Science’s ongoing quest to find the smallest possible objects remains tantalisingly incomplete, as physicist Prof Andy Parker explains.

Physics has a problem with small things. Or, to be more precise, with infinitely small things.

We imagine that we can move any distance we like, no matter how small.

This perception was exploited by Zeno in one of his famous paradoxes. Achilles could never actually get anywhere since the distance he would have to cover could be halved an infinite number of times – halfway there, halfway again, and so on. He would have to take an infinite number of ever-smaller steps to reach his goal.

Mathematicians have explained this apparent paradox, and are completely comfortable with infinite numbers, as well as infinitely small distances and objects. Their answers are used in physics to describe the world inside the atom.

But nature is not so comfortable with this. When we try to describe something as a “point” – an infinitely small object, that throws up some of the most intractable problems in physics.

Since all of particle physics relies on “point-like” particles, reacting to forces in tiny spaces, one can anticipate trouble.

This duly appears in the form of nonsense answers when the equations are used at the smallest distances.

Physicists are therefore increasingly suspicious of points, and asking whether in fact Nature has a limit for the smallest possible object, or even whether there is a smallest possible space.

**Russian ****D****olls**

The quest for the smallest building blocks of Nature probably stretches back to the first caveman who tried to put a sharp edge on a flint.

The Greeks gave us the concept of billiard-ball shaped atoms which stick together to make up the materials we see, and this picture is still in most peoples’ minds today.

Over a century ago, JJ Thomson managed to extract electrons from atoms in Cambridge, and he was followed in 1932 by Cockcroft and Walton, who split the atomic nucleus with a cleverly designed particle accelerator.

These turned out to be only the first Russian Dolls.

Successive experiments, using more and more powerful accelerators, revealed that the nucleus was composed of protons and neutrons, and that they in turn were made of quarks.

The evidence for the Higgs boson recently produced at the Large Hadron Collider at Cern is the latest of these.

But all attempts to split quarks or electrons, even using the awesome power of the LHC have failed.

The basic building blocks seem to be points, certainly smaller than 0.0000000000000000001 metres across.

To infinity

One can see where the problem comes from. All the forces in nature get stronger at short distances.

Newton’s famous “inverse-square law” of gravity, for example, says that the force of gravity gets four times stronger if you halve your distance from an object.

If we imagine particles as points, you can make the distance between two of them as small as you like, so the force becomes infinite. Ultimately this would break up the fabric of space, creating a foam of black holes. That would certainly slow Achilles down!

Physicists can normally sidestep this problem, using the fuzziness built into quantum mechanics which allows matter to behave as particles or waves.

You may also have heard of Heisenberg’s Uncertainty Principle which does not allow us to know exactly where anything is. So even though a particle might be a point, its location is uncertain, and in the equations it looks like a fuzzy ball – problem solved!

Well almost – we don’t actually know how to apply quantum mechanics to gravity, and so we still get stuck with nonsensical predictions such as the complete collapse of space if we try to describe strong gravitational fields, like those inside black holes…..

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