I dont think time works the way of the movies would like you to believe.
You have your basic timeline which people think of,then theres the multiverse or multitimeline
(fig1)
A(now)----------->B(past)------------->A(now)
(fig2)
A(now)----------->B(past)------>C(now)----------D(future)
Now in fig1 you see whats considered standard movie timetravel,you leave from point A present to the past,then go back to the future,its just a,b then back to a.
Nonononono
See the moment you go back in the past your very presence is an alteration and has to kinda write itself all the way up to the present,so A becomes C
and the Future becomes D.
Ok so what happens when i meet myself?
well youve already changed things by being there,and now youre meeting yourself,
or so you think!!!
you are meeting yourself but your actually meeting a copy,a multiversal copy.
To make this clearer
A(past)------>B(present)------->C(future) (normal)
Your at B,you go to the past A and the moment you do that from your perspective B does not exist,
so B becomes C
A-----B-----/Cut off/A-------C>>>>>D future (time altered)
The normal timeline still exists maybe in a parallel universe,except your no longer in it,your just changing the probabilites where youre at,as you still exist in parallel universes on quantum probabilities,if its probable you exist elsewhere then its also probable for you to meet these copies,theres no actual harm in that if the original A/B timeline is accepted to exist on a quantum scale.
You have to accept though that cos you create a C/D line that the present will not be the same as what it was before,every second you spend in the past is altering the run of things,the shops you visit,the people you talk to and so on.
If you were to go back in the past from where youre at in the C/D line then its the same:
C-----D----/cut off/C------E>>>>>F future (altered again)
The problem that it doesnt fix is memory,for instance YES there very well could be parallel universes but i dont have memorys of other copies of myself.
WHY should time travel be an exception to the rule?
If certain events dont happen because i changed them,how is it i have memory of the events even though they never happened?
And parallel universes will not solve this problem cos as i said we dont get memory from these universes in natural law,so the questions about memory remain.
Multi timeline sounds ok,but its gonna follow the same physics as far as memory is concerned.
Although saying that as your in a different universe it should mean you keep your memorys from the previous timeline,i say SHOULD but im unsure.
We can know how mass,energy and so on works elsewhere and can transfer to and fro naturally,but thats not using memory,it just does it,
when your doing these things your only doing them based on memory,if memory is wrecked from this procedure the whole thing gets cancelled out.
It kinda forces you to accept the multiverse idea,so that memory is carried forward from where you was to where youre now at.