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I crack the cover of Brian Cox and Jeff Forshaw’s new book, Why Does E=mc2, and I’m thinking of all the well-worn relativity clichés: Einstein running at the front of a beam of light, trying to catch up; time slowing down; a ball bearing placed on the fabric of spacetime. As a Seed editor and an aficionado of popular physics texts, I should be able to tackle a higher-level physics book. I’ve always assumed that a true understanding of Einstein’s theory of relativity was beyond the comprehension of anyone other than a professional physicist. Here, I’ve documented my journey to truly understand the science.
Cox and Forshaw’s book is an explanation of the hard physics behind the special theory of relativity. Although they promise to write in plain English, use very little math, and assume no prior knowledge of the subject matter, I begin the read with a suspicion it will still be hard work. But I’m excited.
Chapter 1: Space and Time
The 16th century Italian astronomer Galileo was the first to popularize the idea that motion is relative—our cars move relative to the road, the Earth moves relative to the Sun, the Sun moves relative to the center of the Milky Way. Galileo, though, thought time was immutable.
Galileo was one of the fathers of empirical investigation—the use of experimental observations rather than pure reason to verify claims—and Cox and Forshaw drive home the importance of experimentation to modern scientific thinking: “If there is no way of observing it or its consequences, you haven’t made a contribution to the scientific understanding of the universe.” Galileo simply looked through a telescope and overturned millennia of “common sense” consensus, but of course the physics of Einstein and his predecessors often lies beyond that which we can directly perceive. Modern physics deals with the very small (particle physics), very large (cosmology), and other physical extremes that are far outside the realms of our senses, and so I, probably as Galileo would, find its observations difficult to understand.
Galileo refuted absolute motion primarily because it could not be experimentally proven, and while I momentarily find myself frustrated at what appears to be a detour into abstract mental exercises, the authors remind me that Galileo’s relativity paved the way for the idea that space isn’t absolute either and eventually to some very practical applications of relativity. (More on that later.)
Chapter 2: The Speed of Light
I’ve breezed through the first two chapters and am excited to get into the physics. The chapter opens with the experiments of Michael Faraday, an English chemist and physicist who was born some hundred years before Einstein when scientists were busy tinkering with newly discovered electricity. Faraday, using only wire, magnets, a compass, and a fascination with electricity, devised experiments that essentially led to a fundamental discovery: Electric currents make magnetic fields, and moving magnets generate electric currents. Faraday’s finding, called electromagnetic induction, is the basis all of our power stations and electric motors and electric pumps in our refrigerators.
In a cool aside, the authors explain why equations like Faraday’s are so powerful. By quantifying the components of a problem, equations often reveal relationships that are not immediately apparent from the results of experiments, which can lead to a much deeper and more profound understanding of nature.
Some of the most important equations in history, the ones that led to Einstein’s E=mc2 (an explanation of which I see won’t arrive at for another three chapters), emerged from an extension of Faraday’s work by the Scottish physicist James Clerk Maxwell. Maxwell discovered equations that described all of the electric and magnetic phenomena Faraday and others had observed. Maxwell established that light, electricity, and magnetism were all aspects of one thing: electromagnetism. The same equations that described the propagation of light could also explain how electricity produced magnetism, and vice versa. This landmark symbiosis is often referred to as the “second great unification in physics.” (The first was Newton’s unification of physics and astronomy.)
It’s the end of my first day of reading, and I’m looking back over my notes and only then do I notice that we’ve yet to actually discuss Einstein. But I’m quite enjoying the historical-biographical tone of the book and feel like I’ve gotten to know Galileo, Faraday, and Maxwell in a new light.
Chapter 3: Special Relativity
German physicist Albert Einstein once worked in a patent office. Who knew? I say this in jest, as it’s impossible for the authors to introduce Einstein (finally) or his “miracle” year of 1905 (the year he discovered special relativity) without mentioning a chestnut like this one. Einstein developed his special theory of relativity based on the work of two previous scientists: Maxwell, whose equations suggested that the speed of light is constant, and Galileo, who said that absolute motion cannot be experimentally confirmed. From these axioms, Einstein set out to describe what happens to time and space if light is a constant. In other words, unlike a high-speed race car inching up behind a competitor, Einstein worked from the premise that you can never catch up to a beam of light. What he found was that if the speed of light is constant, then space and time are relative.
In a nutshell, if I’m flying around a particle accelerator on the back of a muon at 300 kilometers per hour (they actually can reach speeds close to those of light), my life would be extended by about one-tenth of a millisecond from the perspective of Brian Cox, who works at the Large Hadron Collider and would be standing on the sidelines measuring my trip. But what about from my perspective? Muons live for 2.2 seconds when standing still, which I would appear to be.
But according to special relativity, space also shrinks in exact proportion to how much time stretches, so the muon’s life is the same length to either party. These strange time dilation properties of relativity have been experimentally proven many times over in particle physics and inside particle accelerators like the LHC at CERN. They are even applied to our satellite GPS systems, which contain clocks that must be adjusted by a few microseconds a day.
Chapter 4: Spacetime
The chapter kicks off by acknowledging the “historical road” that the authors have taken so far; we’re now leaving that road, which worries me. We jump right into some basic concepts of physics. The first is “invariance,” the idea that a property of a system is conserved, such as momentum. A great example, mentioned in the book, is the Moon’s gravitational pull upon the Earth’s oceans, which creates the tides. Through friction, the tidal bulge gradually slows the Earth’s spin. As the Earth’s spin slows, that momentum transfers to the Moon. This energy moves the Moon four centimeters further from the Earth every year.
Invariance matters a lot at this point in the story because the classical conception of space and time has been undermined pretty definitively by special relativity. In the wake of Einstein’s paper in 1905, physicists began working toward new ways to explain the relationship between space and time. It was German mathematician Hermann Minkowski who first mathematically described space and time as a four-dimensional spacetime just two years after Einstein’s special relativity. By regarding the speed of light in his equations as a constant, he was also able to preserve “causality,” the preservation of the order of cause-and-effect-related events in the universe. In other words, in physics the math should not conclude that you ate breakfast before you woke up.
Cox and Forshaw provide a much-needed pep talk mid-chapter: “Very few people understand difficult concepts the first time they encounter them, and the way to deeper understanding is to move forward with small steps.” Does this mean I’m being self-defeating by reading 60 pages in one sitting while taking notes?
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