|
Deriving Lorentz factor by means of dynamics of gases. Let's take some fluid medium. p - pressure R - density V - velocity C - sound speed (in this fluid) First, let's derive momentum equation (if you know it, you can skip this part). Let's examine change of momentum of a fluid element: F1-F2=(dm*v2-dn*v1)/dt F=p*S, dm/dt=R*S*v p1*S1-p2*S2=R2*S2*v2^2-R1*S1*v1^2 ~ S1(R1+p1*v1^2)=S2(R2+p2*v2^2) ~ Let's denote pressure in free fluid as p0, and suppose that adiabatic exponent is very close to 1. Let's examine moving fluid element: p+R*v^2=p0 (p/p0)=1-(R/p0)*v^2 c=sqrt(p/R) (p/p0)=1-(v/c)^2 (c'/c)=sqrt(p/p0) ~~~ (c'/c)=sqrt(1-(v/c)^2)=gamma ~~~ So interaction speed has decreased and all time intervals have stretched: dt=dt0/gamma. Can it be a mere coincidence? It explains two "purely relativistic" effects from etheral point of view: - Muons reaching earth surface - Transverse Doppler effect I'm not sure if above derivation is 100% correct, but at least it's fun ;) |
| |
| |
| |
| |
 | 
|
| |
| |
|
| |
| |
| |
|
| |
| |
| |
|