You can also twist the spins of electrons in an atom and in the process add a tiny amount of energy, but when you do this with quarks the effects are huge. You need to add a few hundred megaelectronvolts of energy. For comparison, the mass of a nucleon is 940 MeV. This means you need a fairly large accelerator to do this. The delta particle is not very stable. It exists for a few short moments and then decays back into a proton or neutron, kicking out the added energy in the form of a new particle. If we look at the energy of that ejected particle we see that it is on average 300 MeV, which means the delta is 30% more massive than the original proton or neutron. But not all of the ejected particles have energy of exactly 300 MeV. In fact they have a distribution, centered at 300 MeV and with a width of 120 MeV. We can use Heisenberg’s uncertainty principle and convert this into time and find that the lifetime of the delta particle is 5.6 × 10−24 s.
A time of 10−24 s is also called a yoctosecond. It takes light about half a yoctosecond (ys) to cross the diameter of a proton and so it is not surprising that this is the timescale for events inside of protons and neutrons. The W boson has a lifetime of 0.3 ys and the Z boson has a lifetime of about 0.25 ys. We have not seen anything significantly faster than this. Will we some day? I do not know. But as I said before, a yoctosecond is about the time it takes for light to cross a proton. That is not a coincidence. For a proton to be excited the whole structure of the proton is involved and so the time is related to how long it takes light to cross that structure. If someday we find smaller structures, perhaps something inside of quarks, then I would not be surprised to find events that are even faster.
9
Deep and Epic Time
In the previous chapter we talked about the second, the time of a heartbeat. We said it was a chunk of time in which a cesium-133 atom could undergo a transition with a resonance of 9,192,631,770 Hz. We also talked about events that take less than a second: lightning strikes, nerve pulses, atomic transitions and the lifetime of subatomic particles. But we do not measure our lifetime in seconds. We measure events of our lives in terms of days, seasons, years, decades and even centuries. The basic SI (Système International, i.e. the metric system) unit of time is the second, but these other units have real value. The year, the week and the hour are directly tied to our experiences and it is hard to imagine functioning in a world without them. But they are a human construct, and as such we could have picked some other division of time, and in fact in the past we have.
The Chinese historically divided the day in various ways. Sometimes they divided the day into twelve shichen, a double long hour. Alternatively they divided the day into one hundred ke. In this sense, the ke is a type of decimal time. But the ke and the chichen did not compliment each other well. So at various times in Chinese history, the ke was redefined as 96, 120 and 108 per day. There were also a number of shorter time units such as the fen and miao, which are similar to the minute and second.
Hindu time is very complex, and spans from epic times, measured in trillions of years, to parts of seconds.
In the Middle Aages the church developed eight canonical hours: matins, lauds, prime, terce, sext, none, vespers and compline. These were times in the day to stop and pray, particularly important in monastic life. They were based on a Judaic tradition and are much like the five daily prayers in the Islamic world today. But they are not really “hours” in the sense we use that word today. Rather, they are events within the day.
In Europe, the day has been divided into twenty-four hours for centuries with a few interruptions. The most notable exception was during the French Revolution. I am going to describe the clock and calendar of the early French Revolution so we can see how time may have been measured, as well as understand why it is not measured that way today.
In 1793 decimal time was introduced into France. In this system the day was divided into ten hours, and those hours were subdivided into minutes and seconds. Since this system re-used the words, hour, minute and second it would get confusing when I compare them to our standard units, so I will refer to them as decimal hours, decimal minutes and decimal seconds. One day had ten decimal hours, one decimal hour had one hundred decimal minutes and each decimal minute had one hundred decimal seconds. Since the decimal and the standard time units are based on the common day we can compare them. What jumps out at me in Table 9.1 is that these times are not so radically different from what we are use to, especially the second. If your heart beats 70 beats in a standard minute, a fairly normal rate, then it beats once every decimal second.
Table 9.1 Comparison of decimal and standard time.
Decimal time
Standard time
1 decimal hour
2.4 standard hours
1 decimal minutes
1.44 standard minutes
1 decimal second
0.864 standard seconds
Decimal time was the official way of recording time in the young French Republic and it was closely related to the French Republican Calendar or revolutionary calendar. In this calendar every week, or décade, had ten days and every month had three weeks. Under this system a year—one trip of the Earth around the Sun—would take 12 months, five and one quarter days (or 2.5 decimal hours). The year is still an important unit of time and even the Enlightenment could not change when we should put seeds in the ground to grow things.
The calendar was not an easy sell. In it there are only 32 décades (weeks) each year and each décade only had one day of rest. To make it more palatable a mid-décade half-day holiday was added, and those five or six days that did not fit into the twelve months were declared “complementary days,” or national holidays, to be taken in the middle of our September.
The reason the French revolutionary leaders went to such lengths was to try and break the power of the church. The revolution was a secular movement; it was a rising up against not only the monarchy, but also against the Church, which authorized and endorsed the king and court. In the eyes of the revolution, the Gregorian calendar—the calendar filled with the days of the saints—as well as Sunday—the day of worship—together represented a stranglehold that the Church held on society. By wiping the calendar clean, they tried to weaken the hold of the Church.
The revolutionary calendar was colorful. Since days were no longer named after saints, they needed new names and the gardens of France provided them, for example Hyacinthe (hyacinth) on April 28 and Fraise (strawberry) on May 30. The complementary days and holidays were even more colorful: there were fetes de la Vertu, du Génie, du Travail, de l’Opinion and La Fête des Récompenses. Finally leap day became La Fête de la Révolution.
The decimal calendar and clock were adopted in 1793 but did not survive. The clock was discarded in 1795 and the calendar in 1806. On the same day that the decimal clock was discontinued, the metric system, with its meter and kilogram, was adopted as the standard of the new republic. This leads us to the question, why has the meter thrived whereas decimal time has vanished? The main reason is that the meter unified commerce and decimal time did not. Prior to the introduction of the meter there were dozens of length standards, most of them unique to a local market. It was frustrating to a merchant who would buy, for example, a length of rope in one market and sell it as a shorter rope in the next city. It was also paralyzing to a tax collector. How could you enforce a uniform law or regulation in which lengths and weights had no uniformity? So the meter and the kilogram were welcomed with open arms, especially by people who traveled between markets. Decimal time, however, did not offer this advantage. Time was already uniform across France and most of Europe. Ironically the watch and clockmakers of France lost business. Before the revolution watch- and clockmakers such as Abraham-Louis Breguet were setting the standards for the rest of the world, creating state-of-the-art timepieces. However the ten-hour watch was provincial and barely sold even within France. Decimal time was a failure because it did not unify.
***
No matter what system is used, a clo
ck and calendar still need to be synchronized with the rotation rate of the Earth and the time to orbit the Sun. Days and years are very real. So, we have ended up measuring time in the most curious set of units. Sixty seconds is a minute and sixty minutes make an hour. Then twenty-four hours make a day. But why 60 and 24? We inherited these numbers from the Babylonians and Sumerians who were using base sixty more than 4000 years ago. But why has its use persisted? In part it is because there seems to not be any overwhelming reason to change a system that gets the job done and is universally understood. But also it is very easy to divide these two numbers into a lot of factors. Sixty can be divided into 2, 3, 4, 5, 6, 10, 12, 15, 20 and 30, which is a pretty impressive list. It is the smallest unitary perfect number, which may not be the reason it is chosen, but instead is related to the fact that you can spend a quarter or a third of an hour on a task, which is harder to do in decimal time. Twenty-four is also no slouch, being divisible by 2, 3, 4, 6 and 12, all of which are handy numbers when trying to divide up the day into shifts or watches.
When you look at the success of the 24-hour clock and the metric system, it makes one realize that the meter has become the world standard not just because the conversion between centimeter and kilometer is easier than inches to miles, but because the meter replaced confusion, whereas decimal time did not.
***
Now we will look at events that happen on ever-increasing timescales, starting with events that take a few minutes and working our way up to the age of the universe. To be consistent with the previous chapter I should label all times in seconds, but most of us do not have a real feel for how much time a million seconds represents. So I will end up using a mixture of common units.
What are events in nature that take more than a second? The average lifetime of a neutron is 880.1 s or 14 min 40 s. This number comes with a lot of caveats. A neutron bound into the nucleus of hydrogen or carbon-12, or in fact any stable isotope can sit quietly through the ages, stable and not decaying. But pluck that neutron out of that nucleus, remove it from its safe haven, its nest, and in less than a quarter of an hour it will decay. For the moment I leave this observation as just a curiosity.
Under ideal conditions, some bacteria can divide in 20 min, a potentially frightful prospect if it is a pathogen and when you think about exponential growth. The eruption of Stromboli happens a few times an hour. Old Faithful, the geyser in Yellowstone, erupts every 45–125 min. All these events happen frequently, but not with perfect regularity. As we look for events with longer and longer time periods we do not find real uniformity until the 24-hour day.
One rotation of the Earth about its axis: a day, 24 hours or 86,400 seconds. It is one of the most significant chunks of time in human existence. I can imagine a year of 500 days, or even living in a place without seasons and so effectively without a year. But the day is ingrained into our biology. Even on the space station, where the sun rises every hour and a half, the crew still lives on a 24-hour clock. As was described in the last chapter, up until a few decades ago the day set the standard for time. But the Earth day is unique only in our tiny corner of the cosmos. If we lived on the surface of Jupiter our day would last only 10 hours from noon to noon. On Venus a solar day lasts about 117 Earth days, with the Sun rising in the west and setting in the east.
On Earth a day is 24 h, whereas the amount of time to rotate once around our axis when compared to the stars is 23 h, 56 min. The first is called a solar day and the second a sidereal day (see Figure 9.1). They are quite similar because our day is fast compared to a year. If you picture our orbit as a circle, after one rotation on our axis we have traveled about 1° around the circle, and so need to rotate an additional degree to see the Sun centered in the sky again.
The Moon is an interesting case. Its orbital time is equal to its rotation, which is different from the time between full moons. The orbital and rotation time is 27.3 days, the time from full moon to full moon, called the synodic period, is 29.5 days. The difference is like the difference between the solar and sidereal day, both caused because the Earth moves around the Sun. But what is so interesting about the Moon is the synchronization of the rotation and orbit, which we see because only one side ever faces the Earth. The Moon is not just a passing rock, accidentally in our orbit. Its formation and evolution must be intimately tied to that of the Earth.
Figure 9.1 Solar versus sidereal time. Starting at (A) the Earth orbits the Sun and rotates on its axis to (B) a day later. After 23 h 56 min—a sidereal day—it has rotated 360° and faces the same stars. After 24 h—a solar day—it has rotated 361° and faces the Sun.
Still, what I am looking for is a clock with which to measure long time periods. The time periods of the orbits of planets are another potential celestial clock. One significant difference between planet-days and planet-years is that there is a strong trend between the position of the planet and the length of its year. This is not true of the length of its day. The further out the planet’s orbit, the longer its orbital time (see Table 9.2). At first we might think it takes longer because it has further to go. But Johannes Kepler (1571–1630) spotted the real trend here. As his third law of planetary motion says, “the square of the orbital period is proportional to the cube of the semi-major axis.” This means that the outer planets not only have a longer distance to travel to orbit the Sun, but they are also traveling slower.
A good feature of using planet-years as opposed to days as a standard is that they are predictable: they are governed by Kepler’s laws. If I am looking for a very slow celestial clock with which to measure the age of the universe, I will want to use something with a very large orbit. Neptune takes 165 Earth years to circumnavigate the Sun, and Pluto (even if it is not really a planet) takes 248 Earth-years to finish a lap. Archimedes wrote The Sand Reckoner only about 9 Pluto-years ago. But there are things in our own solar system that have even longer periods.
Table 9.2 Days and years of the planets.
Comets have orbits just like planets, even if they are highly eccentric and elongated, but they are still governed by Kepler’s laws. Most famous of comets is undoubtedly Halley’s comet, named after Edmond Halley (1656–1742), Astronomer Royal of Great Britain. Halley realized that this comet returned every 76.7 years. Halley’s comet shows up on the Bayeux tapestry, with ominous foreboding for King Harold and the Battle of Hastings (1066), about a dozen Halley’s-comet-years ago.
However, Halley’s comet barely ventures beyond the orbit of Neptune and so is a frequently seen comet. The comet Hale–Bopp has an orbit period of 2,400 years. That means that Stonehenge is only about two Hale–Bopp years old. The comet Hyakutake, which passed us in 1996, last passed us about 17,000 years ago. But it was caught by Jupiter’s gravity and slingshotted into an even greater orbit. We should not expect to see it return for about 140,000 years. In fact, this event points out one of the problems with using comets as clocks. They can easily have their orbits altered by the gravity of the planets and other things they pass. Or they may cease to exist, like the comet Shoemaker–Levy 9, which collided with Jupiter in 1994.
Still, I am looking for a slower clock that could measure even more ancient time. So I need to look for something with even a larger orbit.
***
Nearly a billion times larger than the solar system are galaxies and within each one stars are orbiting the center of the galaxy. This should be the ultimate clock. Our Sun, in fact our whole solar system, is zipping around the Milky Way at 230 km/s. At that rate, and given the size of our galactic orbit, it will take about 230 million years to make one trip around.
A galactic year sounds like a good unit to measure out the eons of deep time. But like planetary days, it is not quite as universal as we would like. We sometimes think of galaxies as giant solid pin-wheels with stars embedded in them. But they are not solid and the stars are not rotating together. Since the stars are still in orbit we might still expect them to follow Kepler’s laws. They do not follow the rule that “the square of t
he orbital period is proportional to the cube of the semi-major axis,” but their motion is still governed by the laws of physics.
Kepler’s laws occupy a unique niche in the history of science. They are very precise, and they are based upon observation. But when originally posed, they were without a theoretical foundation. Within that same century, Newton penned his gravitational law and derived Kepler’s three laws of planetary motion. Deriving those laws in many ways vindicated Newton. You can derive Kepler’s laws from Newton’s gravity if you assume that the planets are orbiting a mass that is concentrated in the center of the system. In our solar system, over 99% of the system’s mass is in the Sun. In galaxies, the mass is not so concentrated. You can still use Newton’s law of universal gravitation, but you need to account for the distribution of matter, including the elusive dark matter. What we see is that orbital speeds are nearly constant for most stars in the galaxy, someplace between 200 and 250 km/s. Of course those stars out on the edge of the galaxy’s spirals have a long path and so a long orbit time.
The solar system travels once around the Milky Way every 230 million years or so. We really are talking deep time now, with the age of the universe at about 60 galactic years. We do not know of any system larger than galaxies that have this sort of periodic, or almost periodic, motion, and therefore we will have to look for slower clocks elsewhere. Let us just quickly review our timekeepers up to now and see what we have missed.
How Big is Big and How Small is Small Page 15