Do We All See the Same Color

This is something I've been wondering since I was a kid (along with "why do I exist?" "why do I see out of these eyes?). 

When I look at red, I see a color. But does everyone else see the same color? What I see as red, you might see what I would call "blue." There's no way to know. You've called it "red" all your life. I've called it "blue" all my life. But until we can see what others see, there's no way to know.

Now, I find this unlikely. The color of light is determined by its wavelength because light is electromagnetic radiation (just like radio waves and infrared and microwaves you use to pop popcorn). So when electromagnetic radiation (EMR) of a certain frequency hits your retina, it sends a signal to your brain saying "this is this color of light." But does your brain interpret that input the same as my brain.

I suppose someday if we can see what others see though technology, we might confirm that red is red for everyone. Until then, this is pure speculation.

Do you think everyone sees the same colors? Or do you think I'm nuts? Let me know in the comments below.

UPDATE: I just read an article that says this is a common dorm-room discussion. I never stayed in the dorms when I was in college, so I guess I never had this discussion.