Talk:Half-life

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Quantum mechanics is important[edit]

Yes it IS difficult to understand. How the heck do you know that half sample has "decayed"? You have to measure it! And doing so are you sure that "the moon will still be there"? Please take a look at Schrödinger's cat article first. I suspect that also recent changes performed by people with "UNI physics papers" haven't fully understood its relation with quantum physics even if there is a very interesting wikipedia article about various interpretations of quantum mechanics not to mention the minority ones. Please note that this article has been rated as Start-Class on the project's quality scale and as "High-importance" on the project's importance scale. Have a nice week-end!
Maurice Carbonaro (talk) 08:24, 20 July 2012 (UTC)

Maurice just put a link to observer (quantum physics), and before that (but I deleted them) links to Measurement in quantum mechanics#Philosophical problems of quantum measurements, Schrödinger's cat, and "[[Boolean algebra (logic)|Quantum Boolean algebra]]". (The last one is strange, the Boolean algebra article says nothing about quantum.) But I don't think any of these links should be there.
Decays can often be measured with a Geiger-Müller tube. Every time a particle decays, the computer goes "CLICK". If you start with five atoms, and you hear three CLICKS, then there are two atoms left. You are "observing" it in the same everyday, trivial sense as you would observe anything in the world. Maybe it's true that people generally need to think more deeply about what "observation" means in everyday life, because it is more complicated than it seems---I personally don't think so, but reasonable people can disagree. (The "If a tree falls in a forest" thought experiment has been around for centuries.) But that doesn't mean that every place on wikipedia where some everyday thing is "observed" should include a discussion or link to the deeper analysis of observation. For example, the Tacoma Narrows Bridge (1940) article says in the second paragraph that the bridge was "observed" to rock in the wind. Should we add a link to observer (quantum physics)? In the Wedding of Prince William and Catherine Middleton article, it says the wedding was "watched" by 36.7 million people. Should the word "watched" have a link to observer (quantum physics)? I hope you think these two examples are silly! But really there is no difference between "observing" that my television screen is showing a royal wedding and "observing" that my Geiger-Müller tube has clicked three times. Discussing quantum mechanics is off-topic in both cases. --Steve (talk) 12:40, 20 July 2012 (UTC)
Hallo Steve (talk), thanks for giving me the opportunity to exchange views with you on this topic. Please let me tell you that I have been a physics university student albeit dropping out. That was 25 years ago and, believe me, I think I had plenty of time to think about half-life, quantum physics and its relationship to our "trivial everyday world" as we perceive it or, better, how we get conscious about it. Roger Penrose (b.1931), for example, seems to me the scientist that has dedicated a consistent part of his life in analyzing the relationship between consciousness and physics. He wrote and made "trivial" two essays about the subject: The Emperor's New Mind in 1989 which I read thoroughly and Shadows of the Mind which unfortunately I didn't have time to read yet. Citing your examples about the "Tacoma Narrows Bridge (1940) observed to rock in the wind" (well, are we talking about physics here? Then it should be a case of mechanical resonance!) or the "Wedding of Prince William and Catherine Middleton event watched by 36.7 million people"... Ok so people watched it but how? On computers, television sets? These "gadgets" work thanks to millions of transistors that use quantum tunnelling. And even if they weren't like, for example your Geiger-Müller tube this doesn't mean that a many-worlds interpretation is not possible. No, I don't think we should add links to "quantum physics" to the "Weddings of european Royals" as I don't even think these articles should be on any kind of encyclopedia at all like Talk:Wedding dress of Kate Middleton. Last but not least I guess you would think differently about your Geiger-Müller tube if it was in a sealed box containing the Schrödinger's cat: because, let's suppose you have these 5 atoms in the box and this cat would die once your instrument triggers a click at the third atom decaying... How would you know unless you open the box and check if the cat is alive or not? Huh!? So I guess that the main problem here is that we should decide if this encyclopedia should move towards article that have a deeper level of understanding or remain trivial. And for "deeper level of understanding" I mean talking about psychoanalysis like subconscious and collective subconscious. I don't know if you are aware of the fact that physicist Wolfgang Pauli (1900-1958) had a nervous breakdown and a mystical crisis towards the end of his life and he searched Carl Jung (1875-1961) for help. So talking about "this stuff" is not so trivial as it could look like at a superficial glance. What do you think about it? (You are more than welcome to continue this talk with private e-mails) Have a nice Sunday! Maurice Carbonaro (talk) 05:55, 22 July 2012 (UTC)
Again, my problem is putting your mention of quantum mechanics here in this article. I have no problem with mentioning quantum mechanics when quantum mechanics is the topic of the article or essential for understanding it. People are reading this article to learn about half life.
  • Quantum mechanics is not necessary to understand half life. For example, you can understand probabilistic decay and half-life by spinning thousands of roulette wheels over and over, and whenever a ball lands on "00" it triggers a mechanism that destroys the wheel. Primary school students for generations have been successfully learning the meaning of probability without understanding a thing about quantum mechanics.
  • Quantum mechanics is not helpful to understand half life. After you have thought deeply about the ontological status of observation, you are not in any better position to understand what the word "half-life" means, nor how to measure or calculate a half-life, nor how to use half-lives to better understand nuclear waste disposal or carbon dating or whatever.
  • Mentioning quantum mechanics is actually counterproductive for understanding half-life. Some readers will say "Yikes, half-life has to do with quantum mechanics?? Better give up on reading this section! This is way beyond my capabilities to understand!"
People look up a topic in an encyclopedia to learn about that specific topic--in this case, Half-life. Therefore each article should be about--and only about--that specific topic. Otherwise an encyclopedia would only have one article, called "Things that people ought to know", and that article would be zillions of words long.
As for the scientific accuracy of that section, it says "one can start with a single radioactive atom, wait its half-life, and then check whether or not it has decayed". It does not say one word about what the status of the radioactive atom was before the checking occurred. Therefore, the sentence is scientifically accurate, and interpretations of quantum mechanics are irrelevant for this sentence. --Steve (talk) 15:53, 22 July 2012 (UTC)
Whateva...! You may find interesting the last changes to the "phenomenon" article in the ==See also section== (I have added a link to the Psychoid archetype). Please feel free to undo... starting a conversation in the talk page. Thanks for your interest in the matter.Maurice Carbonaro (talk) 11:12, 31 July 2012 (UTC)

More on quantum mechanics[edit]

As an example, the radioactive decay of carbon-14 is exponential with a half-life of 5730 years. A quantity of carbon-14 will decay to half of its original amount after 5730 years, regardless of how big or small the original quantity was <!--*************"(...) regardless of how big or small the original quantity was (...) "?!?!?!? WOW! Now, I wonder how this latter sentence is NOT connected with 'quantum physics"... How could possibly some "original quantity" "KNOW" which is the amount that we WILL MEASURE IN THE FUTURE in order for us to KNOW if it has decayed or NOT? How is that we are going to pick up and consider the "whole amount of something" and NOT the "wrong half of something" that will NOT decay OR that will decay completely??***********--> --Maurice Carbonaro (talk)

I moved this hidden comment out of the main article. Please keep talk on the talk page, that's what it's there for! --Steve (talk) 12:40, 7 August 2012 (UTC)
You make it very clear that you have the belief that you are guaranteed to have exactly half the original quantity left after one half-life, and that it cannot happen that all of it has decayed or none of it has decayed after one half-life. If this belief were true, then you would be correct that there would have to be some mystical and supernatural explanation. The atoms would have to magically "know" what you will measure in the future, or Destiny would forbid you from measuring the wrong thing, or who knows what.
But this belief is not true!! Not only is it not true, but there is an entire section in the article about how it's not true, and an animation which visually demonstrates the fact that it is not true. I know you read that section because you were discussing it above. But obviously you missed the entire point of it! Sadly, I don't know how to make it any clearer.
So it seems to me that this article has been a complete failure in communicating anything about half-life to you. I suggest that you try to learn what half-life is from a different source like [1] [2] [3]. Maybe one of those will be a more successful teacher. When you finally understand it, you can come back and offer some suggestions about how to make this article clearer. -Steve (talk) 13:03, 7 August 2012 (UTC)
A symmetrical blue cloud that decreases in intensity from the center outward
In quantum mechanics, the behavior of an electron in an atom is described by an orbital, which is a probability distribution rather than an orbit . In the figure, the shading indicates the relative probability to "find" the electron, having the energy corresponding to the given quantum numbers, at that point.

' "I think I can safely say that nobody understands quantum mechanics." '

Richard Feynman (1918-1988), 
The Character of Physical Law (1965)
Chapter 6, “Probability and uncertainty - the quantum mechanical view of nature”


Hallo there Steve (talk). Thanks for taking my hidden comments to the talk page. I guess you are taking for "deterministically granted" what is instead a "probabilistic measurement". Infact there is an entire section in the article called Half_life#Probabilistic_nature_of_half-life. So going back to the half-life article there is a very low probability (IMHO) that the entire "many identical atoms undergoing radioactive decay" could decay ALLTOGETHER just after a microsecond instead of the probabilistic given half-life of "many identical atoms undergoing radioactive decay"' (for instance "zillions of years" like 1.6416 Yottaseconds which is the estimated half-life of the "stable" 20983Bi[smuth] radioactive isotope). From this image on the right I have taken from the Electron#Quantum_mechanics article/section you will see that in quantum realm we talk about "probabilities". And this is comparable to the "half-life" probabilities we are talking about because in half-life there are mainly beta decays involved. So I am still of the opinion that quantum mechanics is involved in half-life: yes. And I am sure you know that too.
"What cats have to do with quantum mechanics? Better keep on reading this section! This should be in my capabilities to understand!"
As well as there is a philosophical thought experiment called "If a tree falls in a forest and no one is around to hear it, does it make a sound?" that "has been going on for centuries"... there is also a thought experiment called "Schrödinger's cat" that started "going on" from only last century. What's a cat got to do with quantum mechanics then? There is no failure in communication between us: in one of your previous comments you stated that inserting in the article the concept that half life had to do with quantum mechanics would have "scared" the average reader. (I quote: "Some readers will say "Yikes, half-life has to do with quantum mechanics?? Better give up on reading this section! This is way beyond my capabilities to understand") So... what? Cheers. Maurice Carbonaro (talk) 08:04, 8 August 2012 (UTC)
As far as I can tell your argument is: "Understanding probability is essential for quantum mechanics. Understanding probability is also essential for understanding half-life. Therefore understanding quantum mechanics is essential for understanding half-life." This is obviously fallacious. If that's not your argument, then you should restate it because I did not catch it.
Now you're also making the argument: "Quantum mechanics is important for understanding the mechanism of radioactive decay. Half-life is important for understanding the consequences of radioactive decay. Therefore understanding quantum mechanics is essential for understanding half-life." (If that's not your argument, you should restate it because I did not catch it.) This is also, obviously, fallacious. Half-life can be used to understand any exponential decay, including coin-flipping experiments. While radioactive decay is an important example of exponential decay, understanding its mechanism--which usually involves virtual particles, quantum tunneling, neutrinos, etc.--is not helpful for understanding the exponential decay itself. It is just a distraction, it wastes the reader's time and attention without helping them understand half-life any better.
Yes, there is an extremely low but nonzero probability that 100% of 1 trillion atoms of 20983Bi[smuth] will all decay within one microsecond. I see how you might have been misled by a sentence in the article so I edited the wording to say "half on average remains" rather than "half remains".
By the way, I use quantum mechanics every single day as part of my job. I have taught it to college students. You don't need to explain to me what quantum mechanics is. It is true that I join the overwhelming majority of quantum physicists in believing that quantum mysticism (which you apparently subscribe to) is religion at best, or easily falsified at worst. But that's not the main point. The main point is that discussing quantum mechanics - even if quantum mysticism was true - would be off-topic in this particular article. --Steve (talk) 15:14, 8 August 2012 (UTC)
IMHO I understand that you would like the article written under the Copenhagen interpretation which is just one of the many interpretations of quantum mechanics. At this point I suggest to insert a template at the beginning of the article that states this fact like the following:


No. As I explained above in great detail, half-life has nothing to do with quantum mechanics. Or at any rate, it has (more or less) the same amount of relation to quantum mechanics as any random article on wikipedia does. There is no mention of quantum mechanics in this article and it should remain that way. People who subscribe to different interpretations of quantum mechanics will nevertheless have exactly the same understanding of half-life.

I have a guess at what you're trying to get at. This article, like every other article on wikipedia (I mean that literally), implicitly assumes the philosophy of realism -- there is one universe in which things objectively happen. For example, if you are talking to your neighbor, you might say

  • Realism: "It's raining"
  • Non-realism 1: "I have the perception that it is raining"
  • Non-realism 2: "I don't know about what's happening in other universes ... but in this universe, it is raining.
  • Non-realism 3: etc. etc.

Again, look at a random wikipedia article, and you'll see that it uses "realist" descriptions, not the non-realist descriptions, starting from the very first sentence (e.g. "Michael Jackson was a musician..." rather than "I have the perception that Michael Jackson was a musician..."). Do you suggest therefore that every article on wikipedia should have that banner you made above?

In your own everyday life, which kind of description do you use? Realism or non-realism?

I believe that it is possible---indeed, a very good idea---to describe everyday things in realist terms even if realism is not fundamentally true. I don't think that people should apologize or qualify statements like "It is raining". (Or "The atom has radioactively decayed" or whatever.) Regardless of its fundamental truth or falsehood, realism has an obvious practical value in talking to people and making decisions in everyday life ... not to mention writing encyclopedia articles!! :-) --Steve (talk) 12:47, 24 August 2012 (UTC)

The acceptance of the Copenhagen interpretation among physicists[edit]

Hallo there Steve (talk),
back to this talk after almost 5 months.
Well I dunno if you have taken a look at the Copenhagen_interpretation#Acceptance_among_physicists article/section.
I quote:

(...) According to a poll at a Quantum Mechanics workshop in 1997,[1] the Copenhagen interpretation is the most widely-accepted specific interpretation of quantum mechanics, followed by the many-worlds interpretation.[2] Although current trends show substantial competition from alternative interpretations, throughout much of the twentieth century the Copenhagen interpretation had strong acceptance among physicists. Astrophysicist and science writer John Gribbin describes it as having fallen from primacy after the 1980s.[3] (...)

And it's all well referenced as well... it makes you think, huh?
We are in the second decade of the XXI century now...   M aurice   Carbonaro  08:56, 31 January 2013 (UTC)

This is the talk page for the article Half-life. We should not be using it for discussions of anything except how to improve this article.
I explained above in excruciating detail why I think it would be inappropriate, in the half-life article, to discuss quantum mechanics or put links to quantum mechanics articles. (Just like I think it would be inappropriate to discuss quantum mechanics in the Julius Caesar article.) My argument does not rely on the truth or falsehood of any particular interpretation of quantum mechanics. No matter what interpretation of quantum mechanics is correct, quantum mechanics should not be discussed in the half-life article (any more than the Julius Caesar article). If you think that quantum mechanics should be part of this article, then you need to carefully read what I wrote above and specifically respond to it. If you just generally want to discuss quantum mechanics with someone, do it at User talk:Sbyrnes321 or http://www.physicsforums.com/ :-D --Steve (talk) 04:17, 12 February 2013 (UTC)


Please avoid wp:sarcasm and wp:pas. I don't see how "Julius Caesar" could have something to do with quantum mechanics. And anyway I am endorsing the fact that this article seems to be mainly written according to the Copenhagen interpretation, which is just *ONE* of the quantum mechanics interpretations. Usually talk pages shouldn't be used for "general conversations" about the subject of the article. According to the definition of "quantum mechanics" (QM – also known as quantum physics, or quantum theory) is a branch of physics dealing with physical phenomena at microscopic scales, where the action is on the order of the Planck constant.. Considering the concept of "Julius Caesar" in his "wholeness" obviously there is nothing to do with the "quantum world" ... but if we start talking about radioactive decay I guess we have all the right to state that we are dealing with phenomena that belong to the quantum world at a Planck scale. I have checked last 500 contributions made on the Interpretations of quantum mechanics article and didn't find one single contribution by User "Sbyrnes321" (that's you) not to mention Talk:Interpretations of quantum mechanics. I beg your pardon but I must say that I have strong reservations that you haven't wholly understood what all "quantum mechanics" is about. Is not that I am saying that I master the whole subject... but... well... at least I am open to discuss about it. On wikipedia. Not on external links (thanks anyway). BTW "(...) excruciating detail (...)" doesn't apply very much to quantum physics where the Heisenberg uncertainty principle makes sense. Please avoid considering phsyics subjects as ballast tanks that haven't got anything else to do with each other. I wrote "physics" not "ancient Rome history". Thanks for reading you. Catch you L8R. (I am available for private e-mailing).   M aurice   Carbonaro  09:01, 13 February 2013 (UTC)
Which part of the article is written "according to the Copenhagen interpretation"? Can you please point to a specific sentence? If you believe that that sentence is written according to the Copenhagen interpretation, then how would you rewrite it to not be according to the Copenhagen interpretation?
It is my opinion that this article, like the Julius Caesar article, is neither "according to the Copenhagen interpretation" nor "according to some other interpretation", because the article has nothing to do with quantum mechanics. As I wrote above, quantum mechanics is related to the mechanism of radioactive decay, while half-life is related to the consequences of radioactive decay. The previous sentence is not evidence of a connection between half-life and interpretations of quantum mechanics. By the same token, rotational inertia is related to the mechanism of flipping coins, while half-life is related to the consequences of flipping coins. The previous sentence is not evidence of a connection between half-life and rotational inertia. Even if there was no such thing as radioactive decay or atoms or quantum mechanics in our universe, we would still invent the exact same concept of half-life, not even slightly modified, to describe other random exponential-decay processes.
I do not dogmatically regard different physics subjects as unrelated ballast tanks. When two aspects of physics are related to each other, I am enthusiastic about pointing out the connection. For example, I recently wrote an article describing the various mathematical relations between thermal diffusion, viscosity, electron flow in semiconductors, etc. But I am always opposed to making up a connection where none actually exists (or as I call it, "going off on unrelated tangents"). Just because two things are part of physics does not mean that they are connected. The Tsiolkovsky rocket equation article should not include a discussion of Wannier functions, even though both are physics. My opinion / guess from this conversation (and I could be wrong) is that you don't have a deep, thorough, detailed, quantitative understanding of either quantum mechanics or half-life, and you noticed some superficial overlap between the two things, e.g. they both involve the word "radioactive". I think you jumped from there to the (incorrect) conclusion that these two things are kinda part of the same subject. They're not. It's just superficial.
As for credentials, I am a PhD physicist who uses quantum mechanics every day as part of my job. No, I haven't edited the Interpretations of quantum mechanics article. Does that prove my ignorance??? I did write the majority of Measurement in quantum mechanics back in 2007 for what it's worth. And much of density matrix and many many others. But I hope that my arguments stand for themselves! :-D --Steve (talk) 04:34, 14 February 2013 (UTC)



Thanks for answering.
Okay let's put it this way then Ph.D. Byrnes.
This article has been rated for a long time as "Start-Class" on the project's quality scale (i.e. "Provides some meaningful content, but the majority of readers will need more.") and as High-importance on the project's importance scale (which is divided in four grades: Top, High, Mid, Low).
IMHO I don't believe you need a Ph.D. to suspect that there is something strange about this article if we are all stuck at this paradoxical point. This should make us wonder:
does this mean that the article is far for being "complete"?
You are setting a difference between "mechanisms" and "consequences" which IMHO clearly states your holistic causalism view of *all* physics which is something I don't endorse, but which I respect and which AFAIC is known as "Copenhagen interpretation".
Consequences of flipping coins? With all due respect I have visited this latter page and honestly I found it a forced oversemplification.
Not to mention the "capitalistic interpretation" (not the "Copenhagen" one) of substituting coins for atoms. (and I am not even a communist!) :D LOL.
BTW have you ever heard of
Because I would be really interested in what do you think about these two (living) guys and the latter concept. Even privately because I don't like being publicly accused for "going off on unrelated tangents". ;-) Stating that you are "always opposed to making up a connection where none actually exists" rings me a bell of someone else that opposed speculating on "pure void" (What was *there* before the Big Bang? Quantum vacuum?). Please let's try to have a nice and relaxed week-end.   M aurice   Carbonaro  08:46, 16 February 2013 (UTC)
I'm sorry that I was condescending before...
Mechanisms vs consequences: I don't think I am making any deep philosophical point here! Here is a more pedestrian example. (1) The Krebs cycle is an important mechanism for Julius Caesar's being alive. (2) The Roman Empire is an important consequence of Julius Caesar's being alive. (3) Nevertheless, it is OK that the article Roman Empire does not discuss the Krebs cycle. Do you agree with (1-3)? If so, then it seems you have the same philosophical view of consequences versus mechanisms as I do! You're just disagreeing with me about the facts of this one particular case. :-D
Is the Julius Caesar article written "according to the Copenhagen interpretation"? What about Tsiolkovsky rocket equation? I'm just trying to understand what you're arguing, these questions are not rhetorical or mocking.
There are about 16,000 physics articles on wikipedia right now. Is it your opinion that a discussion of the various interpretations of quantum mechanics (and/or synchronicity, etc. etc.) should be in all 16,000 of these articles? Or half of them? Or 1% of them? Or what? Am I correct to understand that each physics article which lacks a discussion of the various interpretations of quantum mechanics is "written according to the Copenhagen interpretation"? If not, what is the criteria by which you to judge an article to be "according to the Copenhagen interpretation"?
If you ask me about Capra, Josephson, and synchronicity, I will give you the same answer as if you ask me about the possibility of extraterrestrial intelligence, or about financial regulations: This is a topic that has nothing to do with half-life. No matter whether you think Josephson is a visionary or a lunatic, or if you've never heard of him, you can still understand half-life equally well! I hope people formulate knowledgeable opinions about Capra, Josephson, and synchronicity, just like I hope people formulate knowledgeable opinions about the possibility of extraterrestrial intelligence. But I don't think we should be teaching about it in this particular article. :-P
I don't see how it's a "paradox" that this article is rated start-class. Quite generally across wikipedia physics articles, almost nobody ever changes that page rating, even when the page gets dramatically better or worse. No one feels that it's their place to change the rating. I personally don't think that this article is start-class. That rating is just one person's opinion, and even worse, it's an opinion about an older version of the article. Can the article be improved by expanding it? Yes, I won't deny that. For example, the article could be improved by adding a table of the half-lives of important nuclides, etc. etc. But the article could also be made worse by expanding it, if the expansion is off-topic (like a discussion of financial regulations, to take an extreme example). I am arguing that discussing interpretations of quantum mechanics is in the latter category. --Steve (talk) 23:13, 17 February 2013 (UTC)
Just to add my two cents... Half life is a classical description of reality. See my talk post below which discusses half life in the context of a chemical system. I don't think a discussion of quantum physics is really appropriate for a half-life discussion. First, its meaning breaks down when you move from classical systems described by continuous differential equations (of which half life arises from) to discrete systems based on probabilities. In addition, atomic decay is an odd issue in that most of it can be described by classical physics. For example, neutron energy is a mass problem, not a wavelength issue such as with the photon. So the discussion of quantum mechanics, here, seems like a non sequitur, which puts me in agreement with Steve. Sean Egan (talk) 21:29, 28 February 2013 (UTC)

Proposing section on application of half life to chemistry[edit]

Many chemistry students Google "Half-life" only to be forwarded to this page. I want to add a section on the application of half life through a derivation. I know this has been done before, but I feel that it isn't as clear as it could be. Students often need to see steps which spell out not only the math, but the reasoning. I also see a lot of contention regarding quantum mechanics and nuclear decay. (Nuclear decay doesn't really follow QM as much as it does classical physics, but whatever...) I'm proposing a chemical example, which is definitely described by classical physics. Tell me what you guys think! I'd like to add it as an aside or as a collapsable example:

Consider the following first order decay of A to B.

A\rightarrow B

We could describe half life through this by solving the differential equation which follows the conversion from A to B via a rate constant k, and then solve for the time when half of A is gone.

\frac{d[A]}{dt}=-k[A] \frac{d[A]}{[A]}=-kdt

We will integrate this differential equation from Ai, or the initial concentration of A to Af, or the final concentration of A.

\int_{[A]_{i}}^{[A]_{f}}\frac{d[A]}{[A]}=\int_{t=0}^{t}-kdt

ln[A]_{f}-ln[A]_{i}=-kt+k(0)

ln\frac{[A]_{f}}{[A]_{i}}=-kt

We may raise both sides to the power of e, thus eliminating the natural log:

e^{ln\frac{[A]_{f}}{[A]_{i}}}=e^{-kt}

\frac{[A]_{f}}{[A]_{i}}=e^{-kt}

[A]_{f}=[A]_{i}e^{-kt}

We now have an equation which solves for the final concentration of A. Assume that we want to know at what time only half of A will be left. We could set Af equal to 1/2 of Ai:

[A]_{f}=\frac{1}{2}[A]_{i}

This simplifies our equation to:

\frac{1}{2}[A]_{i}=[A]_{i}e^{-kt}

Where we may cancel Ai to yield

\frac{1}{2}=e^{-kt}

We could then solve for t by taking the natural log of both sides, and then divide by -k to solve for the time at which only half of A remains, which would be the half-life:

\frac{ln\frac{1}{2}}{-k}=t

\frac{0.693}{k}=t

I believe this gives a better understanding of where the half comes from in half-life. It's described by these equations as the time at which half of the initial species remains. Does anyone agree? Sean Egan (talk) 21:13, 28 February 2013 (UTC)

I like the idea of starting the article with a (brief) discussion of exponential decay in general -- where it comes from, what interesting properties does it have, etc. Some of the text could be copied from exponential decay.
But I wouldn't put the differential equation derivation (above) into that discussion. I would guess that 95% of readers of this article don't know the first thing about calculus, then another 4.9% are capable of kinda following the math but only a hazy idea of what it means, and only the last 0.1% will understand the concept better by reading through the math there. (By the way, I'm speaking very specifically about what you proposed, as I understand it. I'm not against math in articles in general -- I've added math to tons of articles including this one -- but it needs to be placed and described appropriately.) Anyway, the differential equation stuff is already in exponential decay, perhaps it could be summarized more briefly with a link to exponential decay. Just my opinion :-D --Steve (talk) 20:19, 19 November 2013 (UTC)

Move Section - Probabilistic Nature of Half Life[edit]

Many high school and under graduate students come to this page for a description of half-life which will help them in their studies. I suggest we move the probabilistic nature of half life to the end of the article, as it is furthest from what the average user on this site would be looking for, and is probably the most confusing. Please see my previous talk post as an example of what I believe to be relevant, important aspects of the concept of half life. Sean Egan (talk) 21:34, 28 February 2013 (UTC)

I agree that this section needs to be moved, but I think that the beginning of the article needs a lot more attention. I would recommend that it be rewritten in the standard method of an undergraduate physics text on radioactive decay. That means just a little more history on the term other than mentioning Rutherford, followed by the samll set of standard formulas - basically just

N(t) = N_0 e^{-\lambda t} \,

and

t_{1/2} = \frac{\ln (2)}{\lambda} = \tau \ln(2)

Then you introduce the standard units of measurement and give a few examples possibly with a supporting graph or picture.

After that, then one can talk about the probabilistic nature of the phenomenon observed in physics, but this needs to be addressed in terms of the solution of the time dependent Shrodinger equation, the transition probabilty, Fermi's Golden Rule, and the energy-time uncertainty relationship. Not just in terms of the law of large numbers, or focusing too much on the boolean character of the decay phenomenon.

I acknowledge that this is not the Exponential decay article, which offers most of this detail.. But that's also a good reason that the probabalistic interpretation needs to be moved out of the first part of the article (the probabalitic interpretation is only in regards to nuclear decay, or another discrete random process). HappyDa (talk) 05:44, 7 March 2013 (UTC)

It's agreed then, we should change up this article. I'll wait to see if anyone else has any thoughts, as I've noticed quite a few recent posts to this talk page. If I don't hear anything else, I'll start moving content around. I also agree with your concern regarding the beginning of the article. I don't think it serves the community well as it is, and should be expanded. I wrote a derivation of half life above this talk post in terms of chemical species, but I could re-write it in terms of nuclear decay. I wouldn't have to copy all the equations, but just the main idea. Does anyone have a problem with that ? Sean Egan (talk) 18:55, 7 March 2013 (UTC)
Well I'm not sure I agree, actually.. I don't think this article needs to jump into derivations right off the bat either. I think that all you need to do is introduce the exponential decay formula, define its variables, and then show what happens when you substitute:
N = \frac{1}{2} N_o
That leads you to the second formula, defining the half life. There is no mention of math or physics in that part - it's just a feature of exponential decay.
That being said, I think that if there should be any leaning towards a particular branch of science when doing the explanation, I would think it should be physics. This term is widely known for its application in nuclear radioactive decay, as that's where it was coined. I certainly don't think that the derivation of the term should start by its application in study of chemical species. If that is mentioned, it should be in a section of its own, but not in the introduction or the first section - it should be more like the Half-life in biology and pharmacology section. HappyDa (talk) 06:37, 8 March 2013 (UTC)
So you don't agree that we should move the probabilistic section down the page? If not, I'll let it sit there. In addition, I had some students take a look at the current definitions of half life. It took 4 freshman physics students quite a while to figure out what was being stated. I think there could be some additional clarity. For example, one student was interested in knowing where the exponential and natural logarithms come from. Why do they arise? This isn't currently stated. Sean Egan (talk) 19:31, 14 March 2013 (UTC)
I agree that the probabilistic section needs to be moved down, yes. I just didn't agree that the front section should be introduced in terms of chemical species - that's what you were suggesting above, and I think it should be introduced in terms of nuclear radioactive decay, just like it is now. We just need to expand it a bit, and yes, the probabilistic section is way too prominent, and it is not explained very clearly. HappyDa (talk) 04:01, 15 March 2013 (UTC)

I think the problem with the probabilistic section is not that it is in the wrong place but that it desperately needed shortening and copy-editing. (I think I wrote it originally ... Sorry! :-P ) I just shortened it ... hope that helps ... :-D --Steve (talk) 02:11, 19 November 2013 (UTC)

Simple table at the top[edit]

The table at the top of the article simply illustrates the concept in numerical sequence. The introduction of 1/e (in red?) seems to serve no purpose and breaks the "halving sequence" the table illustrates - also the formatting creates errors. The use of math formatting for the simple fractions involved seems rather pointless. Restored original. Vsmith (talk) 13:30, 3 October 2013 (UTC)

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