In this post I will be refering to S.Hawking's lecture: http://www.hawking.org.uk/the-beginning-of-time.html
I have a couple of questions regarding the Imaginary time and the Big Bang.
In the article mentioned above, it is said that "The no boundary proposal, predicts that the universe would start at a single point, like the North Pole of the Earth. But this point wouldn't be a singularity, like the Big Bang".
This statement clearly tells us that the No Boundary condition and the Big Bang theory opposes each other with respect to initial singularity in real time.
My questions are:
1) Is it possible that the No Boundary condition proposal can still allow the Big Bang singularity in real time?
2)Can I just say that the concept of Imaginary time is equivalent to an extra-time dimension with certain properties and call it "t_2"? or How this Imaginary time dimension is different from extra time dimentions proposed in other theories like 3 time-dimensions theories?
I do not have mathematical background in Cosmology other than the standard level General Relativity, but these questions are free to be answered in any depth possible. Thank you!
3)How this No boundary condition explain the origin of the universe without the Big Bang singularity when this singularity is intuitive?