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• aaronll
In summary, particles have a probabilistic lifetime and the probability of decay is independent of how old the particle is. This can be seen in the half-life, which corresponds to a decay constant and gives the probability of decay within a certain time interval. The probability of decay can be calculated using the formula P = 1 - e^(-λt), with a decay constant λ = -ln(0.5)/t1/2. This means that on average, if we observe a large number of particles for a time equal to their average lifetime, we will see that some decay instantly and some decay later than the lifetime interval, but the overall average lifetime will still hold true. This probabilistic behavior is similar to the probabilistic interpretation of
aaronll
If I have a particle with a average lifetime of 15min, if I take 10 particles confined in a box, after 15 min there will be 5 particles.
After 15min 2.5 particles and so on... , but so, at the end there will be the last particle that decades.
That particle lived far longer than 15min, but is the same kind of other particles.
So why some particles lives less and some more? Are related to when they are "born" ( I know this word is bad)

And for particle with an enormous lifetime, e.g. 10^20 years, I can take a large number of particles, like 10^20, and see if there is a decay in some time interval,for example 1 years, if there is not i can say that almost its lifetime is 10^20 years.
But how those particle doesn't decay, for lucky, when I experiment on them?

thank you

aaronll said:
If I have a particle with a average lifetime of 15min, if I take 10 particles confined in a box, after 15 min there will be 5 particles.
No. That's a half life, not an average lifetime.

aaronll said:
So why some particles lives less and some more?
It's completely probabilistic.

No. That's a half life, not an average lifetime.It's completely probabilistic.
Yes, I meant half life ( excuse me ).

So it's probabilistic, but... why? It's like when we calculate expectation value of an observable according to probabilistic interpretation of wave function? So we "found" some value with some probability to found if we measure it, but why we found a particular value it's a "mystery".
it's the same things?
To me thinking that a particle has a probabilistic lifetime it's very strange.Last question: if we take a particles, randomly (we cannot say when it was "born") so statistically we can observe it for a time equal to its average lifetime? We can observe some that disappear instantaneously, and some later than lifetime interval, but on average is the lifetime, is correct?

thanks

aaronll said:
To me thinking that a particle has a probabilistic lifetime it's very strange.
It is strange. But that's how nature behaves.

Also, nuclei don't "wear out" the probability of a nucleus to decay is independent of how old it is.

aaronll said:
Last question: if we take a particles, randomly (we cannot say when it was "born") so statistically we can observe it for a time equal to its average lifetime? We can observe some that disappear instantaneously, and some later than lifetime interval, but on average is the lifetime, is correct?
Right. And it doesn't matter when it was born, as long as it exists when you start the measurement.

aaronll said:
If I have a particle with a average lifetime of 15min, if I take 10 particles confined in a box, after 15 min there will be 5 particles.
As noted above, you really mean the half-life, ##t_{1/2}##, not the average lifetime.
Also, nuclei don't "wear out" the probability of a nucleus to decay is independent of how old it is.
In general, a half-life corresponds to a decay constant (probability of decay, per unit time) of $$\lambda = \frac {-\ln 0.5} {t_{1/2}}$$ For the given example, $$\lambda = \frac {0.693} {15~\rm{min}} = 0.0462~\rm{min^{-1}}$$ If you pick any particle, it has a probability of 0.0462 = 4.62% of decaying within the next minute, regardless of how long it has lived already.

Last edited:
If a particle is certainly present at ##t=0## then the probability that it decays within the time interval ##[0,t]## is
$$P_{\text{decay}}=1-\exp(-\lambda t).$$

Oops, I shouldn't have blindly assumed the first-order approximation.

The exact calculation above gives P = 0.0451 = 4.51%.

## 1. What is particle lifetime (half-life)?

Particle lifetime, also known as half-life, is the amount of time it takes for half of a sample of particles to decay or disintegrate into other particles or energy.

## 2. How is particle lifetime (half-life) measured?

Particle lifetime is measured by observing the decay of a large sample of particles over time. The half-life is determined by the amount of time it takes for half of the particles to decay.

## 3. What factors affect particle lifetime (half-life)?

The factors that affect particle lifetime include the type of particle, the energy of the particle, and the environment in which the particle exists.

## 4. What is the significance of particle lifetime (half-life) in particle physics?

Particle lifetime is an important concept in particle physics as it helps to understand the stability and behavior of particles. It also provides valuable information about the fundamental forces and interactions between particles.

## 5. Can particle lifetime (half-life) be altered or manipulated?

Yes, particle lifetime can be altered or manipulated through various methods such as changing the energy of the particles or manipulating the environment in which the particles exist. However, this is a complex process and is not yet fully understood.

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