Session E4: Other Topics

Cramer's rule, Quarks Fractional electric charge, A scientific exploration or a possible mathematical electric charge value?

In linear algebra, [Cramer's rule][1] is an explicit formula for the solution of a system of linear equations with as many equations as unknowns. 2u+1d=1 1u+2d=0 $a_1d+b_1u=c_1$, $a_2d+b_2u=c_2$ $u=\frac {c_1b_2-c_2b_1}{a_1b_2-a_2b_1}$ and $d=\frac {a_1c_2-a_2c_1}{a_1b_2-a_2b_1}$ u=+2/3 d=-1/3 now i think an up quark has no electric charge and infact this is down quark which has electeric charge of (+1,-1), then fractional electric charge completely breakdown 2u(0)+1d(+1)=+1 1u(0)+d(-1)+d(+1)=0 which means probabilities is associated with unknown parameters, Thus, Quarks fractional electric charge value is possible charge of quarks ``not'' accurate value. And also it is consisted with neutron decay, While bound neutrons in stable nuclei are stable, free neutrons are unstable; they undergo beta decay with a mean lifetime of just under 15 minutes (881.5 $\pm$ 1.5 s). (thanks god!) Free neutrons decay by emission of an electron and an electron antineutrino to become a proton, a process known as beta decay $n^0 \to p^{+1}+e^{-1}+\overline \nu_e$ \\[4pt] [1]: http://en.wikipedia.org/wiki/Cramer's\_rule   

In the nucleus density gravitation is greater than electrostatic force

Let's compare the density gravitation and electrostatic force between two protons. Temporarily, gravitational constant is believed to be accurate in the following discussion. Proton mass is about 1.67x10$^{-27}$kg, radius is about r$=$1.0x10$^{-15}$m H$=$6.67x10$^{-11}$k$=$9x10$^{9}$ Proton charge is e$=$1.6x10$^{-19}$coulomb Proton density is p1$=\frac{1.67\times 10^{-27}}{\frac{4}{3}\pi r^{3}}=$ $\frac{1.67X10^{-27}}{4.1762X10^{-45}}=4X10^{17}$kg/m$^{3}$ F$_{\mathrm{d}} \quad =$H$\frac{p_{1}^{2}}{R^{2}}$ F$_{\mathrm{e}}$ $=K\frac{e^{2}}{R^{2}}$ Obviously F $_{\mathrm{d}} \quad_{\mathrm{>>}}$ F $_{\mathrm{e}}$, Tt is apparent that F$_{\mathrm{d}}$ is much greater than F$_{\mathrm{e.}}$.   

The Real Meaning of the Spacetime-Interval

The spacetime interval is measured in light-meters. One light-meter means the time it takes the light to go one meter, i.e. $3\cdot 10^{-9}$seconds. One can rewrite the spacetime interval as: $\Delta s^{2}=c^{2}(\Delta t)^{2}-[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}]$. There are three possibilities: a)$\Delta s^{2}=$0 which means that the Euclidean distance $L_{1}L_{2}$ between locations $L_{1}$ and $L_{2}$ is travelled by light in exactly the elapsed time $\Delta t$. The events of coordinates (x, y, z, t) in this case form the so-called light cone. b)$\Delta s^{2}>0$ which means that light travels an Euclidean distance greater than $L_{1}L_{2}$ in the elapsed time $\Delta t$. The below quantity in meters: $\Delta s=\sqrt {c^{2}(\Delta t)^{2}-[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}} ]$ means that light travels further than $L_{2}$ in the prolongation of the straight line $L_{1}L_{2}$ within the elapsed time $\Delta t$. The events in this second case form the time-like region. c)$\Delta s^{2}<0$ which means that light travels less on the straight line $L_{1}L_{2}$. The below quantity, in meters: -$\Delta s=\sqrt {-c^{2}(\Delta t)^{2}+[(\Delta x)^{2}+(\Delta y)^{2}+(\Delta z)^{2}} ]$ means how much Euclidean distance is missing to the travelling light on straight line $L_{1}L_{2},$ starting from $L_{1}$ in order to reach $L_{2}$. The events in this third case form the space-like region. We consider a diagram with the location represented by a horizontal axis $(L)$ on \textit{[0, }$\infty ),$ the time represented by a vertical axis $(t)$ on \textit{[0, }$\infty ),$ perpendicular on $(L),$ and the spacetime distance represented by an axis ($\Delta s)$ perpendicular on the plane of the previous two axes. Axis ($\Delta s)$ from \textit{[0, }$\infty )$ is extended down as $(-\Delta s)$ on \textit{[0, }$\infty ).$