#### Introduction

In a 2012 interview, Florida Senator Marco Rubio, a U.S. presidential candidate for 2016, was asked “How old do you think the Earth is?” He responded, somewhat coyly: “Whether the Earth was created in 7 days, or 7 actual eras, I’m not sure we’ll ever be able to answer that.” Keep in mind that Rubio sits on the Science and Space Subcommittee in the U.S. Senate Committee on Commerce, Science and Transportation, which oversees by far the largest scientific research budget in the world.

Paul C. Broun (R-Ga.), who serves on the U.S. House Science and Technology Committee, was more direct: “I don’t believe that the earth’s but about 9,000 years old. I believe it was created in six days as we know them.”

To a scientific mind, such statements are incredible. Yet they are fairly representative of the public at large. For example, a 2014 Gallup poll found that 42% of Americans believed that God created humans essentially in their present form, within the past 10,000 years. A 2010 poll in Australia found that roughly 35% of Australians believed that humans lived at the time of dinosaurs.

#### Radiometric dating

So how do scientists measure the age of the earth and its fossil layers? How reliable are these dates?

The primary technique for measuring these ages is *radiometric dating*. Radiometric dating is rooted in the rates of radioactive decay of various nuclear isotopes, which rates have been measured carefully in numerous laboratories beginning in the early 20th century. Radioactive decay is in turn a very basic physical phenomenon, well understood as a consequence of quantum mechanics, one of two cornerstones of modern physics, and has been precisely confirmed in thousands of very exacting experiments. For these reasons, scientists have considerable confidence in these dates when they are measured properly in accordance with procedures that have been developed and refined over several decades.

Some of the most commonly used radiometric schemes are Argon-argon, Lead-lead, Potassium-argon, Rubidium-strontium, Uranium-lead and Uranium-thorium. Each method has its own particular range of applicability, based on the half-life involved. Uranium-thorium dating, for instance, can be used to date specimens up to about 500,000 years old (since the half-life of the U-Th decay is 75,000 years), but Rubidium-Strontium dating can be used to date specimens billions of years old (since the half-life of the Rb-Sr decay is 48.8 billion years).

#### Some technical details

The amount of a radioactive isotope that remains in a given rock sample can be measured using a mass spectrometer, which nowadays can be found in many scientific laboratories. In mathematical terms, radioactive decay is governed by a simple exponential formula, taught in many high school math classes:

P_{1} = P_{0} e^{-L t}

where e = 2.71828… is the well-known math constant, P_{0} is the original amount of the radioactive material, P_{1} is the amount after time t, and L is the decay constant for the radioactive isotope. This decay constant L can be expressed in terms of the half life T (the time it takes for one-half of the material to decay) as L = 0.693147 / T. In other words, if we know P_{1} and P_{0}, or even merely their ratio, we can solve the above equation for the time t.

However, usually it is not possible to apply this formula directly, because, for instance, in many cases we do not know the original amount of the radioactive isotope when the rock was solidified. Also, such a calculation does not provide us with any statistical error margin to double-check the result.

Fortunately, scientists have developed several methods, including the “isochron” method, that not only circumvent the difficulty of not knowing the original amounts, but also provide a very reliable means of statistical validity checking. These methods are based on “linear regression,” an elementary scheme taught in high school statistics classes to fit data points to a straight line, which is built into most spreadsheet programs for personal computers.

Suffice it to say that the overall methodology for determining radiometric dates is entirely straightforward, using equipment and experimental techniques that have been highly refined over the last 50 years since radiometric dating was first developed. For some additional technical details, including the actual formulas used, see Radiometric dating.

#### A sample isochron graph

Here is just one example of an isochron graph, which is entirely typical among the tens of thousands of examples that could be mentioned. Note how breathtakingly close these points are to the fitted line, thus confirming with high statistical confidence the validity of the resulting date:

The data for the this graph is a set of measurements of basaltic achondrites (meteorites). The corresponding date obtained from this isochron graph (based on the slope of the line), is 4.396 billion years, plus or minus 0.18 billion years.

#### How reliable are these dates?

As with any experimental procedure in any field of science, these measurements are subject to certain “glitches” and “anomalies,” as noted in the literature. Young-earth creationists make great hay of these examples, but their criticisms don’t hold much water. They are instances of the “forest fallacy” — finding fault with the bark on a handful of trees, then trying to claim that the forest does not exist. For additional discussion, see Reliability of radiometric dating, this response by noted geologist Brent Dalrymple, and this response by Roger Wiens, a Los Alamos physicist.

#### Half lives and the age of the earth

In any event, there is a simple way to see that the earth must be at least 1.6 billion years old, which does not require any mass spectrometers, isochron graphs, calculus or statistical software (provided one accepts a few very-well-established measured rates of radioactivity). Consider this list of all known radioactive isotopes with half-lives between 10^{6} and 10^{15} years, and which are not themselves produced by any natural process such as radioactive decay or cosmic ray bombardment:

Isotope | Half-life (years) | Found in nature? | Isotope | Half-life (years) | Found in nature? |

In-115 | 4.41 x 10^{14} |
yes | Gd-152 | 1.08 x 10^{14} |
yes |

Ba-130 | 7.00 x 10^{13} |
yes | Pt-190 | 6.50 x 10^{11} |
yes |

Sm-147 | 1.06 x 10^{11} |
yes | La-138 | 1.02 x 10^{11} |
yes |

Rb-87 | 4.97 x 10^{10} |
yes | Re-187 | 4.12 x 10^{10} |
yes |

Lu-176 | 3.76 x 10^{10} |
yes | Th-232 | 1.40 x 10^{10} |
yes |

U-238 | 4.47 x 10^{9} |
yes | K-40 | 1.25 x 10^{9} |
yes |

U-235 | 7.04 x 10^{8} |
yes | Pu-244 | 8.00 x 10^{7} |
yes |

Sm-146 | 6.80 x 10^{7} |
yes | Nb-92 | 3.47 x 10^{7} |
no |

Pb-205 | 1.73 x 10^{7} |
no | Cm-247 | 1.56 x 10^{7} |
no |

Hf-182 | 8.90 x 10^{6} |
no | Pd-107 | 6.50 x 10^{6} |
no |

Tc-98 | 4.20 x 10^{6} |
no | Bi-210 | 3.04 x 10^{6} |
no |

Dy-154 | 3.00 x 10^{6} |
no | Fe-60 | 2.62 x 10^{6} |
no |

Tc-97 | 2.60 x 10^{6} |
no | Cs-135 | 2.30 x 10^{6} |
no |

Gd-150 | 1.79 x 10^{6} |
no | Zr-93 | 1.53 x 10^{6} |
no |

(In the above chart, years are displayed in scientific notation: i.e., 1 x 10^{6} = 1 million; 1 x 10^{9} = 1 billion, etc.)

All of the above isotopes are readily produced in nuclear reactors, so there is every reason to believe that they were formed along with stable isotopes, in roughly the same abundance as nearby stable isotopes of similar atomic weight, when the material forming our solar system was produced in an ancient stellar explosion. A quick calculation shows that after an elapsed period of 20 times the half-life of a given isotope, the fraction 1/2^{20} = 1/1048576 (i.e., roughly one part in one million) of the original isotope will remain, which is a small but nonetheless detectable amount. Similarly, after 30 half-lives, roughly one part in one billion will remain, and after 40 half-lives, roughly one part in one trillion will remain, which is near the current limit of detectability.

Now note that an absolutely clear-cut fact is revealed in the above table: **every** isotope in the list with a half life less than 68 million years is absent in nature, evidently because all traces of these isotopes have decayed away, yet **every** isotope with a half life greater than 68 million years is present at some detectable level. This is incontestable evidence that the material from which our earth and solar system was formed is at least 20 x 68 million (= 1.36 billion) years old, and, more likely, is at least 40 x 68 million (= 2.72 billion) years old.

#### Conclusion

In short, the conclusion that the earth and its fossil layers are very old is supported by an overwhelming weight of evidence, with literally tens of thousands of carefully conducted peer-reviewed studies behind it. The methodology is based on the most fundamental physics, and the methodology is, forgive the pun, rock-solid.

Some creationists assert that we cannot know that the laws of physics and radioactive decay were the same millions of years ago. But scientists really do have “time machines.” For example, in 2011, when a researcher team led by Peter Nugent at the Lawrence Berkeley National Laboratory discovered a Type Ia supernova in the Pinwheel Galaxy, 21 million light-years away, they quite literally were peering into the past 21 million years ago. And yet they witnessed the laws of physics in general, and of radioactive decay in particular, played out in exquisite detail, exactly as in present-day laboratories on earth.

Some have said that the last of the flat-earth believers did not give up until they held a GPS receiver (or an iPhone or Android handheld) in their bare hands and measured the exact latitude-longitude coordinates of their position. Will the last of the young-earth creationists not give up until they can measure the age of a rock sample with their own bare hands?

That day is almost here. A kickstarter-funded firm known as Consumer Physics has designed a handheld, consumer-oriented optical spectrometer, which can be used to measure the molecular constituents of an item that you shine its built-in light upon. True, it may be a stretch to think that these could be used to measure the isotopic concentrations of elements used in radiometric dating, but maybe not much of a stretch. With prices of such devices continuing to fall, a gift of Moore’s Law of electronic technology, the day when one can literally measure the geologic age of a sample cannot be very many years away.