Five-minute Explainer: Special Relativity

Note: The section “A Constant Speed of Light” was revised on 28 Jan 19. Some slight inaccuracies were corrected regarding the relativistic treatment of time, and some vague wording was clarified regarding the same.

This is going to be the the briefest history of time ever. When I’m done, my goal is for you to understand not only that motion changes time and space but how and why.

Einstein created the theory of special relativity to answer these questions, and it does so in a very satisfying and complete way which physicists still haven’t improved on. It may surprise you to know that the paper in which he originally described it was only thirty-one pages long.

Postulates

Before we start, we need just the slightest background here on what Einstein had to work with when he came up with special relativity. Namely, he used two assumptions.

  • The laws of physics are the same for any point of view which seems stationary to the observer. This is known as the principle of relativity. It means that it’s physically impossible to distinguish between whether I’m moving or the world is moving if I were to jump up and down. Both are true at the same time. You can take whichever point of view you like. That stationary point of view is called an inertial frame of reference.
  • The speed of light is always the same in all inertial frames of reference, regardless of the speed of whatever is emitting the light.

There are some additional assumptions you have to bake in, like conservation laws and so on, but none of those would strike you as terribly strange, and they’re subtle enough points that they don’t bear discussing here.

From those two assumptions, which are today called postulates, the rest of the theory emerges. Remember that carefully—every strange part of special relativity is an emergent consequence of those two postulates. No alternative to the theory could work without some change to the postulates, and at the time Einstein was working, he was almost certain they were true. Einstein merely carried the assumptions to their logical conclusion: special relativity.

The Principle of Relativity

Einstein loved to visualize things, and he used trains to illustrate his theory originally because of the train station in Bern, Switzerland. We’ll use trains, too. To make things even easier to visualize, we’ll not deal with light directly but instead use a thought experiment involving a thrown ball.

Imagine a person standing still on the ground can throw a ball at 100 kilometers per hour. The ball crosses a distance of 27.78 meters in 1 second. The thrower can always throw at that speed, so over the course of 1 second, the distance traversed is always 27.78 meters.

Now imagine this same person is standing on a train car. The train is moving at 30 kilometers per hour. They throw the ball in the direction of travel at 100 kilometers per hour. How far does the ball travel?

For an ordinary ball, the distance traveled depends on where you stand. The person throwing the ball on the train sees nothing out of the ordinary because they too are moving along. They see the ball travel at 100 kilometers per hour, and so they likewise see the ball cross 27.78 meters in 1 second. This accords with the first postulate, the principle of relativity. No matter that the train is moving. To the person on the train, it might as well be still while the rest of the world moves backward.

However, a person standing stationary on the ground next to the train would see the ball thrown at 130 kilometers per hour because the train’s motion adds onto the ball’s motion. Therefore, the ball travels 36.11 meters over 1 second. The velocities add together.

A Constant Speed of Light

So far, I have described the ordinary, intuitive behavior you would expect in this situation. Now let’s change things up: The ball can never travel at any other speed than 100 kilometers per hour in any direction, regardless of who is standing where or who is in motion compared to whom. This is similar to how light behaves, according to the second postulate.

The person on the train throws the ball, and it travels at 100 kilometers per hour relative to them, crossing 27.78 meters in 1 second. So far, so good! But the person on the ground also sees the ball travel 100 kilometers per hour, despite the velocity of the train being 30 kilometers per hour. The velocity of the train no longer adds onto the velocity of the ball, yet the ball is still in motion when it is thrown.

How far does the ball travel now?

Here, the universe encounters some very awkward bookkeeping problems. If the person on the ground also saw it travel 27.78 meters in 1 second at 100 kilometers per hour, that ball would land somewhere other than where the person on the train sees it land. This train is in motion, along with the ball. We expect it to cover a distance in 1 second equivalent to the motion of the train in addition to the 27.78 meters which the person on the train sees. That’s 36.11 meters. Yet it cannot cross that distance in 1 second because the ball cannot go faster than 100 kilometers per hour.

For the ball to go different places for different people violates causality itself—it would mean cause and effect were broken. Einstein assumed cause and effect would work out because without them, science wouldn’t do us much good for describing the universe. At the same time, however, he had this very annoying issue of how to solve this problem of reconciling time and distance under these conditions. He thought about it until he understood that some of the assumptions he held about what the universe would keep constant were not, in fact, fixed.

The way to resolve the problem above is that the ball does travel only 27.78 meters. How can that be? Because the train itself must get shorter. The person standing stationary on the ground, looking up at the train, would see the train (and everything on it) squished in the direction of travel. The universe solves the bookkeeping problem around the speed of light by altering space itself! In point of fact, those 27.78 meters over which the ball travels would look different to a person standing on the ground compared to someone on the train because they would be shorter meters.

It is the way the universe must work because of the finite and invariant speed of light—or, in our thought experiment, the invariant speed of the ball thrown. It simply cannot be any other way without breaking causality or changing one of the postulates.

While we’ve fixed up the distance problem, though, we’ve created a new problem. Imagine that the person on the train who threw the ball walks over and picks it up after throwing it. They’re moving through a shorter train (at less than the speed limit). If we only contract the length through which they walk, they would cover the distance to arrive to where the ball landed too quickly. This outcome is equally as bad as before, when the distances didn’t work out. How do we solve this?

This problem really bothered Einstein until he let go of the assumption that the universe kept an absolute time clock somewhere. In other words, he discarded the idea that there’s one real, absolute time. This allowed the universe bend time in order to make the math come out right. This means that the solution to the problem is, everything on the train must slow down when the train is in motion relative to an observer.

The sum total of these effects leads to the stationary person on the ground seeing the everything on the train squished in the direction of travel while moving more slowly at the same time. The faster the train goes, the more pronounced these effects become. For the person on the train, they see everything happening there normally, but due to the principle of relativity, they see things on the ground also squished and in slow motion.

There can be no distortion in space without a matching distortion in time, and it appears that space and time are so inextricably bound that it’s easier to deal with them as a single thing called spacetime.

Cause and Effect

By changing the rules the ball followed in our thought experiment, some very unintuitive consequences emerged. As it happens, light really does behave the way the ball does. Because time and space warp for light, they warp for anything moving at any speed, though the speed limit is so high that the effects aren’t obvious in ordinary life.

It was only necessary to change the behavior of the ball—and hold everything else equal—to see the effect of special relativity on time and space. It caused the everything in motion to squish (length contraction) and begin moving in slow motion (time dilation) when seen by the person on the ground next to the train.

In the next five-minute explainer, I’ll describe even more incredible effects which emerge from the invariant speed of light which Einstein and others found later.

I am grateful again to Zuzu O. for her thoughtful suggestions on improving the readability of this post.

Five-minute Explainer: The Conflict Thesis

How do you reach someone who believes the world is flat? How do you convert a global warming denier? How do you confront an anti-vaxxer? You may have noticed, when presenting facts contradicting their arguments, or even pointing out the self-contradictions in their own arguments, that your audience remains intransigent.

Why should this be? Especially where vaccination or global warming are concerned, the stakes ought to be too high to allow vagaries of ignorance to win out. Yet facts don’t cut it. You risk entrenching the other side, and you come away even more convinced of their wrongness. Everyone goes home angry.

There are strategies to take for winning over people with different viewpoints: the best one being to find common ground. This tack has nothing to do with the facts at issue, but it’s the best way forward.

How did we get in this situation where it’s possible to disagree with facts themselves? I propose that it’s not so much that we find ourselves arguing with a reasoned point of view but with an identity.

Meet Alice and Bob

Consider Alice, who believes that human-caused global warming is changing the Earth’s climate (hereafter “climate change”). She’s trying to convince Bob, who just doesn’t believe Alice. Everything he’s heard leads him to believe that there’s just too much doubt to know for sure if the Earth is really warming, and if it is, there’s no way that humans could be the cause.

No matter what Alice says, Bob believes Alice is wrong. What’s Bob’s deal? Fundamentally, this is not a discussion about whose facts win out over whose. Instead the question is about who is arguing from the more meaningful authority.

Some of you might be wondering, well, gosh, Alice isn’t arguing from authority, is she? She has facts and figures and charts and scientific consensus to back up her side. Here’s the problem: science itself has been turned into an authority over the years—in Bob’s mind and even in Alice’s mind.

Let’s leave them to their intractable argument and visit this idea of battling authorities.

The Conflict Thesis

It’s probably a vast oversimplification to consider Alice and Bob above as proxies for science and religion. However, they likely carry feelings that science and religion conflict irresolvably, and elements of that conflict almost certainly underlie several of their attitudes. Where did these feelings come from? What do they mean?

The conflict thesis is not so much a description of the reality of science as it is a historiographical approach to the history of science itself. It’s a belief that religion is inherently and attitudinally adverse to science and vice versa. It permeates Western science education and many current Western religious doctrines.

For most people raised in the United States, the idea of the conflict thesis will feel very familiar—it may conjure up images of Galileo’s house arrest or the Scopes Trial. Many contemporary popular scientists, speakers, and writers have promulgated elements of the conflict model, such as Neil deGrasse Tyson or Isaac Asimov. Quoting Stephen Hawking, who stated the conflict very forthrightly near his latter years,

There is a fundamental difference between religion, which is based on authority, [and] science, which is based on observation and reason. Science will win because it works.

The conflict model is not especially useful, though, for understanding the relationship between religion and science. Historians have mostly moved to more nuanced models for describing the history of science. The evidence available doesn’t support conflict.

Primarily, two episodes in history foment the supposed conflict between religion and science (or more particularly, Christianity and science): the Galileo affair and Darwin’s theory of evolution. In point of fact, before the modern period, religion was such a dominant force in society that scientific thought was not seen as in conflict with religion so much as aiding it by discovering God’s plan. This view is literally ancient: Saint Augustine of Hippo considered God’s word, as written, fallible because of the imperfection of language (PDF download). Therefore, where natural knowledge and science contradicted the Bible, God’s former scripture—creation itself—wins out.

In the case of the Galileo affair, Galileo’s persecution had less to do with the Church’s disagreement about heliocentrism or of Galileo’s supposed heresies than about Galileo running afoul politically of the pope. Heliocentrism as a mathematical model predates Galileo by nearly a century, and (even despite having some contemporary detractors and competing models, such as the complicated Tychonian model), the Church had no problem with its use. The pope also approved the publication of the Dialogue Concerning the Two Chief World Systems before subsequently banning it (possibly because some statements the pope had made within Galileo’s hearing which he had then placed in the mouth of a character he named Simplicio).

This is a five-minute explainer, so I won’t go into other historical examples in detail. Suffice it to say, many episodes of putative conflict in the past (such as the Galileo affair or the Scopes Trial) had political and personal motivations and issues at play as well as, or rather than, pure conflict between religion and science.

The Problem of Authority

So we come back to Alice and Bob. How does the conflict thesis shape their argument?

Recall that I mentioned that Alice and Bob are both fundamentally arguing from authority. This may seem like a sharp tilt on what’s happening, but here’s what I see. The conflict thesis has become common enough to make it into textbooks, popular writing, TV shows, and even public policy. People who believe science and religion can coexist (let alone build on one another) find themselves in a minority.

One of religion’s main functions as an institution is providing a foundation for community via shared mores and beliefs. From this position, religion becomes an authority, and in that capacity, the Christian Church served as a powerful authority for many centuries. The conflict thesis emerges naturally as a way of supplanting that authority in order to center a scientific model of reality.

The problem is that we have exchanged one authority for another. This happened as a natural outgrowth of the process of deconstructing religion as authority. However, science is not designed to be an authority, and it doesn’t function best that way.

Yet it’s taught that way. Consider how scientific news flows to the public—channeled through layers of intermediate journalism: the actual scientific publications, next scientific journalism, then mainstream journalism. Along the way, what remains are names of lofty institutions, their impenetrable facts, and their avatars of a new faith. Worse yet, consider what’s emphasized in school: not processes, not approaches, but perfected facts and great minds beyond impeaching.

Missing is the human element: the struggle with ambiguity, the charting of unknown territory, the failures and blind alleys. Science can contain narratives which empower people, if only we can burnish its anti-authoritarian stance: question everything and everyone. Finding the right questions is within anyone’s power, and science is more about questions than answers.

Resolution for Alice and Bob

Turning back to Alice and Bob again—isn’t that actually what Bob is doing? Questioning Alice? Questioning the science behind climate change? Unfortunately, he’s not really questioning them. This is mere denial because he’s not examining them in any rigorous, critical way. In his mind, however, he may have an anti-authoritarian stance, believing Alice has bought into climate change without critical thought on her part.

Meanwhile, Alice hasn’t taken Bob’s point of view seriously at all. She hasn’t sought to understand it, and therefore she has no idea how to engage critically with it. Maybe his point of view isn’t consistent, rational, or even coherent, but it’s where they have to begin if he’s going to join Alice.

Both sides are merely dismissing the other, and that’s why nobody is making headway. They both fervently believe in what they have learned, and they have bound up their own identities in those beliefs. Unfortunately for both of them, the conflict thesis has interwoven tightly into their beliefs as well, leading them to a place where their systems of thought are thoroughly immiscible.

Even if they can’t bridge the gap between belief systems, though, the hope is that Alice can reach Bob in a way that doesn’t force him to abandon his beliefs, his authority, or even his identity in order to incorporate new knowledge. For this reason, finding common ground is key.

An excellent place for Alice to begin is with this excellent video, Global Weirding with Katharine Hayhoe, produced by KTTZ Texas Tech Public Media and distributed by PBS Digital Studios, to allow her better to reach Bob and understand why butting facts against facts directly (or facts against faith) is a doomed effort.

Winning hearts and minds is about overturning the root of conflict through which we see science and religion. It allows Bob (and Alice!) to entertain multiple ways of seeing the world simultaneously. With the conflict resolved, Alice can move from changing Bob’s mind to adding to what Bob knows instead, and Bob can move from losing foundational beliefs to incorporating new ideas into those foundations.