If you were to go back in time, how would you account for the extra mater in the Universe? Would not every atom in your body, the oxygen in your lungs and all that you brought with you, already exist as something else?
closed as primarily opinion-based by JDługosz, Hohmannfan, bilbo_pingouin, AndyD273, DaaaahWhoosh Oct 26 '16 at 13:15
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
This depends on how your time machine works.
Let's imagine past!William built a time machine back in 1970. The time is finally right to test it, so future!William dusts it off and opens the door. On the other side of the door...is his laboratory in 1970. When he walks through the door, he is in 1970; when he walks back through, he's in 2016.
Conservation of energy applies to a closed system, where nothing is entering or leaving. "The Earth" isn't a closed system, since the Sun is constantly adding energy. "The Universe" on the other hand is generally considered closed, since there's no known method for energy to enter or leave it.
But with your time machine turned on, "the Universe at midnight on January 1, 1970" can't be considered a closed system, because now things can move back and forth between 1970 and 2016. You've effectively forced "the Universe in 2016" and "the Universe in 1970" to be part of a larger closed system in which conservation of energy holds.
This is really weird, and runs counter to our intuitions about physics, but is a logical result of the way this hypothetical time machine works. You aren't actually producing energy out of nowhere; anything which comes through the door in 1970 has departed through the door in 2016.
As a side note: equivalent to conservation of energy is the claim that "nothing depends on time" (via Noether's Theorem). In other words, there's no law of physics which gives different results if your clock is five minutes slow. So if conservation of energy doesn't hold for the Universe in a single instant any more, then time symmetry doesn't either, which could have some interesting consequences...including, a convenient way to handwave any other weirdness in your fictional world's physics. ;)
Well, atoms don't have serial numbers, so there wouldn't be any physical reason your atoms would be identified as your past self's atoms. Especially since many of your atoms are replaced on a regular basis, along with the air in your lungs.
This is essentially a question of where the soul is, and whether your soul or being can be in two places at once. When asked where the soul is, someone wise said, "The same place the music is in the organ."
So, if your characters travel in time, I would not be worried about that. This isn't actually a time travel paradox. If you do want to make difficulty of concurrent existence a thing, that was a major part of Time Cop (I think that was the one). They had it that if you meet yourself, you are pulled together and your flesh slowly fuses with their , disturbingly and painfully.
Whatever else time travel does, it doesn't involve the conservation of matter. Besides the conservation of matter, strictly speaking, only applies to closed systems and there is no reason why this law should apply to the universe as a whole.
It is possible to construct a model where the conservation of matter does have temporal properties. Assume normal matter moving in time has a positive temporal quality, when it is moving backwards in time it now has a negative temporal quality. When you add the two temporal qualities together the nett result is zero.
Once the matter stops moving backwards in time and is now moving forwards in time its temporal quality is gain positive. Adding this to the previous result of zero and the universe is back to the original amount of positive matter in the universe.
This suggests time travel won't have any affect on the conservation of matter. There is no need to account for extra matter in the past, because effectively no extra matter has been added.