## Five-minute Explainer: What Even Are Gravitational Waves?

You might follow the news—which you may find depressing these days—but maybe you don’t follow the science news, which is plenty exciting! Gravity is making waves these days, literally: gravitational waves. In fact, several weeks ago, the LIGO scientific collaboration announced the release of a catalog of gravitational wave sources.

Gravitational-wave detection began just a few short years ago, and only starting in 2017, scientists began to get the first really interesting observations. These most recent events have enabled us to understand fundamental physics better by ruling out or circumscribing a few grand theories of everything, and they have allowed us to see the universe in ways we never could before.

Yet the events themselves are mere “inspiral chirps” which happen in less than a second and usually at a remove of a billion parsecs or more. How can something so brief and so distant, be so meaningful? That’s what today’s explainer is all about.

To get the big deal about gravitational waves, let’s review what we know about gravity.

## What Are Gravitational Waves?

Gravity happens because mass warps space and time. All mass does this, and the warping effect stretches out across the universe infinitely. Even you, as you sit reading this, cause a very tiny change in the space in your vicinity and in the passage of time, and that extends beyond you out into space forever, however faintly.

Two things are important to note, though. First, the degree to which any object warps space around it weakens very sharply as you move away from it. This is because the farther you get from it, the amount of space there is to warp grows exponentially, so the warpage falls off in turn. (This is a kind of conservation law, known as the inverse-square law.) Second, that warpage—that gravity—doesn’t travel instantly. It’s bound by the same speed limit as everything else, just as special relativity requires.

So given these facts, we know that gravity spreads out in much the same way light does. How does it form waves? Waves result from any cyclical phenomenon which traverses a distance. Think of a cork bobbing in a pond. The cork, stationary, merely moves up and down, but the ripples move out in waves. Waves made of gravity can therefore ripple outward anytime a source of mass changes in a repeating way.

This is what gravitational waves are—cyclical changes in gravity. The ones we can detect result from vastly large masses spiraling in toward one another extremely rapidly and colliding. Their circling motion causes the gravity from them to ripple out in a pattern of repetitive change—in waves—as the masses revolve around each other. This spiraling pattern causes the masses to alternate positions quickly, sometimes lining up or sometimes sitting side-by-side (from our point of view). As they revolve, they also draw closer and closer to one another. Finally, when the masses collide, the wave source stops in a sudden “inspiral chirp”—so called because the gravitational wave is so rapid and stops so suddenly, it sounds like a chirping sound when played as audio.

## How Do We Detect Them?

We detect gravitational waves with a lasers, of course. Actually, it’s a bit more complicated. There are multiple lasers. And we bounce them down tunnels (called “arms”) over four kilometers long—long enough that the Earth curves downward by a meter over their length—and back.

When a gravitational wave ripples through a LIGO facility, the phenomenon literally causes those arms to change shape and size according to general relativity. The facility is a vast instrument called an interferometer which causes the lasers to interfere with one another in a very specific and measurable way.

The idea is that a pair of lasers are fired over a very great distance (through the arms) and bounced back to the detector, which is a specialized kind of digital camera. When they bounce back, they’re meant to interfere with each other in a very precise way because of how they overlap when they hit the detector. However, minute vibrations upset the delicate interference pattern, and the detector can see that.

The lasers have to be so long because they’re directly measuring very tiny warpages in the shape of spacetime itself. Gravitational waves ripple out from violent but brief, distant events, and so these instruments must be extraordinarily sensitive. LIGO reports that at its most sensitive, it can detect a change in distance ten-thousandth the width of a single proton. The facility in Hanford, Washington, detects vibrations so sensitive that it can pick up ocean waves crashing on the beach several hundred miles away.

Using multiple facilities located in different locations, it’s possible to detect gravitational waves very quickly using advanced, purpose-made software (used to separate the data from the noise) and roughly locate the source in the sky.

## What Do We Do With This Information?

Gravitational-wave detection is one of the newest and most profound breakthroughs in recent observational cosmology. Even merely detecting a gravitational wave is a feat not to be understated—it signifies that we have directly measured a ripple in the fabric of spacetime itself and further cemented the theory of general relativity. It took nearly a century after their first theoretical prediction to achieve a direct detection.

Gravitational-wave astronomy gives us our first look at the universe beyond electromagnetic radiation (light, infrared, x-rays, and so on). We are finally able to see the ripples of the pond in which we all live, not just the specks of light. Gravity behaves differently than EM radiation in several important ways, so it promises new insights into massive phenomena like neutron stars, supermassive black holes, and the like—all at incredible distances difficult to observe otherwise. The promise of revelations into the formation of galaxies, exotic phenomena, dark matter, or even the creation of the universe all await.

Already, though, we’ve seen the birth of a new form of astronomy altogether called multi-messenger astronomy which combines both gravitational wave observations along with traditional radio or optical telescopic observations of the same event. Until now, humanity has only ever been able to see the light from the stars and make educated guesses about distance, mass, and so on. What’s more, we still have more questions than answers about how EM radiation and gravity relate to one another. The most fundamental explanations of all of creation, from the subatomic level to the cosmic level, depend on answers to these questions.

The first event observed via both gravity and light was called GW170817. Gravitational waves from this event was detected by three detector facilities in real time, and a corresponding gamma-ray burst (the most violent kind of explosion in the universe) was found at the same location in the sky by dozens of observatories. This event, which is thought to be two neutron stars colliding, has already taught us new things and begun to constrain models of fundamental physics.

For example, since it was observed via both light and gravity, we can compare the time it took for both to reach us and see what differences may exist. Some grand unifying theories of everything thought that perhaps gravity would take longer to cross the distance to us because it had to travel differently (through hidden, “compactified” spacetime dimensions, for example). Since that didn’t happen, those theoretical physicists will have to go back to the drawing board.

Gravity travels unattenuated by dust and unscattered over vast distances. Events like GW170817 travel over distances only affected by other masses, allowing us to “see” the universe in a different and maybe clearer way. Some scientists hope that we may even find primordial gravitational waves leftover from the earliest epochs of the universe, before even light could emerge because matter was too dense. Gravitational waves may let us pierce the wall of creation’s primordial fire and look beyond into nearly the very earliest moments of the universe itself.

## What’s Next?

Gravitational-wave astronomy and multi-messenger astronomy are extraordinarily young sciences. The data from the events we’ve observed are still being pored over by scientists as they attempt to make or break new theories and find new signals in the noise.

In the future, we may be able to put extraordinarily large interferometers into space which extend over massive distances and which would not be subject to earthly vibrations such as trucks, oceans, footfalls, or earthquakes. One such planned project is called LISA. We would be able to observe many more sources of waves with such a detector, even ones within our own galaxy. Perhaps we will even find sources of gravitational waves we never even expected. We’re standing at the verge of a whole new universe.

## Five-minute Explainer: What Is Gravity?

This essay continues from the previous one in this series, “Five-minute Explainer: Why Is Mass Equivalent to Energy?”

An old story relates that Newton figured out gravity when an apple fell on his head. Newton himself doesn’t mention the apple falling on his head—this appears to be a later embellishment—but he does mention the apple anecdote a couple of times in his dotage. John Conduitt remembered,

In the year 1666 [Newton] retired again from Cambridge to his mother in Lincolnshire. Whilst he was pensively meandering in a garden it came into his thought that the power of gravity (which brought an apple from a tree to the ground) was not limited to a certain distance from Earth, but that this power must extend much further than was usually thought.

Why not as high as the Moon said he to himself & if so, that must influence her motion & perhaps retain her orbit, whereupon he fell a calculating what would be the effect of that supposition.

This anecdote describes a key quality of gravity as understood then: its nature as an occult force—something working mysteriously and unseen across space.

Before Newton, it was known that the planets moved according to well known laws (Kepler’s laws) which allowed their motions to be predictable. It was not understood, however, why they should move in that way. Kepler’s laws merely came from generalizations after many observations.

Philosophers at the time were troubled that the planets appeared to have no reason to move as they did. Aristotelian thought required that something must drive the planets in their motions. If concentric spheres of quintessence did not, what could this be? For a while, we believed space might be full of a kind of fluid which moved in vortices which propelled the planets like clockwork. This explanation was unexpectedly successful for decades precisely because it did not require belief in occult forces—which is to say, it didn’t require something invisible to reach magically over distances and cause a thing to happen without touching it. It pushed instead of pulled.

Newton had looked at the apple and realized nothing had pushed it to the ground. It seemed to have fallen of its own accord. Newton then extrapolated this idea out beyond the garden into the stars. Once he did, a compact set of laws allowed him to explain all the motions of the heavens very tidily. His explanation, eventually known as the Principia, laid the groundwork for fundamental physics for centuries to come. It was a feat on par with Euclid’s Elements and fully completed the Scientific Revolution which Galileo had inaugurated.

## From Hypotheses to Theories

In the second edition of the Principia, Newton tacked on some notes by popular demand. In this General Scholium, he explained that he was in no position to explain what gravity could tangibly be. Famously, he said, “Hypotheses non fingo” (“I do not feign hypotheses [of what gravity could be]”). He described nature as he found it, and the explanation worked. That’s how the matter lay for centuries.

One problem is that, over time, we observed that Newton’s explanations were not perfect after all. There were subtle but galling errors which cropped up in very rare circumstances (such as predicting where Mercury would be over time). Another problem was more metaphysical—Newton’s laws only explained how gravity worked, not what it was.

Einstein solved both problems in a single stroke with general relativity. His theory of general relativity followed in the decade after special relativity as a consequence of the latter. The general theory extended the special one to more situations and provided a more fundamental explanation of universal phenomena, particularly gravity.

## Equivalence All the Way Down

If you’ve made it this far, you’ve read how energy is an impetus to change over time. Motion can be a form of energy because it can impart motion on another object, accelerating it. Energy is also equivalent to mass, and mass to energy—even at rest. Finally, you’ve seen how motion itself changes energy, space, and time relative to someone observing the motion.

Now we add a new equivalence—one so incredible in its implications that Einstein called it his “happiest thought.” It’s now simply known as the equivalence principle, special enough to stand alone by that name. It states that it’s impossible to distinguish between acceleration and gravity in any real, physical way.

That is to say, if you were trapped in some enclosed box and unable to see outside, you could not devise any instrument which would be able to tell you whether that box were accelerating in some direction steadily (and therefore drawing you toward the floor) or within a gravitational field (which would accomplish the same effect). Therefore, experiencing acceleration is equivalent to experiencing a gravitational field.

Einstein realized this in November 1907. From that point, he realized that energy, mass, space, time, and gravity were all inseparably linked, and he spent the next several years feverishly working toward a general theory of relativity to explain how it all works. The explanation he came up with in 1915 works so well that its predictive power overturned Newton and has held up even to this day.

## Motion in a Bottle

As a result of special relativity, we saw that motion warps space and time. We also know that motion relative to an observer represents kinetic energy, which is equivalent to any other form of energy. Finally, we know that energy is equivalent to mass and vice versa. The final piece of the puzzle to put into place here is that, since motion—and therefore energy—warps time and space, so does mass.

Think of mass as bottled motion. Mass–energy equivalence lets us treat mass as energy which has congealed, more or less, into one place. As I said in the last essay, it’s not enough to think of mass and energy as distinct things sharing some properties—they are a single substance. Therefore, all the same properties and consequences which apply to one form also apply to the other. That means that all the warping effects which apply to energy—to motion—also apply to mass.

So mass warps time and space, but what does this actually mean in reality? The result is gravity! Gravity is an emergent consequence of how mass warps time and space, exactly the same way motion warps time and space due to special relativity. Gravity is in fact not a force reaching mysteriously across distances but instead a bending of space and time which changes the paths of objects traveling through that space and time, leading them inexorably closer to one another.

## The Conservative Appeal of Gravity

Let’s dispense with the tired bowling-ball-on-a-rubber-sheet imagery and talk about what that last paragraph actually means. We can begin with the classic assumptions about how objects behave. Newton’s laws state that objects in motion tend to stay in motion, or at rest, unless acted on. They also state that there’s always an opposite and equal reaction for every action.

These are, at their heart, conservation laws. For things to behave otherwise would mean creating or destroying energy. An action must impart an opposite and equal reaction, or energy would go missing. An object at rest must stay at rest, or energy would spontaneously appear. An object in motion must stay in motion, or energy would vanish.

In flat space, therefore, moving objects tend to stay the course in order to conserve energy. You can trace the line of how the object moves geometrically as a straight line. Now if we introduce a mass nearby, space and time contract and stretch, respectively, in the vicinity of that mass. The object’s path still needs to conserve energy, and in order to do so, the line we trace now curves closer to the mass. It appears as if the object “falls” inwards toward the mass—exactly as you’d expect from a gravitational field.

## Occult Forces and Fictitious Forces

We no longer need an “occult force” to explain the mechanism of gravity. General relativity—which geometrically describes space and time as it bends under the influence of mass and energy—provides the complete picture.

As it turns out, gravity is not a force at all in the ordinary sense. It only appears to exert a force in the way that a merry-go-round in motion appears to make a ball curve through the air when you throw it from one side to the other. Gravity plays a similar trick on us: we’re constantly on a path through time and space which, were it not for the gigantic rock beneath us, would cause us to curve inexorably toward the center of the Earth. Since the Earth itself interrupts our course, we press against it, and it against us, which imparts the force we’re familiar with.

## Making Waves

By uniting conservation laws and a handful of postulates, we can fully explain the substance and behavior of gravity. When we combine this knowledge with the speed limit of the universe, we see that even gravity takes time to travel, which means that changes in gravity take time to travel. This allows gravity to ripple across space and time. We’ll now be prepared to look at these waves in the next explainer.

## Five-minute Explainer: Why Is Mass Equivalent to Energy?

This essay continues from the previous one in this series, “Five-minute Explainer: Special Relativity.”

The most recognizable equation of the twentieth century equates mass to energy.

$$E = mc^2$$

Specifically, this equation relates a very small quantity of mass to a huge quantity of energy. Why should that be true? What does it imply?

It follows as a consequence of special relativity—one which emerged only after Einstein and his friends worked out the initial theory when they considered how energy is conserved.

## Energy: Always Transforming Yet Never Changing

The conservation of energy means that it is never created or destroyed; it only changes form. This cosmic bookkeeping of energy suggests that its different forms are in fact the same underlying phenomenon which is conserved in quantity through each transformation. We should look at this idea more closely, though.

What is energy? This is actually a hard question to answer in an univocal way, but we should adopt a definition useful for our purposes. I will describe energy as that quantitative property of an object which provides an impetus to change over time.

For example, kinetic energy is capable of accelerating an object. Chemical energy is capable of inducing a chemical reaction and changing one substance into another. Nuclear energy is capable of driving a nuclear reaction, thereby disassembling an atomic nucleus. All these forms of energy are equivalent in their respective quantities.

Being equivalent, they may endlessly transform from one form to another. Friction is an example of a phenomenon by which kinetic energy becomes heat energy. We can turn heat back into motion (assuming we could capture it with perfect efficiency, though we can’t) by using the heat to drive a turbine. We can turn the rotational motion of a turbine into electrical energy using induction, and we can transform that into light, sound, motion, magnetism, or heat all over again.

Everyday life relies on hundreds of examples of energy transformations. Even if we can’t capture and reuse energy with total efficiency, we always can always measure it and account for it. Since energy is always perfectly conserved, it makes sense to think of energy as a single phenomenon which changes form endlessly.

## Energy in Motion

Now we need to understand how special relativity agrees with conservation of energy. In our thought experiment for special relativity, we watched a train pass by at 30 kilometers per hour. Let’s revisit that train.

While the train is in motion, it has energy—kinetic energy—relative to an observer standing on the ground watching it pass. The faster the train goes, the more velocity it has, the more kinetic energy it acquires, and so on.

However, our observer standing on the ground has already noticed odd effects due to the cosmic bookkeeping which makes special relativity work. That train is getting shorter, and the time on the train is getting slower. Our thought experiment has significantly exaggerated the effects of special relativity because we’ve lowered the speed limit of the universe to 100 km/h. Otherwise, everything we see obeys the actual laws of physics.

Kinetic energy is only dependent on the mass and velocity of an object: as both increase, so does the kinetic energy. This fact remains true whether you consider special relativity or not. However, instead of being half the product of the mass and the square of the speed, as in classical mechanics, the kinetic energy instead tends toward infinity as we approach the speed limit in relativistic physics. As motion begins to warp time and space the closer we come to the speed limit, it must make similar adjustments to kinetic energy.

## Points of View in Collision

If kinetic energy didn’t consider the speed limit of the universe, energy would not be conserved properly. Stranger yet, these consequences affect not only energy but mass. We can show this with an example.

Imagine watching from the train as someone throws a ball at 100 km/h to us standing still on the ground watching the train pass at 30 km/h. The person who threw it—who is moving along at the same speed with the ball—doesn’t see anything out of the ordinary with the ball’s motion, energy, or momentum. It moves at 100 km/h relative to them because that’s the speed at which they threw it.

From our vantage point on the ground, we also see the ball arrive at 100 km/h because that’s the speed limit of the universe. The train has been moving at 30 km/h, and so the train imparted some kinetic energy onto the ball, even if the train could not in fact make the ball go any faster than the speed limit. Although the ball is stuck moving at the speed limit, it took some kinetic energy from the train regardless. We know this because the ball imparted an opposite and equal reaction to the train as it was thrown. This means the train lost some energy, and that energy has to go somewhere—so it went into the ball.

We catch the ball at 100 km/h, but the ball somehow has more kinetic energy—and more momentum—than it should because it was thrown from a 30 km/h train. We feel that additional energy in the impact when we catch it. It makes a louder thud in our catcher’s mitt, too. Yet it’s not going any faster than a 100 km/h ball thrown from the ground.

What could be happening here? Here’s more cosmic bookkeeping: since we know the ball cannot move any faster than 100 km/h in our thought experiment, some other quantity has to increase to make up the difference. We also know that kinetic energy relates velocity and mass to one another. The only two things which impart more energy to an impact is adding a heavier object or making it go faster. Therefore, if velocity must stay constant, then mass must increase as a result. We are forced to conclude that the energy imparted onto the ball has added to the mass content of the ball instead of the velocity.

The amount of mass added isn’t much, to be sure—just enough to make up the difference between one ball thrown at 100 km/h and another ball thrown at 130 km/h. Remember also that we’ve lowered the speed limit of our imaginary universe, which exaggerates all the effects. In reality, the speed limit is actually about 1,079,252,848.8 km/h, so differences in speed impart vanishingly tiny bits of mass because ordinary, everyday speeds are tiny in proportion to the universal speed limit, $$c$$. The difference in mass to “make up” the missing velocity is usually quite small.

Velocity isn’t the only quantity which “turns into” mass, due to the way energy transforms. All forms of energy are equivalent, so they all represent some amount of mass which can be quantified and calculated.

Once we take this idea to its logical conclusion, we hit upon the unavoidable consequence that the relationship works in reverse as well—that all forms of mass also are equivalent to energy and are quantifiable as such. Even mass at rest has some energy content, the amount of which grows as the mass is set into motion. Motion merely increases the mass–energy.

## The Implications of Mass–energy Equivalence

As we just worked out, the math works out such that any tiny bit of mass adds up to an enormous amount of energy, thanks to the fact that the speed of light is so fast. For this reason, it took us a very long time to notice or test this phenomenon.

For example, one kilogram is equivalent to almost ninety quadrillion joules of energy. That’s the same energy output as a twenty-one megaton bomb, or four-fifths the energy output of the 2004 Indian Ocean earthquake and tsunami. In the other direction, the output of a sixty-watt incandescent bulb over an hour—both its light and heat—weighs only 2.4 nanograms, or about the mass of thirty red blood cells.

Special relativity implies that mass and energy are in actuality a single underlying phenomenon, called mass–energy, which we encounter in two familiar forms. In other words, they’re not just similar on some level—they literally are the same thing. Consider, for example, that the Earth weighs approximately 2.38 billion metric tons more due just to the rotational energy of spinning than it would if we changed nothing at all except to cause it not to spin. To stop the world from spinning would be the equivalent of shedding over thirteen million blue whales of mass.

## Generalizing Relativity

From the seemingly contradictory postulates of the principle of relativity and the invariance of the speed of light, we have been able to learn new things about the very substance of the universe. If we add in one more principle, we generalize special relativity into a much broader and much more powerful theory which overturned Newton’s theory of gravity. I’ll cover that in the next five-minute explainer.

## 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.