Subject: Doesn't Time Travel defy Conservation of Mass / Energy?

According to Kip Thorne and others, time travel is allowed under the Theory of 
Relativity.  Even though some claim that naturally occuring wormholes would be 
tiny (ie. subatomic particles or bosons, if those, would be the only things 
allowed to pass through) they would still allow for the passage of tiny masses 
and energy.  But, if a mass were to travel through space and / or time (say, 1 
Kg of matter), wouldn't that same 1Kg of matter either A -- Blink out of 
existence for a period of time (ie constitute a loss of 1 Kg of matter over the 
entire universe) and / or B -- Reappear in the past, where there was already 
that 1Kg of matter (ie constitue a gain of 1Kg of matter over the entire 
universe)?  Doesn't that violate conservation of mass / energy?  Or does it 
mean that the singularity of the big bang was a point in 4 dimensions, and 
actually contained all of the matter and energy in the universe for every 
single measure of Planck's Time for its entire existence (a number so large as 
to be deamed infinity)?  Either way, doesn't this prove some flaw in relativity 
or possibly in our understanding of the Big Bang?

Re: Doesn't Time Travel defy Conservation of Mass / Energy?