Did Time Start at the Big Bang? (Patreon)

A hundred years ago we discovered the beginning of the universe. Observations of the retreating galaxies by Edwin Hubble and Vesto Slipher, combined with Einstein’s then-brand-new general theory of relativity, revealed that our universe is expanding. And if we reverse that expansion far enough – mathematically, purely according to Einstein’s equations, it seems inevitable that all space and mass and energy should once have been compacted into an infinitesimally small point – a singularity. It’s often said that the universe started with this singularity, and the Big Bang is thought of as the explosive expansion that followed. And before the Big Bang singularity? Well, they say there was no “before”, because time and space simply didn’t exist. If you think you’ve managed to get your head around that bizarre notion then I have bad news. That picture is wrong. At least, according to pretty much every serious physicist who studies the subject. The good news is that the truth is way cooler, at least as far as we understand it.

Now before … a certain crowd starts with all the “scientists keep changing their minds, they don’t know anything” or “the Big Bang theory is just a theory” let me be very clear:  the evidence for a hot, dense early universe is practically incontrovertible. The cosmic microwave background is a direct line of sight to the universe as it was only a few hundred thousand years after the hypothetical beginning of time. We can see, pretty much directly, that all space and matter in the universe was once crunched at least 1000 times closer together. There’s also relative abundance of the simple elements - hydrogen and helium in particular – whose ratio is exactly what we expect if the entire universe was a dense, billions-of-degrees nuclear furnace for the first several minutes of its existence.

In fact, powerful evidence brings us back to 1 millionth of a second after theoretical beginning of expansion, and a lot of well-tested physics brings us back quite a bit further than that. The Big Bang THEORY is the scientific description of the early hot, dense state, and it’s generally incredibly well tested and agreed on. But just because we can rewind the math a long way doesn’t mean we can rewind it all the way to the supposed the Big Bang singularity at T=0, the beginning of time. In fact there’s powerful evidence that we should NOT rewind Einstein’s equation that far – at least without introducing some very new physics. For one thing, there’s also convincing observational evidence that the time before around 10^-32 seconds included a period of extremely rapid expansion called cosmic inflation. We talked about the reasons we need inflation in a previous episodes, and I’ll come back to it in a bit. Adding that initial growth burst solves a couple of big problems, but it doesn’t change the fact that rewinding the expansion of the universe, even at different speeds still leads us towards the T=zero singularity.

I’m going to come back to why we need to forget the idea of that singularity. Doing so will change the way we think about cosmic inflation, and also about what “the beginning of the universe” even means. But before we kill that whole idea of the Big Bang singularity, we need to understand what we’re killing. What does it really mean for all of space to be compacted to a single point? This idea is especially weird if the universe is infinite.  Now the universe may or may not be infinite, but if we can understand the infinite case, then getting all of this for the finite case is baby stuff, at least by comparison.

It’s tricky to talk about the “size” of an infinite universe. Instead of overall volume or radius, we talk about the size of an expanding infinite universe in terms of the scale factor – the distance between any two points in space at some moment in time relative to their distance at some other reference moment. That reference moment is typically taken as right now, so the scale factor of the universe is currently one. Several billion years ago the scale factor was a half – all points in the universe were half as far apart as they are today. When I talk about “rewinding the expansion” I mean running the clock backwards to track the shrinking scale factor. One way to do that is to keep halving the scale factor. Do that enough times and any two points, no matter how far apart they were, will end up as close together as you like. Do it enough times and the universe can end up as hot and dense as you like. But it’ll still be infinite, spatially. The scale factor is incredibly small, but an incredibly small number times infinity is still infinity.

Rewinding the universe this way doesn’t leave us with a singularity – the singularity is when all points are not just next to each other – but are literally all the same point, at which point temperature and density are infinite. That last tiny step is a doozy – the scale factor goes from incredibly small to zero, so the infinite universe becomes infinitesimal. All points become the same point, and 3-dimensional space becomes zero-dimensional.

That’s the singularity. We say that it didn’t happen in any one place because a point is zero-dimensional. There weren’t spatial dimensions for it to happen in. At the same time, we say the Big Bang happened everywhere at once, because even the tiniest fraction of a second later the universe has infinite size, and everywhere is expanding equally. Even if the universe is NOT infinite, then whatever space there is comes into being at the same time from that singularity.

But what happens to time at the Big Bang singularity? To get that you can’t think about the universe as having one big clock that rewinds and then winks out of existence at the big bang. Or into existence if you’re going forward. No, you have to think about time the way Einstein intended. There is no universal clock – time is relative – clocks are attached to each observer – each moving frame of reference. To see what time does at the Big Bang we have to trace a path through space AND time backwards to the singularity. We trace a path called a geodesic, which in general relativity is the shortest path between two spacetime coordinates. These are the grids we use to map spacetime.

Remember that in our rewind, all points in the universe get arbitrarily close together before merging at T=zero. Well, that’s the same as saying that all geodesics in the universe converge at the Big Bang singularity. In the same way, all lines of longitude converge at the North Pole.

So, each geodesic tracks earlier and earlier times as it approaches the Big Bang – infinite clocks rewinding towards zero – and then they all converge. Then when? Then … nothing. All geodesics end at the Big Bang singularity, and their timelines end with them. Or start, depending on how you think about it. The point is that in the pure Einsteinian picture there IS no before the Big Bang because no timeline in this universe can be traced there. This is called “geodesic incompleteness”, and it also happens at the singularity in the center of a black hole – all timelines end – this time in the forward direction.

The analogy with the North pole is a good one, and Einstein himself used it. Lines of longitude end at the north pole, and it’s meaningless to ask what is north of the north pole, and from the pure Einsteinian point of view it’s meaningless to ask what happened before the Big Bang or after reaching a black hole’s center.

OK, so I’m taking my time to explain something I already told you is wrong. But it’s important because the extreme weirdness of the Big Bang singularity is part of what tells us it’s wrong. Any time you encounter a singularity in the mathematics of a physical theory you have good reason for skepticism. It’s probably telling you that your physical theory is incomplete, and that you pushed that theory too far. That’s what’s happening here. We used general relativity to rewind the universe, but we already know that despite its incredible successes, GR is an incomplete theory. At the crazy densities and temperatures of the Big Bang singularity and just after, GR comes into terrible conflict with quantum mechanics. We’ve talked about that conflict and its possible resolutions before – but the upshot is that we just don’t know how the universe behaves in those conditions. But we DO know that pure general relativity isn’t a good description, and so we probably shouldn’t believe its prediction that all space was compacted into a single point and that this is where time started.

OK, so what are the alternatives? Can we really trace geodesics, and the timelines they embody, through the Big Bang and out the other side? If so, what do we find there? There are several possibilities, and they deserve their own episodes, and we’ll get those to you soon. But to whet your appetite: first up, cosmic inflation can offer a temporary reprieve from the singularity. Eternal inflation suggests that our universe appeared as a regularly-expanding bubble in an unimaginably larger, continuously inflating spacetime. In that case, “before the Big Bang” was a period of exponential expansion that could have lasted indefinitely.  We’ll get into the nitty gritty of that, with its inflatons and bubble universes, real soon.

There are various cyclic universe options. The first cyclic universe idea was the big bounce, in which the gravitational attraction all all matter in the universe was enough to cause it to recollapse – and then presumably bounce outwards again. We now know that there isn’t anywhere near enough matter to do that.

Unless we bring in string theory. The Steinhardt–Turok model suggests that our universe floats in a higher dimensional space, living on geometric objects called branes. Collisions of those branes initiate cycles of expansion and contraction. Roger Penrose’s conformal cyclic cosmology is even weirder, because it postulates that the infinite future boundary of an eternally expanding universe looks just like the Big Bang of a new universe, mathematically. So our heat death is someone else’s Big Bang.

There are less abstract ways to get a new universe out of an old one – for example, an extreme quantum fluctuation could initiate a new Big Bang given infinite time, or the same amount of time could lead to all particles randomly converging back to the same spot. Or maybe black holes birth new universes, as in Lee Smolin’s fecund universe hypothesis. There’s a poetry to that last one – the geodesics approaching the black hole singularity become the geodesics emerging from a new Big Bang singularity.

People love cyclic universes and regenerating universes – they appeal to our sense of narrative. They also appeal to our intuition for causality - things happen because prior events cause them. Many of our ideas just push back the uncomfortable something-from-nothing moment. Physicists have a thing or two to say about that – from quantum fluctuations from nothing to Steven Hawking’s timeless interpretation of eternal inflation that draws on the holographic principle. All things we’ll discuss in the future, as we travel beyond the beginning of spacetime.