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Q: What exactly is the vacuum catastrophe and what effects does this have upon our understanding of the universe?

Physicist: The vacuum catastrophe is sometimes cited as the biggest disagreement between theory and experiment ever. They disagree by a factor of at least 10107.

According to quantum field theory the energy of empty space can’t quite be zero. In fact, QFT gives us an exact value for how much energy empty space should have. Although we can never access that energy, it does have a gravitational effect.

One of the (many) things the Voyager probes did was allow us to estimate how strong those gravitational effects are. Unfortunately, they determined that the theoretical predictions are way, way, way off (too high).

There’s a short paper here aimed at the undergraduate physics crowd that covers this better than I do.

It’s a catastrophe because QFT is otherwise a stunningly accurate theory (the most accurate ever, by far). But, at the end of the day, you have to fall back on observation, so something about our favorite theory is wrong.

One result of the Heisenberg Uncertainty Principle is that it’s impossible for a system to be in a zero-energy state. In a nutshell: if a particle definitely has zero energy, then it’s definitely not moving and its momentum is zero. However, to get that level of certainty you need the position to be completely uncertain and (for various reasons) that’s untenable. You can run through this mathematically, and you find that systems always have just a tiny bit more than zero energy, and that that energy is proportional to , where is the frequency of the particle/system in question. That little bit of energy is called the “ground state energy” or just “ground energy”.

The same thing applies to all particle fields, but rather than generalize, I’ll just talk about light: the electromagnetic (EM) field. It turns out that every frequency of the EM field, at every point in space, is its own tiny system (not at all obvious; that falls out of the math). As a result, instead of a tiny ground state energy for a single system, in any given region of space you have lots of systems. These form the ground state energy density, which is more commonly known as the “zero point energy”.

As a quick aside, a lot of people get very excited about zero point energy, but shouldn’t. Setting aside the fact that harvesting it would violate the Uncertainty Principle (which is set in stone pretty good), to generate usable energy you still need to drop things from high energy states to low energy states. For example, there’s a tremendous amount of potential energy to be gained by dropping all of the ocean’s water to the bottom of the ocean (a waterfall as tall as the ocean is deep would generate a lot of hydroelectric power). Of course, first we just need to pump all the water out. Then we can gain energy by pouring it all to the bottom (so, the net energy gain is at best zero).

Back to the point: So there’s a ground state energy for each frequency of light. Looking at all the frequencies up to you find that the ground state energy density is proportional to (again, not obvious).

But there are a lot of frequencies out there! As far as we know, there may be no upper limit, which would imply that the ground state energy is infinite. There are a lot of ad hoc estimates (that tend to be extremely high), based on the highest energy photons we can make with our accelerators, or the highest energy photons observed, or the highest energy photon it even makes sense to consider (if the frequency is too high, the wavelength is short enough that space gets “grainy”… sort of). All of these estimates maintain that the zero point energy is stupefyingly huge.

However, all energy and matter creates gravity, so you’d expect that all that extra stuff would affect how gravity works. Specifically, you’d expect the velocity of orbiting objects to all be about the same, regardless of the size of the orbit (still: not obvious). But, to the best of our ability to measure (which is pretty good), no effect has been seen at all in terms of the movement of stars and planets and whatnot.

So why not just abandon the whole zero point energy idea? Why not say: “it’s clearly not around, so let’s move on”? Because you can detect it! Curveball!

The electric field inside of a conductor is zero (in a super-conductor at least). This principle is responsible for things like the shininess of metal and Faraday cages. In between two conducting surfaces the electric field can only assume wavelengths shorter than the distance between the plates (and thus only frequencies above a certain cut-off), because the plates nail down the field by forcing it to be zero.

This is a little like saying you’d expect to find big, low-frequency, waves in the ocean, but not in a cup.

Since the region in between the conducting surfaces is missing all the “tiny systems” corresponding to those low freuencies, there’s a slightly lower energy density between two conducting surfaces than outside of them (never mind that both densities may be huge), and this manifests as a tiny pressure that pushes the surfaces together. If there were no zero point energy at all, then you wouldn’t see this effect.

So, just like quantum field theory predicted, there is some ground state energy (1 point for QFT). However, the theory also predicts that there should be so much energy that its gravitational effects would overwhelm the gravity of everything else (whoops).

As far as what this means for our understanding of the universe: we’re missing something. But this is old-hat for scientists. As a people, we’re used to dealing with unknowns and weird experimental results. It’s just that, in physics at least, the last century has been one big prediction/verification win after another. A stumbling block like this stands out because we’ve been doing so well.

The vacuum catastrophe may lead to another big paradigm shift, or a slight correction, or who knows. Other small weirdnesses, like nuclear decay and Mercury’s orbit, have led to the creation of entirely new fields, like particle physics and general relativity.

We’re probably just not taking something into account, but it’s a big something whatever it is.

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