one end of the spectrum just found gravity waves, is working on dark matter, split the atom, and asks is time travel possible - and - at the other end we have the ant shavers.
Time travel would be impossible for living things (to remain alive). Don't forget the Earth is spinning at 25,000 mph, and revolving around the sun at God knows what speed, and if certain theories are correct the whole solar system is moving outward from where it used to be to wherever it's going. If you traveled back in time even 1 minute you might find yourself buried in the earth or floating in outer space.
...if certain theories are correct the whole solar system is moving outward from where it used to be to wherever it's going.
Although the galaxy has us in a gravitational lock, sure spin around and migrate as everything is spinning around a super massive black hole in the center of the galaxy.
You can find plenty of scientific articles about this online; you just have to weed out the cranks.
The best known method of time travel to the future is by traveling very close to the speed of light, especially near a black hole.
Some think that it may be possible to travel to the past - but that involves traveling faster than the speed of light, not usually considered possible.
Although some theories say it may be acheived by linking two spinning black holes with a wormhole and repeatedly traveling through the wormhole.
Not exactly a practical proposition.
Then we have Quantum mechanics that posits that 'entangled' particles are linked instananeously across astronomical distances, much faster than the speed of light so who knows where that might lead.
Look up at a clear night sky and see the stars at all that old light. Same goes for the Sun with the 8.3 minutes old light that bathes the planet - just don't look at our local star as it will cause eye damage.