Dear Dr B: What are the chances of the universe ending out of nowhere due to vacuum decay?

“Dear Sabine,

my names [-------]. I'm an anxiety sufferer of the unknown and have been for 4 years. I've recently came across some articles saying that the universe could just end out of no where either through false vacuum/vacuum bubbles or just ending and I'm just wondering what the chances of this are occurring anytime soon. I know it sounds silly but I'd be dearly greatful for your reply and hopefully look forward to that

Many thanks

[--------]”

Dear Anonymous,

We can’t predict anything.

You see, we make predictions by seeking explanations for available data, and then extrapolating the best explanation into the future. It’s called “abductive reasoning,” or “inference to the best explanation” and it sounds reasonable until you ask why it works. To which the answer is “Nobody knows.”

We know that it works. But we can’t justify inference with inference, hence there’s no telling whether the universe will continue to be predictable. Consequently, there is also no way to exclude that tomorrow the laws of nature will stop and planet Earth will fall apart. But do not despair.

Francis Bacon – widely acclaimed as the first to formulate the scientific method – might have reasoned his way out by noting there are only two possibilities. Either the laws of nature will break down unpredictably or they won’t. If they do, there’s nothing we can do about it. If they don’t, it would be stupid not to use predictions to improve our lives.

It’s better to prepare for a future that you don’t have than to not prepare for a future you do have. And science is based on this reasoning: We don’t know why the universe is comprehensible and why the laws of nature are predictive. But we cannot do anything about unknown unknowns anyway, so we ignore them. And if we do that, we can benefit from our extrapolations.

Just how well scientific predictions work depends on what you try to predict. Physics is the currently most predictive discipline because it deals with the simplest of systems, those whose properties we can measure to high precision and whose behavior we can describe with mathematics. This enables physicists to make quantitatively accurate predictions – if they have sufficient data to extrapolate.

The articles that you read about vacuum decay, however, are unreliable extrapolations of incomplete evidence.

Existing data in particle physics are well-described by a field – the Higgs-field – that fills the universe and gives masses to elementary particles. This works because the value of the Higgs-field is different from zero even in vacuum. We say it has a “non-vanishing vacuum expectation value.” The vacuum expectation value can be calculated from the masses of the known particles.

In the currently most widely used theory for the Higgs and its properties, the vacuum expectation value is non-zero because it has a potential with a local minimum whose value is not at zero.

We do not, however, know that the minimum which the Higgs currently occupies is the only minimum of the potential and – if the potential has another minimum – whether the other minimum would be at a smaller energy. If that was so, then the present state of the vacuum would not be stable, it would merely be “meta-stable” and would eventually decay to the lowest minimum. In this case, we would live today in what is called a “false vacuum.”

Image Credits: Gary Scott Watson.

If our vacuum decays, the world will end – I don’t know a more appropriate expression. Such a decay, once triggered, releases an enormous amount of energy – and it spreads at the speed of light, tearing apart all matter it comes in contact with, until all vacuum has decayed.

How can we tell whether this is going to happen?

Well, we can try to measure the properties of the Higgs’ potential and then extrapolate it away from the minimum. This works much like Taylor series expansions, and it has the same pitfalls. Indeed, making predictions about the minima of a function based on a polynomial expansion is generally a bad idea.

Just look for example at the Taylor series of the sine function. The full function has an infinite number of minima at exactly the same value but you’d never guess from the first terms in the series expansion. First it has one minimum, then it has two minima of different value, then again it has only one – and the higher the order of the expansion the more minima you get.

The situation for the Higgs’ potential is more complicated because the coefficients are not constant, but the argument is similar. If you extract the best-fit potential from the available data and extrapolate it to other values of the Higgs-field, then you find that our present vacuum is meta-stable.

The figure below shows the situation for the current data (figure from this paper). The horizontal axis is the Higgs mass, the vertical axis the mass of the top-quark. The current best-fit is the upper left red point in the white region labeled “Metastability.”

Figure 2 from Bednyakov et al, Phys. Rev. Lett. 115, 201802 (2015).

This meta-stable vacuum has, however, a ridiculously long lifetime of about 10⁶⁰⁰ times the current age of the universe, take or give a few billion billion billion years. This means that the vacuum will almost certainly not decay until all stars have burnt out.

However, this extrapolation of the potential assumes that there aren’t any unknown particles at energies higher than what we have probed, and no other changes to physics as we know it either. And there is simply no telling whether this assumption is correct.

The analysis of vacuum stability is not merely an extrapolation of the presently known laws into the future – which would be justified – it is also an extrapolation of the presently known laws into an untested energy regime – which is not justified. This stability debate is therefore little more than a mathematical exercise, a funny way to quantify what we already know about the Higgs’ potential.

Besides, from all the ways I can think of humanity going extinct, this one worries me least: It would happen without warning, it would happen quickly, and nobody would be left behind to mourn. I worry much more about events that may cause much suffering, like asteroid impacts, global epidemics, nuclear war – and my worry-list goes on.

Not all worries can be cured by rational thought, but since I double-checked you want facts and not comfort, fact is that current data indicates our vacuum is meta-stable. But its decay is an unreliable prediction based the unfounded assumption that there either are no changes to physics at energies beyond the ones we have tested, or that such changes don’t matter. And even if you buy this, the vacuum almost certainly wouldn’t decay as long as the universe is hospitable for life.

Particle physics is good for many things, but generating potent worries isn’t one of them. The biggest killer in physics is still the 2nd law of thermodynamics. It will get us all, eventually. But keep in mind that the only reason we play the prediction game is to get the best out of the limited time that we have.

Thanks for an interesting question!