The Great Unknown: Seven Journeys to the Frontiers of Science

 "Just as I can talk about space having a shape, I can also talk about space-time having a shape. My initial instinct is to think of time as a line, which makes it very difficult for me to think of anything other than a line that is finite and therefore has a beginning and an end, or a line that is infinite. But there are other possibilities. Since time and space make up four dimensions, I must consider shapes that I can’t see. I need mathematics to describe them. But I can picture shapes representing parts of space-time that enable me to understand what I mean by the question of what happened before the Big Bang. For example, imagine there was only one spatial dimension, so that space-time is two-dimensional. This creates a surface that I can see, like a rubber sheet that I can play with and wrap up in interesting ways. I think most people’s model of two-dimensional space-time would be an infinite flat sheet with time extending infinitely backward and forward and space also one-dimensional and infinite. But, as I explored in the last Edge, space could be finite. I could wrap space up to make a circle and then time would extend this circle to make space-time look like a cylinder. I could, of course, join the cylinder up to make a bagel- or torus-shaped space-time. That would make time finite too. In this model of space-time I could loop around and return to a previous moment in history. Logician Kurt Gödel proposed solutions to Einstein’s equations of general relativity that have this feature. Gödel, as I shall explain in my final Edge, greatly enjoyed messing with people’s logical expectations. But Gödel’s circles of space-time are generally regarded as curiosities, because going back in time causes too many problems when it comes to causality. Possible shapes for a two-dimensional space-time To get a more realistic picture of space-time, I need to create a geometry that takes into account our current model of the history of the universe, which includes a beginning: the Big Bang. To see this point in my two-dimensional space-time universe, I could wrap up the surface so that it looks like a cone. The universe, which is just a circle, shrinks as I go back in time until I hit the point at the end of the cone. This is where time begins. There is nothing before that. No space. No time. Just a point of infinite density. This is a good model for something rather like the Big Bang. Or, rather than pinching space-time at a point, perhaps it could look like a sphere—like the surface of the Earth. This has its own implications for how I answer the question of what happened before the Big Bang. If I head south along a line of longitude, then when I hit the South Pole there is a sudden flip and I find myself on another line of longitude on the other side. But these are just numbers that we give to these points on the Earth’s surface. It doesn’t actually represent a discontinuous flip in the shape, just a jump in the way that we measure it. So by changing the coordinates, what appears to be a singular point can look quite smooth. This is one of Hawking’s ideas for time. Perhaps I should try to embed space-time in a shape such that this point that seems to show time stopping is actually just the south pole of the shape. After all, how do you answer the question, what’s south of the South Pole? The question doesn’t really make sense. It is striking that often when a question arises to which it seems we cannot know the answer, it turns out you need to acknowledge that the question is not well posed. Heisenberg’s uncertainty principle is not really an expression of the fact that we cannot simultaneously know both the momentum and position of a particle, so much as that these two things don’t actually exist concurrently. Similarly, attempts have been made to show that the question “What happened before the Big Bang?” isn’t one whose answer cannot be known. Rather, the question does not really make sense. To talk about “before” is to suppose the existence of time, but what if time existed only after the Big Bang?"

Start reading this book for free: https://read.amazon.com/kp/kshare?asin=B01IOHQ8P6&ref_=kar_wh_ca