Uhm... this has been around for 25 years. FIOS popularized it, but other companies have been using them for a long time. If you mean as small as a microprocessor, that's IBM, not HP.
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That would be very useful and dramatically increase speed. IBM is working on something like that. Unfortunately, since no PCs use PPC processors anymore, I think servers will benefit the most, at least until the other processors catch up.
RAM is already as close to the cpu as possible and it's still not fast enough, most of the time you CPU is actually waiting for the RAM. Electricity through insulated copper travels at about 80% the speed of light, eliminating that lag will dramatically increase speed.
If that were to be implimented, would you have to have an OS that supports it? Or would it give automatic benefits?
It's be a hardware benefit, so nothing would change in the software, not even at the HAL.