Simultaneity in relativity

Let there are two inertial frames of references S and S’. S is the stationary frame of reference and S’ is the moving frame of reference. At time t=t’=0 that is in the start, they are at the same position that is Observers O and O’ coincides. After that S’ frame starts moving with a uniform velocity v along x axis.Let two events in frame S occur simultaneously at positions P1 and P2. The coordinates of the P1 will be (x1,y1,z1,t1) and of P2 will be (x2,y2,z2,t2). The events will be simultaneous (occur at the same time) according to the observer in frame S. Therefore

t1 = t2                                                              (1) Continue reading “Simultaneity in relativity”

Einstein mass energy relation discussion and derivation

Einstein’s mass energy relation:

You must have known the relation E = mc2. Let us derive it:

Derivation:

Consider an object of rest mass m’. If force is applied to the object such that it starts moving with relativistic velocity (that is comparable with the speed of light), then its mass will also vary with variation of mass with velocity relation

m = m’/(1-v2/c2)1/2 (1)

Now suppose that work dw will be done due to this force. If the object is displaced along x axis, then work will be:

dw = Fdx

or  dw = (dp/dt)dx      (because from Newton’s 2nd law F = dp/dt)

or  dw = [d(mv)/dt]dx   (because p =mv)

Differentiate R.H.S.

dw = (mdv/dt + vdm/dt)dx    (here m is also a variable quantity, thus m is also differentiated)

or dw = mdvdx/dt + vdmdx/dt

or dw = mvdv + v2dm                                       (2) Continue reading “Einstein mass energy relation discussion and derivation”