Is fundamental science a victim of its own success?

Some 500 years ago, there was one scientific phenomenon that was, without controversy, extremely well-understood: the motion of the celestial objects in the sky. The Sun rose in the east and set in the west with a regular, 24 hour period. Its path in the sky rose higher and the days grew longer until the summer solstice, while its path was the lowest and shortest on the winter solstice. The stars exhibited that same 24 hour period, as though the heavenly canopy rotated throughout the night. The Moon migrated night-to-night relative to the other objects by about 12° as it changed its phases, while the planets wandered according to the geocentric rules of Ptolemy and, later, refinements put forth by others.

For over 1000 years, this Earth-centered view of our Universe went largely unchallenged, and became nearly universally accepted.

We often ask ourselves, “How was this possible?” How did this geocentric picture of the Universe hold up, without any of science’s greatest minds contesting it, for generation after generation for more than a millennium? There’s this common narrative that due to dogmatism, like the unchallengeable facts of Earth being stationary and the center of the Universe, no one was even allowed to question these so-called facts. But the truth is far more complex. The reason the geocentric model held sway for so long wasn’t because of the oft-ascribed problem of groupthink, but rather because the evidence supporting a geocentric Universe fit it so well: far better than any of the alternatives that had been put forth. The biggest enemy of progress isn’t groupthink at all, but the unrivaled successes of the leading, already-established theory. Today, although many complain about “groupthink” as a major problem in science, it’s actually the successes of our current picture of the Universe that present the greatest difficulties when searching for a scientific revolution.

This chart, from around 1660, shows the signs of the zodiac and a model of the solar system with Earth at the center. For decades or even centuries after Kepler clearly demonstrated that not only is the heliocentric model valid, but that planets move in ellipses around the Sun, many refused to accept it, instead hearkening back to the ancient idea of Ptolemy and geocentrism.

Although we normally consider Copernicus, and his 16th century treatise, the beginnings of heliocentrism, that’s not exactly true. It might not be a particularly well known fact, but the idea of a heliocentric Universe goes back (at least) over 2000 years. All the way back in the 3rd century BCE, the legendary scientist Archimedes published a book called The Sand Reckoner, where he begins contemplating the Universe beyond Earth. Although he isn’t quite convinced by an argument against geocentrism, he recounts the (now lost) work of his contemporary, Aristarchus of Samos, who put forth the following idea:

“His hypotheses are that the fixed stars and the sun remain unmoved, that the earth revolves about the sun on the circumference of a circle, the sun lying in the middle of the orbit, and that the sphere of the fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the earth to revolve bears such a proportion to the distance of the fixed stars as the center of the sphere bears to its surface.”

In other words, way back when the Great Wall of China was being built, Aristarchus proposed that the Sun and the stars were stationary, that the Earth revolves around the Sun, and that the stars are so distant that the Earth’s distance vs. the Sun’s size is about the same ratio as the distance to the star’s vs. the size of Earth’s orbit. (The latter ratio is actually about 580 greater than the former ratio.) The work of Aristarchus was recognized as having great importance: for two major reasons that, surprisingly, have nothing to do with the idea of heliocentrism.

The observed path that the Sun takes through the sky can be tracked, from solstice to solstice, using a pinhole camera. That lowest path is the winter solstice, where the Sun reverses course from dropping lower to rising higher with respect to the horizon, while the highest path corresponds to the summer solstice.

Why do the heavens appear to rotate? This was an enormous question of the time. When you look at the Sun, it appears to move through the sky in an arc each day, where the arc that’s observable from Earth is merely a fraction of a 360° circle: corresponding to an apparent motion for the Sun of about 15° each hour. The stars also move in precisely the same fashion: where the entire night sky seems to rotate about the Earth’s north or south pole (depending on your hemisphere) at that exact same rate, about 15° per hour. The planets and Moon do nearly the same thing, just with the tiny, extra addition of their nightly motion (~12° per night for the Moon; ~1° per night for a planet like Jupiter) relative to the background of stars.

The issue is that, based on these observations alone, there are two conceptual ways that are equally good at accounting for these observed motions.

1. The Earth is stationary, and the heavens (and everything in them) rotate about the Earth with a rotational period of 360° every 24 hours. Atop that, the Moon and planets have a slight, extra motion superimposed atop that: motion that could be accounted for by their additional motion through space.
2. The stars and other heavenly bodies are all stationary, while the Earth rotates about its axis, with a rotational period of 360° every 24 hours. And, in addition, the Moon and planets have a slight, extra motion superimposed atop that: motion that could be accounted for by their further motion through space.

If all we saw were the objects in the sky, either one of these explanations could fit the data perfectly well.

Satellites, planes, and comets transit across the night sky under stars that appear to rotate above Corfe Castle on August 12, 2016 in Corfe Castle, United Kingdom. The apparent motion of the objects in Earth’s sky could either be explained by the Earth rotating beneath our feet or by the heavens above rotating about a fixed Earth. Simply by watching the skies, we cannot tell these two explanations apart.

And yet, practically everyone in the ancient, classical, and medieval world went with the first explanation and not the second.

Why? Was this a case of dogmatic groupthink?

Hardly. There were two major objections that were raised even back in the ancient world to the second scenario: the scenario of a rotating Earth. Neither one of these objections was successfully addressed until much more modern times: during the Renaissance.

The first objection is that if you dropped a ball on a rotating Earth, it shouldn’t fall straight down from the perspective of someone standing on the Earth. Instead, the ball should fall straight down while the person on the Earth moved along with the (rotating) Earth: motion that should appear different from the straight-line motion of the falling ball. This was an objection that persisted through the time of Galileo, and was only resolved with an understanding of relative motion and the independent evolution of horizontal and vertical components for projectile motion. Today, these properties form the basis of what’s known as Galilean relativity.

The second objection was even more severe, though. If the Earth rotated about its axis every 24 hours, then your position in space would differ by the diameter of Earth — about 12,700 km (7,900 miles) — from the start of the night to the end of the night. That difference in position should result in what we know astronomically as parallax: the shifting of closer objects relative to the more distant ones.

The stars that are closest to Earth will appear to shift periodically with respect to the more distant stars as the Earth moves through space in orbit around the Sun. Before the heliocentric model was established, we weren’t looking for “shifts” with a ~300,000,000 kilometer baseline over the span of ~6 months, but rather a ~12,000 kilometer baseline over the span of one night: Earth’s diameter as it rotated on its axis. The distances to the stars are so great that it wasn’t until the 1830s that the first parallax, with a 300 million km baseline, was detected. Today, we’ve measured the parallax of over 1 billion stars with ESA’s Gaia mission.

If the stars were actual objects in space at great distances from Earth, then the closest ones should appear to exhibit this parallax relative to the more distant ones: after sunset, the closest stars should appear to shift by a small but noticeable amount relative to their positions just before sunrise. And yet, no matter how acute their vision was, nobody had ever observed a parallax for a single one of the thousands of stars visible in the sky. If they were at different distances and the Earth was rotating, we’d expect to see the closest ones shift position from the beginning of the night to the end of the night.

Despite this prediction, no parallax was ever observed for more than 1000 years: until the 1830s, in fact, well after the invention of the telescope. With no evidence for a rotating Earth right here on Earth’s surface, and no evidence for parallax (and hence, a rotating Earth) among the stars in the heavens, it became difficult to ascribe the apparent motions of the Sun, stars, and other heavenly objects by hypothesizing a rotating Earth. The data didn’t support that hypothesis, while the alternative explanation of a stationary Earth and a rotating sky — or a “celestial sphere” beyond Earth’s sky — wasn’t contradicted by any observables. For that reason, the “rotating celestial sphere” option emerged as the favored explanation.

This Foucault pendulum, on display in action at the Ciudad de las Artes y de las Ciencias de Valencia in Spain, rotates substantially over the course of a day, knocking down various pegs (shown on the floor) as it swings and the Earth rotates. This demonstration, which makes the rotation of the Earth very clear, was only concocted in the 19th century.

Were we wrong? In hindsight, we absolutely were.

The Earth does rotate, but we didn’t have the tools, knowledge, or the precision available to us in order to make quantitative predictions for what we’d expect to see. It turns out that the Earth does rotate, but the key experiment that allowed us to observe it on Earth, the Foucault pendulum, wasn’t developed until the 19th century. Similarly, the first parallax wasn’t seen until the 19th century either, owing to the fact that the distance to the stars is enormous, and it takes the Earth migrating by millions of kilometers over weeks and months, not thousands of kilometers over a few hours, for the best telescopes of the time to detect it. (The largest parallax for any star is for Alpha Centauri, whose maximum parallax is just 0.74 arc-seconds, or about 1/5000th of a degree.)

The problem was that we didn’t have the evidence at hand to tell these two predictions apart, and that we (incorrectly) conflated “absence of evidence” with “evidence of absence.” We couldn’t detect a parallax among the stars, which we expected for a rotating Earth, so we concluded that the Earth wasn’t rotating. We couldn’t detect an aberration in the motion of falling objects, so we concluded that the Earth wasn’t rotating. We must always keep in mind, in science, that the effect we’re looking for, that we haven’t seen yet, might actually be present: including at precisions that are just below the threshold of where we’re capable of measuring.

61 Cygni was the first star to have its parallax measured and published (back in 1838), but also is a difficult case due to its large proper motion. These two images, stacked in red and blue and taken almost exactly one year apart, show this binary star system’s fantastic speed. If you want to measure the parallax of an object to extreme accuracy, you’ll make your two ‘binocular’ measurements simultaneously, to avoid the effect of the star’s motion through the galaxy. Gaia is exceptionally good at characterizing the orbits of nearby stars with small separations from their companion, but faces more challenges with more distant, wider binary systems.

Still, Aristarchus was able to make important advances that did survive throughout the ages, and that were quite significant for his time. First off, he demonstrated that he wasn’t dogmatic about his own ideas, as he was able to set his heliocentric ideas aside: instead using light and geometry within a geocentric framework to concoct the first method for measuring the distances to the Sun and the Moon, and hence to also estimate their sizes. Although his values were way off — mostly due to “observing” a dubious effect now known to be beyond the limits of human vision — his methods were sound, and modern data can accurately leverage Aristarchus’s methods to calculate the distances to the Sun and the Moon, as well as the physical sizes of each one.

It wasn’t until the 16th century that there was revived interest in Aristarchus’s heliocentric ideas, as that’s when Nicolaus Copernicus came onto the scene. Copernicus noted that the most puzzling aspect of planetary motion, the periodic “retrograde” motion of the planets, could be equally well-explained from two perspectives.

1. Planets could orbit according to the geocentric model: where planets moved in a small circle that orbited along a large circle around the Earth, causing them to physically move “backward” at occasional points in their orbit.
2. Or planets could orbit according to the heliocentric model: where every planet orbited the Sun in a circle, and when an inner (faster-moving) planet overtook an outer (slower-moving) one, the observed planet appeared to change direction temporarily.

One of the great puzzles of the 1500s was how planets moved in an apparently retrograde fashion. This could either be explained through Ptolemy’s geocentric model (left), or Copernicus’ heliocentric one (right). However, getting the details right to arbitrary precision was something neither one could do. It would not be until Kepler’s notion of heliocentric, elliptical orbits, and the subsequent mechanism of gravitation proposed by Newton, that heliocentrism would triumph by scientific standards.

Why do the planets appear to make retrograde paths? This, then, became the key question for astronomers and those who studied Earth’s place in the Universe. Now, humanity had two potential explanations with vastly different perspectives, yet both were capable of producing the phenomenon that was observed. On the one hand, we had the old, prevailing, geocentric model, which accurately and precisely explained what we saw. On the other hand, we had the new, upstart (or resurrected, depending on your perspective), heliocentric model, which could also explain what we saw. At least, they could both qualitatively explain what was observed. But in science, it’s the best quantitative explanation, the one that accounts for “how much” of an effect we see, that will win out.

Unfortunately, the geocentric predictions in the 16th century were more accurate — with fewer and smaller observational discrepancies — than the heliocentric model’s predictions. Copernicus could not sufficiently reproduce the motions of the planets with a heliocentric system even as well as the geocentric model could, no matter which parameters he assigned to the various circular orbits of the planets. In fact, to remedy this, Copernicus even attempted to add in epicycles to the heliocentric model, seeking to improve the orbital fits. Even with this ad hoc fix, his heliocentric model, although it generated a renewed interest in the problem, did not perform as well as the geocentric model in practice.

Mars, like most planets, normally migrates very slowly across the sky in one predominant (known as prograde) direction. However, a little less than once a year, Mars will appear to slow down in its migration across the sky, stop, reverse directions, speed up and slow down, and then stop again, resuming its original motion. This retrograde (west-to-east) period stands in contrast to Mars’s normal prograde (east-to-west) motion, and presented a scientific challenge for centuries.

It wouldn’t be until the 17th century that the heliocentric model finally gained support and overthrew the geocentric model in a legendary scientific revolution. But why did it take so long? The reason it took close to 2000 years isn’t because of groupthink or a lack of imagination, but rather it took so long was because of how successful the geocentric model was at describing what we observed, and how poorly the alternatives fared in comparison. The positions of the heavenly bodies could be modeled exquisitely using the geocentric model, in a way that the heliocentric model could not reproduce.

It was only with the 17th century work of Johannes Kepler — who tossed out the Copernican assumption (that he himself once adhered to) that planetary orbits must be reliant on circles — that led to the heliocentric model finally overtaking the geocentric one. What was most remarkable about Kepler’s achievement wasn’t:

• that he used ellipses instead of circles,
• that he overcame the dogma or groupthink of his day,
• or that he actually put forth laws of planetary motion, rather than merely a model of it.

Instead, Kepler’s heliocentrism, with elliptical orbits, was so remarkable because, for the first time, an idea had come along that described the Universe, including the motion of the planets, better and more comprehensively than the previous (geocentric) model could.

Tycho Brahe conducted some of the best observations of Mars prior to the invention of the telescope, and Kepler’s work largely leveraged that data. Here, Brahe’s observations of Mars’s orbit, particularly during retrograde episodes, provided an exquisite confirmation of Kepler’s elliptical orbit theory. Kepler put forth his 1st and 2nd laws of planetary motion in 1609, with his 3rd law coming 10 years later: in 1619.

There are always three hallmarks of any scientific revolution, where a new theory comes along looking to supplant and replace the old one.

1. The new theory succeeds wherever the old theory did.
2. The new theory explains an observed phenomenon that the old theory couldn’t account for.
3. And the new theory, in comparison to the old theory, makes differing predictions that we can then go out and test.

In particular, the (highly eccentric) orbit of Mars, which was previously the biggest point of trouble for Ptolemy’s model, was an unequivocal success for Kepler’s ellipses. Under even the most stringent of conditions, where the geocentric model had its greatest departures from what was predicted, the heliocentric model had its greatest successes. That’s often the test case: look where the prevailing theory has the greatest difficulty, and try to find a new theory that not only succeeds where the prior one fails, but succeeds in every instance where the prior one also succeeds.

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Kepler’s laws paved the way for Newton’s law of universal gravitation, and his rules apply equally well to the Earth-moon system, to Jupiter’s and Saturn’s moons within the Solar System, and to the motions of planets of exoplanetary systems here in the 21st century. One can complain about the fact that it took some ~1800 years from Aristarchus until heliocentrism finally superseded our earlier geocentric notions, but the truth is that until Kepler and the advent of elliptical orbits, there was no heliocentric model that matched the data and observations as well as Ptolemy’s model did.

The Muon g-2 electromagnet at Fermilab, ready to receive a beam of muon particles. This experiment began in 2017 and continues to take data, having reduced the uncertainties in the experimental values significantly. Theoretically, we can compute the expected value perturbatively, through summing Feynman diagrams, getting a value that disagrees with the experimental results. The non-perturbative calculations, via Lattice QCD, seem to agree, however, deepening the puzzle of the muon’s anomalous magnetic moment.

In fact, it’s easy to envision a slightly different version of human history, where the geocentric model would hold sway for even longer periods of time. The only reason this scientific revolution occurred when it did is because there were already well-established “cracks” in the theory: places, such as for the orbit of Mars (and, to a lesser extent, Mercury) where observations and predictions failed to perfectly align. Whenever there’s a mismatch between what’s predicted and what’s measured, that’s where the opportunity for a new revolution may arise, but even that is not guaranteed. It leads to some fascinating questions that puzzle scientists even today.

• Are dark matter and dark energy real, or is this an opportunity for a revolution?
• Do the different measurements for the expansion rate of the Universe signal a problem with our techniques, or are they an early indication of potential new physics?
• What do non-zero neutrino masses indicate; a simple mixing, as in the case of quarks, or the first step toward a leap beyond the Standard Model?
• And what of the muon g-2 experiment? Is this a case where experiment differs from theory, or a case where we’ve simply made theoretical mistakes in our calculations?

It’s important to explore all possibilities, even the most wild ones, but to always ground ourselves in the reality of observations and measurements we can make. If we ever want to go beyond our current understanding, any alternative theory has to not only reproduce all of our present-day successes, but to succeed where our current theories cannot. That’s why scientists are often so resistant to new ideas: not because of groupthink, dogma, or inertia, but because most new ideas never clear even the first of those epic hurdles, and are inconsistent with the established data we already possess. Whenever the data clearly indicates that one theoretical alternative is superior to all the others, however, a scientific revolution is inevitably sure to follow.