Saturday, September 16, 2006

Age of the Earth Series - 3

Lecture 3 - Creationist Arguments Against Radiometric Dating Techniques

In this lecture, the third in my series of lectures on the age of the earth, I intend to highlight the most common arguments I come across in creationist literature and from creationists themselves against radiometric dating techniques. I will use the information from the first two lectures to show why each and every one of these is false. Then in my next lecture, I'll show why all the supposed proofs of a young earth are also false.

Clearly I won't be able to cover every single argument in either this lecture or the next. I cannot claim to have read every single piece of creationist propaganda ever. But I'm pretty experienced in this field, having had many debates with many creationists, and having read many creationist texts and websites. So I hope to give a good insight into their methods and arguments, and strong rebuttals for them all.

Argument 1: You have to know the initial conditions of a rock to date it, including how much parent and daughter were in a rock. This is impossible, because noone was there when it formed

Well, now we've heard the first two lectures, this is a simple argument to answer. Even the simplest Uranium-Lead methods use minerals that exclude lead chemically, and thereby excluding the possibility of non-radiogenic lead being present within the rock at formation.

K-Ar dating uses the fact that Argon is an inert gas and will bubble away at formation - any atmospheric argon-40 that is trapped at formation will also be trapped with atmospheric Argon-36, in a ratio of 295 parts to 1 (the atmospheric ratio of Ar-40 to Ar-36). We can therefore measure the Argon-36 in a sample and work out how much Argon-40 is non-radiogenic, and remove this from our calculations. Since the K-Ar method uses potassium salts, which are hard and crystalline in a strong ionically bonded lattice, we can be sure that no Potassium-40 has been lost or added since formation.

In isochron methods, we need no information whatsoever about the starting concentrations of elements, only the gradient of the isochron. In fact, as we have seen, even if we did need these starting ammounts, the y-intercept of the isochron gives us these directly - we can actually measure the starting ammounts using the isochron method.

Argument 2: Radiometric dating assumes closed system behaviour - that nothing leaks out or gets into a sample post-formation. Therefore any open system behaviour will make radiometric dating unreliable.

Again, this is simply not true. As we know from isochron methods, the isochron will tell us if open system behaviour has occured - because it will not be a straight line. Therefore we cannot get a "false" date from an isochron without knowing it.

Furthermore, the Ar-Ar methods and the Concordia/Discordia method both can deal with open system behaviour - in fact the latter is *designed* to deal with such behaviour. A discordia cannot exist unless there has been open system behaviour!

Argument 3: Radiometric dating of samples often gives different ages for different methods

Actually, this is just false - the power and strength of radiometric dating is that, as we have shown in lecture 2, we often get massive levels of agreement from many different methods of dating. Of course, given the hundreds of thousands of dating samples now taken, there are bound to be some that will give discordant readings - a mixing isochron here and there - a K-Ar date disrupted by open-system behaviour - and inherited isochron.

But the bulk majority of radiometric dating samples do come back with similar dates over many different and independent techniques. There is now more than sufficient evidence from these to conclude with a high degree of certainty that the earth is old.

Argument 4: Carbon-14 dating is reliant on calibration, you have to know how much C-14 was in the atmosphere at any one time, and you can't know that.

Despite the fact that Carbon-14 dating has never been used by any credible scientist to date the age of the earth - and despite the fact that most biblical archaeology relies on C-14 dating, I see this argument an awful lot.

Firstly, you'll have noted from lectures 1 and 2 that I didn't mention C-14 dating. That's because it is never used to date the age of the earth. This is for two reasons - firstly that it can only date things up to 55,000 years old, because of the short half life of C-14 - and the earth is 4.5 billion years old. Secondly, it does need objects of known age to calibrate it - the creationist argument is partially right - we already have to know that the earth is 50,000 years old because we have to have an object known to be 50,000 years old to make C-14 work.

However, secondly, we do have such objects. We find out the ammount of C-14 in the atmosphere at any one time in the past 50,000 years using 3 methods. Firstly, dendochronology - the study of tree rings. Secondly, varves, seasonal deposition of sediment in sea beds that give a year by year record of the earth's atmosphere going back tens of thousands of years. Thirdly, stalactites and stalagmites are useful to cross check the former two methods.

Argument 5: It is impossible to make accurate measurements of half life - especially for long lived isotopes like Rb-87, whose supposed half life is 47 billion years. Has anyone been around that long to check it?

Half life is actually measured from the activity of a sample (how many decays there are per second from a known quantity of sample), not from waiting around 47 billion years to see if half has decayed.

Basically, in order to establish the half-life of an element, the only thing we need to know is: what is the probability of any one atom decaying in any one second? What that means is, if we take a large enough sample with enough atoms in it (a sample of 1 gram of Rb-87 will contain 7 thousand billion billion atoms), and measure how many atoms decay for a long enough time, we will be able to work out the probability of any one atom decaying in any one second.

From this we can very accurately establish the half life, sufficiently accurately for the "error" in our estimation of half life to be negligable compared to random statistical errors in methods of dating.

Argument 6: But what if half life has changed? There is no way of going back into the past and measuring it?

Having had the previous 5 arguments answered a million times, creationists are now getting desperate. They know fine well that many methods of radiometric dating agree - and they know they are very well tested. So they are trying to come up with something that could be more fundamentally wrong with radiometric dating, in this case, the idea that during the year of Noah's Flood - the half life of elements changed such that 4.5 billion years of decay occured in a single year.

Methods of measuring decay rates in the past:

There are, as you can expect, many problems with this assertion. The first problem is that it is actually possible to measure half life in the past through several methods. The first method is to use a time machine, and look into the past. By "time machine" I mean "telescope". You see, if you look out of your window and look at the sun, you're not seeing the sun right now, you're seeing it 8 minutes ago. That's how long the light has taken to reach you. If I look at a sun that is very far away, say 4000 light years, I will see 4000 years into the past. We have studied stars hundreds of thousands of light years away - and we have measured decay of radioactive elements within those stars.

Another method of reassuring ourselves that decay rates have not changed is by looking at Uranium decay chains / series. I mentioned these in lecture 1. You see, these chains settle down to a steady state - called a "secular equilibrium" - where the ammounts of each element in the chain remain the same. The ratio of each element to each other element at secular equilibrium is determined by the ratio of their half-lives. What that means is that, if half lives had changed say, 4000 years ago, every decay chain would have been disturbed. Then if the half-lives had changed back to present day values say, 3999 years ago, it would take another 2-3 million years for these chains to go back into secular equilibrium. In other words, if this creationist assertion were true, we should find a total of zero uranium decay chains at secular equilibrium. In fact, we find many.

There are other methods of measuring decay rates in the past, although they are more complex. For example, the neutron absorbtion ratio from natural nuclear reactors such as the Oklo reactor can be used to measure physical constants and decay rates in the long past. But discussion of these sorts of methods is outwith the scope of this lecture, enthusiasts can write to me to find out.

Other problems with half-life dramatically changing:

There are several other problems with the idea that half-life has dramatically changed. Firstly, as we learnt in lecture 1, we have a good understanding of the theory behind nuclear physics, and what causes a nucleus to be radioactive. We know that radical change to half-life would involve radical change to the constants in the Semi-empirical mass formula. There is no reason at all why this should occur just because there was a worldwide flood. Not only that, God would have to arrange it such that all elements had the same percentage change in decay rate so that radiometric dates would agree - how or why he would do so is open to question. What physical constants he might alter to do this are unknown.

However, there is a much bigger problem with the idea of half life changing dramatically, and that problem is heat. We learnt in lecture 1 that the reason nuclei decayed is that they were unstable - they had too much energy. The Semi-empirical mass formula is actually a measure of the energy each nucleus has. In other words, radioactive decay happens because nuclei have too much energy, they are unstable, and they need to get rid of some energy to become more stable.

What that means is that all radioactive decay produces heat. There are no exceptions to this rule. If it doesn't release energy, it isn't radioactive decay. In fact, radioactivity produces a lot of heat. We all know this - because we all know what happens when you make unstable nuclei like Uranium split apart in a process called fission (thus releasing the energy of several decays at once). You get a big explosion. Hiroshima style. Or you get a nuclear power plant. In fact, the reason the core of the earth is still hot, despite it loosing heat, is because of natural radioactivity keeping it hot.

Now creationists want 4.5 billion years worth of decay to have happened in a year. That means an increase in radioactivity of about 450 billion percent. Sure, the clever ones among you are saying "does all that energy mean the rocks would melt and isochrons would be reset and Argon would be released?" And yes, I guess it does. But more worryingly, it means that large parts of the earth would be vapourised or melted. That obviously hasn't happened in the last 4000 years. Heat is a more general problem for "flood geology" actually - what with the heat produced from all the continents shifting at several meters per second, and of course the idea that almost all the igneous rock was produced in that time.

Argument 7: What about pressure and heat - do these not affect half-life and make radiometric dating inaccurate?

The answer to this is generally no. We have subjected light elements to hundreds of thousands of atmospheres of pressure and pretty extreme heat, and we have only seen minute changes to radioactive decay. The reason for this is that the nucleus where decay occurs is pretty immune to either chemical environment or outside pressure. It is not involved in chemical bonding, and the forces within it are so powerful as to render even massive external pressure negligable.

The only exception to this is for bound-state beta decay in a plasma. Let me explain. Beta-decay is when a neutron turns into a proton and an electron. In bound state beta decay, this electron does not escape, but actually starts orbiting the new nucleus. Such decay is common in Rhenium-187 in the interior of stars, where the heat from the stars has stripped many or all of the outer electrons of the Rhenium, and therefore bound state beta decay can occur.

In other words, when beta-decaying elements exist in a plasma state, with their outer electrons ripped away, beta-decay can happen much more quickly in a "bound-state" form. 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!

Argument 8: What if God made the earth mature, like he made Adam mature, and created the star-light in transit?

This final question intrudes slightly on the topic of Lecture 5 - the theology of an old earth, but it is worth dealing with here. Most people who are ignorant of the evidence for an old earth, and ignorant of the science of cosmology, advance this kind of argument because they don't think through the actual implications.

When we look up at the stars we just see points of light. They're pretty. We can lie back on the grass with our girlfriends and gaze up at them, and hope that the romance of the situation will lead to a snog and a grope. It is easier to believe that God might just have created the light in transit to give us a such a great view, and a better chance at a snog and a grope.

But when scientists look at stars, they don't just see points of light. They look through telescopes, and see all sorts of wonderful details - but the most important detail of all is that these stars are not static. Stuff happens in them. Events. Things are going on. From radioactive decay, to cosmic jets, to supernovae expanding and contracting - these stars are a hotbed of activity! If God created the light in transit therefore - there is only one conclusion we can make about all this activity - all of these events we see. They never happened.

God made them up, like Steven Speilberg makes a CGI movie sequence up. If we observe a star going nova 500,000 light years away - the supernova we see forming never formed. That star might not actually exist, for all we know, because we have never really seen it. All of the decays we counted, all of the expansion we measured, all of the flashes and movement we saw - was all an elaborate hoax - a movie reel - a piece of divine CGI animation.

All the chicks love a scar

We all build up scars in our lives, and stretch marks, and various other annoyingly permanent but occasionally impressive blemishes. They remind us of how we became who we are - of the period where we lost weight quickly - that time we fell off our bikes when we were 6 - the tooth we chipped playing rugby. Scars are permanent reminders of real incidents in our past - our life history is written in them - we weren't created yesterday.

Sadly, there are still people around whose minds have been so bent and twisted by religious fundamentalism, that they believe the earth *was* created yesterday. Or, more specifically, about 6,000 years ago. They say that, if God created Adam mature, why should He not create the earth mature? But I have news for them. If God created Adam, he didn't create him with a scar on his navel from an operation on his gall bladder. Nor would Adam have possessed scarring from a bilateral hernia, nor a BCG injection scar. His teeth would have been perfect and new, and showed no signs of the wear and tear they would have gone through in teenage years, because he didn't have teenage years. His little toes would never have been broken, because he'd never broken them. He would have had no stretch marks, because he would never have grown. Adam didn't have a history, and God isn't a liar.

The earth has so many scars. Of great meteor impacts that eradicated dinosaurs in the Cretaceous, and rocked the end-Permian era. Of animal tracks buried under layers of sediment, built up over millions of years. The fossils of beings the likes of which we've never seen, the radioactive elements in the rocks that contain them, the order of the strata in which the rocks lie - ghosts of a past, a real history, that haunt the modern day creationist. And even when we turn our gaze away from the earth beneath us towards the heavens, using our telescopes to see stars hundreds of thousands of light years away, are we to seriously believe that we observe a faked history? Are we to imagine that the God of truth created images of supernovae exploding, and coded these images into light, and put that light in transit toward earth - even though the supernovae never existed - and the explosions never occurred?

And I'll let you ponder those questions for a little while longer, as I create lecture 4 in this series!

Wednesday, September 13, 2006

Wednesday, September 13, 2006
September 13th ONE MORE BLOW!!!!
Well here's the deal... We have been on the phone all morning with Docs trying to get her transferred to another Hospital for a Second Opinion. Problem with that is the Docs at U of M are talking these other hospitals out of accepting Emmie-Rose for the Second Opinion that Rightfully We are allowed to receive.

We called Toledo back for a letter of acceptance and explaination to send to the Insurance Company for an appeal. In turn, The Doc tells Us that They have spoken to U of M and U of M has discouraged them from taking her due to another Ethics Committee meeting that We werent even told about or asked if We wanted to attend. The way the Docs at U of M are going We will NEVER get an Unbiased opinion. The Ethics Committee is now involved at Toledo even though they have NOT even assessed Emmie-Rose's condition firsthand and without an overturn decision by that Committee, the Doc that is willing to take her case is not allowed to do so.

They have now taken it upon Themselves to take away her TPN (nutrients She needs to grow, her "food") and her Blood Transfusions, Platelets and Lipids. She has had all of these things since birth until last Sunday when She had her surgery. They told Us She would die in two days, a week later She is still here and We asked them to give her her TPN, Blood and Platelets back and they did (yesterday). Yesterday they called a meeting to let Us know that "THEY" have "decided" amongst themselves that they are going to NOT feed her anymore or offer Her anymore Blood, Platelets or anything else that will help her to grow. So basically they want to starve her and let her blood run out so She can die. What does that sound like to you??? Torture if you ask ME!!

We just dont understand how a group of people who call themselves "doctors" can just "decide on a whim" that because this Child isnt "PERFECT" in their eyes that She isnt worth fighting for. They keep feeding Us the line "Well, do you know how hard it is going to be down the line/in the future". WHO CARES ABOUT TOMORROW, Lets work on today. They feel that Emmie-Rose is a "dead" issue and they have been just waiting for her to die. GUESS WHAT PEOPLE, LOOK WHO's STILL HERE!! NOW WHAT????????????? So their next course of action is to keep everything away from her that She has needed since birth and see if that makes her die. They let her blood get so low that that could have killed her. They are tired of dealing with Emmie-Rose because they see Her as "imperfect" and thats what they want to save is the ones that are going to make it "Long term". Who knows but the Lord who will make it the next 2 minutes let alone a yr from now. Obviously, U of M is trying to play "god" here and take it amongst themselves to kill Her at this point.

We need an Unbiased Second Opinion that We are entitled to as well as requested from the U of M team. We need someone out there to give Our Little Girl the chance. We want Her to live or die with Respect and Dignity that any Human being has the right to have. U of M is just completely giving up on a Living Human Being and that is NOT Right. We need to fight for Our Loved Ones and Stand Up for them when No One else will. Emmie-Rose is a fighter and until the Lord calls Her home, Mommy and Daddy are going to be fighting for Her every step of the way. There is a reason She is here and touching so many lives in the process. As long as She is going to fight, So are We.

Please Help Us!! IF Anyone has any contacts to help Us out with this situation, please either post or email Us. We need help from Everyone to Help Our Little Girl to get the Care She so deserves. This is a very time sensitive thing, We need to move quickly before U of M decides to take things into their own hands with more bad decisions.

Stephanie and Chris
Emmie-Rose's Mommy and Daddy

We need help finding a Doc to accept her and look at her without hearing one side only. If anyone knows a Neonatologist, a Ped Surgeon, Ped Doc with Nicu experience... Please pass Our story on. We need to move pretty fast.

Thanks for reading!

Please Continue the Prayers!!


posted by ShopGirl2U2000 @ 10:27 AM

Age of the Earth Series - 2

Lecture 2 - Complex Dating Methods

In this lecture, we'll go through the various more complex methods of radiometric dating - talking first about Argon-Argon Plateaus, second about isochron methods, and lastly about the Uranium-Lead Concordia Discordia method, the most complex of all.

These methods of dating are extremely powerful, and build in clever mechanisms to test or eliminate the so-called "assumptions" that creationists often criticise geochronologists for making. That's why it's very important to understand them, and to read this lecture carefully before we go on to lecture 3 - where we will show creationist arguments against radiometric dating to be false.

The Argon-Argon Plateau

We talked in lecture 1 about the K-Ar method of dating - comparing the Potassium and Argon in a rock to find its age. This method uses exactly the same parent and daughter isotopes as the potassium-argon method. In effect, it is a different way of telling time from the same clock. Instead of simply comparing the total potassium with the non-air argon in the rock, this method has a way of telling exactly what and how much argon is directly related to the potassium in the rock. Even though it has been around for nearly half a century, the argon-argon method is seldom discussed by groups critical of dating methods.

In the argon-argon method the rock is placed near the center of a nuclear reactor for a period of hours. A nuclear reactor emits a very large number of neutrons, which are capable of changing a small amount of the potassium-39 into argon-39. Argon-39 is not found in nature because it has only a 269-year half-life. The rock is then heated in a furnace to release both the argon-40 and the argon-39 (representing the potassium) for analysis. The heating is done at incrementally higher temperatures and at each step the ratio of argon-40 to argon-39 is measured. In other words, the sample is heated in steps, say 10 degrees, and for each step, how much Ar-40 and Ar-39 that is dislodged is measured.

If the argon-40 is from decay of potassium within the rock, it will come out at the same temperatures as the potassium-derived argon-39 and in a constant proportion. On the other hand, if there is some excess argon-40 in the rock it will cause a different ratio of argon-40 to argon-39 for some or many of the heating steps, so the different heating steps will not agree with each other. In other words, Ar-40 / Ar-39 should be constant for each step, unless Ar-40 has either been added or subtracted from the rock during the time it's been existent. From this we form the Argon-Argon Plateau:

In this sample, a real sample by the way, the Ar40/Ar39 ratio is fairly constant over the temperature steps. This means the rock has not been disturbed, and we have taken, in this case, 25 different and independent measurements of age that have all come out the same. This is a very powerful evidence that the rock is as old as the method claims. It also tests the assumption that argon has not been added or taken away from the rock.

It also means that we can use this method on partially metamorphised rocks. If a rock has gone through a period of heating - but only been partially melted, the argon-40 at the lower temperature steps will have leaked away. But the argon-40 that was harder to dislodge, that only came out at the higher temperature steps, will have remained constant. We will then get a partial-plateau - with lower ratios at the lower temperature steps, but then a constant plateau at higher temperature steps. This method therefore gives us a way of measuring age even in rocks that have been partially metamorphised.

It also tells us definitively if a rock has been tampered with. Here is a "bad" Ar-Ar plateau for reference:

As you can see - the plateau is never constant. Although more of the harder to get out Argon-40 remains at higher temperature, the plateau is never truly flat. This method tells us when a rock is unsuitable for dating then, because argon has been leached. Inspirational stuff. God bless science.

Isochron Methods

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.

However 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.

In the rubidium-strontium method, rubidium-87 decays with a half-life of 48.8 billion years to strontium-87. Strontium has several other isotopes that are stable and do not decay. When the rock first cools, all parts of the rock have the same strontium-87/strontium-86 ratio because the isotopes were mixed in the magma - and because Sr-87 and Sr-86 are chemically indistinguishable - a mineral cannot distinguish chemically between them. At the same time, some of the minerals in the rock have a higher rubidium/strontium ratio than others. Rubidium has a larger atomic diameter than strontium, so rubidium does not fit into the crystal structure of some minerals as well as others. In other words, Rubidium is chemically distinguishable from Strontium. Therefore the Rb-87/Sr-86 ratio will vary from mineral to mineral. Over time, the Rb-87/Sr-86 ratio decreases as Rb-87 decays to Sr-87. Similarly, the Sr-87/Sr-86 ratio increases over time, as Sr-87 is formed from Rb-87.

The result of this is an isochron, as seen above. This is a plot, for several different minerals, of Sr-87/Sr-86 on the Y-axis and Rb-87/Sr-86 on the X-axis. At the start, you will have a straight flat line, because although there will be different Rb-87/Sr-86 ratios for different minerals, the Sr-87/Sr-86 ratio will be the same, as these are chemically indistinguishable. As time goes on, you will get increasing slopes of line, like this:

The gradient of the line is therefore proportional to the age. Notice also that where the line cuts the Y-axis, we get the exact starting ratios of all the elements, in other words, this method tells us directly what the elemental composition of a rock was to start off with. Enthusiasts can write to me and I'll send them the mathematics behind deriving the age from the gradient.

But the most clever thing about this method is the fact that, if any of our assumptions about the rock are wrong - if the rock has been interfered with - if elements have spread or scattered or left or entered - we won't get a straight line. The very existence of a straight line is proof, in and of itself, that our assumptions were correct.

In a few very rare instances the rubidium-strontium method has given straight lines that give wrong ages. This can happen when the rock being dated was formed from magma that was not well mixed, and which had two distinct batches of rubidium and strontium. One magma batch had rubidium and strontium compositions near the upper end of a line, and one batch had compositions near the lower end of the line.

In this case, the minerals all got a mixture of these two batches, and their resulting composition ended up near a line between the two batches. This is called a two-component mixing line. It is a very rare occurrence in these dating mechanisms, but at least thirty cases have been documented among the tens of thousands of rubidium-strontium dates made.

However, there is a mathematical test (the Reciprocal test) for mixing lines - plus exactly half of all mixing lines are negative - and anyhow, if a two-component mixture is suspected, a second dating method can be used to confirm or disprove the rubidium-strontium date. The agreement of several dating methods is the best fail-safe way of dating rocks - because mixing lines do not agree with other dating methods. So other than mixing, for which we can test and that we know is rare - this is an excellent method of telling the time.

Uranium-Lead Concordia/Discordia

The U-Pb method relies on the decays of U-235 and U-238. These two parent isotopes undergo series decay involving several intermediate radioactive daughter isotopes before the stable daughter product is reached. We have already covered the basic U-Pb method in Lecture 1.

Two simple independent “age” calculations can be made from the two U-Pb decays: U-238 to Pb-206, and U-235 to Pb-207. However, what if lead has leaked out? We found out in lecture 1 that the minerals that Uranium-Lead dating is performed with, like zircons, chemically exclude lead - that also means that during metamorphism and heating lead tends to leak out, giving an artificially young age. How can we get around this problem?

The answer is using a Concordia/Discordia plot. The U-Pb concordia-discordia method circumvents the problem of lead loss in discordant systems and provides an internal check on reliability. This method involves the U-238 and U-235 decays and is used in such minerals as zircon, a common accessory mineral in igneous rocks, that contains uranium but no or negligible initial lead. This latter requirement can be checked, if necessary, by checking for the presence of Pb- 204, which would indicate the presence and amount of initial lead.

In a closed lead-free system, a point representing the 206Pb/238U and 2O7Pb/235U ratios will plot on a curved line known as concordia. The location of the point on concordia depends only on the age of the sample:

In other words, a rock that has not undergone any deformation or metamorphism or leaching will lie on a concordia plot - this means that both U-235 and U-238 methods are in agreement on age, basically. As the rock gets older, it progresses up the concordia plot.

If at some later date (say, 2.5 billion years after formation) the sample loses lead in an episodic event, the point will move off of concordia along a straight line toward the origin (again, the maths of this I'll send to the enthusiast). At any time after the episodic lead loss (say, 1 billion years later), the point Q in the last diagram will lie on a chord to the concordia connecting the original age of the sample and the age of the lead loss episode. As you can see in the diagram, the chord intercepts the concordia at 1 billion years (the time between the last metamorphic event and present day) and 3.5 billion years (the true age of the sample).

This chord is called discordia. If we now consider what would happen to several different samples, say different zircons, from the same rock, each of which lost differing amounts of lead during the episode, we find that at any time after the lead loss, say today, all of the points for these samples will lie on discordia:

As we can see, by drawing the concordia and plotting the discordia from measurements, we can now find the true age of the rock and when the metamorphic event that caused the discordia occured. This is a very powerful method of dating therefore - not only is it self-checking of assumptions - it is actually built specifically to deal with open system behaviour. As we will see in lecture 3 - creationists complain that dating methods have to assume a closed system - that no elements will leak in or out of the sample during the time of its existence. We now know that isochron methods and Ar-Ar methods can handle this - now we've learnt that U-Pb Concordia/Discordia is actually built specifically to deal with this. By the way, the above graph is from a real sample, from the Morton Gneiss, Minn. This rock was also measured at around 3.6 billion years old by several other dating methods.

Dating with multiple methods

As you can see from the results below, amazingly concordant dates are a common feature of radiometric dating using many different methods. These results are from the Amitsoq Gneisses of Western Greenland:

In this case, the gneisses were dated several times using U-Pb, Lead-Lead (another name for Concordia/Discordia methods), Rb-Sr isochron methods, and a couple of lesser used isochron methods, lutetium-hafnium and samarium-neodymium. All the dates agreed to within bounds of error with an age of 3.61 billion years old. The different methods of completely independent, there is no reason that they should agree other than that they represent the real age of the rocks. We will talk about such fallacious creationist claims that these similar results could be caused by a speeding up of radioactive decay rates in lecture 3.

However, that aside, dating with many methods which come up with the same result is a hugely powerful evidence that the earth really is very old. The oldest rocks yet found are about 4.3 billion years old, in Western Australia, making scientists conclude that the earth itself is about 4.5 - 4.6 billion years old in total, giving time for some cooling and rock formation. This age could move back as older rocks are found.

I hope this gives you a good insight into the complex methods of radiometric dating, and that it was not too complex to follow.