Maximum Processing Power allowed by the Laws of physics?

[Alasuya]

Hello, I have a few questions regarding computational power. In the far off future, I imagine creating a realistic virtual reality, a cybernated solar system composed of a sun like star and numerous habitable planets and moons with the same complexity of life on Earth. For this solar system I would like to create 100,000 computed humans in it. All of them would have consciousness. And perhaps the ability to even download my own consciousness into these virtual worlds.

But there are issues with this concept, the first one is no one knows exactly why we are conscious beings, that is currently being researched, the second being is processing power, all of this simulation would require huge levels of computation power. IBM researchers estimate that even just one human brain considering it's complexity would compute at 36.8 petaflops, or 36.8 quadrillion of data per sec.

What is the theoretical max limit of computing power for a computer one kilogram?
Seth Lloyd calculates an upper theoretical bound for a 1 kg computer of 5*10^50 logical operations per second carried out on ~10^31 bits.
Are his calculations accurate to what the true upper limit is?

Sources would obviously be greatly encouraged.

Edited August 17, 2013 by Alasuya

[EdEarl]

It is possible to make a single atom transistor; however, it may not be reliable and requires leads to other transistors to make circuits. Let's assume one needs 1000 atoms per transistor for a reliable circuit with interconnections.

 

The atomic weight of silicon is about 28.

 

Avogadro's constant is 6.02214129(27)×10²³ mol⁻¹.

 

Thus 6.02214129(27)×10²³ atoms of silicon weighs 28 grams.

 

1kg / 28 g = 1000/28

 

Thus; 1kg of silicon is 1000/28 × 6.02214129(27)×10²³ atoms ~= 215×10²³ atoms = 2.15 × 10²⁵ atoms.

 

At 1000 atoms per transistor in an integrated circuit, means there could be 2.15 × 10²² transistors.

 

It is been a long time since I did a mole weight calculation; perhaps I made a mistake.

 

If my calculations are correct, 10^31 bits is high for 1 kg silicon or any other atom.

 

Current processing speed is about 5 GHz. (5× 10⁹) Thus, 5*10^50 logical operations per second logical operations per second is very high for a single core computer today, but parallel processing allows scaling to any composite speed. Even with speed improvements promised by quantum computing, 5*10^50 logical operations per second seems very high to me for 1kg silicon or any other atom.

 

Gamma rays are 10¹⁸ and higher frequency, which may mean switching times can be much faster than 10⁹, but we do not know where the limit is. Even if switching speeds can be 10²⁵, it is a long way to 5*10⁵⁰. But, like absolute zero, theoretical maximums are beyond reality.

[md65536]

If my calculations are correct, 10^31 bits is high for 1 kg silicon or any other atom.

Yes, but it's a theoretical maximum. And even then, it's only a theoretical maximum given certain assumptions (eg. transistor logic and one transistor per atom). Those are probably reasonable assumptions, but theoretical maximums can be overcome if the assumptions change, and that sometimes happens. Certainly that's a high number for today.

It is possible to make a single atom transistor; however, it may not be reliable

That could potentially be a benefit in more authentically simulating a human brain.

 

But there are issues with this concept, the first one is no one knows exactly why we are conscious beings, that is currently being researched, the second being is processing power, all of this simulation would require huge levels of computation power.

And there may be massive shortcuts that allow a huge amount of simulated detail to be processed in parallel, or shared among objects. Some people imagine simulating all the atoms in a system individually, but perhaps it's possible to do a few calculations that can be used by all of them. Perhaps there is a huge amount of brain work that can be done once and used by all the simulated brains. I can't imagine what any such short-cut might be, but by the time we're simulating brains (if ever), I'm sure people (or sims!) will discover tons of news ways to do it better and cheaper than we can imagine possible today.

[Sato]

I read this paper a while ago, that seems to discuss the theoretical maximum when taking account for time dilation. I think it applies here.

http://arxiv.org/pdf/0907.1579.pdf