Monday, January 15, 2018

Like Doppler

Another view of the torus photon's time trip backwards is,


baring in mind that the kinetic energy along the time dimension is mc2mc2.  As we account for total energy across space and time dimensions,

Δforward=12m(c+vboom)2+mc2(12mv2boom+12mc2+mc2+mc2)Δforward=12m(c+vboom)2+mc2(12mv2boom+12mc2+mc2+mc2)

Δforward=mcvmc2=mc(vc)Δforward=mcvmc2=mc(vc)

which is just the required energy to to accelerate a particle from (vi=vvi=v) to (vf=cvf=c) in the expression,

E=mcvfvidvE=mcvfvidv

from the post "No Poetry for Einstein" dated 06 Apr 2014.

If this discrepancy is solely compensated for by one particle,  mc2mc2 along one timeline of existence,

Δt=Δforwardmc2=vc1Δt=Δforwardmc2=vc1

As v<cv<c, Δt<0,  a negative value indicates backward in time at the instance T when the torus collapses.  In term of τ,

Δτ=1Δt=1vc1

Δτ=11vc

Both expressions are different from the one in the previous post "Light Speed Back In Time" dated 15 Jan 2018,

Δt=vc

Δτ=cv

because previously the focus is on one particle along its timeline.  In this post, the total energy across both timelines are considered with the discrepancy compensated solely by one particle.  Both timelines are kept in view.

vboom is not the speed of the torus photon source.  It is assumed that vboom is in the same direction as c.  If vboom acquires a negative value.

Δτ=11vc=11+vc

vboom can acquire a negative value when the photon ray is observed from the side moving at right angle to the line of sight.  To establish a common reference given two Δτ values, we use the geometric mean,

Δτ+=11vc

Δτ=11+vc

Δτ=Δτ+Δτ=11+vc11vc

This geometric mean is the ray mc2, that appear previously in this derivation,

Δt=Δforwardmc2   or

Δτ=mc2Δforward

So,

Δτ1=Δτ+Δτ=1v2c21vc=mc2Δforward=fof1

f1=1vc1v2c2fo

and

f2=1+vc1v2c2fo

which look like the transverse Doppler effect but has nothing to do with a moving source.  It is a ray moving in a medium that collapses the torus photons to vboom that in turn eject torus photons upon further collisions at vboom.  A ray through a region of gas that emitted the torus photons.

OK??