Stephen Hawking and imaginary time

The imaginary time axis is drawn orthogonal to the real time axis. Credit: Wikimedia commons

Update 14/03/2018 Professor Stephen Hawking died today. See his obituary here. From all I have read he remained an ardent atheist his whole life. And he never really understood the worldview issue in cosmology and the origin of the universe. This proves that even very smart people can get it wrong. Nevertheless he gave us much to ponder, debate and learn. 


What is imaginary time? I don’t mean the time you spend day-dreaming but the concept in physics, promoted by theoretical physicist Stephen Hawking. It is used in some quantum mechanics and special relativity theory. Imaginary time is where the usual time dimension undergoes a Wick rotation (a phase rotation)1 so that its coordinates are multiplied by the imaginary number the square root of -1, represented by the symbol i. In such a situation time theoretically behaves like a spatial dimension.

Stephen Hawking Credit: Wikipedia

Hawking wrote:2

“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?” (emphasis added)

Positivism is the philosophy that we cannot determine what is real, but we can only propose hypotheses and test those against what we observe. Hawking is an atheist—an anti-theist—and has spent some time attempting to show that the Creator is unneeded in the universe.

Hawking claims that imaginary time is as real as real time, only that it is travelling in a different direction.3 He claims that ‘before’ the big bang time was imaginary and thus there was no time. Imaginary time may have “always existed” he said, but because we have no idea of what the laws of physics were ‘before’ the big bang, and there is no way to measure what happened ‘before’ the big bang, hence there is no point including time back then in a discussion of our universe. Continue reading

The singularity—a ‘Dark’ beginning

Did the universe form spontaneously from nothing?

“The universe burst into something from absolutely nothing – zero, nada. And as it got bigger, it became filled with even more stuff that came from absolutely nowhere. How is that possible? Ask Alan Guth. His theory of inflation helps explain everything.”—front cover of the April 2002 issue of Discover magazine

First years

Figure 1: The first several hundred million years after the big bang is when the universe was in its Dark Ages. No ionized hydrogen meant that no sources of light were available during that period. Larger image available from http://www.astro.caltech.edu/~george/reion/.

“Spontaneous creation of the universe from nothing”is the title of a 2014 paper authored by He, Gao and Cai, published in the American Physical Society journal Physical Review D, one of America’s most prestigious journals dealing with physical theory. It purports to outline a so-called mathematical proof that the universe did indeed burst into something from nothing. Continue reading