# The Nature of Space and Time (New in Paper)

Stephen Hawking
Roger Penrose
Pages: 160
https://www.jstor.org/stable/j.ctt7szq2

1. Front Matter
(pp. i-iv)
(pp. v-vi)
3. Foreword
(pp. vii-viii)
Michael Atiyah

The debate between Roger Penrose and Stephen Hawking recorded in this book was the high point of a six-month program held in 1994 at the Isaac Newton Institute for Mathematical Sciences at the University of Cambridge. It represents a serious discussion of some of the most fundamental ideas about the nature of the universe. Needless to say, we are not yet at the end of the road; uncertainties and controversy still persist and there is plenty to argue about.

Some sixty years ago there was a famous and extended debate between Niels Bohr and Albert Einstein about the foundations of...

4. Acknowledgments
(pp. ix-2)
5. CHAPTER ONE Classical Theory
(pp. 3-26)
S. W. Hawking

In these lectures, Roger Penrose and I will put forward our related but rather different viewpoints on the nature of space and time. We shall speak alternately and shall give three lectures each, followed by a discussion on our different approaches. I should emphasize that these will be technical lectures. We shall assume a basic knowledge of general relativity and quantum theory.

There is a short article by Richard Feynman describing his experiences at a conference on general relativity. I think it was the Warsaw conference in 1962. It commented very unfavorably on the general competence of the people there...

6. CHAPTER TWO Structure of Spacetirne Singularities
(pp. 27-36)
R. Penrose

In the first lecture by Stephen Hawking, singularity theorems were discussed. The essential content of these theorems is that under reasonable (global) physical conditions, singularities must be expected. They do not say anything about the nature of the singularities, or where the singularities are to be found. On the other hand, the theorems are very general. A natural question to ask is, therefore, what the geometric nature of a spacetime singularity is. It is usually assumed that the characteristic of a singularity is that the curvature diverges. However, this is not exactly what the singularity theorems by themselves imply.

Singularities...

7. CHAPTER THREE Quantulll Black Holes
(pp. 37-60)
S. W. Hawking

In my second lecture, I’m going to talk about the quantum theory ofblack holes. It seems to lead to a new level of unpredictability in physics over and above the usual uncertainty associated with quantum mechanics. This is because black holes appear to have intrinsic entropy and to lose information from our region of the universe. I should say that these claims are controversial: many people working on quantum gravity, including almost all those who entered it from particle physics, would instinctively reject the idea that information about the quantum state of a system could be lost. However, they have...

8. CHAPTER FOUR Quantum Theory and Spacetime
(pp. 61-74)
R. Penrose

The great physical theories of the twentieth century have been quantum theory (QT), special relativity (SR), general relativity (GR), and quantum field theory (QFf). These theories are not independent of each other: general relativity was built on special relativity, and quantum field theory has special relativity and quantum theory as inputs (see fig. 4.1).

It has been said that quantum field theory is the most accurate physical theory ever, being accurate to about one part in about 1011. However, I would like to point out that general relativity has, in a certain clear sense, now been tested to be correct...

9. CHAPTER FIVE Quantum Cosmology
(pp. 75-104)
S. W Hawking

In my third lecture, I shall turn to cosmology. Cosmology used to be considered a pseudoscience and the preserve of physicists who might have done useful work in their earlier years, but who had gone mystic in their dotage. There were two reasons for this. The first was that there was an almost total absence of reliable observations.

Indeed, until the 1920s about the only important cosmological observation was that the sky at night is dark. But people didn’t appreciate the significance of this. However, in recent years the range and quality of cosmological observations has improved enormously with developments...

10. CHAPTER SIX The Twistor View of Spacetime
(pp. 105-120)
R. Penrose

Classicality of cats. Stephen argued that because a certain region of spacetime is inaccessible we are forced into the density matrix description. However, this is not sufficient to explain the classical nature of observations in our region. The density matrix that corresponds to finding either a live cat |live) or a dead cat |dead) is the same density matrix that describes the mixture of the two superpositions,

$\frac{1}{{\sqrt 2 }}\left( {\left| {{\rm{live) + }}} \right|{\rm{dead)}}} \right)$

and

$\frac{1}{{\sqrt 2 }}\left( {\left| {{\rm{live) - }}} \right|{\rm{dead)}}} \right)$

Thus the density matrix alone does not say whether we see either a live or a dead cat or else...

11. CHAPTER SEVEN The Debate
(pp. 121-138)
S. W. Hawking and R. Penrose

These lectures have shown very clearly the difference between Roger and me. He’s a Platonist and I’m a positivist. He’s worried that Schrodinger’s cat is in a quantum state, where it is half alive and half dead. He feels that can’t correspond to reality. But that doesn’t bother me. I don’t demand that a theory correspond to reality because I don’t know what it is. Reality is not a quality you can test with litmus paper. All I’m concerned with is that the theory should predict the results of measurements. Quantum theory does this very successfully. It predicts that the...

12. AFTERWORD TO THE 2010 EDITION The Debate Continues
(pp. 139-142)
S. W. Hawking and R. Penrose

In the years following the original publication ofThe Nature of Space and Time, there have been many important developments, both on the observational and theoretical sides. Yet, despite this increased knowledge, our two points of view appear to have diverged even further, rather than come together to a clear, common understanding. This is, no doubt, indicative of the vast amount that is not yet known about the foundations of physics, and of the nature of quantum gravity in particular. In this new afterword, we give a brief outline of where our respective views have taken us and of the...

13. References
(pp. 143-145)