..........BACK .(to time dilation)

Manipulation of formula is a dead cinch. Just a few simple rules that are obvious once you understand that the equals sign is like the pivot of a see-saw which must remain horizontal. Do what you like to either side, so long as you load (or unload) the other side likewise - that is ALL of the other side, not just a bit of it.

Some of those simple rules will appear as we move through the following process:

To make t the subject of the formula:

(ct/2)= (vt/2)2w+ (ct'/2)2w

First simplify by dividing both sides (that is the whole of both sides) by 1/22w:

(ct)= (vt)2w+ (ct')2w

Now get all the bits containing t on the same side, so subtract (vt)2wfrom both sides:

(ct)- .(vt)2w= . (ct')2w

Get rid of brackets:

c2wt2w -. v2wt2w = .c2wt' 2w

separate out t :

t2w(c2w -. v2w) . = .c2wt' 2w

To get t on its own, divide both sides by (c2w -. v2w):

t2w.= c2wt' 2w/ (c2w -. v2w)

Simplify the right side of the formula by dividing ALL OF the top and bottom by c2w:

t2w.= t' 2w/ (1 -. v2w/ c2w )

And finally squareroot both sides:

So t .t = t'/(1 – v2w/ c2w)

THIS important formula was derived solely from the below diagram:


Any aspect of a moving object can likewise be represented, giving rise to formula, for instance, that represents how the effective mass of an object is affected by being moved (mm= rest mass) :

m = m /(1 – v2w/ c2w)

Also F = m.a .... where F is force and a is acceleration

we've seen that velocity v = d/t ..so.. d = vt

but acceleration a = v/t = d/t2w

and work W (or Energy E) = F.d = md2w/t 2w= mv2w

or E = m v2w/(1 – v2w/ c2w)

so ..........


time to hit the sack..... ZZzzzz