universe - How can something happen when time does not exist?

I saw this documentary hosted by Stephen Hawkins.

And if I didn't get it wrong, it says that there was no time before the big bang, time was created there.

So how can anything happen when there is no time (eg: the creation of time and the universe)? Is this what he calls a 'singularity'? Which I could think like this: when there is no time nothing can happen, except during this singularity.

Of course I don't know of a law that says 'when there is no time nothing can happen..', I just came up with it, as something intuitive.

Answer

General relativity is a local theory. That means it describes spacetime near the point you're looking at but it doesn't say anything about the large scale structure of spacetime.

Now this may seem unrelated to your question, but actually it's key to why we say that time started at the Big Bang. If we make a few apparently sensible assumptions about the universe we can solve the Einstein equation and get the FLRW metric. This metric allows us to start at our current position and trace back towards the Big Bang to see what happens. As we do this we are calculating a geodesic, which is simply the curve in spacetime followed by a freely moving object. The key point about this is that from some point on our geodesic, e.g. me sitting typing this, we use the metric to calculate the immediately preceeding points, then from there we use the metric to calculate even earlier points and so on back in time towards the Big Bang.

The problem is that as we calculate back towards the Big Bang the metric gets larger and larger, and at the moment of the Big Bang it becomes infinite. You can't do arithmetic with infinity. It might be fun to speculate what $\infty$ times 0 is, but when this sort of expression crops up in Physics it means we have to admit we can't calculate what's going on.

This is why you'll often hear it said that time started at the Big Bang. It's because we can't calculate backwards in time from that point. Now that doesn't necessarily mean there was no time before the Big Bang, it just means we have no way of calculating it from General Relativity. If you believe Loop Quantum Cosmology, this predicts that there was a bounce at the Big Bang, so we can follow geodesics back through the Big Bang and into an earlier universe. However this is highly speculative.

Incidentally, you get exactly the opposite effect if you fall into a black hole. If you launch yourself into a static black hole your geodesic is described by a metric called the Schwarzchild metric. The metric allows you to calculate your path towards the centre of the black hole (the singularity) but when you reach the center the metric becomes infinite and you can't calculate it any further. It's often said that time stops at the central singularity in a black hole.