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No.
At present you have two hurdles. One is the complete lack of any mini DisplayPort adapters other than the two by Apple (both for a computer with mDP.). The second is the fact that even with a "monitor end mDP" cable, the only thing it can convert to is full-size DP. (Unless Apple is going against past precedent and hiding a second signal type in that display..). Which means even with said cable, you'd have to have DP on your computer. At present there is no way to add DP to your MacBook.
edit: Followup now that I'm at home on a real keyboard...
So to expand: "DisplayPort" is an industry standard from the industry-standards organization VESA. The standard defines both a physical port, as well as a new method of signaling for the display data. Apple's mini DisplayPort is a custom physical plug (that Apple is willing to license free,) that uses this industry-standard signal. The problem is that the signal is new, and not at all backward compatible. The specification for the
plug says that manufacturers are allowed to make their own custom physical adapters to drive other devices (such as DVI, VGA, etc,) using the existing physical pins; but that doesn't help us with the
signal.
Apple's 24" LED Cinema Display uses the new DisplayPort signal over Apple's new mini DisplayPort plug. So even with an adapter that can change the mini DisplayPort plug into something else, you still need a computer that can output the DisplayPort signal. The new Apple MacBooks all have this. A few (you can count them on your fingers,) video cards for PCs have DisplayPort. But there are no converters to turn the older DVI signal into a DisplayPort signal. All "DisplayPort to DVI adapters" you see are physical plug adapters for use on video cards that can push a DVI signal through their DisplayPort plug. (Much as how the "DVI-I" standard carries both the digital DVI-D signal as well as an analog VGA signal; allowing you to use a physical adapter to get VGA out of a DVI port.) But for that, you still need to have a device that supports the DVI signal. Again, unless Apple goes against their nature, the new product ONLY supports the DisplayPort signal. (Many monitor manufacturers make LCDs with both DVI and VGA. The moment Apple put DVI on their monitor, VGA was dead. I imagine this is the same. DisplayPort-only, no DVI signal lurking anywhere on the monitor.)
Apple makes physical adapters to turn mini DisplayPort on the MacBooks into VGA or DVI for monitors; but, again, these just pass through the VGA or DVI signal that Apple has on the pins of the plug in the notebook. One of the reasons for the delay in the Dual-Link DVI adapter is that it physically cannot be a simple 'pin-adapter'. DisplayPort has enough pins for single-link DVI or VGA; but not for Dual-Link DVI. This means that the DL-DVI adapter is doing some kind of signal translation to get a DL-DVI signal out of not-enough-pins. It could be that it is truly converting a DisplayPort signal into a DL-DVI signal; or it could be Apple using custom signaling that isn't technically DVI compliant out of the mini DisplayPort, such that it needs active help to convert it back to DL-DVI. This would also explain why the DL-DVI adapter costs $100. It's not just a physical plug change.
It is possible that someone could make a "signal changer" to allow DVI-equipped computers to connect to a DisplayPort-only monitor, but, like the DL-DVI adapter, it won't be cheap, since it has to be an active signal translator. In addition, Apple's is the first DisplayPort monitor to *NOT* include a DVI port; so at present, the market would be
very limited. (Heck, you can count the number of DisplayPort-equiped monitors on
one hand, and that's without including your thumb...)
Some might point to the third-party adapters that were made for Apple's old retired "ADC" monitor connection to convert it to DVI as a mark that people are willing to target a product at a small market. Unfortunately, the ADC connection used DVI signaling deep down, it was just a custom physical plug. The adapter "only" had to convert the physical plug, then add a power brick. (ADC was really just a DVI connection plus power and USB in one physical cable.) No signal translation necessary. Unlike what would be needed here.
Now, if you had a MacBook
Pro,
and someone makes a "mini DisplayPort monitor to standard DisplayPort video card" adapter, you would be able to do it; but, again, it's not cheap. Companies make devices that plug into the ExpressCard slot to convert it to an external PCI Express expansion box. This allows you to plug a desktop-style video card into this box, then connect that through the adaptor into your ExpressCard slot. (See
Asus XG Station.) You would have to use a video card that has native DisplayPort, and you would lose video performance because your video card would be connecting at 1x PCI-E instead of the standard 16x PCI-E. But you could do it. (Oh, and those expansion box devices are ridiculously expensive...)
So, back to my short answer: No, it's not going to happen.
Edit 2: Some companies do make native ExpressCard video cards; so it's possible that someone might make an ExpressCard video card with a DisplayPort output, which would be nice, since DP is smaller than DVI. If that happens, you could upgrade a MacBook Pro to run the new monitor... But that's asking an awful lot.