Figure 3.

Rubidium-Strontium. In nearly all of the dating methods, except potassium-argon and the associated argon-argon method, there is always some amount of the daughter product already in the rock when it cools. Using these methods is a little like trying to tell time from an hourglass that was turned over before all of the sand had fallen to the bottom. One can think of ways to correct for this in an hourglass: One could make a mark on the outside of the glass where the sand level started from and then repeat the interval with a stopwatch in the other hand to calibrate it. Or if one is clever she or he could examine the hourglass' shape and determine what fraction of all the sand was at the top to start with. By knowing how long it takes all of the sand to fall, one could determine how long the time interval was. Similarly, there are good ways to tell quite precisely how much of the daughter product was already in the rock when it cooled and hardened.

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Figure 4 is an important type of plot used in rubidium-strontium dating. It shows the strontium-87/strontium-86  ratio on the vertical axis and the

Figure 4. A rubidium-strontium three-isotope plot. When a rock cools, all its minerals have the same ratio of strontium-87 to strontium-86, though they have varying amounts of rubidium. As the rock ages, the rubidium decreases by changing to strontium-87, as shown by the dotted arrows. Minerals with more rubidium gain more strontium-87, while those with less rubidium do not change as much. Notice that at any given time, the minerals all line up--a check to ensure that the system has not been disturbed.

Figure 5. The original amount of the daughter strontium-87 can be precisely determined from the present-day composition by extending the line through the data points back to rubidium-87 = 0. This works because if there were no rubidium-87 in the sample, the strontium composition would not change. The slope of the line is used to determine the age of the sample.

rubidium-87/strontium-86 ratio on the horizontal axis, that is, it plots a ratio of the daughter isotope against a ratio of the parent isotope. At first, all the minerals lie along a horizontal line of constant strontium-87/strontium-86 ratio but with varying rubidium/strontium. As the rock starts to age, rubidium gets converted to strontium. The amount of strontium added to each mineral is proportional to the amount of rubidium present. This change is shown by the dashed arrows, the lengths of which are proportional to the rubidium/strontium ratio. The dashed arrows are slanted because the rubidium/strontium ratio is decreasing in proportion to the increase in strontium-87/strontium-86. The solid line drawn through the samples will thus progressively rotate from the horizontal to steeper and steeper slopes.

All lines drawn through the data points at any later time will intersect the horizontal line (constant strontium-87/strontium-86 ratio) at the same point in the lower left-hand corner. This point, where rubidium-87/strontium-86 = 0 tells the original strontium-87/strontium-86 ratio. From that we can determine the original daughter strontium-87 in each mineral, which is just what we need to know to determine the correct age.

It also turns out that the slope of the line is proportional to the age of the rock. The older the rock, the steeper the line will be. If the slope of the line is m and the half-life is h, the age t (in years) is given by the equation

t = h x ln(m+1)/ln(2)

For a system with a very long half-life like rubidium-strontium, the actual numerical value of the slope will always be quite small. To give an example for the above equation, if the slope of a line in a plot similar to Fig. 4 is m = 0.05110 (strontium isotope ratios are usually measured very accurately--to about one part in ten thousand), 

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we can substitute in the half-life (48.8 billion years) and solve as follows:

t = (48.8) x ln(1.05110)/ln(2)

so t = 3.51 billion years.

The Samarium-Neodymium, Lutetium-Hafnium, and Rhenium-Osmium Methods. All of these methods work very similarly to the rubidium-strontium method. They all use three-isotope diagrams similar to Figure 4 to determine the age. The samarium-neodymium method is the most-often used of these three. It uses the decay of samarium-147 to neodymium-143, which has a half-life of 105 billion years. The ratio of the daughter isotope, neodymium-143, to another neodymium isotope, neodymium-144, is plotted against the ratio of the parent, samarium-147, to neodymium-144. If different minerals from the same rock plot along a line, the slope is determined, and the age is given by the same equation as above. The samarium-neodymium method may be preferred for rocks that have very little potassium and rubidium, for which the potassium-argon, argon-argon, and rubidium-strontium methods might be difficult. The samarium-neodymium method has also been shown to be more resistant to being disturbed or re-set by metamorphic heating events, so for some metamorphosed rocks the samarium-neodymium method is preferred. For a rock of the same age, the slope on the neodymium-samarium plots will be less than on a rubidium-strontium plot because the half-life is longer. However, these isotope ratios are usually measured to extreme accuracy--several parts in ten thousand--so accurate dates can be obtained even for ages less than one fiftieth of a half-life, and with correspondingly small slopes.

The lutetium-hafnium method uses the 38 billion year half-life of lutetium-176 decaying to hafnium-176. This dating system is similar in many ways to samarium-neodymium, as the elements tend to be concentrated in the same types of minerals. Since samarium-neodymium dating is somewhat easier, the lutetium-hafnium method is used less often.

The rhenium-osmium method takes advantage of the fact that the osmium concentration in most rocks and minerals is very low, so a small amount of the parent rhenium-187 can produce a significant change in the osmium isotope ratio. The half-life for this radioactive decay is 42 billion years. The non-radiogenic stable isotopes, osmium-186 or -188, are used as the denominator in the ratios on the three-isotope plots. This method has been useful for dating iron meteorites, and is now enjoying greater use for dating Earth rocks due to development of easier rhenium and osmium isotope measurement techniques.

Uranium-Lead and related techniques. The uranium-lead method is the longest-used dating method. It was first used in 1907, about a century ago. The uranium-lead system is more complicated than other parent-daughter systems; it is actually several dating methods put together. Natural uranium consists primarily of two isotopes, U-235 and U-238, and these isotopes decay with different half-lives to produce lead-207 and lead-206, respectively. In addition, lead-208 is produced by thorium-232. Only one isotope of lead, lead-204, is not radiogenic. The uranium-lead system has an interesting complication: none of the lead isotopes is produced directly from the uranium and thorium. Each decays through a series of relatively short-lived radioactive elements that each decay to a lighter element, finally ending up at lead. Since these half-lives are so short compared to U-238, U-235, and thorium-232, they generally do not affect the overall dating scheme. The result is that one can obtain three independent estimates of the age of a rock by measuring the lead isotopes and their parent isotopes. Long-term dating based on the U-238, U-235, and thorium-232 will be discussed briefly here; dating based on some of the shorter-lived intermediate isotopes is discussed later.

The uranium-lead system in its simpler forms, using U-238, U-235, and thorium-232, has proved to be less reliable than many of the other dating systems. This is because both uranium and lead are less easily retained in many of the minerals in which they are found. Yet the fact that there are three dating systems all in one allows scientists to easily determine whether the system has been disturbed or not. Using slightly more complicated mathematics, different combinations of the lead isotopes and parent isotopes can be plotted in such a way as to 

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minimize the effects of lead loss. One of these techniques is called the lead-lead technique because it determines the ages from the lead isotopes alone. Some of these techniques allow scientists to chart at what points in time metamorphic heating events have occurred, which is also of significant interest to geologists.

The last 5 radiometric systems listed up in Table I have far shorter half-lives than all the rest. Unlike the radioactive isotopes discussed above, these isotopes are constantly being replenished in small amounts in one of two ways. The bottom two entries, uranium-234 and thorium-230, are replenished as the long-lived uranium-238 atoms decay. These will be discussed in the next section. The other three, Carbon-14, beryllium-10, and chlorine-36 are produced by cosmic rays--high energy particles and photons in space--as they hit the Earth's upper atmosphere. Very small amounts of each of these isotopes are present in the air we breathe and the water we drink. As a result, living things, both plants and animals, ingest very small amounts of carbon-14, and lake and sea sediments take up small amounts of beryllium-10 and chlorine-36.

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The cosmogenic dating clocks work somewhat differently than the others. Carbon-14 in particular is used to date material such as bones, wood, cloth, paper, and other dead tissue from either plants or animals. To a rough approximation, the ratio of carbon-14 to the stable isotopes, carbon-12 and carbon-13, is relatively constant in the atmosphere and living organisms, and has been well calibrated. Once a living thing dies, it no longer takes in carbon from food or air, and the amount of carbon-14 starts to drop with time. How far the carbon-14/carbon-12 ratio has dropped indicates how old the sample is. Since the half-life of carbon-14 is less than 6,000 years, it can only be used for dating material less than about 45,000 years old. Dinosaur bones do not have carbon-14 (unless contaminated), as the dinosaurs became extinct over 60 million years ago. But some other animals that are now extinct, such as North American mammoths, can be dated by carbon-14. Also, some materials from prehistoric times, as well as Biblical events, can be dated by carbon-14.

The carbon-14 dates have been carefully cross-checked with non-radiometric age indicators. For example growth rings in trees, if counted carefully, are a reliable way to determine the age of a tree. Each growth ring only collects carbon from the air and nutrients during the year it is made. To calibrate carbon-14, one can analyze carbon from the center several rings of a tree, and then count the rings inward from the living portion to determine the actual age. This has been done for the "Methuselah of trees", the bristlecone pine trees, which grow very slowly and live up to 6,000 years. Scientists have extended this calibration even further. These trees grow in a very dry region near the California-Nevada border. Dead trees in this dry climate take many thousands of years to decay. Growth ring patterns based on wet and dry years can be correlated between living and long dead trees, extending the continuous ring count back to 11,800 years ago. "Floating" records, which are not tied to the present time, exist farther back than this, but their ages are not known with absolute certainty. An effort is presently underway to bridge the gaps so as to have a reliable, continuous record significantly farther back in time. The study of tree rings and the ages they give is called "dendrochronology".

Calibration of carbon-14 back to almost 50,000 years ago has been done in several ways. One way is to find yearly layers that are produced over longer periods of time than tree rings. In some lakes or bays where underwater sedimentation occurs at a relatively rapid rate, the sediments have seasonal patterns, so each year produces a distinct layer. Such sediment layers are called "varves", and are described in more detail below. Varve layers can be counted just like tree rings. If layers contain dead plant material, they can be used to calibrate the carbon-14 ages.

Another way to calibrate carbon-14 farther back in time is to find recently-formed carbonate deposits and cross-calibrate the carbon-14 in them with another short-lived radioactive isotope. Where do we find recently-formed carbonate deposits? If you have ever taken a tour of a cave and seen water dripping from stalactites on the ceiling to stalagmites on the floor of the cave, you have seen carbonate deposits being formed. Since most cave formations have formed relatively recently, formations such as stalactites and stalagmites have been quite useful in cross-calibrating the carbon-14 record.

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What does one find in the calibration of carbon-14 against actual ages? If one predicts a carbon-14 age assuming that the ratio of carbon-14 to carbon-12 in the air has stayed constant, there is a slight error because this ratio has changed slightly. Figure 9 shows that the carbon-14 fraction in the air has decreased over the last 40,000 years by about a factor of two. This is attributed to a strengthening of the Earth's magnetic field during this time. A stronger magnetic field shields the upper atmosphere better from charged cosmic rays, resulting in less carbon-14 production now than in the past. (Changes in the Earth's magnetic field are well documented. Complete reversals of the north and south magnetic poles have occurred many times over geologic history.) A small amount of data beyond 40,000 years (not shown in Fig. 9) suggests that this trend reversed between 40,000 and 50,000 years, with lower carbon-14 to carbon-12 ratios farther back in time, but these data need to be confirmed.

What change does this have on uncalibrated carbon-14 ages? The bottom panel of Figure 9 shows the amount

Figure 9. Ratio of atmospheric carbon-14 to carbon-12, relative to the present-day value (top panel). Unlike long-term radiometric dating methods, radiocarbon relies on knowing the fraction of radioactive carbon-14 in the atmosphere at the time the object being dated was alive. The production of carbon-14 by cosmic rays was up to a factor of about two higher than at present in the timescales over which radiocarbon can be used. Data  for the last 11,800 years comes from tree-ring counting, while the data beyond that age comes from other  sources,  such as from a carbonate stalagmite for the data shown here. The bottom panel shows the offset in  uncalibrated ages caused by this change in atmospheric composition. Tree-ring data are from Stuiver et al.,  Radiocarbon 40, 1041-1083, 1998; stalactite data are from Beck et al., Science 292, 2453-2458, 2001.

of offset in the uncalibrated ages. The offset is generally less than 1500 years over the last 10,000 years, but grows to about 6,000 years at 40,000 years before present. Uncalibrated radiocarbon ages underestimate the actual ages. Note that a factor of two difference in the atmospheric carbon-14 ratio, as shown in the top panel of Figure 9, does not translate to a factor of two offset in the age. Rather, the offset is equal to one half-life, or 5,700 years for carbon-14. This is only about 15% of the age of samples at 40,000 years. The initial portion of the calibration curve in Figure 9 has been widely available and well accepted for some time, so reported radiocarbon dates for ages up to 11,800 years generally give the calibrated ages unless otherwise stated. The calibration curve over the portions extending to 40,000 years is relatively recent, but should become widely adopted as well.

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It is sometimes possible to date geologically young samples using some of the long-lived methods described above. These methods may work on young samples, for example, if there is a relatively high concentration of the parent isotope in the sample. In that case, sufficient daughter isotope amounts are produced in a relatively short time. As an example, an article in Science magazine (vol. 277, pp. 1279-1280, 1997) reports the agreement between the argon-argon method and the actual known age of lava from the famous eruption of Vesuvius in Italy in 79 A.D.

There are other ways to date some geologically young samples. Besides the cosmogenic radionuclides discussed above, there is one other class of short-lived radionuclides on Earth. These are ones produced by decay of the long-lived radionuclides given in the upper part of Table 1. As mentioned in the Uranium-Lead section, uranium does not decay immediately to a stable isotope, but decays through a number of shorter-lived radioisotopes until it ends up as lead. While the uranium-lead system can measure intervals in the millions of years generally without problems from the intermediate isotopes, those intermediate isotopes with the longest half-lives span long enough time intervals for dating events less than several hundred thousand years ago. (Note that these intervals are well under a tenth of a percent of the half-lives of the long-lived parent uranium and thorium isotopes discussed earlier.) Two of the most frequently-used of these "uranium-series" systems are uranium-234 and thorium-230. These are listed as the last two entries in Table 1, and are illustrated in Figure 10.

Figure 10. A schematic representation of the uranium-238 decay chain, showing the longest-lived nuclides. Half-lives are given in each box. Solid arrows represent direct decay, while dashed arrows indicate that there are one or more intermediate decays, with the longest intervening half-life given below the arrow.

Like carbon-14, the shorter-lived uranium-series isotopes are constantly being replenished, in this case, by decaying uranium-238 supplied to the Earth during its original creation. Following the example of carbon-14, you may guess that one way to use these isotopes for dating is to remove them from their source of replenishment. This starts the dating clock. In carbon-14 this happens when a living thing (like a tree) dies and no longer takes in carbon-14-laden CO₂. For the shorter-lived uranium-series radionuclides, there needs to be a physical removal from uranium. The chemistry of uranium and thorium are such that they are in fact easily removed from each other. Uranium tends to stay dissolved in water, but thorium is insoluble in water. So a number of applications of the thorium-230 method are based on this chemical partition between uranium and thorium.

Sediments at the bottom of the ocean have very little uranium relative to the thorium. Because of this, the uranium, and its contribution to the thorium abundance, can in many cases be ignored in sediments. Thorium-230 then behaves similarly to the long-lived parent isotopes we discussed earlier. It acts like a simple parent-daughter system, and it can be used to date sediments.

On the other hand, calcium carbonates produced biologically (such as in corals, shells, teeth, and bones) take in small amounts of uranium, but essentially no thorium (because of its much lower concentrations in the water). This allows the dating of these materials by their lack of thorium. A brand-new coral reef will have essentially no thorium-230. As it ages, some of its uranium decays to thorium-230. While the thorium-230 itself is radioactive, this can be corrected for. The equations are more complex than for the simple systems described earlier, but the uranium-234 / thorium-230 method has been used to date corals now for several decades. Comparison of uranium-234 ages with ages obtained by counting annual growth bands of corals proves that the technique is 

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highly accurate when properly used (Edwards et al., Earth Planet. Sci. Lett. 90, 371, 1988). The method has also been used to date stalactites and stalagmites from caves, already mentioned in connection with long-term calibration of the radiocarbon method. In fact, tens of thousands of uranium-series dates have been performed on cave formations around the world.

The uranium-234 / thorium-230 method is now being used to date animal and human bones and teeth. Previously, dating of anthropology sites had to rely on dating of geologic layers above and below the artifacts. But with improvements in this method, it is becoming possible to date the human and animal remains themselves. Work to date shows that dating of tooth enamel can be quite reliable. However, dating of bones can be more problematic, as bones are more susceptible to contamination by the surrounding soils. As with all dating, the agreement of two or more methods is highly recommended for confirmation of a measurement. If the samples are beyond the range of radiocarbon (e.g., > 40,000 years), a second method for confirmation of thorium-230 ages may need to be a non-radiometric method such as ESR or TL, mentioned below.

Non-Radiometric Dating Methods for the Past 100,000 Years

We will digress briefly from radiometric dating to talk about other dating techniques. It is important to understand that a very large number of accurate dates covering the past 100,000 years has been obtained from many other methods besides radiometric dating. We have already mentioned dendrochronology (tree ring dating) above. Dendrochronology is only the tip of the iceberg in terms of non-radiometric dating methods. Here we will look briefly at some other non-radiometric dating techniques.

Ice Cores. One of the best ways to measure farther back in time than tree rings is by using the seasonal variations in polar ice from Greenland and Antarctica. There are a number of differences between snow layers made in winter and those made in spring, summer, and fall. These seasonal layers can be counted just like tree rings. The seasonal differences consist of a) visual differences caused by increased bubbles and larger crystal size from summer ice compared to winter ice, b) dust layers deposited each summer, c) nitric acid concentrations, measured by electrical conductivity of the ice, d) chemistry of contaminants in the ice, and e) seasonal variations in the relative amounts of heavy hydrogen (deuterium) and heavy oxygen (oxygen-18) in the ice. These isotope ratios are sensitive to the temperature at the time they fell as snow from the clouds. The heavy isotope is lower in abundance during the colder winter snows than it is in snow falling in spring and summer. So the yearly layers of ice can be tracked by each of these five different indicators, similar to growth rings on trees. The different types of layers are summarized in Table III.

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Ice cores are obtained by drilling very deep holes in the ice caps on Greenland and Antarctica with specialized drilling rigs. As the rigs drill down, the drill bits cut around a portion of the ice, capturing a long undisturbed "core" in the process. These cores are carefully brought back to the surface in sections, where they are catalogued, and taken to research laboratories under refrigeration. A very large amount of work has been done on several deep ice cores up to 9,000 feet in depth. Several hundred thousand measurements are sometimes made for a single technique on a single ice core.

A continuous count of layers exists back as far as 160,000 years. In addition to yearly layering, individual strong events (such as large-scale volcanic eruptions) can be observed and correlated between ice cores. A number of historical eruptions as far back as Vesuvius nearly 2,000 years ago serve as benchmarks with which to determine the accuracy of the yearly layers as far down as around 500 meters. As one goes further down in the ice core, the ice becomes more compacted than near the surface, and individual yearly layers are slightly more difficult to observe. For this reason, there is some uncertainty as one goes back towards 100,000 years. Ages of 40,000 years or less are estimated to be off by 2% at most. Ages of 60,000 years may be off by up to 10%, and the uncertainty rises to 20% for ages of 110,000 years based on direct counting of layers (D. Meese et al., J. Geophys. Res. 102, 26,411, 1997). Recently, absolute ages have been determined to 75,000 years for at least one location using cosmogenic radionuclides chlorine-36 and beryllium-10 (G. Wagner et al., Earth Planet. Sci. Lett. 193, 515, 2001). These agree with the ice flow models and the yearly layer counts. Note that there is no indication anywhere that these ice caps were ever covered by a large body of water, as some people with young-Earth views would expect.

Table III. Polar ice core layers, counting back yearly layers, consist of the following:

Varves. Another layering technique uses seasonal variations in sedimentary layers deposited underwater. The two requirements for varves to be useful in dating are 1) that sediments vary in character through the seasons to produce a visible yearly pattern, and 2) that the lake bottom not be disturbed after the layers are deposited. These conditions are most often met in small, relatively deep lakes at mid to high latitudes. Shallower lakes typically experience an overturn in which the warmer water sinks to the bottom as winter approaches, but deeper lakes can have persistently thermally stratified (temperature-layered) water masses, leading to less turbulence, and better conditions for varve layers. Varves can be harvested by coring drills, somewhat similar to the harvesting of ice cores discussed above. Overall, many hundreds of lakes have been studied for their varve patterns. Each yearly varve layer consists of a) mineral matter brought in by swollen streams in the spring. b) This gradually gives way to organic particulate matter such as plant fibers, algae, and pollen with fine-grained mineral 

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matter, consistent with summer and fall deposition. c) With winter ice covering the lake, fine-grained organic matter provides the final part of the yearly layer. Regular sequences of varves have been measured going back to about 35,000 years. The thicknesses of the layers and the types of material in them tells a lot about the climate of the time when the layers were deposited. For example, pollens entrained in the layers can tell what types of plants were growing nearby at a particular time.

Other annual layering methods. Besides tree rings, ice cores, and sediment varves, there are other processes that result in yearly layers that can be counted to determine an age. Annual layering in coral reefs can be used to date sections of coral. Coral generally grows at rates of around 1 cm per year, and these layers are easily visible. As was mentioned in the uranium-series section, the counting of annual coral layers was used to verify the accuracy of the thorium-230 method.

Thermoluminescence. There is a way of dating minerals and pottery that does not rely directly on half-lives. Thermoluminescence dating, or TL dating, uses the fact that radioactive decays cause some electrons in a material to end up stuck in higher-energy orbits. The number of electrons in higher-energy orbits accumulates as a material experiences more natural radioactivity over time. If the material is heated, these electrons can fall back to their original orbits, emitting a very tiny amount of light. If the heating occurs in a laboratory furnace equipped with a very sensitive light detector, this light can be recorded. (The term comes from putting together thermo, meaning heat, and luminescence, meaning to emit light). By comparison of the amount of light emitted with the natural radioactivity rate the sample experienced, the age of the sample can be determined. TL dating can generally be used on samples less than half a million years old. Related techniques include optically stimulated luminescence (OSL), and infrared stimulated luminescence (IRSL). TL dating and its related techniques have been cross calibrated with samples of known historical age and with radiocarbon and thorium dating. While TL dating does not usually pinpoint the age with as great an accuracy as these other conventional radiometric dating, it is most useful for applications such as pottery or fine-grained volcanic dust, where other dating methods do not work as well.

Electron spin resonance (ESR). Also called electron paramagnetic resonance, ESR dating also relies on the changes in electron orbits and spins caused by radioactivity over time. However, ESR dating can be used over longer time periods, up to two million years, and works best on carbonates, such as in coral reefs and cave deposits. It has also seen extensive use in dating tooth enamel.

Cosmic-ray exposure dating. This dating method relies on measuring certain isotopes produced by cosmic ray impacts on exposed rock surfaces. Because cosmic rays constantly bombard meteorites flying through space, this method has long been used to date the ' flight time' of meteorites--that is the time from when they were chipped off a larger body (like an asteroid) to the time they land on Earth. The cosmic rays produce small amounts of naturally-rare isotopes such as neon-21 and helium-3, which can be measured in the laboratory. The cosmic-ray exposure ages of meteorites are usually around 10 million years, but can be up to a billion years for some iron meteorites. In the last fifteen years, people have also used cosmic ray exposure ages to date rock surfaces on the Earth. This is much more complicated because the Earth's magnetic field and atmosphere shield us from most of the cosmic rays. Cosmic ray exposure calibrations must take into 

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account the elevation above sea level because the atmospheric shielding varies with elevation, and must also take into account latitude, as the magnetic shielding varies from the equator to the poles. Nevertheless, terrestrial cosmic-ray exposure dating has been shown to be useful in many cases.

We have covered a lot of convincing evidence that the Earth was created a very long time ago. The agreement of many different dating methods, both radiometric and non-radiometric, over hundreds of thousands of samples, is very convincing. Yet, some Christians question whether we can believe something so far back in the past. My answer is that it is similar to believing in other things of the past. It only differs in degree. Why do you believe Abraham Lincoln ever lived? Because it would take an extremely elaborate scheme to make up his existence, including forgeries, fake photos, and many other things, and besides, there is no good reason to simply have made him up. Well, the situation is very similar for the dating of rocks, only we have rock records rather than historical records. Consider the following:

• There are well over forty different radiometric dating methods, and scores of other methods such as tree rings and ice cores.
• All of the different dating methods agree--they agree a great majority of the time over millions of years of time. Some Christians make it sound like there is a lot of disagreement, but this is not the case. The disagreement in values needed to support the position of young-Earth proponents would require differences in age measured by orders of magnitude (e.g., factors of 10,000, 100,000, a million, or more). The differences actually found in the scientific literature are usually close to the margin of error, usually a few percent, not orders of magnitude!
• Vast amounts of data overwhelmingly favor an old Earth. Several hundred laboratories around the world are active in radiometric dating. Their results consistently agree with an old Earth. Over a thousand papers on radiometric dating were published in scientifically recognized journals in the last year, and hundreds of thousands of dates have been published in the last 50 years. Essentially all of these strongly favor an old Earth.
• Radioactive decay rates have been measured for over sixty years now for many of the decay clocks without any observed changes. And it has been close to a hundred years since the uranium-238 decay rate was first determined.
• Both long-range and short-range dating methods have been successfully verified by dating lavas of historically known ages over a range of several thousand years.
• The mathematics for determining the ages from the observations is relatively simple.

The last three points deserve more attention. Some Christians have argued that something may be slowly changing with time so all the ages look older than they really are. The only two quantities in the exponent of a decay rate equation are the half-life and the time. So for ages to appear longer than actual, all the half-lives would have to be changing in sync with each other. One could consider that time itself was changing if that happened (remember that our clocks are now standardized to atomic clocks!). And such a thing would have to have occurred without our detection in the last hundred years, which is already 5% of the way back to the time 

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of Christ.

Beyond this, scientists have now used a "time machine" to prove that the half-lives of radioactive species were the same millions of years ago. This time machine does not allow people to actually go back in time, but it does allow scientists to observe ancient events from a long way away. The time machine is called the telescope. Because God's universe is so large, images from distant events take a long time to get to us. Telescopes allow us to see supernovae (exploding stars) at distances so vast that the pictures take hundreds of thousands to millions of years to arrive at the Earth. So the events we see today actually occurred hundreds of thousands to millions of years ago. And what do we see when we look back in time? Much of the light following a supernova blast is powered by newly created radioactive parents. So we observe radiometric decay in the supernova light. The half-lives of decays occurring hundreds of thousands of years ago are thus carefully recorded! These half-lives completely agree with the half-lives measured from decays occurring today. We must conclude that all evidence points towards unchanging radioactive half-lives.

Some individuals have suggested that the speed of light must have been different in the past, and that the starlight has not really taken so long to reach us. However, the astronomical evidence mentioned above also suggests that the speed of light has not changed, or else we would see a significant apparent change in the half-lives of these ancient radioactive decays.

Some doubters have tried to dismiss geologic dating with a sleight of hand by saying that no rocks are completely closed systems (that is, that no rocks are so isolated from their surroundings that they have not lost or gained some of the isotopes used for dating). Speaking from an extreme technical viewpoint this might be true--perhaps 1 atom out of 1,000,000,000,000 of a certain isotope has leaked out of nearly all rocks, but such a change would make an immeasurably small change in the result. The real question to ask is, "is the rock sufficiently close to a closed system that the results will be same as a really closed system?" Since the early 1960s many books have been written on this subject. These books detail experiments showing, for a given dating system, which minerals work all of the time, which minerals work under some certain conditions, and which minerals are likely to lose atoms and give incorrect results. Understanding these conditions is part of the science of geology. Geologists are careful to use the most reliable methods whenever possible, and as discussed above, to test for agreement between different methods.

Some people have tried to defend a young Earth position by saying that the half-lives of radionuclides can in fact be changed, and that this can be done by certain little-understood particles such as neutrinos, muons, or cosmic rays. This is stretching it. While certain particles can cause nuclear changes, they do not change the half-lives. The nuclear changes are well understood and are nearly always very minor in rocks. In fact the main nuclear changes in rocks are the very radioactive decays we are talking about.

There are only three quite technical instances where a half-life changes, and these do not affect the dating methods we have discussed.

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2. Physical conditions at the center of stars or for cosmic rays differ very greatly from anything experienced in rocks on or in the Earth. Yet, self-proclaimed "experts" often confuse these conditions. Cosmic rays are very, very high-energy atomic nuclei flying through space. The electron-capture decay mentioned above does not take place in cosmic rays until they slow down. This is because the fast-moving cosmic ray nuclei do not have electrons surrounding them, which are necessary for this form of decay. Another case is material inside of stars, which is in a plasma state where electrons are not bound to atoms. In the extremely hot stellar environment, a completely different kind of decay can occur. ' Bound-state beta decay' occurs when the nucleus emits an electron into a bound electronic state close to the nucleus. This has been observed for dysprosium-163 and rhenium-187 under very specialized conditions simulating the interior of stars (Phys. Rev. Lett., 69, 2164-2167; Phys. Rev. Lett., 77, 5190-5193, 1996). All normal matter, such as everything on Earth, the Moon, meteorites, etc. has electrons in normal positions, so these instances never apply to rocks, or anything colder than several hundred thousand degrees.

As an example of incorrect application of these conditions to dating, one young-Earth proponent suggested that God used plasma conditions when He created the Earth a few thousand years ago. This writer suggested that the rapid decay rate of rhenium under extreme plasma conditions might explain why rocks give very old ages instead of a young-Earth age. This writer neglected a number of things, including: a) plasmas only affect a few of the dating methods. More importantly, b) rocks and hot gaseous plasmas are completely incompatible forms of matter! The material would have to revert back from the plasma state before it could form rocks. In such a scenario, as the rocks cooled and hardened, their ages would be completely reset to zero as described in previous sections. If this person's scenario were correct, instead of showing old ages, all the rocks should show a uniform ~4,000 year age of creation. That is obviously not what is observed.

3. The last case also involves very fast-moving matter. It has been demonstrated by atomic clocks in very fast spacecraft. These atomic clocks slow down very slightly (only a second or so per year) as predicted by Einstein's theory of relativity. No rocks in our solar system are going fast enough to make a noticeable change in their dates.

These cases are very specialized, and all are well understood. None of these cases alter the dates of rocks either on Earth or other planets in the solar system. The conclusion once again is that half-lives are completely reliable in every context for the dating of rocks on Earth and even on other planets. The Earth and all creation appears to be very ancient.

It would not be inconsistent with the scientific evidence to conclude that God made everything relatively recently, but with the appearance of great age, just as Genesis 1 and 2 tell of God making Adam as a fully grown human (which implies the appearance of age). This idea was captured by Phillip Henry Gosse in the book, "Omphalos: An Attempt to Untie the Geological Knot", written just two years before Darwin's "Origin of Species". The idea of a false appearance of great age is a philosophical and theological matter that we won't go into here. The main drawback--and it is a strong one--is that this makes God appear to be a deceiver. However, some 

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people have no problem with this. Certainly whole civilizations have been incorrect (deceived?) in their scientific and theological ideas in the past. Whatever the philosophical conclusions, it is important to note that an apparent old Earth is consistent with the great amount of scientific evidence.

As Christians it is of great importance that we understand God's word correctly. Yet from the middle ages up until the 1700s people insisted that the Bible taught that the Earth, not the Sun, was the center of the solar system. It wasn't that people just thought it had to be that way; they actually quoted scriptures: "The Earth is firmly fixed; it shall not be moved" (Psalm 104:5), or "the sun stood still" (Joshua 10:13; why should it say the sun stood still if it is the Earth's rotation that causes day and night?), and many other passages. I am afraid the debate over the age of the Earth has many similarities. But I am optimistic. Today there are many Christians who accept the reliability of geologic dating, but do not compromise the spiritual and historical inerrancy of God's word. While a full discussion of Genesis 1 is not given here, references are given below to a few books that deal with that issue.

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APPENDIX: Common Misconceptions Regarding Radiometric Dating Methods

There are a number of misconceptions that seem especially prevalent among Christians. Most of these topics are covered in the above discussion, but they are reviewed briefly here for clarity.

1. Radiometric dating is based on index fossils whose dates were assigned long before radioactivity was discovered.

This is not at all true, though it is implied by some young-Earth literature. Radiometric dating is based on the half-lives of the radioactive isotopes. These half-lives have been measured over the last 40-90 years. They are not calibrated by fossils.

2. No one has measured the decay rates directly; we only know them from inference.

Decay rates have been directly measured over the last 40-100 years. In some cases a batch of the pure parent material is weighed and then set aside for a long time and then the resulting daughter material is weighed. In many cases it is easier to detect radioactive decays by the energy burst that each decay gives off. For this a batch of the pure parent material is carefully weighed and then put in front of a Geiger counter or gamma-ray detector. These instruments count the number of decays over a long time.

3. If the half-lives are billions of years, it is impossible to determine them from measuring over just a few years or decades.

The example given in the section titled, "The Radiometric Clocks" shows that an accurate determination of the half-life is easily achieved by direct counting of decays over a decade or shorter. This is because a) all decay curves have exactly the same shape (Fig. 1), differing only in the half-life, and b) trillions of decays can be counted in one year even using only a fraction of a gram of material with a half-life of a billion years. Additionally, lavas of historically known ages have been correctly dated even using methods with long half-lives.

4. The decay rates are poorly known, so the dates are inaccurate.

Most of the decay rates used for dating rocks are known to within two percent. Uncertainties are only slightly higher for rhenium (5%), lutetium (3%), and beryllium (3%), discussed in connection with Table 1. Such small uncertainties are no reason to dismiss radiometric dating. Whether a rock is 100 million years or 102 million years old does not make a great deal of difference.

5. A small error in the half-lives leads to a very large error in the date.

Since exponents are used in the dating equations, it is possible for people to think this might be true, but it is not. If a half-life is off by 2%, it will only lead to a 2% error in the date.

6. Decay rates can be affected by the physical surroundings.

This is not true in the context of dating rocks. Radioactive atoms used for dating have been subjected to extremes of heat, cold, pressure, vacuum, acceleration, and strong chemical reactions far beyond anything experienced by rocks, without any significant change. The only exceptions, which are not relevant to dating rocks, are discussed under the section, "Doubters Still Try", above.

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7. A small change in the nuclear forces probably accelerated nuclear clocks during the first day of creation a few thousand years ago, causing the spuriously old radiometric dates of rocks.

Rocks are dated from the time of their formation. For it to have any bearing on the radiometric dates of rocks, such a change of nuclear forces must have occurred after the Earth (and the rocks) were formed. To make the kind of difference suggested by young-Earth proponents, the half-lives must be shortened from several billion years down to several thousand years--a factor of at least a million. But to shorten half-lives by factors of a million would cause large physical changes. As one small example, recall that the Earth is heated substantially by radioactive decay. If that decay is speeded up by a factor of a million or so, the tremendous heat pulse would easily melt the whole Earth, including the rocks in question! No radiometric ages would appear old if this happened.

8. The decay rates might be slowing down over time, leading to incorrect old dates.

There are two ways we know this didn't happen: a) we have checked them out with "time machines", and b) it doesn't make sense mathematically. Both of these points are explained in the section titled, "Can We Really Believe the Dating Systems?"

9. We should measure the "full-life" (the time at which all of the parent is gone) rather than the half-life (the time when half of it is gone).

Unlike sand in an hourglass, which drops at a constant rate independent of how much remains in the top half of the glass, the number of radioactive decays is proportional to the amount of parent remaining. Figure 1 shows how after 2 half-lives, 1/2 x 1/2 = 1/4 is left, and so on. After 10 half-lives there is 2^-10 = 0.098% remaining. A half-life is more easy to define than some point at which almost all of the parent is gone. Scientists sometimes instead use the term "mean life", that is, the average life of a parent atom. The mean life is always 1/ln(2) = 1.44 times the half-life. For most of us half-life is easier to understand.

10. To date a rock one must know the original amount of the parent element. But there is no way to measure how much parent element was originally there.

It is very easy to calculate the original parent abundance, but that information is not needed to date the rock. All of the dating schemes work from knowing the present abundances of the parent and daughter isotopes. The original abundance N₀, of the parent is simply N₀ = N e^kt, where N is the present abundance, t is time, and k is a constant related to the half life.

11. There is little or no way to tell how much of the decay product, that is, the daughter isotope, was originally in the rock, leading to anomalously old ages.

A good part of this article is devoted to explaining how one can tell how much of a given element or isotope was originally present. Usually it involves using more than one sample from a given rock. It is done by comparing the ratios of parent and daughter isotopes relative to a stable isotope for samples with different relative amounts of the parent isotope. For example, in the rubidium-strontium method one compares rubidium-87/strontium-86 to strontium-87/strontium-86 for different minerals. From this one can determine how much of the daughter isotope would be present if there had been no parent isotope. This is the same as the initial amount (it would not change if there were no parent isotope to decay). Figures 4 and 5, and the accompanying explanation, tell how this is done most of the time. While this is not absolutely 100% foolproof, comparison of several dating methods will always show whether the given date is reliable.

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12. There are only a few different dating methods.

This article has listed and discussed a number of different radiometric dating methods and has also briefly described a number of non-radiometric dating methods. There are actually many more methods out there. Well over forty different radiometric dating methods are in use, and a number of non-radiogenic methods not even mentioned here.

13. "Radiation halos" in rocks prove that the Earth was young.

This refers to tiny halos of crystal damage surrounding spots where radioactive elements are concentrated in certain rocks. Halos thought to be from polonium, a short-lived element produced from the decay of uranium, have been found in some rocks. A plausible explanation for a halo from such a short-lived element is that these were not produced by an initial concentration of the radioactive element. Rather, as water seeped through cracks in the minerals, a chemical change caused newly-formed polonium to drop out of solution at a certain place and almost immediately decay there. A halo would build up over a long period of time even though the center of the halo never contained more than a few atoms of polonium at one time. "Hydrothermal" effects can act in ways that at first seem strange, such as the well-known fact that gold--a chemically un-reactive metal with very low solubilities--is concentrated along quartz veins by the action of water over long periods of time. Other researchers have found halos produced by an indirect radioactive decay effect called hole diffusion, which is an electrical effect in a crystal. These results suggest that the halos in question are not from short-lived isotopes after all.

At any rate, halos from uranium inclusions are far more common. Because of uranium's long half-lives, these halos take at least several hundred million years to form. Because of this, most people agree that halos provide compelling evidence for a very old Earth.

14. A young-Earth research group reported that they sent a rock erupted in 1980 from Mount Saint Helens volcano to a dating lab and got back a potassium-argon age of several million years. This shows we should not trust radiometric dating.

There are indeed ways to "trick" radiometric dating if a single dating method is improperly used on a sample. Anyone can move the hands on a clock and get the wrong time. Likewise, people actively looking for incorrect radiometric dates can in fact get them. Geologists have known for over forty years that the potassium-argon method cannot be used on rocks only twenty to thirty years old. Publicizing this incorrect age as a completely new finding was inappropriate. The reasons are discussed in the Potassium-Argon Dating section above. Be assured that multiple dating methods used together on igneous rocks are almost always correct unless the sample is too difficult to date due to factors such as metamorphism or a large fraction of xenoliths.

15. Low abundances of helium in zircon grains show that these minerals are much younger than radiometric dating suggests.

Zircon grains are important for uranium-thorium-lead dating because they contain abundant uranium and thorium parent isotopes. Helium is also produced from the decay of uranium and thorium. However, as a gas of very small atomic size, helium tends to escape rather easily. Researchers have studied the rates of diffusion of helium from zircons, with the prediction from one study by a young-Earth creationist suggesting that it should be quantitatively retained despite its atomic size. The assumptions of the temperature conditions of the rock over time are most likely unrealistic in this case.

16. The fact that radiogenic helium and argon are still degassing from the Earth's interior prove that the Earth must be young.

The radioactive parent isotopes, uranium and potassium, have very long half-lives, as shown in Table 1. These parents still exist in abundance in the Earth's interior, and are still producing helium and argon. There is also a time lag between the production of the daughter products and their degassing. If the Earth were geologically very young, very little helium and argon would have been produced. One can compare the amount of argon in the atmosphere to what would be expected from decay of potassium over 4.6 billion years, and in fact it is consistent.

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17. The waters of Noah's flood could have leached radioactive isotopes out of rocks, disturbing their ages.

This is actually suggested on one website! While water can affect the ability to date rock surfaces or other weathered areas, there is generally no trouble dating interior portions of most rocks from the bottom of lakes, rivers, and oceans. Additionally, if ages were disturbed by leaching, the leaching would affect different isotopes at vastly different rates. Ages determined by different methods would be in violent disagreement. If the flood were global in scope, why then would we have any rocks for which a number of different methods all agree with each other? In fact, close agreement between methods for most samples is a hallmark of radiometric dating.

18. We know the Earth is much younger because of non-radiogenic indicators such as the sedimentation rate of the oceans.

There are a number of parameters which, if extrapolated from the present without taking into account the changes in the Earth over time, would seem to suggest a somewhat younger Earth. These arguments can sound good on a very simple level, but do not hold water when all the factors are considered. Some examples of these categories are the decaying magnetic field (not mentioning the widespread evidence for magnetic reversals), the saltiness of the oceans (not counting sedimentation!), the sedimentation rate of the oceans (not counting Earthquakes and crustal movement, that is, plate tectonics), the relative paucity of meteorites on the Earth's surface (not counting weathering or plate tectonics), the thickness of dust on the moon (without taking into account brecciation over time), the Earth-Moon separation rate (not counting changes in tides and internal forces), etc. While these arguments do not stand up when the complete picture is considered, the case for a very old creation of the Earth fits well in all areas considered.