This is something I've always been intrigued by. I can't help but think the collective consciousness of the population would have been significantly changed over such a enormous length of time. Would I know the names of Old Kingdom kings? Were our traditions and views on life and death the same? Heck, could we even have communicated with each other?
Edit: grammar
There's always more to be said on the topic, but I've touched on this in a few past posts.
I can't recommend Assmann's The Mind of Egypt: History and Meaning in the Time of the Pharaohs highly enough if you're interested in the intellectual history of ancient Egypt.
Imagining the Past: Historical Fiction in New Kingdom Egypt by Colleen Manassa and Never Had the Like Occurred: Egypt's View of its Past edited by John Tait are also relevant and interesting.