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Friday, December 26, 2014

Stargate

If we stare down one of the space dimension with one time dimension curled around it,


where r is very small.  tg is at light speed, v=c.  If it is possible to slow down time,

tgft<c   (in ticks per second)

such that,

tgft=rω

r=1ωtgft<cω

where both ω and r are physically manageable number, consider the equation from the post "Time Travel Made Easy" again,

tgft=1mc2(tgitEΔh+tgiEΔht)+tgit ---(*)

tgit=c

tgft=1mc2(cEΔh+tgiEΔht)+c

tgiEΔht=mc2tgftcEΔhmc3

tgi=2πaψnc

aψnEΔht=12π{mc3tgftc2EΔhmc4}

aψn=12π{mc4(EΔht)1+mc3tgft(EΔht)1c2EΔh(EΔht)1}

Since,

EΔht<0

aψn=12π{mc4(|EΔht|)1mc3tgft(|EΔht|)1+c2EΔh(|EΔht|)1}

replacing aψno=12πmc4(|EΔht|)1

aψn=aψno{11ctgft+1mc2EΔhtt}

From (*)

tgft=1mc2(tgitEΔhtt+tgittEΔht)+tgit

tgft={2tmc2EΔht+1}tgit --- (**)

So,

aψn=aψno{1{2tmc2EΔht+1}+1mc2EΔhtt}

aψn=aψno{tmc2EΔht}

aψn=12πc2.t

The particle travels at a forward velocity of,

vtele=12πc2

Is this speed possible?  Yes, time speed has been slowed down, that implies greater than light speed space travel.  However we are NOT traveling through space this way.

At time t=0, just before t=0,

aψn,t=0=aψno{11ctgft+1mc2EΔhtt0}

aψn,t=0=aψno{11ctgft}

in this case, tgft0, and the teleported distance is aψnt=0.  As with the case considered in the post "Teleportation", with

tgft=constant

 the particle return velocity is,

aψno1mc2EΔhtt=12πc2.t=vtele.t

vtele=12πc2

At t>0 however,

vtele=12πc2

It seems paradoxical that the particle can be at different locations and have different velocities just before and after t=0.  The trick here is,

tgft={2tmc2EΔht+1}tgit = constant

The expression EΔht.t is held constant such that 

tgft={2tmc2EΔht+1}tgit

from (**) is a constant.  This means

 EΔht=At

where A is a constant.

This way, only the situation for t=0 applies and as will be discussed below t0.

The problem is, if EΔht is induced in a particle, how to turn it off when it is at a distance aψn,t=0 away?

Simple, we beam the particle through another portal that induces EΔht.  After passing through the second portal, EΔht=0.  Equation (*) collapses to,

tgft=tgit

as at t=0,  EΔh=0.

And the particle does not return from x=aψn,t=0,  t0.



Since time, tg is curled around x where itg=x as required in the post "Time Travel Made Easy".  x is perpendicular to the circular plane containing tg.  The portal is directional.  This sort of teleportation unfortunately is restricted to line of sight.  Unless we can draw a straight line between the two points, teleportation is not possible.

And the billion dollar question is, how to induce EΔht=At in a particle?