Is travelling back in time possible?

It seems to me there are 3 possible reasons why we might never be able to travel backwards in time:

1. We will never create the technology to do so, either because civilisation ends before the technology is invented or because the technology required is simply beyond the ability of human beings to invent.
   
2. Because the laws of physics prohibit the possibility of traveling backwards in time.
   
3. Because the past doesn't exist. So we can't travel to the past for the same reason we can't travel to Narnia.

I suspect we will never travel backwards in time, and that is because the the past doesn't exist i.e "3".