- #1

Cerenkov

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I'm trying to pin down something Stephen Hawking was referring to in his book, A Brief History of Time.

*During the next few years I developed new mathematical techniques to remove this and other technical conditions from the theorems that proved that singularities must occur. The final result was a joint paper by Penrose and myself in 1970, which at last proved that there must have been a big bang singularity provided only that general relativity is correct and the universe contains as much matter as we observe. There was a lot of opposition to our work, partly from the Russians because of their Marxist belief in scientific determinism, and partly from people who felt that the whole idea of singularities was repugnant and spoiled the beauty of Einstein’s theory. However, one cannot really argue with a mathematical theorem. So in the end our work became generally accepted and nowadays nearly everyone assumes that the universe started with a big bang singularity. It is perhaps ironic that, having changed my mind, I am now trying to convince other physicists that there was in fact no singularity at the beginning of the universe – as we shall see later, it can disappear once quantum effects are taken into account.*

Ok, this is the 1970, Hawking - Penrose paper. https://royalsocietypublishing.org/doi/pdf/10.1098/rspa.1970.0021

But is there a paper where Hawking 'takes these quantum effects into account'?

Can it be found here... http://www.hawking.org.uk/publications.html ?

Any help given at a basic level would be appreciated.

Thank you,

Cernkov.