Frames of Reference

Previously:  v=v’+V, r=r’+R, etc

Medium for light waves? “eather”

Interferometer: E1+E2=Etot, Intensity = |Etot|^2

Vearth=30km/s

c=3×10^8m/s

B=V/C = 10^-4

t1=2(l1/c)*(1/(1-B^2))

t2=2(l2/c)*(1/root(1-B^2))

Assuming ether at rest

(t1-t2)@theta=0 – (t1-t2)@theta=90  = B^2*(l1+l2)/c

Michaelson kept getting B=0

Fitzgerald-Lorentz contraction: dx = dx/gama

gama=1/root(1-B^2)

Einstein-> 1. No such thing as absolute motion, no preferred coordinate system… its all relative

if the ether is at rest there is a preferred system.

2. All inertial observers see the same value for ‘c’

light plays by its own rules: not v=v’+V

Lorentz-Xform

r=ct and r’=ct’ then r!=r’+R

[x';y';z';ct']=L*[x;y;z;ct] where (r^2-c^2*t^2)=(r’^2-c^2*t’^2)

this is fullfilled by:

x’=gama(x-ct*v/t)

y’=y

z’=z

ct’=gama(ct-xv/c)

transform matrix [gama, 0, 0, -gamaB; 0, 1, 0, 0; 0, 0, 1, 0; -gamaB, 0, 0, gama]

Time dilation

t2-t1= gama ((t2-t1)-(x2-x1)*v/c^2))… taken from ct’=gama(ct-xv/c) -> t’=gama(t-xv/c^2)

if X2=X1

dt’=gamadt  iff |B|<1

dt’ > dt

In the same way you can do Time dilation you can also do length contraction.