Nothingness = a closed spherical spacetime of zero radius
Can you imagine nothingness? Right now I am reading a book titled, Why Does the World Exist?: An Existential Detective story. About halfway through the book, I came across a wonderful passage. The author, Jim Holt, speaks with physicist Alex Vilenkin about the difficulty in imagining sheer nothingness. Vilken helps make this possible with a thought experiment: Imagine spacetime as the surface of a sphere. Now suppose that this sphere is shrinking, like a balloon that is losing air. The radius grows smaller and smaller. Eventually—try to imagine this—the radius goes all the way to zero. The surface of the sphere disappears completely, and with it spacetime itself. We have arrived at nothingness. We have also arrived at a precise definition of nothingness: a closed spacetime of zero radius. This is the most complete and utter nothingness that scientific concepts can capture. It is mathematically not only devoid of stuff but also of location and duration.
With this characterization in hand, Vilenkin was able to do an interesting calculation. Using the principles of quantum theory, he showed that, out of an initial state of nothingness, a tiny bit of energy-filled vacuum could spontaneously “tunnel” into existence. How tiny would this bit of vacuum be? Perhaps as little as one hundreth-trllionth of a centimeter. But that, it turns out, is good enough for cosmogonic purposes. Driven by the negative pressure of “inflation,” this bit of energetic vacuum would undergo a runaway expansion. In a couple of microseconds it would attain cosmic proportions, issuing in a cascading fireball of light and matter—the Big Bang!
Ted Talk: Jim Holt: Why Does the Universe Exist?