Explaining Einstein’s Theory of Special Relativity

From a lecture series presented by The Great Courses

Einstein’s theory of special relativity clarified a lot of confusion circulating in the scientific community about the nature of light waves. This theory is still quite difficult to wrap your head around, though. We’ll use some mind-boggling, yet concrete, examples to illuminate this theory that forever changed our understanding of space and time.

Photograph of handwritten forumula for relativity surrounded by equations

Relativity: A Counterintuitive Concept

The word “relativity” is apt because, according to special relativity, certain quantities—like the distance between points space, and the durations of time between events—are different to different observers. Distances in space and lengths of time don’t have objectively correct values.

If the question is how far apart from one another are two points in space, then the correct answer depends on the frame of reference when the measurement is made.

And the same thing is true for measurements that involve lengths of time. Quantities such as these are indeed relative to one’s frame of reference. If you’re hearing about this for the first time, it almost certainly seems very strange, and very counterintuitive.

And it should. Relativity is very strange. And it is very counterintuitive.

This is a transcript from the video series What Einstein Got Wrong. Watch it now, on The Great Courses Plus.

Special relativity describes phenomena that are not at all like those that you regularly experience. Human beings are strongly hardwired to intuitively understand how objects move through space and time.

This is the case because, over millions of years, early humans and other hominids were more likely to survive and reproduce if they could do things like evade predators and find food. These are the kinds of things that one can do better if they have a solid working conception of both space and time.

As a result, natural selection gradually caused our ancestors to evolve useful instincts and intuition for both space and time. But none of our hunter-gatherer ancestors ever had much to gain by understanding how objects behave when they move at speeds close to the speed of light.

We have very poor intuition for this kind of phenomena because it wasn’t useful to our ancestors. In order for us to understand these strange and counterintuitive ideas, we can’t expect to rely on our instincts.

Instead, we have to train ourselves to think differently. It can be done, but it requires some work.

The Speed of Light in Action

Let’s consider an example. Imagine that I am holding a meter stick and that you are moving toward me along the direction that the meter stick is pointed. As you pass by me, you measure the distance from one end to the other of my meter stick. As long as you are moving at a speed that is much slower than the speed of light, you’ll measure this distance to be one meter, just as you would expect.

But if instead, you zip by at a speed comparable to the speed of light, you’ll find that your measurement yields a different—and perhaps more surprising—result. For example, if you are moving at 60,000 miles per second—which is about a third of the speed of light—you’ll measure the length of the meter stick to be about 94 centimeters, or about 6 percent shorter than its length when measured at rest.

If you were moving at 90 percent of the speed of light, it shrinks even further, to about 44 centimeters. And at 99.9 percent of the speed of light, you’ll measure the meter stick to be just under 4.5 centimeters long.

In addition to space, surprising things also occur in connection to time in Einstein’s theory of special relativity. Picture a mechanical alarm clock. Now imagine that you set the alarm to go off in one hour. To anyone that is either stationary or that is moving far less than the speed of light relative to the clock, they will measure that an hour passes before the alarm goes off.

bronze vintage alarm clock isolated on white background
Surprising things occur in connection to time in Einstein’s theory of special relativity.

But to someone that is moving at a third of the speed of light, it will take about 1 hour and 4 minutes. At 90 percent of the speed of light, it takes 2 hours and 18 minutes. And at 99.9 percent of the speed of light, this length of time—which was only an hour in its rest frame—gets stretched to over 22 hours, almost a full day.

Learn more about Einstein’s general theory of relativity

Time Travel and the Twin Paradox

The most famous illustration of this kind of phenomena is an example known as the twin paradox. So, picture two identical twins.

One grows up to be a banker and stays on Earth for her entire life. The other grows up to become an astronaut and travels at 99.9 percent of the speed of light to a distant solar system that is 50 light years away from us.

Once arriving there, she quickly turns around and returns the same way she came, again traveling at the same speed of 99.9 percent of the speed of light. To those of us on Earth, the astronaut’s round-trip journey of 100 light years takes just over 100 years to complete.

Minkowski’s Twin Paradox diagram.
Twin Paradox diagram

But time passes differently in the astronaut’s moving frame of reference. As far as the astronaut is concerned, only about 4.5 years pass between the start and finish of her journey.

This means that the ship’s clocks all measure that 4.5 years have passed and the astronaut only ages 4.5 years. But on Earth, 100 years of time and history have passed. And the twins are no longer the same age. In what was only 4.5 years of time for the astronaut was 100 years of time for the banker on Earth. In all likelihood, everyone that the astronaut knew before leaving on her journey had grown old and died before she got back home.

Just take a second to consider how weird and spectacular this result is. For all intents and purposes, the astronaut in this example has just traveled into the future—making this an example of time travel.

By moving at nearly the speed of light, the astronaut slowed down the very passing of time in her frame of reference, allowing her to move rapidly into the future. The closer your speed is to the speed of light, the faster that you can move through time.

To something that is moving at exactly the speed of light, time ceases to make much sense at all. To such an object, all events that will ever happen simply happen simultaneously. Therefore, to a beam of light, there is just no such thing as the past, present, or future. There is only a simultaneous series of events.

To summarize these ideas and put them into context and perspective, according to Einstein and special relativity, distances in space are contracted or shortened to observers that are in moving frames of reference. And in a similar fashion, time passes more slowly in moving frames of reference.

Furthermore, the closer one gets to the speed of light, the more pronounced these effects become. These effects are not illusions. They are not merely some kind of problem with observers mis-measuring lengths in space or durations of time.

The reality is that a meter stick is only a meter long in one particular frame of reference—its rest frame. And what takes an hour according to one observer can be much longer or shorter to another observer.

Learn more about quantum entanglement

The Legacy of Einstein’s Relativity Theory

These ideas of Einstein’s radically changed our notions about both space and time. From Newton up to Einstein, physicists had been imagining a world in which lengths and durations were objective quantities, that everyone would agree upon—at least given a high-quality measurement.

But Einstein showed this is not always the case. Space and time are not the simple and objective quantities they’d long been thought of as. There are some quantities that are the same to all observers, but these are the exception and not the rule. For example, observers in all frames of reference will measure the same value for the speed of light.

Over the past century, physicists have carried out numerous experiments intended to test the predictions of special relativity. And over and over again, they find perfect agreement.

When Einstein proposed this theory in 1905, it was viewed with skepticism by many of his colleagues. At best, it was seen as speculative, and at worst it was seen as nonsense. But the repeated success of this theory eventually left no serious scientist skeptical of its validity.

With the discovery of special relativity, Einstein overthrew many of physics most longstanding notions, forcing us to reimagine our very conceptions of space and of time.

From the lecture series What Einstein Got Wrong, taught by Professor Dan Hooper

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Minkowski’s Twin Paradox diagram.  Image created by Bartosz [CC BY-SA 3.0 (http://creativecommons.org/licenses/by-sa/3.0/)], via Wikimedia Commons