If you have a cake baking in the oven and someone stomps on the floor or slams a door, will the cake collapse? Or was this just a way for my mother to keep me quiet for 3 or 4 hours?
Second part of the question…what kind of cake takes 4 hours to bake?
Some baked goods, souffle and poundcakes (for example), can collapse in the way you describe.
Cakes don’t take 4 hours to bake.
Unless you have really bad flooring even a souffle will not collapse.
I have baked cakes at sea before. No problem.
You will not recreate those conditions even with the worst flooring.
A poundcake can collapse if you slam the oven door, my brother did this once.
Of course, a lot of people believe that and will tell people to be quiet around the oven.
I think it is the cold air from opening an oven rather than vibrations. And four hours is far to long to back a cake. A half hour is probably enough.
It’s the only way Mom could get some peace and quiet in the house.
Tell a gaggle of kids that they need to be quiet or the delicious cake in the oven will be ruined, and they’ll be *very *quiet.
With four rowdy boys in the house, Mom baked a lot of cakes. 
What cakes are you making? I suppose if you’re making something very flat, some recipes might take as little as 30 minutes, but most of mine are more on the order of 45 minutes to an hour, and some take a bit longer. The longest bake time I know if is for some meringues, which can stay in the oven at a low temperature for several hours. I agree that four hours is way to long for any cake, but jason’s time perception might have been a bit different when he was seven.
The delicate cakes are almost all air and egg with a little flour. Slamming an oven door at a critical point can cause them to collapse. I haven’t collapsed a cake for a few decades, but a certain oven with extremely strong door springs did in a couple cakes. Most cakes people make are not so delicate and I don’t think a kid screaming in the kitchen will deflate any cake, but jumping may.
"Second part of the question…what kind of cake takes 4 hours to bake? "
There are cakes the Brits would likely call “pudding” that take hours, though I can’t think of one taking four. Typically involve being baked in a water bath, and subject to collapse, IME. Whatfrom, dunno.