I have noticed on 4-lamp F40T12 magnetic rapid start troffers where the tubes are closer together, it seems like the inner tubes are dimmer than the outer ones.  It seems prominent on a cold start, and with the diffuser down/removed.  Why is this?  I would think they would be the same brightness or brighter because the are next to the other tubes that give off heat, and the ballasts.

The F40T12 are rated in free air 25degC. Due to the large surface, it mean quite cold operation during the reference setup, so when the maker want to reach the best efficacy figure, he will optimize the lamp for that cold operation.
And that mean, any real arrangement with restricted air circulation (reflector above,...) and mainly other tubes very close by, mean the tube s will operate above the optimum temperature, so with too high mercury pressure. And that mean the hotter running lamp become farther from the ideal temperature, so the performance will degrade more.

So the ballast runs at a lower power than?

Are both ballasts the same? And are the tubes all the same age?

As for the ballasts being the same, I have not looked, but could.  The tubes were all bought new and installed the same day. (11-23-2013)

Interesting. Maybe the ballasts are different, or maybe one ballast is beginning to go bad. As they age the inner tubes are more likely to dim due to heat (sometimes the phosphor will turn grey) if the fixture gets a lot of use, but since the tubes are new that possibility is ruled out.

So the ballast runs at a lower power than?

No.
Said in other words, the middle tubes simply overheat more than the outer ones.

Than, how are they dim at start up when they are cold?

Indeed, that is strange.

Other idea came to my mind: I don't know the difference you observe, but couldn't that be your eye is just lying to you? The side lamps have dark area on their sides, so because of the contrast look brighter, than the middle lamps, which have only the lighted lamps around, so no such contrast...

I agree with medved.  Have you tried closing the cover and see how it looks then?  Have you swapped the tubes, inner for outer, just to see if maybe you got a somewhat dud tube?  If it is a big difference, you probably have a weaker ballast that is not fully driving the tubes.  If the fixture originally had full power .8 amp ballasts and someone replaced one with a .76 amp or less type, then there is your obvious difference.

The diffuser is up (I actually did it after the photo) and the inner tubes still look darker.  I tried to double check and make sure, it is not my eyes lying to me.  There is a diffuser next to it where the tubes are further apart from each other and the are the same brightness on each side.  One side also has SuperSavers and the other has 2 full 40W tubes.