Can Matrioshka brains run simulated universes to the subatomic level?

The advanced civilization in my story have harnessed the power of many of the stars in their galaxy and using them for different purposes, one being Matrioska brains. Some of these super computers will be to run the AI in the real world as well as for other calculations, Others will be to run detailed virtual worlds. The earliest Simulations will be Computer simulated worlds with artifical life within but later the advanced species will try to create simulations to the subatomic level.

It has been stated that a Matrioshka brain with the full output of the sun can simulate 1 trillion to a quadrillion minds, how this translates to how much world/simulation space can exist and to what detail i am not sure. I believe our sun's output per second is $$3.86 \cdot 10^{26}$$ W and our galaxies is $$4\cdot 10^{58} \ W/s$$, although with 400 billions stars in our galaxy I am not sure how of that energy is from other sources than the stars.

If we look past the uncertainty of subatomic partcles we have $$10^{80}$$ particles in a space of $$10^{185}$$ plank volumes in our observable universe, if we use time frames of $$10^{-13}$$ seconds this gives $$10^{13}$$ time frames per real second. With $$10^{80}$$ particles we can have $$10^{160}$$ interactions for a full simulation but a simulation where only the observed/ observable details needs to be simulated can run off much less computing.

Multiple Matrioshka brains can be linked together for higher computational needs, they will be limited to the speed of light in the real universe for information to be updated but this does mean a whole galaxy could run as one super computer for billions or trillions of years with the longer lived stars.

This question and the one mentioned in the question are similar to mine but I don't think they mention the energy needed and how it relates to Matrioshka brains. What Technology is Needed to Virtually Simulate...Everything?

With the known energy output of stars and the levels of computing needed to simulate a universe down to the quantum scale is there a way of knowing with near future or plausible advanced computing, how many stars could simulate a universe like our own?

• I am not sure W per second makes any sense, because W is already J/s – L.Dutch - Reinstate Monica Jun 6 '20 at 13:32
• Just a quick note: For proper chemical simulations of atoms you will need a femtosecond time step. In your proposed simulation a single time step equals 100 ps, which is way, way too fast for subatomic processes and chemical reactions. – Bdrs Jun 6 '20 at 13:38
• How many quantum states can those 10^80 partlcles have? Without the computer being able to simulate even just the quantum states for each and every particle simultaneously - for which it would need many more states to process it than the number of particles in the universe - then you're stuck. Doesn't even that simple task necessitate a computer with more particles than the universe? (That's even without calculating superpositions of quantum states and positions, vectors and masses). So how could an answer be less than a universe-worth of energy-mass? – A Rogue Ant. Jun 6 '20 at 13:50
• Well, maybe if you're only looking at the observed/ovservable details, then maybe. If you want everything, then it's maybe possible to calculate the energy required, but it would possibly invoke extra-dimensional space, Branes of the interdimensional variety. Hmm, a computer only partly in this universe, pocket-sized, but that has the computing power of several universes. I think you might need an M-theory specialist to flesh out the details though. – A Rogue Ant. Jun 6 '20 at 14:04
• W per second sounds like "I pay you 10 \$ per hour, per hour" – L.Dutch - Reinstate Monica Jun 6 '20 at 14:29

I will try to answer your question at least in parts by just reduce it to some smaler equations I am able to handle (as neither astrophysics nor nuclear/quantumphysics are my speciality). Same reason is why I will not check the numbers you gave in your question. (Edit: I exactly did that now, all numbers you gave and I used I checked for mistakes. Found none. ^^)

As the ability of a Matrioshka brain using the power of our sun is given as 10^9 to 10^12 minds, I will calculate its computing power in floating operations per second (flops). I think a 'mind' is used as equivalent for one human brain. The computing power of a human brain is roundabout 10^13 flops so the Matrioshka brain has a computing power of 10^22 to 10^25 flops. Lets use the higher value here. As you want to simulate the universe in steps of femtoseconds (regarding the comments) that equals 10^10 flopfs (floating operations per femtosecond) for a MB using the sun.

The power of all stars in our galaxy is 10^32 times that of our sun, so a network of MBs using our whole galaxy is 10^42 flopfs. As we have 10^80 particles we would need 10^38 of these galaxy-MBs just to check for every timeframe if a particle interacts with any other particle or not. And that's just for the check. We still have to check what kind of interaction those particles have.

Hubble revealed an estimated number of 10^11 galaxies in his visible range. We would need 10^27 times that. Just for the checking. (Edit: I just read scientific estimations go on to 10^12 galaxies in the observable universe, so we 'just' would need 10^26 times the output of our observable universe just for checking all particles in itself for interactions. Conclusion stays the same.)

So my answer is: no. We will not be able to simulate a whole universe even with this kind of technology.

why not have the Matrioshka brain also be a quantum Computer?

a quantum Computer the size of a city can also run a universe sized simulation. SO I would imagine that if you were to upscale this to be a Matrioshka Brain, you should be able to do the task of running a simulated universe right down the the subatomic level no problem.

as a game designer, you wouldn't need to have everything rendered at once, only what was being simulated at that time. I use Unity 6, and we use scenes. So something like that should work

• "A quantum Computer the size of a city can also run a universe sized simulation": any computer can run a universe simulation if you don't expect the results to be accurate. If you expect the results to be accurate then sorry, but no, it cannot. (And what makes you think that Unity or any other game engine has anything to do with simulating the functioning of even the smallest part of the universe?) – AlexP Jun 7 '20 at 8:27
• just using unity as an example. but you can make a universe simulation using a game engine of your choice, but what you will get will vary greatly. It depends on many things really. – Mr. Anderson Jun 7 '20 at 17:51