Originally Posted by SpongeDad

In the sense of center of mass (COM), if you're COM is moving up a steep hill at 10mph and you stand, you're probably moving 90% of the bike weight (your body) forward faster than 10mph, meaning the bike itself has to either slow down or go backwards (just for a moment). Now, I suppose you could apply sufficient force just as you started standing up that you keep things moving forward.

Even if all the wheel does is slow down, someone close on your wheel could bump it.

Originally Posted by waterrockets

It depends on your frame of reference. As the rider who's standing, it appears that you are moving forward when you stand, because your frame of reference is anchored at the bike.

If you're another rider, your frame of reference is your own bike. When the guy in front stands up, his weight moves forward relative to his bike, but his COM continues at the same speed. Since the bike is lighter and the COM didn't move relatively, the bike moves closer to yours.

The effect would be much smaller if we just rode much heavier bikes

Originally Posted by unterhausen

it's basically the reverse of throwing your bike at the line. If there is someone on my wheel, I make an effort to stand smoothly and without throwing the bike backwards. It takes some effort.

Originally Posted by Phantoj

It has nothing really to do with gravity.

Originally Posted by nafun

It's not so mysterious. When some people stand, the first thing they do is pull themselves forward off the saddle with their arms. When you do this, you are pulling the bike back by the handlebars. If the first thing you do is push hard on the pedals and let your legs raise you off the saddle, then the bike doesn't jump back.