Recognizing that it’s no easy task to pin down the essential features of science, let’s return to the story at hand. In Lecture Two we saw how a piece of Einstein’s general theory of relativity became a striking and inspiring case study of successful science for figures like Popper. This time, we rewind further, to Einstein’s special theory of relativity, first published in 1905 when Einstein was only 26.
This was a revolutionary advance in physics, though here we’re more interested in the philosophical impact—which is just as significant. The term “special” doesn’t mean “especially brilliant,” but rather “a special case of relativity.” Special relativity applies to constant-velocity motion, where objects move without forces that accelerate or redirect them. I’ll occasionally call this “inertial motion.” The general theory of relativity, by contrast, applies to all motion—accelerated as well as uniform—and so in a sense is the “grander” of the two. For our purposes, though, sticking with the simpler special theory will do.
An important historical note: many of the concepts most often attributed to Einstein weren’t originally his. His genius lay less in inventing the raw pieces of the theory than in weaving them together into a consistent framework, which was the truly difficult part.
We already know that inertial motion—motion at constant speed in a straight line—can only be described relative to some chosen frame of reference. Galileo argued this in the early 1600s: a ball rolls the same way on land as it does on a ship gliding steadily across calm waters. Clearly this was a thought experiment, since no ship actually sails in a perfectly uniform way, but his insight holds. You can sense when a ship speeds up or turns; but with the windows closed, there’s no experiment you can run that tells you whether you’re stationary or coasting smoothly forward. This idea came to be called the “principle of Galilean relativity.”
Since mechanical laws don’t distinguish between one state of steady motion and another, we might as well treat any inertial state as if it were at rest. In this sense, Einstein didn’t invent relativity—he extended and generalized Galileo’s principle.
Put differently: suppose you and I drift past one another in deep space. Neither of us can determine who is “truly” moving. All we can say is how each of us moves relative to the other. The natural temptation is to conclude that the question “which one is really in motion?” has no real meaning—at least no empirical meaning, since no test could answer it. But the situation is a little trickier than that. Other parts of physics—notably electromagnetism and light—seemed to suggest there might be some way to define “absolute” motion.
Here’s why: James Clerk Maxwell, the 19th-century Scottish physicist, had shown that light behaves like an electromagnetic wave. At the time, waves were assumed to require a medium—like water for ocean waves or air for sound. The medium for light was thought to be the “aether,” through which light rippled as sound ripples through air.
Think of sound in water. If you’re still with respect to the water, you’ll record the same speed of sound in every direction. But if you swim through the water, the sound’s measured speed will vary: it will seem faster if you’re heading toward the wave, slower if you’re moving away. The same logic applies to catching or fleeing from a thrown baseball: relative to you, its speed depends on your own motion.
Notice the trick—we’re talking about how things appear to you as the moving observer, not about the “true” underlying motion.
By the same reasoning, light should act this way too. If the Earth is plowing through the aether at a steady pace, then measurements of light’s speed should vary depending on the direction. In one direction, Earth would be “chasing” the light, so the light should seem slower; in the opposite direction, Earth would be moving away, so the light should seem faster.
Now, it wasn’t obvious that moving relative to the aether was identical to moving relative to space itself, but since the aether was thought to permeate everything, it looked like a natural candidate for an absolute frame of reference.
Here’s the kicker: experimenters repeatedly tried to detect Earth’s motion through the aether, but no matter what point in Earth’s orbit they measured from, they always got the same answer—the same speed of light. This was baffling. It was as if a baseball always approached you at the same speed whether you ran toward it or away from it.
Einstein didn’t discover this puzzling constancy of light speed—it had already been observed in experiments and predicted in Maxwell’s theory decades earlier. What Einstein did was far more daring: he accepted the experimental results at face value and sought a way to reconcile them with relativity.
This set up a genuine puzzle: on the one hand, relativity tells us that all steady motion is relative; on the other, light insists on traveling at a fixed speed no matter who’s moving. At first glance, those two principles flatly contradict each other.
Let’s spell it out. Galilean relativity says that to speak of motion you must reference some frame—“I’m going 55 miles per hour relative to the highway.” But light, in a vacuum, is said to move at about 670 million miles per hour, and that’s not relative to anything. Even if you were to chase after a beam of light at tremendous speed, the light would still recede from you at exactly 670 million miles per hour.
So it looked as though one of the principles had to be false. Nearly everyone assumed the culprit was the claim that light’s speed is constant regardless of the observer. But those stubborn experimental results wouldn’t vanish.
Scientists, unwilling to abandon the older framework, resorted to some desperate patches. One suggestion was that Earth dragged along a bubble of aether around it, meaning that locally we were always at rest with respect to the medium. Another, even more radical, was that instruments themselves were altered by motion: measuring rods shrank and clocks slowed whenever Earth moved through the aether.
That sounds bizarre, though it wasn’t entirely implausible within 19th-century physics. If electromagnetic forces held matter together, and those forces propagated through the aether, then perhaps motion through the medium distorted objects. Still, this “explanation” was a stretch: it said the speed of light really did vary, but conveniently, all our measuring tools were distorted in just the right way to hide it from us.
Einstein’s leap was to stop fighting the evidence. He accepted the data as it stood. Instead of assuming the contradiction was real, he asked whether the contradiction only appeared because we were holding on to unexamined assumptions about space and time.
The first step was to broaden the principle of relativity. Galileo had said that no mechanical experiment could reveal whether you were at rest or moving steadily. Einstein extended that: no experiment of any kind—mechanical, electromagnetic, or otherwise—can distinguish one uniform motion from another. And light, like Newton’s laws, obeys this principle.
But this reconciliation came with radical consequences. Different observers, moving relative to one another, would inevitably disagree about fundamental things: whether one event happened before another, or how long an event lasted.
To dramatize this, let’s borrow a thought experiment from physicist Brian Greene. Imagine two presidents, Enginefacer and Caboosefacer, about to sign a treaty. To ensure fairness, they sit equidistant from a light bulb in the middle of a train car, which is rolling at constant velocity across the border between their nations. When the car’s midpoint passes the border, the bulb flashes. Each president, upon seeing the flash, immediately signs. From their perspective inside the train, both sign simultaneously.
But observers standing on the platform see something different. To them, Enginefacer is moving toward the flash while Caboosefacer is moving away. Since light travels at the same speed in both directions, the beam reaches Enginefacer first. Thus, from the platform’s frame, Enginefacer signs earlier.
So which is right? The train observers or the platform observers? The astonishing answer is: both. Each perspective is correct within its own frame. The question “which signing came first?” has no answer until a frame of reference is specified.
This leads to equally strange results for time. If you and I are gliding past each other, my measurements will tell me that your clock runs slow, while you will say the same about mine. It feels impossible—surely both clocks can’t be slower than the other—but that impossibility rests on the pre-relativistic assumption that there’s a single, absolute timeline. Einstein showed that assumption was the mistake.
The same logic applies to space. To me, your meter stick looks contracted; to you, mine does. In our own frames, though, each appears normal.
Let’s look at another well-known illustration. Imagine we measure a barn and a pole at rest, side by side, and confirm they’re exactly the same length. Now picture someone sprinting at seven-tenths the speed of light, carrying the pole through the barn. From our vantage point at the barn, the pole appears shortened, so it seems both barn doors could close with the pole inside.
But from the runner’s perspective, things are reversed: the barn is what has contracted, not the pole, so the barn is too short to ever contain it.
So what actually happens? Both, depending on the frame. We see the doors close around the runner; the runner sees the back door still open and the pole sticking out before the front door shuts. At first this looks contradictory, but the tension vanishes if you calculate when light signals, traveling at their maximum speed, reach each observer from the critical points (the ends of the pole and the barn doors). Once you factor in the travel time of those signals, the apparent paradox dissolves.
Of course, nobody has ever run through a barn at relativistic speeds. But experiments with subatomic particles confirm the strange consequences of special relativity. Muons, for instance, normally decay very quickly. Yet when accelerated close to the speed of light, they “live” about ten times longer, because from our perspective, their clocks slow dramatically.
For us, the exact physics isn’t the main concern. What matters is the conceptual shock: physicists had assumed they knew what they meant by words like “simultaneous” or “length.” Einstein forced a reconsideration: those concepts only make sense when tied to the procedures of measurement and observation.
That realization profoundly shaped both science and philosophy. For decades, much of the debate revolved around how to connect scientific concepts securely to experience.
One of the first to push this idea was not a professional philosopher but a Nobel-winning physicist, P. W. Bridgman. Drawing inspiration from special relativity, he argued that the lesson was conceptual: never again should abstract ideas blind us to what experiments reveal.
Scientists had overlooked the constancy of light’s speed because their theories got in the way. Einstein succeeded by working through the implications of the data instead of forcing the data to match old assumptions. Bridgman’s response was a new view called operationalism.
According to operationalism, every scientific concept must be defined in terms of the operations used to measure or detect it. Take “length”: instead of defining it philosophically as “the amount of space something occupies,” Bridgman says it just is the procedure of laying a meter stick along an object and recording the number. If the object is longer than the stick, you move the stick and keep counting. The operation itself provides the meaning.
His idea was that if we had insisted on defining simultaneity operationally, we would never have been surprised by relativity. Since no signal can travel faster than light, observers moving relative to one another cannot agree on whether distant events happened at the same time. If we had tied the concept directly to measurement, the relativity of simultaneity would have been obvious instead of shocking.
Let’s see how operationalism works when applied more broadly. Strictly interpreted, each measurement procedure defines a distinct concept. For example, “temperature as read by an alcohol thermometer” is technically different from “temperature as read by a mercury thermometer.” If we swap instruments, we’ve switched the operation—and therefore the meaning.
At first glance that sounds manageable, but problems appear quickly. How finely do we draw the line between operations? Does “testing acidity with blue litmus paper while wearing a lab coat” count as the same operation as “testing acidity with blue litmus paper while wearing overalls”? They differ in one respect, however trivial. Bridgman might say in principle we should count these as separate, though in practice we don’t bother. But even if we ignore such trivialities, the challenge remains: how exactly should operations be individuated?
Another issue is that operational definitions can’t regress forever. Eventually, they must bottom out in basic, unanalyzed acts—like “look at the scale and write down the number.” At some stage, scientists must assume certain observations are immediate and unproblematic. Bridgman accepted this, but it sets him apart from philosophers like Karl Popper, who denied that there is a privileged layer of “pure” observation immune from further critique.
Even with these difficulties, operationalism proved highly influential in the early 20th century. In psychology especially, it shaped practice: diagnosing “depression,” for some schools of thought, simply meant scoring below a threshold on a particular test. No extra meaning was allowed beyond the operational definition. The appeal was clear—psychology is complicated, so tying concepts to standardized procedures ensured consistency.
But most philosophers now view operationalism as too restrictive. If every concept must be fully defined by a single measuring operation, science either loses important meanings or cheats by smuggling them back in. Bridgman’s view risked crippling inquiry.
Take “weight” as measured with a pan balance. If the pans balance, the objects weigh the same; if one side falls, that side is heavier. Straightforward enough—except this presumes no hidden forces are interfering. But how do we operationally guarantee that? We could add steps: check for someone pressing on the scale, test for magnetic fields, and so on. Yet the list of possible disturbances is endless. Clearly, our notion of weight isn’t reducible to just the pan balance’s behavior—we assume the balance is tracking something real, not defining it.
The same holds for thermometers. We assume that alcohol and mercury thermometers measure the same property. We even talk about temperatures too small for current instruments to detect. That confidence shows we treat “temperature” as something out there, not something created by the act of measurement.
Here’s another example: a thermometer plunged into the sun would explode, killing the observer. Yet we still believe the sun has a temperature, and we seek instruments capable of measuring it. That assumes an independent concept of temperature—one not reducible to current operational methods.
And this, ironically, is what operationalism was meant to eliminate. Einstein’s revolution had warned against sneaking in extra meaning beyond measurement. Bridgman took that warning seriously, but his solution proved too rigid.
Still, his operationalist call made an important contribution: it reminded scientists to anchor their terms in measurable practice rather than abstract speculation. As we’ll see later, this idea has a long philosophical history, and thinkers had been grappling with these issues for centuries. What Einstein did was make them freshly urgent.
