Einstein’s last paper of 1905 is the shortest of them all. A mere two pages, “Does the Inertia of a Body Depend Upon Its Energy Content?” looks at aspects of his special relativity paper in more detail. The paper reads like a casual hypothesis. Almost “here’s a crazy idea, and it might explain a few odd things.” What Einstein derives is his most famous equation, E = mc^2.
The equation doesn’t actually appear in the paper, but is trivially derived from its results. In the work, Einstein noted that the relative nature of time and space meant that the kinetic and potential energy of a mass were also relative to the observer. Normally these would be the sum total energy of a mass, but if this was the case the energy of a mass wouldn’t be conserved. So Einstein derived a relativistic energy relation such that energy would be conserved. In doing this, he demonstrated that a mass should have a mass energy or “rest energy” in addition to its kinetic and potential energies. This connection between a body’s mass and its energy is what the famous equation represents.
At the end of the paper Einstein notes that this relation might explain the strange behavior of radium salts, which seemed to emit particles with far more energy than could be produced by simple chemistry. He turned out to be right, because not only are mass and energy connected, but mass can become energy and energy can become mass. We now know that radium emits high energy particles by transmuting into other elements that have less mass. The lost mass is transformed into energy.
As an astronomer, the most impressive aspect of this short work is the fact that it gave us a real understanding of the stars. In the 1800s the only known mechanism by which the Sun and stars could shine was through gravitational heating. Just as putty can get warm if you squeeze it, the Sun could be heated by its gravitational weight. But this would only allow a star to shine for about 20 million years, and geology had clearly shown the Earth was millions if not billions of years old. Einstein’s famous equation solved that problem. The sun and stars are mostly made of the light elements hydrogen and helium, and those can’t be split into lighter elements. But perhaps the tremendous heat and pressure of a sun’s core could fuse lighter elements into heavier ones. In 1939, Hans Bethe demonstrated how four hydrogen atoms could be fused into a single helium atom. A helium atom has less mass than four hydrogen, so the result was helium plus energy. We then learned how helium could become carbon, nitrogen and oxygen, and on to heavier and heavier elements, all producing energy along the way.
This gave us far more answers than we expected. It not only gave us fusion as the source of a star’s power, but eventually explained from whence the diversity of elements came. Hydrogen and helium fusing into heavier elements. Exploding stars scattering those elements across the cosmos. New stars forming, with planets, one of which is home to us. From a single, simple equation we came to know that we are the dust of stars.
Paper: Einstein, Albert. Ist die Trägheit eines Körpers von seinem Energieinhalt abhängig? Annalen der Physik 18 (13): 639–641 (1905)
We live in a universe of space and time. Events occur at a particular time, and in some location in space. In this way, space and time can be seen as a background against which things happen. Throughout most of human history, this background was seen as absolute. Each event occurs at a unique point in space and time, and in principle everyone can agree what that point is. Intuitively, it makes a lot of sense. In our everyday lives the Earth seems to be an unmoving rock, and acts as a point of reference for everything we do. Sure, we now know the Earth moves around the Sun, but it doesn’t feel that way. When Galileo and others began proposing a more sophisticated view of physics, the intuitive view of spacetime as an immutable background remained. Galileo argued that the motion of objects was relative to each other, but that motion could always be measured relative to the “fixed” space. For Galileo, speed was relative, but spacetime was not. When Newton developed his theories of physics and gravity, he also assumed that spacetime was fixed and absolute.
The success of Newton’s physics seemed to confirm the absolute nature of spacetime, and the assumption remained largely unquestioned for two centuries. But as we came to understand light, the idea became less intuitive. According to Maxwell’s equations, the speed of light is the same for all light. That’s because electromagnetic waves propagate at the same rate. But water waves propagate through water, and sound waves through air, so what do light waves propagate through?
The most popular idea was that light moved through a luminiferous aether. This aether couldn’t be observed directly, but it was thought to be stationary relative to the background of space. Some proposed that this aether could in fact be the absolute frame of reference for the universe. But if that’s the case, then your measurement of the speed of light should depend upon your motion relative to the aether.
Suppose you were on the platform of a train moving at 10 m/s (20 mph). If you measured the speed of sound in the direction you are moving, you would get a speed of 330 m/s. That’s because the sound is traveling through the air at 340 m/s, but you are traveling through the air in the same direction at 10 m/s, so the sound is moving 330 m/s relative to you. In the same way, if you measured the speed of sound in the opposite direction, you would get 350 m/s because of your motion. This is a key feature of waves traveling through a medium: they can be different in different directions because of your motion through the medium.
Then in 1887, Albert Michelson and Edward Morley performed an experiment to measure this difference in the speed of light. But what they found was the speed of light was always the same. No matter what direction light traveled, no matter how they oriented their experiment, the speed of light never changed. This was not only surprising, it violated the fundamental assumption of an absolute reference frame. It seemed the speed of light (and only the speed of light) is absolute, and this made no sense at all.
This is the puzzle Einstein sought to resolve in his paper “On the Electrodynamics of Moving Bodies.” In this paper Einstein noted that in order for the speed of light to be an absolute constant, either Maxwell’s equations or Newton’s concept of space and time had to be wrong. Somewhat surprisingly, Einstein argued for the latter. Specifically, he argued that the “grid” of space and time was relative to the observer. He demonstrated this by looking at a property known as simultaneity. In Newton’s view, two events seen to occur at the same time will be seen to be simultaneous for all observers. But Einstein showed that the constancy of light required this concept of “now” to be relative. Different observers moving at different speeds will disagree on the order of events.
Rather than a fixed background, space and time is a relation between events that depends upon where and when the observer is. This relativity of space and time led to strange predictions, such as time dilation, which were later found to be true. It’s a concept that’s still difficult to fully understand, but is absolutely necessary for modern devices such as GPS.
Tomorrow: Einstein looks at the connection between matter and energy, and finds that relativity could explain the light of the stars.
Paper: Einstein, Albert. Zur Elektrodynamik bewegter Körper. Annalen der Physik 17 (10): 891–921 (1905)
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