In Newtonian physics, the speeds of two objects are added or subtracted to get the speed of one object as viewed from the other. For example, suppose we throw a ball at twenty miles per hour (mph) toward an oncoming train moving at eighty mph. A passenger on that train would see the ball moving toward them at one hundred mph, and the person throwing the ball would see it traveling at twenty mph. The ball travels at different speeds depending on the observer’s reference frame.
One of the things that puzzled physicists toward the end of the nineteenth century was that light always seemed to travel at the same speed regardless of the frame of reference, unlike the ball thrown at the train. Suppose a beam of light is traveling at 670 million mph (the speed of light) toward an oncoming spaceship traveling at 10 million mph. We might think that a passenger on the spaceship would measure the speed of the oncoming light at 680 million mph, adding velocities like the train and baseball. No, the passenger would measure the speed of the oncoming light at 670 million mph, not 680 million mph. Einstein realized that Newtonian physics and electrodynamics (the physics of light) do not agree with each other. One of them had to change.
In 1865, James Clerk Maxwell published four equations now known as Maxwell’s equations, which describe the behavior of electric and magnetic fields. These equations describe waves of alternating electric and magnetic fields, and other phenomena. The speed of these waves can be calculated using constants related to the strength of electric and magnetic fields. This speed is equal to the measured speed of light, establishing the connection between electromagnetic waves and light. Other forms of electromagnetic waves include radio waves, microwaves, infrared, ultraviolet, and X-rays.
Maxwell’s equations also show that the speed of light in a vacuum is a universal constant that does not change with the speed or direction of an observer’s frame of reference. The speed of light remains the same when it travels in different directions, such as when reflected by a mirror. This is because Maxwell’s equations are isotropic and do not depend on the direction light travels.
When light travels through matter, like water or glass, the charged particles in the matter, such as electrons and atomic nuclei, interact with the light’s electric and magnetic fields. This slows light down. Consequently, light achieves its highest speed in a vacuum. We will ignore the complication of light changing speed in matter and focus on the behavior of light in a vacuum. A discussion of relativity is complicated enough in a vacuum where the speed of light always has the same value.
In 1905, Albert Einstein published four papers widely regarded as the beginning of modern physics. This revolution swept through the field in the early twentieth century, although it went largely unnoticed at the time. One of these papers, “On the Electrodynamics of Moving Bodies,” introduced his Theory of Special Relativity.
Why is Einstein’s Special Theory of Relativity so special? Einstein recognized that this theory only applied to the case of reference frames traveling at a constant speed in a straight line. In a future blog post, we will look at Einstein’s General Theory of Relativity, which includes accelerating frames and gravity.
The Special Theory of Relativity is based entirely on two postulates, or assumptions. The first postulate is a restatement of Galilean relativity: we cannot feel or measure whether we are moving at a constant speed in a straight line or standing still without looking outside our frame of reference. We can only determine the speed of a reference frame relative to other frames. There is no experiment we can perform inside our spaceship, without looking outside, that will ascertain our absolute speed. You might remember that this leads us to the conclusion that there is no such thing as absolute speed and no special reference frame in the universe that is standing still.
The second postulate of special relativity states that the speed of light in a vacuum always has the same value of 670 million mph, regardless of our frame of reference. Einstein reasoned this from the fact that experiments have not found any indication that light propagated through any aether, but was, in fact, isotropic and traveled at the same speed regardless of direction.
Einstein reasoned with thought experiments that enabled him to visualize and think through the consequences of these two postulates. Some of these results seem very weird and outrageous because in our normal experiences, we do not encounter speeds approaching the speed of light. Some of these results are famous, such as the equation E = mc2.
Suppose we are watching a spacecraft as it accelerates to speeds approaching the speed of light. We would observe these three things happening to the spacecraft:
• Time slows down
• Objects become shorter along the direction of travel
• The ship becomes more massive (evidenced by a decrease in acceleration at constant thrust)
The occupants of the spacecraft would not observe these changes. Instead, they would see our frame of reference speeding away in the opposite direction. They would see our time slowing down, our things getting shorter, and us getting more massive. Remember, everything is relative to your frame of reference.
We may wonder why we don’t experience these strange things when looking at moving objects. The slowing of time and the shortening of objects are only observed on objects moving at speeds close to the speed of light, 670 million mph. We generally don’t experience anything close to these speeds, even in space without the atmosphere to slow them down.
Speeds of various objects compared to the speed of light.
In a future blog post, we will see how these strange effects follow from Einstein’s two postulates.
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