The Vacuum Catastrophe

Today I’ve decided to talk about the vacuum catastrophe, a.k.a. the cosmological constant problem, a.k.a. “the worst theoretical prediction in the history of physics”.

For the last several decades, physics has been brilliant at coming up with better and better theoretical models of the universe. Two of the best-studied (and most widely accepted and utilized) physical theories are general relativity and quantum mechanics. You probably knew that already.

You might also have heard that the two models are inconsistent with each other: quantum mechanics treats spacetime as a (most of the time) static “background” on which particles interact and propagate. Conversely, general relativity describes the dynamics of the spacetime background itself as it couples to matter.

Despite their differences, there are certain situations where both theories can be succesfully applied to the same physical system. One example is black holes: Stephen Hawking famously predicted that, when you consider quantum particles in the warped spacetime around a black hole, the combined theories predict the steady emission of electromagnetic radiation, resulting in the black hole’s evaporation.

Cosmic Expansion

In 1929, Hubble recorded the first evidence that the universe was expanding. Later on, it would be discovered that not only was the universe getting bigger, but that the rate of expansion was itself increasing (accelerating expansion). As it turned out, general relativity could be adjusted to account for such an accelerated expansion.

This was achieved by the introduction of a positive cosmological constant, often represented as $\mathrm{\Lambda }$. Fitting to observations of the relative movements of distant galaxies yields a very tiny (put positive) value for $\mathrm{\Lambda }$: around $1.1056\times {10}^{-52}{\text{m}}^{-2}$.

According to GR, this indicates that space has a negative pressure everywhere as a consequence of having positive energy density. In other words, cosmology tells us that empty space isn’t empty. On its own, this isn’t a problem. But what does quantum theory have to say about this?

The Quantum Vacuum

Quantum field theory (QFT) also tells us that empty space isn’t empty: it’s filled up with the quantum vacuum. In other words, QFT predicts that empty space is constantly buzzing with activity (particles coming into and out of existence and the like).

There are strong arguments that this should contribute a positive energy density that would result in an expanding universe, and hence gives a quantitative prediction for the cosmological constant. This should be cause for celebration: two fundamentally different theories of physics making predictions about the universe that are consistent with each other.

The Catastrophe

So the problem is, quantum field theory predicts a cosmological constant that is on the order of ${10}^{120}$ (one with 120 zeros after it) times larger than the one seen in cosmology. The only thing that both theoeries get consistent is the sign ($+$) of the constant. Which isn’t much to celebrate.

So far, no universally accepted physical theory provides a convincing reason for this huge discrepancy between the two most successful physics theories of all time.

Conclusion

Hopefully that gives a decent and non-technical introduction to the vacuum catastrophe. I am inclined to find this kind of topic interesting, as it’s indicative of a gigantic rift between two otherwise hugely successful theories. I intend to cover other topics in quantum mechanics and general relativity (as well as more exotic physics!) in future posts.

Take care!

Jamie