March 8, 2011
Life time of particles and Time dilation
I want to correct thePDF file below (I will edit the PDF file itself later)…the values of decay width Vs life time and corresponding decay distance I give to the end of the PDF file here is only true for the Neutral B-meson for which I calculated because neutral B the life time is 1.53 pico sec SO the decay width is 430 x 10^(-6) eV in keeping with Uncertainty Relationship of Heisenberg, SO the lesson learnt from this mistake: One needs to use values of experimental measurement plus the Uncertainty EQuality, otherwise one will obtain arbitrary values consistent with Uncertainity INequality. But the equality must be chosen since it gives the best or the ideal value that is more closer to natural value under a given experimental scenario
I wanted to brush up my ideas of relativity a little. The question in my mind is, Is life times of particles given as a proper time ( in the rest frame of the particle itself ) The answer is the life time (mean) is given for particles at rest, so its the proper time but the observer should also be in the rest frame of the particle. The proper time is (1 over gamma) times the regular time, where gamma is the Lorentz contraction factor and is the inverse of the square root of (1 minus beta square), beta is the ratio of velocity of transformation by speed of light.
SO a muon which has a life time of 2 micro seconds moving at a speed of 3, 5ths of the speed of light would live for 2.5 micro seconds because time would dilate, that is, the life time for the muon observed by someone when it moves fast (apparent life time) will be more. Time dilation is an effect of Special Theory of Relativity where moving clocks run slow that is on a moving train or air plane the clocks ticks slower, it takes more time to execute a process.
I have a related article where (Einstein, Hawking and my ideas) I have described how two particles moving wrt each other is like a particle moving wrt time, so time itself can be thought of like a particle, in that case its easy to intuit how time is relative, if we are moving faster wrt to time, time is moving faster wrt to us. SO we can say from that perspective time is slower or faster.
But the thing here to remember is MOVING CLOCKS run SLOW, therefore in any frame where the particle is moving it would seem that the particle has lived longer than the time given as the particles mean life time. The paradox between the two frames of references, the rest frame of the moving particle and the lab frame or something where this particle is seen to be moving is they each would claim the other frame to be running a slower clock and they both are right, since they each are moving wrt each other, but remember there is something called simultaneity which in itself is relative, ie simultaneity in one frame is not valid in another frame.
SO they both end up measuring a different process unless they adjust for simultaneity and only in such a fictitious scenario they will claim inconsistently. If everything is taken for consideration there is no paradox or inconsistency.
SO the Klong meson lives for 15.3 meters(512 picosecs), the kshort lives for 2.7 centi meters (89.5 picosecs or the time during which light would make through that distance).
The neutral pions live for only 25 nano seconds where as the neutrons live for about 15 minutes. The protons are the oldest living creatures in the particle world, they could live up to several 100 times 10 to the 30 years.
SO in about every 15 minutes one of the neutrons inside a nucleus converts into a proton (plus electron and electron type neutrino ) SO I wonder if all the neutron would vanish in a while inside the nucleus as they will produce protons.
In any case the protons are the ones then that are giving the atom its stability and positive charge. What are the neutrons even doing there and once they convert into a proton, it goes on increasing the number of protons but the number of neutrons goes on decreasing, so what happens after long enough time !!!