Time Travel I

1. Time Travel I by Robert Nemiroff Michigan Tech

2. Physics X: About This Course • Officially "Extraordinary Concepts in Physics" • Being taught for credit at Michigan Tech • Light on math, heavy on concepts • Anyone anywhere is welcome • No textbook required • Wikipedia, web links, and lectures only • Find all the lectures with Google at: • "Starship Asterisk" then "Physics X"  • http://bb.nightskylive.net/asterisk/viewforum.php?f=39

3. Time Travel to the Future Time travel to the future: • allowed by Special Relativity (SR) • basis of the twin paradox • just go really fast for really long and come back • or go near a black hole • can always see what is going on • can send messages and affect things • during travel, on the average, Earth's clocks will appear to run fast compared to your clock • expensive and hard to do

4. Time Travel to the Past Time travel to the past: • has never been done • generally thought not possible • unfundable without clear demonstration • leads to many paradoxes • might not conserve mass, energy, momentum, angular momentum, etc. • popular plot device in science fiction

5. Time Travel: Grandfather Paradox A person travels back in time and kills her/his grandfather.  This happens before (s)he had children.  Therefore, there is no way for the time traveler to be born.  If the time traveler is not born, how can they go back in time to kill their grandfather? This paradox need not involve a grandfather, but could be any direct ancestor including either parent.  In perhaps the simplest case, the person killed could also be the time traveler before they entered the time machine.

6. Grandfather Paradox: Possible Resolutions • Parallel Universes Resolution • One can only time travel to a parallel universe. • History remains intact at the time of arrival. • Anything goes after that. • Restricted Action Resolution • Actions are restricted -- you cannot kill your grandfather (etc.), even if you try • Related to the Novikov Self Consistency Principle.

7. Grandfather Paradox: Possible Resolutions • Destruction Resolution • Killing your grandfather will cause the destruction of the universe (science fiction) • Predestination Resolution • Whatever a time traveler does was really supposed to happen, even if the time traveler didn't know that at the time (science fiction)

8. Time Travel: Ontological Paradox What happens if you get an idea from a time-traveler? If an idea comes from a time traveler from our future, where did the original idea come from?   New information must have an origin.

9. Searching for Time Tourists Hawking Paradox: if time travelers existed, they would be here now.  Since they are not here, time travelers -- and possibly time travel itself -- does not exist. Similar to Fermi Paradox about intelligent alien life. Sagan Corollary: Perhaps they are somehow disguised. • physical laws say they can't be seen • they might not want to be found • for personal gain • to avoid paradoxes in the future

10. Searching for Time Tourists How would we find time tourists? • Big lottery winners? • Images captured in old photographs? • Google searches for events before they happen? • (A personal hobby of RJN.)

11. Time Travel: Chronology Protection Conjecture A conjecture by Hawking that the law of physics will prevent time travel (closed time-like curves in GR) on all but microscopic scales. This applies only to "normal matter", matter that satisfies the GR Weak Energy Condition.   The CPC does not apply to matter with a negative energy density (dark energy). 

12. Novikov self-consistency principle NSCP: It is impossible to create time paradoxes.   OR The probability of something occurring that creates a true time paradox is zero.  HOWEVER "Changing the past" paradoxes are guaranteed self-consistent in that they only create a "closed loop" in a self-adjusted, cyclical, self-consistent way.

13. Novikov self-consistency principle Time Loop Logic: use the NSCP and a time machine to compute things faster than is possible with current computers: Example: How to use the future and a time machine to compute a prime factor F for a very large number N. Algorithm: Establish N.   • Receive F from the future. • If F is a true prime factor of N, send F to the past • If F is NOT a prime factor of N, send F+1 to the past

14. Novikov self-consistency principle Time Loop Logic Note that if F is not a prime factor of N, then the F sent in step 3 will not be the same as the F received in step 1.  This is a time paradox, the the F received must the same F that was sent. Such time paradoxes are not allowed by the NSCP.  Therefore, this cannot happen, and only step 2 can occur.  So one can determine "very fast" if F is a factor.

15. RJN Comment: Instantaneous Time Travel Let's say you go back in time one minute.  When you appear, there is twice your mass around as was before.  Then, when one copy disappears back into the time machine, mass seems to just disappear without going anywhere • Mass and energy conservation appear violated at a high level.  • Even over one minute, the two copies of the time machine would develop a relatively high relative velocity.  This is due to the Earth rotating, the Earth moving about the Sun, etc.  How come you don't come flying out of the time machine at a very high velocity?