The discussion centers around the concept of half-life in radioactive decay, specifically addressing why half-life is independent of the quantity of radioactive substance present. Participants explore definitions, implications, and alternative concepts related to half-life.
Participants express a mix of agreement and disagreement regarding the terminology and implications of half-life. While there is a shared understanding of the definition of half-life, the discussion reveals competing views on the relevance and utility of the concept of "full life" and alternative fractional lives.
Some statements reflect uncertainty regarding the definitions and implications of half-life, particularly in relation to individual atoms and the mathematical modeling of decay. The discussion also touches on the limitations of applying the concept of half-life outside of radioactive decay.
pallidin said:One cannot establish "half' unless one knows the "whole"
Else there is no half.
How is it that nuclear decay "knows" this?
Some type of entanglement?
I thought you said above you were onboard with exponential decay and just wanted to know why? You even gave an example of radioactive decay you accepted. Now you're not accepting it anymore? Did you read the above posts regarding stability?pallidin said:One cannot establish "half' unless one knows the "whole"
Else there is no half.
pallidin said:One cannot establish "half' unless one knows the "whole"
Else there is no half.
How is it that nuclear decay "knows" this?
Some type of entanglement?
Exactly the same exponential decrease happens with charge stored on a capacitor or water draining from a small hole in the bottom of a cylindrical tank. In all cases, the rate of decrease is proportional to the level at any given time.pallidin said:One cannot establish "half' unless one knows the "whole"
Else there is no half.
How is it that nuclear decay "knows" this?
Some type of entanglement?
pallidin said:One cannot establish "half' unless one knows the "whole"
Else there is no half.
How is it that nuclear decay "knows" this?
Some type of entanglement?
QuantumPion said:No. You are thinking of the semantics of the phrase "half-life" incorrectly. The half-life is NOT the time it takes a particular sample to decay by half. There is no difference between the sample you started with, and half of that sample. It is the time it takes ANY AMOUNT to decay by half. The half-life is completely independent of how much material you have. The half-life is defined as:
t_{1/2}=\frac{ln \: 2}{\lambda}
Lambda is the decay constant, which is a particular value for each isotope. The half-life is just a different mathematical representation of this decay constant. Another way of expressing half-life is the mean lifetime, tau:
t_{1/2}=\tau \: ln \: 2
The mean lifetime is the average time it takes for any atom of a particular isotope to decay, even if it is just a single atom by itself.
The nuclear decay of an atom does not know about any other atoms around it. There is no entanglement. This is precisely the point.