I believe a anything between a 3.5 inch and 4.3 inch display is fine. Let's just compare the iPhone and the iPad for a moment. Everything on the iPad is slightly bigger than on the iPhone (if you are going to compare, for example, the app icons). Only slightly.
Now, let's look at the iPad 3's pixel density: 264 pixels per inch. The iPhone has 326 pixels per inch. This means Apple is fine with having bigger icons as long as the pixel density doesn't drop below 264 pixels per inch. Apple is also happy to call a display with 264 pixels per inch a retina display. Now, let's see what Apple's options are if they increase the screen size but doesn't want to lose the 'retina display' term.
- 3.6 inch (960 x 640 resolution): 320 ppi
- 3.7 inch (960 x 640 resolution): 312 ppi
- 3.8 inch (960 x 640 resolution): 304 ppi
- 3.9 inch (960 x 640 resolution): 296 ppi
- 4 inch (960 x 640 resolution): 288 ppi
- 4.1 inch (960 x 640 resolution): 281 ppi
- 4.2 inch (960 x 640 resolution): 275 ppi
- 4.3 inch (960 x 640 resolution): 268 ppi
- 4.4 inch (960 x 640 resolution): 262 ppi
As you can see, up to 4.3 inch everything is fine - and I sincerely believe that any display between 4 inch and 4.3 inches is the 'sweet spot' for mobile displays (depending on how the phone is designed [aspect ratio, thick or thin border, etc.]).
So, before I continue, in short why I looked this up: anything at or above 264 pixels per inch is fine (icons will never become bigger than what you see on the iPad's display) and it allows Apple to use the 'retina display' marketing term.
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So, what is Apple going to choose? We can never know for sure, but there are some basic things we know. First of all, it's very expensive to change a production line (by changing the pixel density of a display). If Apple is going to use a bigger display, than the most reasonable option - from a financial perspective - is to use a display size of which there already is an infrastructure.
This means that, if Apple is going to change the display (and thus the pixel density), the smartest thing to do is to go for a pixel density of which there already is an infrastructure.
So, let's see what pixel densities Apple already uses for their products.
iPhone 4(S): 326 pixels per inch
iPad 3: 264 pixels per inch
That's it. Every other display Apple is shipping (in their Macs, iPods, etc.) has a lower pixel density than 264 pixels per inch - and Apple just will NOT go below that 264 pixels per inch.
This means, from a financial perspective, Apple should choose a display size that offers 264 pixels per inch. If we look at the list of possible screen sizes above, than we see they must choose a display that has a diagonal between 4.3 and 4.4 inches: so let's say about 4.37 inch.
Now, the critics here on this forum will say "they can't go for a 4.37 inch display, it's either a 4.3 or 4.4 inch display". That's not true. The iPhone 4S' display isn't really 3.5 inch either: it's about 3.539 inch (or rounded off: 3.5 inch).
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So I think that, if Apple goes for a bigger display, they'll go for a 4.37 inch (or rounded up: 4.4 inch) display. The infrastructure for producing these display (with a pixel density of 264 pixels per inch) is already there (LG, Samsung and possibly Sharp are already producing 264 ppi-displays for the iPad 3).
It's the most logical decision from a financial perspective (and let's not forget: Apple is commercial company and likes to have as little costs as possible).
That also explains why John Gruber (always very accurate regarding Apple rumours) says Apple is testing a 7.85 inch display (that's quite a specific number) with a resolution of 1024 by 768.
A 7.85" display with a resolution of 1024*768 has a pixel density of 163 pixels per inch. Guess three times. ------ Guessed it already? That's right: that's the same pixel density the iPhone 3GS has. The infrastructure is already there and that's why they probably are testing 7.85" displays
And than we come back to my conclusion: if Apple is going to increase the iPhone's display, it's going to be a display with a screen diagonal of between 4.3 and 4.4 inches.