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By Root 1170 0

atoms 2,500 years ago, no one could have accurately guessed what the true elementary components of matter would turn out to be. Some of the physical theories that apply at small distances are so counterintuitive that even the most creative and open-minded people would never have imagined them if experiments hadn’t forced scientists to accept their new and confounding premises. Once scientists of the last century had the technology to probe atomic scales, they found that the inner structure of matter repeatedly defied expectations. The pieces fit together in a way that is far more magical than anything we will see on a stage.

Any human being will have difficulty creating an accurate visual image of what’s going on at the minuscule scales that particle physicists study today. The elementary components that combine to form the stuff we recognize as matter are very different from what we access immediately through our senses. Those components operate according to unfamiliar physical laws. As scales decrease, matter seems to be governed by properties so different that they appear to be part of entirely different universes.

Many confusions in trying to comprehend this strange inner structure arise from lack of familiarity with the variety of ingredients that emerge at different scales and the range of sizes at which different theories most readily apply. We need to know what exists and to have a sense of the sizes and scales that different theories describe in order to fully understand the physical world.

Later on we will explore the different sizes relevant to space, the final frontier. This chapter first looks inward, starting with familiar scales and ending deep in the interior of matter—the other final frontier. From commonly encountered length scales to the innards of an atom (where quantum mechanics is essential) to the Planck scale (where gravity would be as powerful as the other known forces), we’ll explore what we know and how it all fits together. Let’s now take a tour of this remarkable inner landscape that enterprising physicists and others have deciphered over time.

SCALING THE UNIVERSE

Our journey begins at human scales—the ones we see and touch in our daily lives. It’s no coincidence that a meter—not one-millionth of a meter and not ten thousand meters—is, roughly speaking, the size of a person. It’s about twice the size of a baby and half the size of a fully grown man. It would be rather strange to find that the basic unit we use for common measurements was one-hundredth the size of the Milky Way or the length of an ant’s leg.

Nonetheless, a standard physical unit defined in terms of any particular human wouldn’t be all that useful since a measuring stick should be a length we all agree on and understand.25 So in 1791, the French Academy of Sciences established a standard. A meter was to be defined either as the length of a pendulum with a half period of one second or one ten-millionth of the length of the Earth’s meridian along a quadrant (that is the distance from the Equator to the North Pole).

Neither definition has much to do with us humans. The French were simply trying to find an objective measure that we could all agree on and be comfortable with. They converged on the latter choice of definition to avoid the uncertainties introduced by the slightly varying force of gravity over the surface of the Earth.

The definition was arbitrary. It was designed to make the measure of a meter precise and standard so that everyone could agree on what it was. But one ten-millionth was no coincidence. With the official French definition, a meter stick is something you can comfortably hold in your hands.

Most of us are better approximated by two meters, but none of us are 10, or even three meters in height. A meter is a human scale, and when objects are this size, we’re pretty comfortable with them—at least insofar as our ability to observe and interact with them (we’ll stay away from meter-long crocodiles). We know the rules of physics that apply since they are the ones we witness in our daily existence. Our intuition