“One creates from nothing. If you try to create from something you’re just changing something. So in order to create something you first have to be able to create nothing.” -Werner Erhard
One of the oldest adages in existence is you can’t get something for nothing, as over a million websites will tell you, including not-so-subtly, cartoonstock.
And, most often when people bring this up to me, it’s in an attempt to prove the existence of God — and the insufficiency of the Big Bang — by pointing to the Universe.
Well, let’s take this question as seriously as our knowledge allows us to. (And by that, I mean physically, rather than philosophically or theologically.) In physics, can you get something for nothing? And if so, what can you and can’t you get?
In many ways, yes, you can. In fact, in many ways, getting something when you have nothing is unavoidable! (Although you can’t necessarily get anything you want.)
For example, take a box and empty it, so that all you’ve got is some totally empty space, like above. An ideal, perfect, empty vacuum. Now, what’s in that box?
Did you guess nothing? Well, it turns out that empty space isn’t so empty.
One of the consequences of Heisenberg’s Uncertainty Principle — that you can’t know a quantum state’s energy exactly for a finite duration of time — means that when you’re talking about very short time intervals, there are large uncertainties in the energy of a system. Over short enough timescales, the energies are large enough that particle-antiparticle pairs wink in-and-out of existence all the time!
“That’s crazy talk,” you say. Prove it!
And they did.
Take two identical, uncharged, parallel metal plates, and put them close to one another. The vacuum fluctuations in between the plates cause there to be a pressure pushing the plates together. This isn’t the gravitational force or an electromagnetic force, but a force due to empty space itself.
This experiment — first done in 1948 but repeated many times (under many conditions) — was a rousing success, and has many immediate, far-reaching and fantastic consequences.
Black holes decay!
The space near a black hole is, of course, filled with these particle-antiparticle pairs, just like space everywhere else. But create a pair close to the event horizon, and one of the two can fall in! The other one, being outside the event horizon, can escape, carrying energy away, and becoming real. These particles that escape are known as Hawking radiation.
They provide the seeds for all the structure in our Universe!
When the Universe inflates, or expands exponentially (before the Big Bang), these quantum fluctuations also expand, and get stretched across the Universe faster than they can annihilate one another. These fluctuations show up as regions with slightly more (for positive fluctuations) or less (for negative ones) energy, which then grow into structure (like clusters, galaxies, and stars) and voids as the Universe ages.
And if you start with enough energy, you can take all of the real matter and antimatter pairs that exist, and create more matter than antimatter, giving us a Universe where we have something, today, rather than nothing.
Now, that’s what we know we can get, even from nothing. But there are many things we can’t do, either practically or theoretically: violate charge or energy conservation, decrease the total entropy of the Universe, or figure out where our initially inflating Universe came from. (Yet!) But we definitely can get something for nothing; quantum field theory not only allows it, it demands it. But it remains to be seen whether we can get everything for nothing. If we ever figure it out, I’ll make sure you’re among the first to know!