Long Times and Short Times
By Steven Weinberg
For more than four decades, one of the most captivating and celebrated science communicators of our time has challenged the public to think carefully about the foundations of nature and the inseparable entanglement of science and society. In Third Thoughts Steven Weinberg casts a wide net: from the cosmological to the personal, from astronomy, quantum mechanics, and the history of science to the limitations of current knowledge, the art of discovery, and the rewards of getting things wrong. Weinberg is that great rarity, a prize-winning physicist who is entertaining and accessible. The essays in Third Thoughts, some of which appear here for the first time, will engage, provoke, and inform — and never lose sight of the human dimension of scientific discovery and its consequences for our endless drive to probe the workings of the cosmos. Here is one of the essays.
In The Sand Reckoner, Archimedes showed that he knew how to deal with large numbers by estimating the number of grains of sand needed to fill the universe. Of course he didn’t know the size of the universe; he was using an estimate by Aristarchus of the distance to what was then thought to be the spherical boundary of the universe, on which the stars ride. That didn’t matter much — the point he was making was not about astronomy, but about mathematics. He described large numbers by talking about myriads, and myriads of myriads, and myriads of myriads of myriads of myriads, and so on. This is much simpler in modern terms: a myriad is 10,000, or 10 times itself four times, written 104; a myriad of myriads is 104 times 104, or 108; a myriad of myriads of myriads of myriads is 108 times 108, or 1016, etc. His conclusion, in modern notation, was that it would take no more than 1063 grains of sand to fill the universe.
Archimedes in The Sand Reckoner was concerned with volumes: the volume of the sphere of the stars expressed as a very large multiple of the volume of a grain of sand. Scientists have to deal with very large and very small quantities of other sorts as well, which again we describe using powers of ten. The Utrecht physicists Gerard ’t Hooft and Stefan Vandoren have described the vast range of times encountered in modern physics in a book, Time in Powers of Ten, published originally in Dutch with lovely illustrations by ’t Hooft’s daughter Saskia.
In July 2013 I received an email from ‘t Hooft, asking if I would contribute a foreword to the English language edition of their book. ’t Hooft is one of the great theoretical physicists of our time and an old friend, and anyway I had been thinking about the scales of time encountered in the history of physics and astronomy, so I agreed. The English language edition of the book by ’t Hooft and Vandoren was published by World Scientific Press with the brief essay below as a foreword in 2014.
Ordinary human experience spans a range of times from seconds to decades, the longest intervals of time a mere billion or so times longer than the shortest. But the progress of science has been marked by the scientist’s growing familiarity with time intervals that are very much longer, or very much shorter, than those that are experienced in human lives.
Around 150 bc the Greek astronomer Hipparchus observed that the position of the Sun against the background of stars at the time of the autumnal equinox was gradually changing, at a rate that would take the equinoctal Sun completely around the zodiac in about 27,000 years. Newton later explained this precession of the equinoxes as an effect of a slow wobble of the Earth’s axis of rotation, caused by the gravitational attraction of the Sun and Moon for the equatorial bulge of the Earth. The Earth’s axis is now known to make a complete turn in 25,727 years. Hipparchus had done the first serious scientific calculation of a time interval very much longer than a human lifetime, and found a result that was off by only about 5 percent. In this century we have become used to much longer intervals of time. From the relative abundance of isotopes of uranium we can infer that the material of which the solar system is made was formed in an exploding star about 6.6 billion years ago. Looking farther back, by observing the way that galaxies now rush apart, we can infer that 13.8 billion years ago the matter of the universe was so compressed that there were no galaxies or stars or even atoms — only a hot thick gas of elementary particles.
The extension of our experience to very short time intervals has been even more dramatic. By observing phenomena like diffraction that are associated with the wave nature of light, it became known early in the nineteenth century that a typical wavelength of visible light is about 0.3 ten-thousandths of a centimeter. Light was already known to travel at a speed of about 300,000 kilometers per second, so the period of the light wave, the time it takes light to travel one wavelength, was known to be about 10−15 seconds (a quadrillionth of a second). This is not very different from the time (to the extent that a classical description is relevant) that it takes electrons in atoms to make one complete circuit of their orbits.
Modern elementary particle physics deals with time intervals that are very much shorter. The lifetime of the W particle (the heavy charged particle responsible for the weak force that al- lows neutrons to turn into protons in radioactive nuclei) is only 3.16 × 10−25 seconds, not long enough for a W particle traveling near the speed of light to cross the diameter of an atomic nucleus.
What I find truly remarkable is not just that scientists have come to confront these very long and very short intervals of time. It seems to me even more amazing that our experiments and theories have become sufficiently reliable so that we can now give precise figures, like 13.8 billion years and 3.16 × 10−25 seconds, with some confidence that we know what we are talking about.
