Since relativity is our most profound theory of time, we would like to argue that time
travel is forbidden by relativity.
Einstein had thought that his description of space-time would forbid time travel.
But this is simply wrong.
Not only is time travel not ruled out but we can actually design time machines.
Unfortunately most of these (in principle) successful proposals require negative energy,
or equivalently negative mass, which does not seem to exist in our universe.
This would have predictable properties.
For example, if you have a tennis ball of negative mass, and drop it, it will fall upwards.
It would seem very plausible that anti-matter, discovered in the 1930s, would have negative
mass.
However, theoretically, this is incorrect and we have even done experiments that show
that positrons (the anti-matter partner of electrons) do actually fall downwards.
So negative mass is very counter-intuitive, but that does not mean it is impossible.
This is a rather unsatisfactory argument since it explains why we cannot time-travel in practice
only by involving another idea that we do not really understand.
According to Standard Physics, Time Travel violates the Second Law of Thermodynamics.
That's because by traveling into the past we are going from now (a high entropy state)
into the past, which must have lower entropy.
This argument originated with the English cosmologist, Arthur Eddington, but it's wrong:
the same argument would prevent us from constructing a refrigerator, which is a device for decreasing
entropy locally.
Hence we would need a “time refrigerator” which would allow us to decrease the entropy
in some box at the cost of increasing it overall.
We of course have no idea how to do so, but 200 years ago no one knew how to make a refrigerator!
More seriously, this argument says nothing about time travel into the future.
In practice, it is just as hard for you to travel to next Thursday as it is to travel
to last Thursday.
However, the Second Law argument says absolutely nothing about traveling into the future: let’s
skip tomorrow and move on to Saturday!
There is no doubt that if we could time-travel freely, we would run into paradoxes.
One of them is "The Grandfather Paradox" which is the idea that if you travel back in time
and kill your grandfather, you would not be born at all, meaning you cannot build a time
machine.
The other paradox is the "Where are they?"
This begs the question "if time travel is possible, why aren't we overrun by time tourists"?
Well, Stephen Hawking played on this one differently: he held a party for time travelers and sent
out the invitations afterward!
No one came.
What if free will doesn't exist at all?
In physics, this can be possible, and in that case, although you can travel back to the
past to observe your grandfather, you cannot kill him, since he was not killed in the past.
The putative guests at Steven Hawking’s party did not attend the party, so they cannot
decide in the future to attend.
It is almost impossible for us to imagine that free will does not exist because it is
totally contrary to our everyday experience.
Psychologists have attempted to prove its existence, but the results are less than convincing.
If you wish to visit your house yesterday, you will need to travel through space as well,
since due to the motion of the Earth around the sun and the sun around the galaxy we would
be roughly 20 million kilometers from our present location.
In fact, the problem is worse than this, since the galaxy is also moving as a whole and we
do not even have a fixed space to refer to.
We have got very good at observing what happens in distant galaxies but have absolutely no
influence on them.
Ironically, the stars that we look at are actually time-shifted: even in the case of
the closest star, we are observing it 4 years in the past.
Could we allow for actual modifications of the past, so that we could go back and murder
our grandfather?
The Many-Worlds theory assumes that the universe bifurcates in the present, so there are many
possible futures and we can just imagine extending this to include alternate timelines in the
past.
One timeline plays out with your grandfather alive and successfully producing progeny,
the second with your grandfather dead and you not existing.
This avoids the logical paradoxes and allows you to have free will again.
Maybe the final answer is Steven Hawking’s idea of “chronological protection”: there
is some (as yet unknown) physical principle that forbids time travel.
This idea starts off with “cosmic censorship“ (with Roger Penrose), which states that whenever
a body collapses so completely as to result in the formation of a singularity, a black
hole will be formed so that the singularity will be hidden behind the event horizon.
So we cannot know what goes on inside a black hole because we cannot get information out
of it.
Ideally, we would have an improved theory that would do this automatically for us and
forbid closed time-like curves.
We even have a name for such a theory: quantum gravity, but unfortunately, it does not exist
yet.
So at the moment, this idea is really the tautological one that we cannot time-travel
because we cannot time-travel!
Although it is a very unsatisfactory solution, it may as well be correct.