They can and should play together. Show your older one some games to play with the baby (if the baby is walking, they should be able to find lots to do together, if not, things like peek-a-boo or clapping games...six year olds are great at making babies laught...have him try to get the baby to laugh).
Teach him that, if he needs to take something away from the baby, he can give the baby something else at the same time so the baby won't cry about it.
My youngest likes to race with the biggest kids. Of course, they are faster, but he doesn't care. We also have crawling races and things that the baby can do more easily.
Show him how to be gentle, but also remember that kids get hurt. They need to not play rough, but a one year old falls down, hits his head, knocks things over, much more than most other age groups. No fun, but it does happen -- they are clumsy at that age. Explain this to your older son, and that he needs to be extra careful.
I would also suggest trying to find some alone time with your older son. I know this is hard, but even ten minutes a day can make a big difference. And play some games with him that are geared toward his age group.
Give him a sense of pride in being a big brother...this is very important to an older child, and will help their relationship if he knows what a big part he will play in his brothers life.
Good luck!