Exploring the World of Short Distances: Feynman’s Insight

In Chapter 5 of the Feynman Lectures Richard Feynman takes us on a journey into the realm of small distances, showing how scientists probe the world beyond the limits of direct observation. His explanations are rich with analogies and imagery, making complex concepts more accessible. In this post, we’ll explore his key ideas, unpack his vivid examples, and add further details to bring these fundamental principles to life.

Breaking Down the Metre: From Millimetres to Microns

Feynman begins with a simple idea: subdividing a metre. Anyone can take a ruler and divide a metre into a thousand parts to get millimetres. With some effort and the aid of a microscope, we can go even smaller, dividing a millimetre into microns (micrometres, or 10^-6 metres). But here, a natural barrier arises—our eyes can’t resolve details smaller than about 5 x 10^-7 metres, the wavelength of visible light.

This is where Feynman’s imagery becomes striking: the limit of what we can “see” is set by the very waves that carry the image to our eyes. This constraint isn’t arbitrary—it’s a fundamental property of light itself. To go further, we need a different kind of “vision.”

Beyond Light: The Electron Microscope and X-Rays

When light’s wavelength is too large to reveal finer details, we turn to shorter-wavelength probes. Feynman mentions the electron microscope, which can resolve details down to 10^-8 metres, a scale where we begin to see individual molecules. But even this has limits.

At the atomic level, we rely on X-ray diffraction, a technique that uses the wave nature of X-rays to infer atomic positions. The method works much like triangulation: we shine X-rays on a crystal and analyse how they scatter, revealing atomic arrangements. This leads us to the fundamental building blocks of matter—atoms, with diameters of about 10^-10 metres.

To put this in perspective, imagine shrinking the Earth to the size of a marble. In this shrunken world, an atom would still be smaller than a grain of sand.

The Vast Gap: Atoms vs. Nuclei

At this point, Feynman highlights a fascinating fact: there is a huge size gap between atoms and their nuclei. While atoms are around 10^-10 metres in diameter, their nuclei are about 10^-15 metres—100,000 times smaller! This is a staggering difference, akin to comparing the size of a football stadium to a marble at its centre.

To measure nuclear sizes, Feynman introduces the concept of cross-sections. He paints a picture of a beam of high-energy particles fired at a thin slab of material. These particles zoom past the surrounding electrons, only interacting if they hit the dense nucleus. By counting how many particles pass through versus how many are deflected, we can estimate nuclear sizes. This method has revealed that nuclei range from 1 to 6 femtometres (10^-15 metres), or “fermis”, named after the physicist Enrico Fermi.

Can We Go Even Smaller?

At this point, Feynman asks a profound question: is there a fundamental limit to how small we can measure? We don’t yet have a definite answer, but he hints at deep unresolved mysteries in nuclear forces. Perhaps, at these extreme scales, our very ideas of space and measurement need revision.

He also touches on an important historical debate: should we define length using a natural reference, like the Earth’s size? The metre was originally defined as a fraction of the Earth’s circumference but was later redefined using a platinum bar in France. Even this was found imprecise, leading to today’s definition: a fixed number of wavelengths of a particular light emission.

This evolution shows that measurement itself is a human construct, one that changes as our scientific understanding advances.

The Fundamental Limits of Measurement

Feynman closes with one of the most profound principles in physics: measurement has limits imposed by nature itself. He refers to Heisenberg’s Uncertainty Principle, which states that if we try to pinpoint an object’s position, we lose precision in its momentum. Likewise, time measurements obey a similar uncertainty:

This implies that if we want to measure an event’s timing precisely, we must sacrifice certainty about its energy.

These principles aren’t just mathematical curiosities—they reveal the fundamental wave-like nature of matter. The world isn’t made of tiny, precise points, but rather of probabilities and waves that blur when we probe too closely.

Final Thoughts

Feynman’s discussion of short distances is a masterclass in scientific storytelling. He takes us from the visible world of millimetres and microns to the unseen realm of atoms, nuclei, and beyond. He builds up each concept carefully, using relatable examples, analogies, and vivid imagery.

But the most fascinating takeaway is this: as we dive deeper into the subatomic world, we encounter not just smaller things, but new rules of reality itself. The limits of measurement, the wave nature of particles, and the mysterious forces inside nuclei suggest that at some point, our classical understanding of “space” may no longer apply.

Perhaps, as Feynman hints, solving the mysteries of nuclear forces will require a completely new way of thinking about space and time. And that’s an exciting idea indeed.