Measuring Very Short Periods of Time
Date: Winter 2012-2013
I have been reading about the discovery of subatomic particles in particle accelerators. How do you measure something that lasts only 10^-24 seconds?
Thanks for the question. No instrument can directly detect the lifetime of a particle that lasts for 10^-24 seconds. What one does is the following. In the experiment, one measures the mass of the particle or the energy of the particle. Mass and energy are related by Einstein's E=mc^2 equation. Let us say you are measuring the energy of the particle. The experimental results will (sometimes) look like a bell-shaped curve. We would say that the particle has a distribution of energies. Now, there is an uncertainty relation (a variation on the famous uncertainty principle) that says (deltaE)*(deltaT)>h/(4pi). Now deltaE is the width of the distribution and delta T is the lifetime of the particle. So, you substitute in the width for deltaE and solve for the inequality for deltaT. That is how you estimate the lifetime for a particle that is very short lived.
I hope this helps. Please let me know if you have any more questions.
Particles can leave behind tracks in detectors and the tracks last a lot longer than the particle itself.
Also, some of the particles decay into longer lived "daughter" particles or take part in interactions whose presence is a sure sign of the presence of the original particle.
Kind of a short answer and broad brush answer, but I hope it helps.
As you might guess, scientists do not measure such short time periods directly. Instead they measure something related to the time period. In this case, they measure the range of energy over which the particle is observed.
A particle that lasts a long time after being formed has a very well defined energy, and if you want to make that particle, you have to provide exactly that amount of energy. If you are off by even a little bit, you just do not see anything. But if you hit the right energy exactly, you get a big signal coming into your detector.
But a particle that decays very quickly after being formed does not have a well defined energy. You can make one even if you do not provide exactly the right amount of energy, as long as you are close enough. The shorter the particle's lifetime, the less precise you have to be to form it.
It turns out that there is an equation that relates the lifetime of a particle to the energy range over which it can be formed. That equation is
* = H,
where H is Planck's constant. (Well, there are some other numbers in there, but they are not important here.) So, if you have measured the range of energy over which you see the particle, you can calculate its lifetime as = H / .
No doubt this sounds pretty arcane and not at all intuitive, but it is very closely related (mathematically) to things we see every day, but might not notice unless we were paying very close attention. Most things that vibrate don't vibrate forever; eventually they stop. But how long does it take them to stop vibrating? Well that depends on their environment. If you touch a vibrating guitar string with your finger, it stops vibrating almost immediately. A physicist would say that the guitar string is "damped" by your finger. Here is the thing we do not notice unless we are paying very close attention: a damped string does not have a very well defined resonant frequency. The is related to the over which it can vibrate.
Now you know why physicists sometimes call short-lived particles "resonances".
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Update: November 2011