for the moving twin to return home ensures that the perspectives of the twins are not equally valid. The moving twin feels acceleration, so she is indeed the one making the journey. In this way, the paradox is only coherently described with the full force of General Relativity in order to take account for the acceleration involved. Recall that the presence of gravity slows down the rate of time with respect to a distant observer. Notice also that acceleration can feel like a source of gravity. This means that instead of thinking about the moving twin as accelerating in order to return home, one can think that she encountered a powerful gravity source that temporarily slowed her clock even further while she changed directions in order to get back home. Thus Einstein’s Twin Paradox is saved.