January 21, 2011
Basic, no math, operational
dimension, example, natural unit, Planck
on Size, Energy and Unit, we know that the speed of light better be equal to 1, that simplify the equation of relativity.
now, we impose 1 more things, the Reduced Planck constant, also set to 1. that simplify all equations with angular momentum or spin.
the Angular momentum:
now becomes :
when we want to calculate the real value, we can recover the by considering the dimension. the reduced Planck constant has dimension
January 17, 2011
decay, momentum, natural unit, reverse, time
when we have a decay process, there are many fragments, we can measure their momentum and energy and construct the 4-momentum
we use the c = 1 unit as usual.
to find out the mass before the decay, we can use
the reason for the term “excited mass”, we can see by the following illustration.
consider a head on collision of 2 particles in C.M. frame, with momentum p and energy E1 and E2.
the mass for each one is given by
but if we use the sum of the 4 momentum and calculate the mass,
which is not equal to
in fact, it is larger.
the reason for its larger is, when using the sum of 4 momentum, we actually assumed the produce of collision is just 1 particles, and the collision is inelastic. Thus, if we think about the time-reverse process, which is a decay, thus, some of the mass will convert to K.E. for the decay product.
December 17, 2010
energy, example, GeV, MeV, momentum, natural unit
i just state the formula and the usage of it.
the basic equation is
where E is total energy, p is momentum
here we can see the advantage of using MeV as unit of mass. the equation is now further simplified by using MeV/c as momentum unit.
which is Pythagorean theorem!
the speed of the particle is from the formula
For example, proton mass is 940 MeV/c2, if we say an proton is moving at 94MeV, or a 94 MeV proton. we mean, the KINETIC Energy (K.E.) of proton is 94MeV. The total energy is
Thus, a 94 MeV proton is moving at 41.7% of light speed. by using a right-angle triangle of base 10, side 11, and the hight is Square-Root 21.
another way around is, a proton at 90% speed of light, how much K.E. it has? which is around 3000 MeV or 3 GeV [Giga eV]