Arthur,
Regarding: instantaneous processors and infinite memory not being possible
In any proof regarding observable physics momentum, force, energy, power ... are used as variables in demonstrating relationships that prove something. Relativity is based upon the speed of light and related relationship of meters/second, or space/time.
The problem with this is that all the variables we routinely correlate are also based upon meters/sec and related inseparable space/time.
So by limiting the analysis of physics to inseparable space/time then mathematics limits causality to being composed of inseparable space/time relationships and the related energy.
What I am studying is the potential for a new way of relating to physics that allows for separable considerations that moderate space/time relationships.
An example of the feasibility of doing this is quantum entanglement. In relativity, anything not directly related to space, or not related to time, or not related to either space nor time, can produce observations that appear to be instantaneous though still causally connected.
Saying something is not possible, should be prefaced with "using currently mainstream relationships".
My interest is what fundamental characteristics moderate the ratios of physics.
E = 1/2 mv^2
What are the causal foundations for the functional relationships? I'm not as interested right now in the variables themselves.
"IF" space and time can be separately manipulated (non-relativistic causality), then energy-less causal manipulation becomes feasible.
A new physics based upon non-relativistic quantum causality.
These are just my interests, there is only minor experimental support thus far in the form of intuitively explaining duality, fringe patterns, observable quantum entanglement, decoherence, the Big Bang, alternate dimensional spaces...
If I figure out how to separate any observable feature of a space/time relationship, I'll probably keep it to myself until corruption can globally be eliminated. Imagine space/time manipulation tools in the hands of criminals !!
This is why I proposed making the NSA ethical to usefully monitor everything from the Top/Down:
http://eliminate-all-corruption.pbworks.com
And concurrently fighting corruption from the bottom/up through the teaching of common sense in my essay, from which has spawned a 501(c)3 for teaching common sense at:
http://www.ua-kits.com
The problem with technology is that it is most often used in conjunction with destroying eco-systems (uncontrolled population growth, mining, pesticides, herbicides ...). I do not believe anyone has put any significant effort into considering the broad devastation that space/time manipulation "can" represent.