## Monday, April 10, 2017

### Shrinkage - the physics of shrink rays

It's a trope that's appeared repeatedly in science fiction:  the shrink ray, a device that somehow takes ordinary matter and reduces it dramatically in physical size.  Famous examples include Fantastic Voyage, Honey I Shrunk the Kids, Innerspace, and Ant Man.  This particular post was inspired partly by my old friend Rob Kutner's comic series Shrinkage, where tiny nanotech-using aliens take over the mind of the (fictitious) President, with the aim of turning the world into a radioactive garden spot for themselves.  (Hey Rob - your critters thrive on radioactivity, yet if they're super small, they're probably really inefficient at capturing that radiation.  Whoops.)  Coincidentally, this week there was an announcement about a film option for Michael Crichton's last book, in which some exotic (that is to say, mumbo jumbo) "tensor field" is used to shrink people.

It's easy to enumerate many problematic issues that should arise in these kinds of stories:
• Do the actual atoms of the objects/people shrink?
• If so, even apart from how that's supposed to work, what do these people breathe?  (At least Ant Man has a helmet that could be hand-waved to shrink air molecules....)  Or eat/drink?
• What about biological scaling laws?
• If shrunken objects keep their mass, that means a lot of these movies don't work.  Think about that tank that Hank Pym carries on his keychain....  If they don't keep their mass, where does that leave the huge amounts of energy ($mc^2$) that would have to be accounted for?
• How can these people see if their eyes and all their cones/rods become much smaller than the wavelength of light?
• The dynamics of interacting with a surrounding fluid medium (air or water) are completely different for very small objects - a subject explored at length by Purcell in "Life at Low Reynolds Number".
The only attempt I've ever seen in science fiction to discuss some kind of real physics that would have to be at work in a shrink ray was in Isaac Asimov's novel Fantastic Voyage II.   One way to think about this is that the size of atoms is set by a competition between the electrostatic attraction between the electrons and the nucleus, and the puffiness forced by the uncertainty principle.  The typical size scale of an atom is given by the Bohr radius, $a_{0} \equiv (4 \pi \epsilon_{0} \hbar^{2})/(m_{\mathrm{e}}e^{2})$, where $m_{\mathrm{e}}$ is the mass of the electron, and e is the electronic charge.   Shrinking actual atoms would require rejiggering some fundamental natural constants.  For example, you could imagine shrinking atoms by cranking up the electronic charge (and hence the attractive force between the electron and the nucleus).  That would have all kids of other consequences, however - such as screwing up chemistry in a big way.

Of course, if we want to keep the appearances that we see in movies and TV, then somehow the colors of shrunken objects have to remain what they were at full size.   That would require the typical energy scale for optical transitions in atoms, for example, to remain unchanged.  That is, the Rydberg $\equiv m_{\mathrm{e}}e^4/(8 \epsilon_{0}^2 h^3 c)$ would have to stay constant.  Satisfying these constraints is very tough.  Asimov's book takes the idea that the shrink ray messes with Plank's constant, and I vaguely recall some discussion about altering c as well.

While shrinking rays (and their complement) are great fun in story-telling, they're much more in the realm of science fantasy than true science fiction....

Anonymous said...

Aw, man... and I was thinking this was al real ... :-)

Douglas Natelson said...

Anon, :-)
I do think it's fun sometimes to go through some sci-fi concepts and really play with what's possible or impossible about them. It can be a good exercise and can also expose gaps in our thinking. At the risk of angering the copyright gods, you might enjoy The theory and practice of teleportation, by Larry Niven.

Anonymous said...

Agreed! And I'll defy some gods :-)
Thanks for a nice variety of posts!