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Tuesday, December 30, 2014

Strained And Witchcraft

Consider the relation between time and space,

2π.tct=c

2π.tc=ct

2πtct=c

tct=c2π

In a similar way and considering the direction of these dimensions,

tTt=ic2π

tgt=ic2π

And

xt=xtctct+xtgtgt+xtTtTt --- (*)

xt=c2π{xtc+ixtgixtT}

If all time dimensions are equivalent,

xtc=xtg=xtT

xt=c2πxtc

We also have

(xt)2=(xtc)2+(xtg)2+(xtT)2

 xt=3xtc

This is possible only if,

 xt=xtc=0

At this point we can swap x for tc, since they are both dummy variables and conclude by symmetry that when xt=c2π,  tct=0

However, for the fun of it,

When x wraps around tc,

2π.xt=c

2π.x=ct

2πxt=c

and,

 2πxtc=cttc

So,

xt=xtctct --- (***)

Since,

xtc=xtgtgtc+xtTtTtc

As changes in x and tc does not effect tg and tT, and as far as x is concern tg and tT are equivalent, !?!

xtc=c2πttc=2xtgtgtc=2xtTtTtc

ie.

xtctct=c2π --- (**)

and

xtctctg=2xtg

From which we formulate,

xtctctgtgt=2xtgtgt --- (1)

Similarly,

xtctctT=2xtT

xtctctTtTt=2xtTtTt --- (2)

Therefore (1)+(2),

xtc{tctgtgt+tctTtTt}=2{xtgtgt+xtTtTt}

Substitute (**) into the above,

 c2π{tctgtgt+tctTtTt}=2tct{xtgtgt+xtTtTt}

But,

 xt=xtctct+xtgtgt+xtTtTt

So,

  c2π{tctgtgt+tctTtTt}=2tct{xtxtctct}

But from (***),

xt=xtctct

So,

c2π{tctgtgt+tctTtTt}=0

But,

tct=tctgtgt+tctTtTt

Thus,

c2πtct=0

tct=0

Blasphemy, I know.  The point is,


when xt=c2π, tct=0 and when tct=c2π, xt=0 are consistent.

The factor of 12π appearing before c is the result of circular motion around the orthogonal axis.  A particle traveling in circular motion in space about the time axis is not traveling in time, so time speed equals zero.  Similarly, the same particle traveling in circular motion in time about the space axis has zero space speed.

This relationship can be rewritten as,

v2+v2t=(c2π)2 --- (+)

where v is the particle velocity in space, vt is the particle velocity in time and c a constant.  Pythagoras' Theorem applies because v is perpendicular to vt.  Obviously expression (+) satisfies the boundary value conditions.

More importantly, the time speed limit occurs at c2π not at c, because the particle goes into circular motion.