Stephen Hawking talks about no clear Big Bang and no boundary to space-time!

March 2, 2018 - Hawking says the universe had no clear “bang”. You can wind back the clock to the edges of those first moments of existence, but asking what came before would be like asking why you can keep walking north when you get to the North Pole. Time, as we define it, loses its meaning as the universe shrinks down.

It never quite narrows to a single point. But no one has proved physics works like that - yet.

Hawking proposes a no boundary condition version of space-time. As you approach the beginning space-time is replaced with imaginary time.

In theoretical physics, the Hartle-Hawking state, named after James Hartle and Stephen Hawking, is a proposal concerning the state of the universe prior to the Planck epoch.

Hartle and Hawking suggest that if we could travel backward in time toward the beginning of the universe, we would note that quite near what might have otherwise been the beginning, time gives way to space such that at first there is only space and no time. Beginnings are entities that have to do with time; because time did not exist before the Big Bang, the concept of a beginning of the universe is meaningless. According to the Hartle–Hawking proposal, the universe has no origin as we would understand it: the universe was a singularity in both space and time, pre-Big Bang. Thus, the Hartle-Hawking state universe has no beginning, but it is not the steady state universe of Hoyle; it simply has no initial boundaries in time or space.

The Hartle-Hawking state is the wave function of the Universe - a notion meant to figure out how the Universe started - that is calculated from Feynman’s path integral.

More precisely, it is a hypothetical vector in the Hilbert space of a theory of quantum gravity that describes this wave function.

It is a functional of the metric tensor defined at a (D − 1) - dimensional compact surface, the Universe, where D is the spacetime dimension. The precise form of the Hartle-Hawking state is the path integral over all D-dimensional geometries that have the required induced metric on their boundary. According to the theory, time diverged from three state dimension - as we know the time now - after the universe was at the age of the Planck time.

Such a wave function of the Universe can be shown to satisfy the Wheeler–DeWitt equation.

Imaginary time is a mathematical representation of time that appears in some approaches to special relativity and quantum mechanics. It finds uses in connecting quantum mechanics with statistical mechanics and in certain cosmological theories.

Mathematically, imaginary time is real-time which has undergone a Wick rotation so that its coordinates are multiplied by the imaginary root i. Imaginary time is not imaginary in the sense that it is unreal or made-up (any more than say irrational numbers defy logic); it is simply expressed in terms of what mathematicians call imaginary numbers.

Stephen Hawking popularized the concept of imaginary time in his book The Universe in a Nutshell.

“ One might think this means that imaginary numbers are just a mathematical game having nothing to do with the real world. From the viewpoint of positivist philosophy, however, one cannot determine what is real. All one can do is find which mathematical models describe the universe we live in. It turns out that a mathematical model involving imaginary time predicts not only effects we have already observed but also effects we have not been able to measure yet nevertheless believe in for other reasons. So what is real and what is imaginary? Is the distinction just in our minds?” wrote Hawking.

In the theory of relativity, time is multiplied by i. This may be accepted as a feature of the relationship between space and time, or it may be incorporated into time itself, as imaginary time, and the equations rewritten accordingly.

In physical cosmology, imaginary time may be incorporated into certain models of the universe that are solutions to the equations of general relativity. In particular, imaginary time can help to smooth out gravitational singularities, where known physical laws break down, to remove the singularity and avoid such breakdowns (see Hartle-Hawking state). The Big Bang, for example, appears as a singularity in ordinary time but, when modeled with imaginary time, the singularity can be removed and the Big Bang functions like any other point in four-dimensional spacetime.