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Workout With No Shoes?

I live in a huge apartment building with neighbors beneath me, so I am afraid to exercise with sports shoes on to make too much noise (they tell me all the time that they hear me walking upstairs). But I'm not willing to just do the low-impact exercises all the time, I like to get as much of a workout as my body can handle! Usually I exercise just in my socks on the carpet. Do you guys think it's safe? I'm just getting back into exercising after a long break, but one of the problems I regularly have is joint pain (I'm 28 so I probably shouldn't have it. I can't run because of knee pain). I'm not a physical therapist, so forgive the simple question -- exercise with no shoes, is it ok?