In 1905, Albert Einstein published a paper explaining how to have electromagnetics work without an ether. This theory came to be known as the theory of special relativity, which explains how to interpret motion between different inertial frames of reference — that is, places that are moving at constant speeds relative to each other.
The key to special relativity was that Einstein explained the laws of physics when two objects are moving at a constant speed as the relative motion between the two objects, instead of appealing to the ether as an absolute frame of reference that defined what was going on. If you and some astronaut, Amber, are moving in different spaceships and want to compare your observations, all that matters is how fast you and Amber are moving with respect to each other.
Special relativity includes only the special case (hence the name) where the motion is uniform. The motion it explains is only if you’re traveling in a straight line at a constant speed. As soon as you accelerate or curve — or do anything that changes the nature of the motion in any way — special relativity ceases to apply. That’s where Einstein’s general theory of relativity comes in, because it can explain the general case of any sort of motion. (I cover this theory later in the topic.)
Einstein’s 1905 paper that introduced special relativity, “On the Electrodynamics of Moving Bodies,” was based on two key principles:
The principle of relativity: The laws of physics don’t change, even for objects moving in inertial (constant speed) frames of reference.
The principle of the speed of light: The speed of light is the same for all observers, regardless of their motion relative to the light source. (Physicists write this speed using the symbol c.)
The genius of Einstein’s discoveries is that he looked at the experiments and assumed the findings were true. This was the exact opposite of what other physicists seemed to be doing. Instead of assuming the theory was correct and that the experiments failed, he assumed that the experiments were correct and the theory had failed.
The ether had caused a mess of things, in Einstein’s view, by introducing a medium that caused certain laws of physics to work differently depending on how the observer moved relative to the ether. Einstein just removed the ether entirely and assumed that the laws of physics, including the speed of light equal to c, worked the same way regardless of how you were moving — exactly as experiments and mathematics showed them to be!
Giving credit where credit is due
No physicist works in a vacuum, and that was certainly true of Albert Einstein. Though he revolutionized the world of physics, he did so by resolving the biggest issues of his day, which means he was tackling problems that a lot of other physicists were also working on. He had a lot of useful research to borrow from. Some have accused Einstein of plagiarism, or implied that his work wasn’t truly revolutionary because he borrowed so heavily from the work of others.
For example, his work in special relativity was largely based on the work of Hendrik Lorentz, George FitzGerald, and Jules Henri Poincare, who had developed mathematical transformations that Einstein would later use in his theory of relativity. Essentially, they did the heavy lifting of creating special relativity, but they fell
short in one important way — they thought it was a mathematical trick, not a true representation of physical reality.
The same is true of the discovery of the photon. Max Planck introduced the idea of energy in discrete packets, but thought it was only a mathematical trick to resolve a specific odd situation. Einstein took the mathematical results literally and created the theory of the photon.
The accusations of plagiarism are largely dismissed by the scientific community because Einstein never denied that the work was done by others and, in fact, gave them credit when he was aware of their work. Physicists tend to recognize the revolutionary nature of Einstein’s work and know that others contributed greatly to it.
Unifying space and time
Einstein’s theory of special relativity created a fundamental link between space and time. The universe can be viewed as having three space dimensions — up/down, left/right, forward/backward — and one time dimension. This 4-dimensional space is referred to as the space-time continuum.
If you move fast enough through space, the observations that you make about space and time differ somewhat from the observations that other people, who are moving at different speeds, make. The formulas Einstein used to describe these changes were developed by Hendrik Lorentz (see the nearby sidebar, “Giving credit where credit is due”).
String theory introduces many more space dimensions, so grasping how the dimensions in relativity work is a crucial starting point to understanding some of the confusing aspects of string theory. The extra dimensions are so important to string theory that they get their own topic, topic 13.
Following the bouncing beam of light
The reason for this space-time link comes from applying the principles of relativity and the speed of light very carefully. The speed of light is the distance light travels divided by the time it takes to travel this path, and (according to Einstein’s second principle) all observers must agree on this speed.
Sometimes, though, different observers disagree on the distance a light beam has traveled, depending on how they’re moving through space.
This means that to get the same speed those observers must disagree about the time the light beam travels the given distance.
You can picture this for yourself by understanding the thought experiment depicted in Figure 6-2. Imagine that you’re on a spaceship and holding a laser so it shoots a beam of light directly up, striking a mirror you’ve placed on the ceiling. The light beam then comes back down and strikes a detector.
Figure 6-2:
(Top) You see a beam of light go up, bounce off the mirror, and come straight down.
(Bottom)
Amber sees the beam travel along a diagonal path.
However, the spaceship is traveling at a constant speed of half the speed of light (0.5c, as physicists would write it). According to Einstein, this makes no difference to you — you can’t even tell that you’re moving. However, if astronaut Amber were spying on you, as in the bottom of Figure 6-2, it would be a different story.
Amber would see your beam of light travel upward along a diagonal path, strike the mirror, and then travel downward along a diagonal path before striking the detector. In other words, you and Amber would see different paths for the light and, more importantly, those paths aren’t even the same length. This means that the time the beam takes to go from the laser to the mirror to the detector must also be different for you and Amber so that you both agree on the speed of light.
This phenomenon is known as time dilation, where the time on a ship moving very quickly appears to pass slower than on Earth. In topic 16, I explain some ways that this aspect of relativity can be used to allow time travel. In fact, it allows the only form of time travel that scientists know for sure is physically possible.
As strange as it seems, this example (and many others) demonstrates that in Einstein’s theory of relativity, space and time are intimately linked together. If you apply Lorentz transformation equations, they work out so that the speed of light is perfectly consistent for both observers.
This strange behavior of space and time is only evident when you’re traveling close to the speed of light, so no one had ever observed it before. Experiments carried out since Einstein’s discovery have confirmed that it’s true — time and space are perceived differently, in precisely the way Einstein described, for objects moving near the speed of light.
Building the space-time continuum
Einstein’s work had shown the connection between space and time. In fact, his theory of special relativity allows the universe to be shown as a 4-dimensional model — three space dimensions and one time dimension. In this model, any object’s path through the universe can be described by its worldline through the four dimensions.
Though the concept of space-time is inherent in Einstein’s work, it was actually an old professor of his, Hermann Minkowski, who developed the concept into a full, elegant mathematical model of space-time coordinates in 1907. Actually, Minkowski had been specifically unimpressed with Einstein, famously calling him a “lazy dog.”
One of the elements of this work is the Minkowski diagram, which shows the path of an object through space-time. It shows an object on a graph, where one axis is space (all three dimensions are treated as one dimension for simplicity) and the other axis is time. As an object moves through the universe, its sequence of positions represents a line or curve on the graph, depending on how it travels. This path is called the object’s worldline, as shown in Figure 6-3. In string theory, the idea of a worldline becomes expanded to include the motion of strings, into objects called worldsheets. (See topic 16 for more information. A worldsheet can be seen in Figure 16-1.)
Unifying mass and energy
The most famous work of Einstein’s life also dates from 1905 (a very busy year for him), when he applied the ideas of his relativity paper to come up with the equation E=mc2 that represents the relationship between mass (m) and energy (E).
Figure 6-3:
The path a particle takes through space and time creates its worldline.
The reason for this connection is a bit involved, but essentially it relates to the concept of kinetic energy discussed in topic 5. Einstein found that as an object approached the speed of light, c, the mass of the object increased. The object goes faster, but it also gets heavier. In fact, if it were actually able to move at c, the object’s mass and energy would both be infinite. A heavier object is harder to speed up, so it’s impossible to ever actually get the particle up to a speed of c.
In this 1905 paper — “Does the Inertia of a Body Depend on its Energy Content?” — Einstein showed this work and extended it to stationary matter, showing that mass at rest contains an amount of energy equal to mass times c2.
Until Einstein, the concepts of mass and energy were viewed as completely separate. He proved that the principles of conservation of mass and conservation of energy are part of the same larger, unified principle, conservation of mass-energy. Matter can be turned into energy and energy can be turned into matter because a fundamental connection exists between the two types of substance.
If you’re interested in greater detail on the relationship of mass and energy, check out Einstein For topic (Wiley) or the topic E=mc2: A Biography of the World’s Most Famous Equation by David Bodanis (Walker & Company).
