by Adam Frank
Plato’s students had once spent centuries trying to solve the problem their master bequeathed to them: how to save the appearances of planetary motion. Einstein, like other students of his generation, was also bequeathed a homework problem by his elders: save the aether and explain how the speed of light appears constant even when frames of reference move relative to it.
But Einstein declined to play by these rules. He did not solve the problem—he changed it. While others spent careers trying to explain why the speed of light was constant, Einstein simply assumed the speed of light was constant and built his physics from that foundation.
In the crucial 1905 paper that launched relativity (published while he was still working at the patent office), Einstein reworked physics from the beginning, invoking kinematics—the study of motion—and its paired foundations of time and space. “I understood where the key to this problem lay”, Einstein said to a friend. “An analysis of the concept of time was my solution.”23 Going back to his original thought experiment about lightwave surfing, Einstein recognized that the problem lay in describing phenomena from different frames of reference. Though he called his theory “relativity”, what he was really after was invariants—he wanted to know which parts of physics did not change from one frame of reference to another. To resolve his paradox and find nature’s true invariants, Einstein first abandoned the aether and then let go of Newton’s space and time.
There are two postulates on which all of relativity rests. First, no special frame of reference exists from which the motions of all others can be judged. In other words, there is no “aether frame” for judging motion or rest. All motion is relative motion. Second, the speed of light must be the same for all observers, no matter what their state of motion. It was this second conjecture that opened the door to a strange new world of time and space.
If you are standing on the Earth watching light from a passing star whizz by, you will measure its speed to be 300,000 kilometres per second. A spaceship rocketing away from Earth at 270,000 kilometres per second (90 percent of the speed of light) looking at that same beam of starlight would also see it race by at 300,000 kilometres per second. According to the second postulate, people at every location, regardless of their state of motion, must measure the same speed for light.
To see how strange this behaviour of light is relative to our common experience, imagine two workers on a fast-moving postal delivery train. Both men work in the moving railway car with all doors and windows closed. The workman at the far end of the car heaves a bulky bag of mail to the other. The speed of the bag as it flies through the air is, from the perspective of the other worker, just the speed the first workman gave it when he let it go. The speed of the train does not affect their experience. But now imagine you are standing on a platform as the train roars by and the worker tosses the heavy mailbag to you from the open car. Would you want to catch the mailbag? Not likely. The speed of the bag would now be the speed at which the worker released it plus the speed of the train. From your frame of reference the velocity of the bag and the velocity of train have to be added together.
This addition of velocities is what physicists would have expected for light as well. Einstein, however, had a deeper vision. The second postulate of relativity is equivalent to demanding that the mailbag thrown from the high-speed train travels towards you at the same speed it left the railway worker’s hands, as if the velocity of the train did not exist.
The deeper reason for this behaviour lies in the fact that Einstein made the speed of light an upper bound on all cosmic motion. Nothing can travel faster than light. It does not matter that this upper bound is the speed of something called light. It just matters that there is an upper bound on speed for everything in the universe. This fact alone changes the meaning of time and space.
Einstein realized that if the universe had a speed limit and light ran at the maximum, then something else had to give in order for light to achieve its constancy. As we have seen, every measurement of velocity is a mix of two other measurements, one for length and one for duration. This means that if the speed of light has to be constant, independent of its frame of reference, then measurements of length and duration can not also be independent in this way. Length (space) and duration (time) have to become flexible, changing from one frame of reference to another. In Einstein’s relativity all time became local time and all space became local space.
Gone was Newton’s divine sensorium. Time was not flowing smoothly everywhere through the universe. Instead of a single over-arching Newtonian cosmic time, there was now a relativistic patchwork of times, each measured by observers moving relative to one another. Gone also was the metaphysical majesty of absolute space. In its place stood varying measurements of length made by many moving observers—onlookers will see different lengths for the same object. There is no one length for an object and there is no one time between events. It all depends on how you are moving relative to these events and objects. In just thirty-six pages of his 1905 article, Einstein unhooked time and space from their Newtonian mooring.
The flexibility of space and time in the new physics is cleanly displayed in the famous “twin paradox”. Imagine a pair of identical twins both born at the same time. At age twenty, the more adventuresome twin rockets away in a spaceship. She travels to a distant star thirty light-years away at 99.9 percent of light speed. When she reaches the star she turns around and returns to Earth. The twin back on Earth has been waiting sixty years for her sister to return and is now eighty years old. The space-travelling twin, however, has only recorded about three birthdays during her round trip. That is her duration of the voyage. Her time was not her sister’s time. For the sister who remained on Earth, the duration between the spaceship leaving and the spaceship’s return was far longer than it was for the astronaut twin. The beat of time flowed faster for the stay-at-home sister as measured by everything from clocks in the town square to the pulse in her chest.
FIGURE 5.5. The “twin paradox” of special relativity. Time flows more slowly for a person who takes a round trip to a distant planet at near light speed than it does for everyone (and everything) on the home planet. There is no paradox, really. The different rates of ageing (the flow of time) are just a consequence of “relativistic time dilation”.
The twin paradox demonstrates the relativity of space as well as time. The sister at home measures the distance between the sun and her sibling’s destination as thirty light-years. But the space-travelling twin’s odometer would click off only 1.8 light-years. The twins do not share the same time and they do not share the same space.
The important point to digest in thinking about relativity is that both twins are right. They have both made proper and accurate measurements of length and duration. Einstein’s fundamental insight was that no “right” answer exists for questions about space and time because there is no absolute frame of reference with an absolute space and time from which to judge the answer. Understanding the correct physics requires seeing beyond the separate concepts of space and time. In the physics of Newton, space was one kind of entity and time was another. They were not connected and calculations never mixed measurements of time and measurements of space. Einstein drew space and time together to become part of a larger whole. Once space and time are no longer seen as separate and absolute, then each one can become individually flexible for different observers. My time will not be your time if we are moving relative to each other. My space will not be your space either.
Even the intuitive concept of simultaneity had to be revised in Einstein’s new vision of physics. The intuitive idea—hardwired into our brains—that only one “now” exists and is shared by everyone lies at the heart of much of human social thinking. We all sense that we live in the same present and act accordingly.
Under the physics of relativity, all measures of simultaneity are frame-dependent. A claim that you and a friend on Mars were born at the exact same instant, the same “now”, actually depends on the fr
ame of reference of the person making that time measurement. In one frame of reference, the two events (your birth and your friend’s birth) happened at the same click of a clock. In another frame of reference—where, perhaps, a clock-watching astronaut streamed through the solar system at 99 percent of the speed of light—you were born before your friend. In yet another frame of reference, where a different astronaut was passing through the solar system from the other direction, you were born after your friend. In relativity the simultaneous also becomes the local.
This result—that time flows more slowly for objects moving close to the speed of light, an effect called “relativistic time dilation”—is nothing less than shocking. That there can be no universally recognized, simultaneous present, no “now” for all creation does violence to our intuition because this is not the time we are born into. The problem, of course, is that the time we do recognize is the one our brains evolved us to see. Human bodies rarely moved faster than a few kilometres per hour before the late 1800s. Human minds never communicated with one another across globe-spanning distances using electrical signals before the late 1800s.
Thus we have no hardwired physics modules to provide instinctive understanding of relativity. Our brains evolved to intuit one kind of time. Thousands of years of cultural evolution and material engagement have slowly taken us beyond that hardwiring. With relativity the pathways of our deepest physical reasoning, also born of material engagement, suddenly vaulted us past intuition and revealed an entirely new form of time that would rework the cosmos.
FROM SPACE AND TIME TO SPACE-TIME: GENERAL RELATIVITY
Einstein’s first paper on relativity, published in 1905, did not instantly change the landscape of physics. As Peter Galison wrote, “There were many choices open to a physicist wanting to understand . . . the electrodynamics of moving bodies . . . there were dozens of ideas vying for attention”.24 As physicists sorted through their options, one of Einstein’s early champions would also become his first serious re-interpreter.
Hermann Minkowski, a German mathematician and physicist, was known for casting physics problems into the language of geometry, the language of spatial relationship. In reviewing Einstein’s early papers, Minkowski saw a way to translate relativity into a powerful geometric vocabulary that would alter all future descriptions of cosmology. Relativity, he discovered, was not simply concerned with objects extended in space (the traditional study of geometry); instead, it described the structure of events in space and time taken as a whole.
Events were the real objects of concern in relativity. A light signal emitted from a spaceship was an event. The reception of that light signal at a distant planet constituted a second event. The whole of creation was nothing more than a web of events situated in space and time. Minkowski recognized that what mattered was not the location of these events in three-dimensional space alone or their location in time alone. Instead, relativity provided relationships between a cosmic web of events in something much larger. Minkowski cast relativity into the geometry of space-time, a new four-dimensional reality. Space-time was the new stage on which the drama of physics would be enacted.
“Minkowski insisted that in the old physics of ‘space’ and ‘time’ scientists had been . . . . misled by appearance”, wrote Peter Galison.25 The philosophical implications of the new perspective were startling. Once again the ghost of Parmenides would hover behind a new development in theoretical physics. The future and past took on a different character in the so-called block universe of space-time. In this vision of relativity, next Tuesday, which we consider to be the future, already exists. The past and future are reduced to events that exist together in the totality of a timeless, eternal block of space-time.
While Einstein initially resisted Minkowski’s geometric reworking of his relativity, other physicists saw the 4-D approach as more transparent, approachable and flexible. In fact, it was with the introduction of Minkowski’s space-time geometry that the tide began turning towards Einstein’s ideas.
Einstein himself would soon put space-time geometry to good use. His first efforts in 1905—now called the special theory of relativity—had focused solely on objects moving with constant velocity. By restricting himself to such a limited set of circumstances, Einstein had managed to tease out the mistaken notions of absolute time and absolute space that had remained at the base of physics since Newton. But velocities do change and the way they changed was the essence of Newton’s physics. Newton had clearly shown how changes in velocity—accelerations—occur only through the presence of an imposed force. Forces produce accelerations. Einstein’s next step was to understand the relativity of accelerating frames of reference. Making that leap meant dealing with Newton’s other great achievement—gravity.
Like a film noir detective, Einstein looked at physics and tried to see just the facts. His approach was to find the most basic measurable effects, the elementary facts of experience, and build his theories from there. If two different situations yielded the same experimental results, then those situations were equivalent in the most basic sense of the word. By remorselessly insisting on this logic of equivalence, Einstein forged a link between accelerating frames of reference and gravity.
As he often did in his explorations, Einstein used a thought experiment to work out his next steps. Imagining himself as the sole occupant in a windowless capsule floating in space, Einstein asked, “How could I tell if the capsule was in motion?” Imagine for a moment that you are the capsule’s occupant. The spacecraft is somewhere in deep space with a powerful rocket motor attached at one end. If the motor was turned off, there would be no way to know if the capsule was in motion. It might be stationary with respect to the stars or it might be moving at constant velocity. In either case, you and any equipment you had on board would just float freely inside your little enclosure. No experiment you could perform would reveal any difference between standing still and moving at constant velocity.
Now imagine the rocket motor is turned on. The capsule begins to accelerate. For the first few instants you and your equipment are floating freely, but now the “floor” of the capsule (where the rockets are located) comes rushing up to meet you as the entire enclosure accelerates in response to the rocket. The floor hits you and your equipment, sweeping you up and transmitting the rocket motor’s incessant push. Pinned to the floor, you now feel as if you are being weighed down. You feel pulled towards the floor.
At this exact moment in the thought experiment, Einstein came to his realization: a person inside an accelerating rocket has the same experience as a person in a rocket at rest sitting on a planet’s surface. Gravity and the rocket’s acceleration produce the same effect. An experiment conducted in a closed capsule with the motor blasting cannot distinguish between the force of gravity and an imposed acceleration. The two situations could not be considered different; from a physics perspective, they were equivalent.
This principle allowed Einstein to make a bold conceptual leap. He did away with Newton’s gravitational forces and, building on Minkowski’s formulation of his own theory, substituted the geometry of space-time for Newton’s gravity. The geometry of 4-D space-time now becomes malleable. Space-time is like a flexible fabric that can stretch and bend. The agent turning space-time into bubblegum is Einstein’s relativistic merged matter-energy.
Drop a ball and it accelerates towards the floor. Using the principle of equivalence, Einstein translated acceleration into the ball’s unforced movement through a curved space-time. The Earth, according to Einstein, does not create a gravitational force that pulls on the ball. Instead, it distorts geometry, the very shape of space-time, around it. Remove all imposed forces (like the support of your hand) and the ball is free to do what space-time wants it to do. It is free to fall along the curve of space-time the way water flows down a children’s slide.
To construct his theory, Einstein had to extend Minkowski’s mathematical insights. Ever since Euclid, the great Greek mathematian, scholars assumed
that the geometry of space was flat. In flat space, for example, two parallel lines can be extended forever and never meet, like railway tracks running endlessly into space. It was not until a few decades before Einstein that mathematicians such as Bernhard Riemann began exploring geometry in curved spaces. You have more experience with curved spaces that you might imagine, since you live on one (the surface of the Earth is a curved 2-D space). While Minkowski’s space-time for special relativity was flat, Einstein realized he would need to adapt Riemann’s new mathematics for his general relativistic theory of curved 4-D space-time. The work was hard even for Einstein, who had to be tutored in the details of the new non-Euclidian geometry. After years of work, he published his definitive work on general relativity in 1916.26
FIGURE 5.6. Gravity and the flexible fabric of space-time. In Einstein’s general theory of relativity, gravity is explained as the distortion, or “curvature”, of space-time due to the presence of mass (mass-energy).
The general theory of relativity cleanly extended Einstein’s earlier special theory. Now, individual frames of reference moved on a flexible manifold of reality, a fabric of space-time that could be bent, stretched and folded. Mass-energy caused the distortions of space-time’s fabric, and in turn, space-time guided the movement of mass-energy. Just as in special relativity, measurements of space (length) or time (duration) depended on individual frames of reference. In general relativity, an observer’s location relative to a large body of matter could also affect space and time measurements.
Clocks close to a planet’s surface run slower than those far away. Lengths measured close to a planet’s surface yield smaller values than do measurements taken far out in space.27 Time and space were still separately relative, but now it was the malleable, gumlike geometry of space-time that provided the framework in which to understand their totality. Space had been an empty stage in Newton’s physics. Now, in Einstein’s general relativity, space-time became a central player in the drama of physics and would soon become the platform from which modern cosmology would be launched.
