When small cannot get any smaller, you enter the quantum world of quarks, photons and space-time foam. You're welcome to take a look at this indivisible side of nature, but just remember to leave your common sense at the door.
People as far back as the Greek philosopher Democritus believed that things were built up from irreducible pieces, which he called "atoms."
Isaac Newton himself thought that light was not a wave, but rather a collection of tiny "corpuscules."
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But physicists have only recently acquired tools with sufficient resolution to see nature's inherent graininess.
Here's a quick tour of the quantum underbelly of the things around us.
If you split a banana, and then split it again, and again, and again, you eventually get down to cells, molecules, atoms.
Each atom has a nucleus of protons and neutrons, with tiny electrons buzzing around. Both protons and neutrons contain three quarks.
But the dissection stops there: electrons and quarks are the smallest pieces of ordinary matter.
How small are they? The electron is sometimes said be a few femtometers across (about a trillionth of a hair's width), but this is misleading. Electrons and quarks are more like puffy clouds than rigid balls.
This puffiness is the result of unavoidable quantum uncertainty: You can't precisely know a particle's motion and position at the same time. If you try to hold a quark still, you would have almost no idea where it is.
Such slipperiness makes exact-size measurements meaningless.
Sea of Particles
Quarks of various flavors — up, down, strange, charm, top and bottom — may appear as pairs of quarks and anti-quarks.
Up, down and strange quarks are the most common. For instance, a charm quark may appear with its opposite, a charm anti-quark, in tow on what scientists view as a sea of quarks inside a proton.
A proton is not necessarily spherical, according to work done by Gerald Miller and Michael Frank of the University of Washington.
Depending on the angular momentum of quarks, a proton could be spherical or more like a doughnut, a pretzel or a peanut.
Miller says the variety of shapes is nearly limitless and depends on the momentum of the quarks and the angle between the spin of the quark and the spin of the proton.
If we turn our scalpel on light, we find that its seemingly continuous glow is actually composed of little bundles of energy called photons. Don't bother squinting your eyes to see them, though: a 100-watt bulb emits a billion trillion photons per second.
So was Newton right? Light is a particle, not a wave? The answer is yes and no.
Light acts like a wave when you do an experiment looking for a wave property (like scattering through a pinhole). It behaves like a particle if you test for a particle property (like colliding with electrons).
"You get what you ask for" is a common refrain in quantum physics.
Particle properties can be "quantized" as well. Probably the weirdest example is particle rotation (what is called spin), which, by the way, is nothing like how a planet or a top moves.
First of all, particles have only one rotation speed — they can't speed up or slow down.
And second, the axis of rotation depends on how you look at it.
In an experiment, one detector might report a particle's spin points north, while another detector might say east. And they'd both be right!
The force of gravity has largely resisted this quantum tomfoolery. But some physicists believe that Newton's apple fell from its tree thanks to gravitons — photon-like particles that carry the gravitational attraction.
Falling apples would not generate a lot of gravitons, but colliding black holes would.
Detectors are currently looking for signals from these distant collisions, though it may be many years before any evidence for gravitons is found.
In 1900, the father of quantum physics, Max Planck, solved a long-standing theoretical puzzle by assuming that the energy radiated by a warm body only came out in discrete chunks, called "quanta."
It is perhaps fitting that Planck also devised a set of units that mark the limit of our current quantum theory.
At distances less than the Planck length (10^-35 meters), the gravitational effects of particles become significant, and Einstein's general relativity must be rectified with the quantum paradigm.
Cosmologists describing the Big Bang have no clue what happened in the universe earlier than the Planck time (10^-44 seconds).
Hotter than the Planck temperature (10^32 degrees), the forces of nature are thought to all meld into one.
Even nothing acts strange at the smallest levels. The vacuum is presumably not really empty, but instead filled with "virtual" particles that constantly blink in and out of existence.
This virtual reality follows from a quantum rule that says probable events influence real outcomes.
More specifically, it is possible (though highly unlikely) for particles and anti-particles to pop out of nowhere and then quickly annihilate. Nobody ever sees this happen, but the sum of all this quantum probability is a real energy.
Space and time
The above vacuum energy is not constant: It seethes and fizzles with bubbles the size of the Planck length. This foam warps the fabric of space-time, blurring the answers to when and where.
Essentially, the underlying geometry of the world is not smooth.
Instead, there are "pixels" that cannot be further resolved. Particles do not move continuously, but instead make little quantum leaps from one pixel to the next.
Such quantized space-time, though not yet observed, is the endpoint of smallness, as well as the end of this tour.
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