The Michelson-Morley experiment was brilliantly conceived—in principle. In their travels through the hypothesized luminiferous aether, the beams of light moving back and forth in the same direction as the Earth’s orbit would appear to travel at a different speed than the beams traveling in a direction perpendicular to the orbit. The difference in speeds would result in the waves of light from the two beams becoming misaligned. When they rejoined, a phenomenon known as interference would occur; the beams would not mesh exactly. This would be captured in a ghostly series of bright and dark rings that could be measured by the small telescope lined up with the light beams. So, in effect, Michelson and Morley used the very nature of light itself to build the exquisite ruler that they needed to make such a difficult measurement.
It was a beautiful experiment, one that would live on in the history of science forever—because it was a spectacular failure. Within the capacity of the apparatus and Michelson’s and Morley’s considerable skills, it was clear that the beams of light traveling in different directions had absolutely no discernible difference in speed. This was true regardless of the time of day the measurement was made, the time of year, the position of the marble block, the temperature in Cleveland, or the value of stocks and shares. Either the aether through which the light beams were traveling wasn’t operating according to accepted principles of physics or it just didn’t exist.
The authors described their experiment in painstaking detail in a journal article in the American Journal of Science. Desperate to understand the outcome, they made several proposals as to why they failed to achieve their anticipated result. None sounded too plausible. The only conclusion they could arrive at was that if there really was a luminiferous aether, the Earth couldn’t be moving through it very fast.
Later efforts by both Michelson and Morley and others fared no better. All these brilliantly executed experiments failing to detect anything made it devastatingly hard to proceed with the aether hypothesis. Something was afoot.
The second pivotal development that would eventually return Michell’s dark stars to the scientific consciousness began inside the brain of a young German patent clerk in Switzerland. Up to this point, the mysterious properties of light had continued to challenge and frustrate physicists—until Albert Einstein published his special theory of relativity in 1905. It irrevocably changed our understanding of the nature of reality. In one fell swoop, puzzles such as the fixed speed of light were turned on their heads—suddenly fitting perfectly into place. In fact, Einstein’s extraordinary insight came from studying Maxwell’s equations. It turned out that they already contained the correct mathematical description of nature. It just required someone to figure out what that was.
There are two fundamental postulates in special relativity. The first is that the laws of physics do not change with your frame of reference, a concept that could be traced back to the Italian astronomer Galileo Galilei. You could be sitting in a deck chair on a tropical island or strapped to a rocket traveling at tens of thousands of miles an hour, yet in either case you would deduce the same laws of physics at play anywhere in the universe around you.
With the second postulate, Einstein went out on an inspired limb. He proposed that the speed of light remains a constant, independent of the speed of its source. This is utterly counterintuitive to our everyday experience of the world and the principles of Newtonian mechanics. But it neatly deals with the agonies of Michelson and Morley, does away with the aether, and explains the validity of Maxwell’s equations. It also means that the phenomenon of light is an extremely fundamental part of our universe. Today, lasers and more complex experimental arrangements can measure the speed of light with ultra-high precisions of better than approximately 2 parts in 10 trillion. Einstein was right. Light’s speed in a vacuum simply doesn’t change, irrespective of the motion of its source or observer.
This simple fact has many startling implications for our physical universe. Time itself becomes an important part of any system of coordinates, and the passage of time is relative—it depends on the motion between an observer and any events. The energy carried by moving objects is also modified from the simple classical physics of Newton. Einstein found that even when we see an object as stationary, it still has an energy called its rest mass energy, given by the now famous equation E = mc2. As objects with mass move faster and faster, their apparent total mass, or inertia, increases, approaching infinity if they move as fast as light itself. Einstein reasoned that this meant that no real object with mass could ever reach or exceed the speed of light, since infinite force would be needed to accelerate it to that point.
The special theory of relativity holds in situations in which any relative motion between objects, or between objects and observers, is constant (in other words, where velocities do not change). It was not until a decade later, in 1915, that Einstein published his general theory of relativity that fully incorporated modifications for acceleration and the phenomenon of gravity.
If special relativity was a revolution, general relativity was the complete and utter dismemberment of the physics that had gone before it. One of Einstein’s critical insights was that if you or I were to float weightless out in the distant, empty universe, it would be entirely equivalent to falling in the gravity field of a massive object. This simple observation led him to redefine gravity itself.
The essential point for now is this: general relativity tells us that mass and energy distort the shape of both space and time, curving them as if they were part of a flexible sheet. What we call gravity is really just the way that objects move in this distorted space and time. Even light, which has no mass and a fixed velocity, is subject to its effects. If the path of light is distorted, then light too “feels” the force of this strange phenomenon as its rays are bent around massive objects. Einstein’s relativity was one of the most profoundly disturbing ideas of the age. It is still considered a major conceptual challenge, but it provides the best description we have yet of the nature of the universe.
Figure 3. This is known as an embedding diagram. The distortion of the geometry of three-dimensional space by mass can be represented as a two-dimensional surface that curves and stretches like a rubber sheet. In this case, an object such as a star or planet is in the middle. Without its mass, the coordinate lines would form a perfectly square grid. With its mass, the geometry of space is distorted—bunched up toward the mass and stretched down. The shortest path through this region may no longer be a straight line. We will explore the reasoning behind general relativity in more depth in chapter 3.
A key consequence led on from Einstein’s earlier results. Special relativity had shown that the energy, or wavelength, of light changes with what we measure the velocity of its source to be. A source of light moving toward us will appear bluer, shifted to shorter wavelengths and higher energies. A source moving away will appear redder, shifted to longer wavelengths and lower energies. All the while, the speed of the light stays the same. The size of this effect in our everyday experiences is negligible. Out in the universe, however, objects can move fast enough for these effects to become starkly obvious.
General relativity demonstrated that the same effect occurs in the distorted space and time around massive objects. Light that comes from a source deep inside the distortion around a mass will be seen as shifted to lower energies, or redshifted. The effect is often termed gravitational redshift: photons have lost energy as they have “climbed” out of the gravitational “well” of an object—although their speed remains unchanged. Equally, if an observer is sitting deep inside the distorted space and time around a massive object, then the light arriving from the distant universe will appear to be shifted to higher energies—blueshifted—as it follows its path into the gravity well. Even more disturbing, the distortion of space and time results in events appearing to happen more slowly the closer they are to a large mass, as seen from a distance. Experiments have confirmed this effect. If you had the willpower to sit in a balloon for f
orty-eight hours roughly six miles above the Earth, you would age by almost 0.0000002 seconds more than someone who had stayed on the ground. Gravity slows time, and this is exactly the same phenomenon as the loss of energy associated with a gravitational redshift.
It took many years after Einstein published his theory of general relativity for some of the implications and details to be worked out. Even Einstein himself did not produce a complete model for how an object like a massive star distorts the fabric of the universe around it. However, hot on the heels of his own breakthroughs, a fellow physicist had an insight that would play a vital role in the application of relativity to this problem.
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As unlikely as it seems today, the forty-two-year-old scientist Karl Schwarzschild wrote some of the most impressive works on relativity and quantum physics while stationed at the savage Russian front of the First World War in late 1915. Born to Jewish parents in Germany, Schwarzschild, like Michell, was a polymath with a penchant for astronomy. His genius was recognized in childhood, and by his late twenties he was an established professor in the upper echelons of academia. As war broke out, Schwarzschild dutifully signed up, joining the German artillery. Somehow he continued his scientific work. In a letter to Einstein, he derived a mathematical solution that described the distortion of space and time surrounding a massive spherical object. In a second letter he derived a solution for the curvature of space and time inside such a massive object, assuming it was uniformly dense. Tragically, within six months of sending Einstein his calculations, Schwarzschild died of illness on the front, never to see the ultimate implications of his work.
Paramount in Schwarzschild’s legacy is a formula that now bears his name. The Schwarzschild radius establishes a relationship between the mass of an object and its effect on light. This was the critical link that would eventually demonstrate that Michell and Laplace’s dark stars might actually exist in our universe.
When Michell and Laplace thought about the properties of these massive objects, they mistakenly considered light to be made up of little bodies that would feel the pull of gravity just like a rock or a tennis ball or anything else. According to this theory, we fail to see light emerging from the surface of these stars because it has been pulled back into the star by the force of gravity. But if you could travel toward a dark star, you would begin to encounter these corpuscles of light before they fell back to its surface. If you moved a little closer still, you would see them looping past on their trajectories, like the curving flight of trillions of balls thrown upward and falling back to the ground. All you’d have to do is get close enough, and the light of the dark star would begin to reveal itself.
Remarkably, it is here that Michell’s dark stars come crashing into our modern world. In Michell’s language, at some distance from a sufficiently massive object the velocity required to escape the gravitational pull of that object begins to exceed the speed of light. Light is halted, and the object is dark to the outside universe. Yet we now know from experiment and fundamental theory that light has no mass, and its velocity remains unchanged. It simply follows the shortest path in time and space. Based on the principles of general relativity, what Schwarzschild’s formula suggested was that there is nonetheless a distance from the center of a mass from which light cannot escape further.
Schwarzschild’s radius corresponds to a singularity in his mathematical solution to the distortion of space around a spherical mass. A mathematical singularity is simply a point at which an algebraic expression provides no meaningful answer, like calculating the value of one divided by zero. In the case of Schwarzschild’s wonderful formulation, such a singularity occurs at a particular distance from a massive object and indicates an extreme curvature of space and time. But, intriguing as it may be, is Schwarzschild’s radius just some mathematical tomfoolery, or does it correspond to something observably real? The answer is that while the singularity can be smoothed away by the right choice of mathematical variables, there is nonetheless something remarkable about this location. All paths at this radius turn inward, even for light itself. For you as an outside observer, the light is also redshifted—its wavelength stretched—by an infinite amount. No matter how close you get, you will never see photons coming from within.
Einstein had demonstrated that light is the measuring rod of the cosmos, knit into the very web of the observable universe. It defines the way we experience the world. It defines the way that all matter and energy interact. The Schwarzschild radius is more than a point from which light cannot escape. From the frame of reference of an external observer, it represents the place where time and space seem to come to a halt. If you could place a clock at this location and observe it safely from outside, it would appear to have stopped. Strictly speaking, it would also fade entirely from view, as light coming from it is redshifted to nothingness as it climbs up to you. Anything occurring inside this point, any event, can never be seen in the external universe. For this reason, the Schwarzschild radius is also known as the event horizon.
The most obvious question, and one that came up again and again in the decades following these revelations, was whether such places could actually exist in the cosmos. The mathematical definition of the Schwarzschild radius is a very simple function, a fixed property of the mass of any spherical object. The tricky issue is that the actual value of this radius is very small. For example, while the Earth has a mass of about 13 trillion trillion pounds (6 × 1024 kilograms), its Schwarzschild radius is only about 9 millimeters—less than half an inch.
Figure 4. Another representation of the distortion of space around a massive object. In this case, a dense mass is curving space and time to an extreme state. At the bottom of this funnel is the event horizon. The outside universe receives no information from below this point, since even light cannot escape from this far down the funnel.
Herein lies part of the problem. You would have to pack the entire mass of the Earth within that 9-millimeter radius to create the event horizon. Given the real size of the Earth, there is clearly no point at which space and time ever become distorted enough to prevent the escape of light. Our huge Sun has a mass about 332,000 times greater than the Earth, and a radius of more than 400,000 miles. It would have to be compressed by a factor of more than 200,000 to fit inside its Schwarzschild radius of 3 kilometers, or 1.86 miles. Only then would space and time be distorted enough to prevent the escape of light.
While general relativity had provided a more complete description of the nature of gravity, and a rigorous and satisfying demonstration that dark objects could in principle exist, everyone had a very hard time believing that such nonsensical things could actually be out there.
Ironically, Einstein himself was one of the people arguing against the plausibility of such an object. What Einstein objected to, in company with the mighty English physicist Arthur Eddington and others, was the idea that real places could ever meet the necessary criteria to create an event horizon. There was also no obvious natural process by which any object could be made so compact. This was compounded by the peculiar nature of the event horizon. Time itself would slow to a halt at this point. From the viewpoint of the external universe, this might prevent anything real, with lumps and bumps, from ever vanishing entirely inside this radius. It would be stuck in stasis forever.
There were different ways of framing some of these arguments. Einstein used the example of a cloud of small masses orbiting one another, like stars orbiting in the space and time distortion, or gravity field, of their combined mass. The more compact this cloud becomes, the faster and faster the small masses need to orbit to keep the cloud from succumbing to gravity and collapsing toward its center. If the cloud becomes small enough to shrink within its Schwarzschild radius, then the little objects would have to move faster than the speed of light, which Einstein reasoned was impossible.
Over the next decades, a remarkable cadre of some of the greatest scientists of the twentieth century gradually broke through a series of highly c
omplex and challenging physics problems that would finally resolve this issue. Other extreme environments would turn out to be far more commonplace in the universe than anyone had suspected. These would be the stepping stones to an answer.
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Beginning in the early 1930s, another revolution in science was well under way. This was the formulation of quantum mechanics, the physics of atomic and subatomic scales and the dual nature of matter as both particle-like and wave-like. If general relativity had toppled our previously tidy picture of the nature of reality off its perch, quantum mechanics took it on an extended bender that few people, if anyone, could or still can completely comprehend.
Many scientists played key roles in the development of this new physics, from Einstein himself to Max Planck, Niels Bohr, Werner Heisenberg, and others. In 1927, Heisenberg was the first to formulate one of the most philosophically challenging and strange parts of quantum mechanics—the uncertainty principle. At the core of this extraordinary description of the physical world was the fact that at microscopic scales nature has an inherent “fuzziness.” For example, it is impossible to precisely measure both the location of something and its momentum—its mass multiplied by its velocity. If the location of an object like an electron, which occupies scales on the order of femto-meters (10−15 meters), is known to high precision, then its momentum will be very poorly constrained. Because “measurement” always involves actual interaction—for example, trapping the electron in a tiny space—there is no getting around this. This intrinsic uncertainty to the world opens up all manner of deeply disturbing phenomena, from parallel realities to virtual particles, appearing out of nothingness and vanishing again. Nonetheless, seen through the protective shielding of mathematics, quantum theory is clearly a good description of the universe around us. The behavior of atoms and electrons, of atomic nuclei, and of light and electromagnetism is accurately described by quantum mechanics.
Gravity's Engines: How Bubble-Blowing Black Holes Rule Galaxies, Stars, and Life in the Cosmos Page 3