Planet of Giants

We have been reduced roughly to the size of an inch.

Atoms are mostly empty space. We’ve known this since 1909, when Ernest Rutherford’s researchers Hans Geiger and Ernest Marsden fired alpha particles at gold foil in an attempt to probe the structure of the atom. To their surprise, most of them went straight through. To their even greater surprise, a few of them bounced straight back. This led in short order to the basic model of the atom that we still use today: a tiny, positively charged nucleus containing almost all the atom’s mass, orbited by negatively charged electrons.

It’s this structure of the atom that makes things the size they are. The direction of the electric force between two charged particles depends on whether the charges are of the same sign, or opposite signs. If they are opposite, the force attracts the particles together: if they are the same, the force pushes them apart. Whether the force is attractive or repulsive, it increases the closer the particles get to one another. So the harder you try to push two electrons together, the more strongly they will try to push each other apart again.

Since the outside of the atom is made of electrons, the same thing happens as you try to push atoms together. And that’s what determines the size of objects in the world around us: the balance between the forces that keep atoms together, and the forces that push them apart.

If you’re going to shrink something, then, you have to change that balance. The obvious way is to simply squeeze the atoms closer together, applying enough pressure to overcome the repulsive electric force between the electrons. That’ll work, provided you don’t mind squishing whatever you’re trying to shrink.

If you want to shrink a person, and not turn them into a compressed pellet of dense goo, you’re going to have to be a bit more sophisticated. Instead of increasing the force pushing the atoms together, you could try to reduce the repulsive electric force, making the atoms naturally huddle up closer to each other.

The strength of the electric force depends on a physical constant called the permittivity of free space, usually labelled ε0 (epsilon-nought). The permittivity of a material is a number that tells you how it is affected by an electric field, and ε0 tells you the same thing about space itself. The higher ε0, the lower the force between charges. So, make ε0 bigger, electric fields get weaker, and atoms sit closer together. Shrinking accomplished!

Except… how exactly do you increase ε0? OK, use some mysterious property of the Tardis, fair enough, but what actually would have to be happening?

Well, the reason why ε0 is the size it is, the reason why space even has this property of permittivity at all, is still not entirely understood, but it probably goes something like this. In a normal material, made up of protons and electrons, an electric field makes these particles line up to a greater or lesser extent. Every material has its own molecular structure, its own configuration of protons and electrons, and this determines its permittivity. Empty space doesn’t have protons and electrons in it – that’s why it’s called empty space – but it does have something altogether stranger.

According to the theory of quantum fields, particles can pop in and out of existence for microscopic fractions of time. How long these virtual particles can exist for is governed by Planck’s constant, which is a very small number indeed – and that’s why we’re generally unaware of it happening. But it does mean that what we think of as empty space is in fact a boiling sea of virtual particles, appearing and disappearing in the blink of a quantum eye.

When an electric field passes through some part of empty space, these virtual particles line up with it just like the protons and electrons in a real material. If you want to increase the permittivity of free space, you need to have fewer virtual particles about – and that means reducing Planck’s constant.

So there you have it. Something goes wrong with the Tardis, it somehow reduces Planck’s constant in the bodies and clothes of our time travellers, and everybody shrinks. Job done.

Except… there are some complications. Mucking about with these constants doesn’t just bring atoms closer together. It also changes a lot of other things, including the energy levels of the electrons within the atoms. All of chemistry, and therefore all of biology, is determined by these energy levels. Change these, and you screw up every single process within our bodies. The consequences would at least be mercifully brief.

But let’s say you somehow manage to do this in such a way that everything still works, albeit in a miniaturised form. You still have problems. Breathing, for a start. The oxygen atoms in the air will be much too big for the now-miniaturised alveoli in the lungs, which allow the oxygen to pass into the blood. Seeing will be interesting, too. The light receptors in the eyes will now respond to much shorter wavelengths. For a shrinkage factor of 100, which would roughly shrink an adult down to about an inch, the eyes would see, not visible light, but X-rays. This would be pretty cool, except that there are not many X-rays around at the surface of the Earth – the X-rays from the Sun being absorbed by the atmosphere, which is just as well otherwise we’d all die – and so it would be like wandering about in the dark all the time.

And, even more fundamental and even more inescapable that all of these, there is the matter of weight. Pushing all these atoms together doesn’t change their mass. A person who weighs 70 kg normally will still weigh 70 kg after shrinking. Four such people standing on a table would make it collapse, and crossing soft ground would be impossible as every step would just sink deep into the earth.

All in all, this notion of shrinking people by bringing their atoms closer together doesn’t seem all that clever after all. What happens if we take some of the atoms away instead?

Certainly, removing 99 atoms out of every hundred would shrink a person. But you’d have to be a bit careful about it. Removing atoms blindly would end up destroying the delicate internal machinery of the body’s cells, with fatal consequences. The only way this approach might work is if you take away 99% of each type of cell, like shrinking a wall by removing some of the bricks. The bricks will still work and the wall will still stand, just a little shorter.

Bodies, however, are more complicated than walls. I dare say a length of bone or gut might more or less continue to function with 99% fewer cells. Even the retina might be OK, although the shrunken eyeball will not be able to focus, so one way or another the person ends up blind. But what about the brain? The complex connections between neurons are the basis of all our thoughts and memories, not to mention the unconscious processes that keep our bodies working. Remove 99% of these cells, and you destroy virtually all of the brain, right down to the basic functions that regulate breathing and circulation.

And even if all these problems could be overcome, these is still this fundamental issue of mass. It can’t just vanish – the conservation laws won’t allow it. And evidently it doesn’t just hang around, or our miniature heroes would find themselves drowning in great puddles of organic goo. No, the only way to get rid of mass entirely is to convert it to energy.

How much energy? That’s easy to calculate. Einstein’s famous equation E=mc2 tells us that mass and energy can be turned into one another, with the conversion factor given by the speed of light squared. This factor of c2 works out at just over 20 megatons per kilogram. Shrinking a 70 kg person, therefore, releases just over 1400 megatons of energy. The whole Tardis crew probably amounts to roughly 250 kg, so that’s an energy release of 5000 megatons. (Let’s not even try to figure out the numbers for the Tardis.) This is nearly ten times the size of the entire US nuclear arsenal, and a hundred times greater than Tsar Bomba, the largest bomb ever detonated.

To get an idea of what would happen if all this energy were released in, say, London, we can use one of my favourite web apps: Alex Wellerstein’s NUKEMAP.

DIagram showing blast and heat radii from 5000 MT explosion in London

Blast and heat radii from 5000 MT explosion in London. (Plotted with NUKEMAP.)

The fireball stretches from Croydon to Edgeware. Buildings from Dover to Coventry are blasted to rubble. And everything from Newcastle to Paris is on fire.

Admittedly, this is a crude model. The nukemap is designed to deal with man-made nuclear weapons, and doesn’t necessarily scale up accurately to such colossal power. It also doesn’t take into account the curvature of the Earth, which would be significant on this scale. Finally, using this model means assuming that the energy is released all at once. Just as loose gunpowder will burn rather than explode, a more gradual energy release would not create such a gargantuan blast. However, it would still dump the same amount of heat into a very small volume of the atmosphere, so the firestorm effects at least would be broadly similar. It certainly puts the environmental threat from Forrester’s dastardly insecticide plot into perspective.

So, to conclude, there doesn’t seem to be any way to make miniaturisation work. The best case scenario has the miniature person blindly choking to death in seconds. The worst case scenario incinerates half of Britain. Perhaps it’s best if we never speak of this again.