Sci-fi book about a guy who finds out he can jump between worlds. He travels to another world and runs into his father (or maybe grandfather) who has been missing for a long time. His (grand?)father then askes the man to join him in search of something

[Peter]

The main character then declines his father and goes back to his world. Then he goes to his girlfriend's house and he convinces her to travel between worlds with him. So they do but they get separated and end up in different worlds. So he seeks out his (grand?)father and asks how to find his gf. They go back in time to talk to another guy who is teaching a class at a university.

I think it is set originally in modern London before they start world-jumping. I remember the girlfriend gets stuck in another world that is like the medieval ages and meets a guy who takes her in. They try to start a business in a new city.
Can you help me? I never finished the book and would love to find it and finish it! I originally read it about 3-4 years ago.

[Peter]

I should mention that the guy kind of stumbles onto this whole world traveling/jumping thing and it has something to do with these really old lines that intersect the world's or something like that

[Gloria]

A Leaf on the Wind of All Hallows This sounds like an interim short story in the Outlander Saga, "A Leaf on the Wind of All Hallows," written by Diana Gabaldon. Roger's father went missing after a plane crash. Roger has always suspected his father could travel through time and he goes in search of his father.

[Peter]

Hmm, that sounds similar but I don't think that is it. This one is set in more modern times before they start world jumping. The main character in the one I am talking about knows nothing of this world-hopping/traveling thing before he accidentally stumbles onto it one day.
I am now remembering that he was just walking down the street and this man approaches him claiming to be his father/grandfather and that they both could do this world-traveling/hopping thing. He then shows him by taking him with.