isospin as time axis

[AntonioLao]

The nearly identical mass property of proton and neutron is a direct consequence of the principle of isospin gauge invariance. This was shown by Yang and Mills in the 1950s. However, this intrinsic symmetry is that of local quantized spacetime not of global continuous spacetime of Einstein’s relativities (SR and GR).

This quantized local spacetime symmetry possesses a local infinitesimal axis of symmetry. This axis is invariance under 4 dimensional spacetime. At the local infinitesimal region, it is equivalent to the time axis of all particles: fermions and bosons. In order for any particle to exist, its time axis must not align with the time axis of the true vacuum field. The time axis of the vacuum represents the universal time axis of the entire universe.

A free neutron whose time axis is at a greater angular distance (greater mass) from the vacuum axis loses its angular symmetry in about 15 minutes turning into a proton, an electron, and an electron antineutrino. These particle products possess their unique time axes. However, the angular distance of the proton’s time axis is such that its half-life is [math] 10^{35}[/math] years.

[Guille]

I remember I studied like 4 months ago the half-life of some sub-atomic particles in physics class. I have forgetten everything I learned then, you know, this summer was too full of things to do. Now, can you tell me what the hal-flife of a particle is and means?

At least I remember that it had to do with radiation and that the "half" meant nothing because it was actually the whole life. tell me more!

[AntonioLao]

Mean lifetime is not the same as the half life of a radioactive sample. The mean lifetime associated with an elementary particle is simply the direct average lifetime of all measured lifetimes whereas the half-life of a sample of radioactive material is the time for the number of active nucleii to be reduced to half the original number. The half life is a property of the sample, not a property of the individual members of that sample. If the decay constant associated with the sample is l , then the mean lifetime of the members of that sample can be shown to be 1/l whereas the half life of the sample itself has the value ln2/l .

The mathematically inclined might like to start with the exponential equation N(t) = N(0) e -l t and show that the mean lifetime has the value 1/l by considering the direct average i.e.

In the case of muons, the mean lifetime has the value 2.2ms but the half-life of a sample of muons would have a value of 1.52ms.