In 1965 I read about Penrose’s theorem that any body undergoing gravitational collapse must eventually form a singularity. I soon realized that if one reversed the direction of time in Penrose’s theorem, so that the collapse became an expansion, the conditions of his theorem would still hold, provided the universe were roughly like a Friedmann model on large scales at the present time. Penrose’s theorem had shown that any collapsing star must end in a singularity; the time-reversed argument showed that any Friedmann-like expanding universe must have begun with a singularity. For technical reasons, Penrose’s theorem required that the universe be infinite in space. So I could in fact, use it to prove that there should be a singularity only if the universe was expanding fast enough to avoid collapsing again (since only those Friedmann models were infinite in space).
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.
Penrose’s theorem 彭罗斯定理
Quantum 量子论
1965年，我读到彭罗斯关于任何物体受到引力坍缩必须最终形成一个点的定理。我很快意识到，如果人们将彭罗斯定理中的时间方向颠倒以使坍缩变成膨胀，假定现在宇宙在大尺度上大体类似弗利德曼模型，这定理的条件仍然成立。彭罗斯定理指出，任何坍缩必须终结于一个点；其时间颠倒的论断则是，任何类弗利德曼膨胀模型必须从一个点开始。为了技巧上的原因，彭罗斯定理需要以宇宙在空间上是无限的为条件。所以事实上，我能用它来证明，只有当宇宙膨胀得快到足够以避免重新坍缩时（因为只有那些弗利德曼模型才是空间无限的），必须存在一个点。
以后的几年中，我发展了新的数学技巧，从证明性必须发生的定理中除去了这个和其他技术上的条件。最后的结果是1970年彭罗斯和我的合作论文。那篇论文最后证明了，假定广义相对论是正确的，宇宙包含着我们观测到的这么多物质，则过去必须有一大爆炸点。我们的工作遭到许许多多的反对，部分来自苏联人，由于他们对科学宿命论的信仰；另一部分来自某些人，他们不喜欢整个点的观念，并认为这糟蹋了爱因斯坦理论的完美。然而，人实在不能辩赢数学定理。所以最终我们的工作被广泛接受，现在几乎每个人都假定宇宙是从一个大爆炸点开始的。颇具讽刺意味的是，现在我改变了想法，试图去说服其他物理学家，事实上在宇宙的开端并没有点——正如我们将看到的，只要考虑了量子效应，性则会消失。
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