I'll give you the numeric answer first, for I have spent far too much time exploring this topic to claim sanity and this answer tries to capture the essence of what I've explored. For a numeric approach, this question's answer, there's an estimated 10^120 bits of entropy in the universe. To do the job right you'd have to collect all of that data. For perspective, our new fanged 64-bit computers can't even address all that information. Not even our super advanced 128-bit and 256-bit super computers can do it. Once we get to 512-bit computers, we'll start to make headway.
And now, enjoy. I've tried my best to keep it interesting and lighthearted, but for all I know, it's only interesting to my twisted senses.
Interestingly enough, the computer resources are not actually the hard part.
As someone who works with simulations quite a lot, I always keep a quote from George Box in the front of my mind. Over a century ago, he said the most true statement about science and simulation that I have ever heard. I even have it posted on my wall above my work computer:
All models are wrong; some are useful.
When scientists or engineers create a simulation, we always keep this in mind. This is an important question because, at some point someone will ask "what do we need to do to simulate this particular scenario perfectly?" We have to step back and explain what a simulation is, and its predictive powers and limitations.
Eventually all of these discussions get lumped into one term: "fidelity." We need to know the fidelity that we need to achieve with the simulation. As an example, allow me to give you a simulation of all of our universe, written in python.
t = 0.0 # seconds since the big bang
notDoneYet = True
state = "INIT"
if state == "INIT":
print t, "Big bang occurred"
state = "BOOMING"
if state == "BOOMING" and t > 10**30:
print t, "Crunching from gravitational collapse
state = "CRUNCHING"
if state == "CRUNCHING" and t > 10**31:
print t, "Universe went splat, like a grape under a tire"
notDoneYet = False # okay, we're done here
t += 1 # advance time one step and keep going
I give this example because it clearly does not do what you want it to do, but could arguably be called a simulation. This makes it an excellent driver for pushing towards what you really want from this simulation.
The march to fidelity, and the scurry to collect data
So what you really wanted from this simulation was to be able to model the future state of the universe. Admit it, you want to predict the future, or at the very least put it in a bottle like fireflies captured during the twilight. So let's start pushing on what you really want to see. You want to have a simulation with enough fidelity to make predictions about the state of the universe to at least model the things we've seen before as part of human existence. We'll set a bar to ensure I don't make you read thorough another dozen lines of useless code: the simulations we'll discuss need to be able to model a human with sufficient accuracy to pass a Turing test. This is far below "simulating our universe," but it turns out to be high enough to show where the cracks begin to form.
Clearly we're going to need more advanced models. We're going to need to model the elasticity of human skin, the growth rate of hair, the diameter of our pupils, and so forth. This is a very important side effect of increasing fidelity: you need more coefficients to make sense of it. Sure, we can model a universe with similar laws to ours, but it won't be our universe unless we get all the important details right. The maximum and minimum diameter of our pupils turns out not to be a trivial detail: they define the maximum and minimum F/stop for our eyes, which has dramatic effects on the quality of the imagery our minds must process.
Gathering the uncomfortable data
So we can go out and measure a lot of things. We can determine that my pupils can range from 3-7mm, and my hair grows at a rate of 1.23cm/year. These are pretty non-invasive. However, some of the more important details start to feel invasive. When I approach you and, in the name of science, ask to crack open your chest so I can measure the velocity of the signals within the SA node of your heart, you're going to get touchy. You might even say "no!" How am I going to possibly make a simulation of you if I can't get the data?
The solution is a search for non-intrusive measurements. We're going to make a new rule that, as part of data gathering, we're not going to cut anything solid apart -- we're only going to observe solids from the outside and seek to measure what is inside. That will keep the peace and, you know, avoid getting you labeled as a mad scientist and such.
Minimum precision and the approach of Chaos
So obviously we're not going to get as good of measurements from outside as inside. I can gather the essence of your heart so much easier if I can hold it in my long spindly fingers, pried from your chest, and slowly strip its--- **ahem** sorry about that. Mad scientist is really hard to shake off. I've been going to support groups. It helps to talk about my feelings.
We're going to need to figure out how accurate we need to measure everything. If it's not accurate enough, it wont be a high enough fidelity model to pass our Turing test. But what is enough? Hopefully we can find some rule of thumb like "to get an output with fidelity X, you must measure these variables with precision Y." There should be one, right?
Edward Lorentz thought so too, back in the 1950's. He was a meteorologist studying mathematical models of the weather. He built a toy example because the world was too complex. He made a world where the sun always shone, no clouds, heck, no pesky land/sea boundaries to make things complicated. It was even kind enough to only rain uniformly across the entire globe, rather than the full weather patterns we have. He boiled all of weather down into 10 iterative rules (sounds like a weather man to me!) He ran his simulation, and had it print out data every now and then so he could see the state of variables within the sim. He had one of those awesome ancient dot matirx printers (okay, back then they weren't ancient) that prints on a continuous feed of paper, so he had the sim print out the state on one line: a time, followed by all of the values within the sim.
One day, he saw a behavior that was interesting to him, and he wanted to study it further. He grabbed the printout, punched the numbers in (so he could start from the same state), and told the computer to run at the same speed as before, but print out the numbers at a faster rate so he could see more data (he was trying to conserve paper, so his initial sim didn't output every timestep, just every 10 or something like that). He hit "go" on his computer, and walked off to get coffee.
When he got back, he didn't recognize the results. Where it was supposed to be sunny, it was raining. Where it was supposed to be cold, it was hot. He figured there had to be a bug in the code, but he kept getting the same results every time he punched the numbers in.
Finally, he found out what happened. Internally, the computer was keeping track of each number to 7 digits. However, on the print out, he only printed the first 4 to fit everything on one line. He figured those last few digits would be noisy and wouldn't matter anyway. How wrong he was.
His work was pioneering in the field of Chaotic systems. What is a chaotic system? They're hard to define, but I like to use 3 "rules" which are pretty easy to understand:
- It must be sensitive to initial conditions - small perturbations cause wild fluctuations
- It must be "topologically mixing," meanings changes in one part of the system rapidly diffuse to changes in all other parts of the system
- It must have "dense periodic orbits," which isn't quite as easy to understand as I like, so I often sum it up as "it must not be completely random -- there must be some order to the system" The result of a coin toss is random, but it's not chaotic. The technical meaning of that is hidden behind the phrase "dense periodic orbits."
Lorentz showed a large swath of useful "nonlinear systems" could demonstrate chaotic behavior, weather models being one of them. These systems could not be predicted unless you measured their state exactly. This had a huge impact on computational modeling of the world around us, which can be felt to this day.
How unpredictable? An example was given to me. Let's pretend you could put a grid of sensors, one on every cubic meter of the atmosphere in a massive grid. Each one can perfectly capture every value a meteorologist could ever ask for, for the point that it's at. On Jan 1 12:00am, the sensors all take a reading. This data is fed into the worlds most powerful supercomputer, and it outputs predictions.
By 12:01, it's already wrong. Small vortices which fit between the grid of sensors have already caused measurable changes in some of the readings. By Jan 2, those measurements are already causing a few key places on the earth to receive incorrect forcasts. By Feb 1, you literally cannot predict the weather any better than you could without your sensors.
Digging into quiescence
So we need to put on the mad scientist goggles again. Oh good! They still fit! A bit dirty though We need to get "perfect" measurements of everything, and we're going to do it with style.
We're going to invent the Electron Microscope's big, slightly maniacal brother. It's going to be a swarm of nanomachines which pass through the world like a giant wave. When the swarm hits matter, it dissects it, measures it, and then keeps moving. Sorry to anything hit by the swarm, but it needs to disassemble you permanently. It's hard to fly a swarm through solid bodies, and we need to get to your fiddly bits if we're going to beat Chaos at its game.
In theory, if you could do this fast enough, you could capture the exact state of the universe at a split second (all 10^120 bits of it). However, there's a catch. We can really only move so fast. Unless you worm your way through and permeate every object in existence before measuring, you have to measure as you go. This destructive measurement is, needless to say, traumatic. People are going to be screaming, and there's a scientific term to describe that (besides simply "All in a good day's work as a mad scientist," of course).
Simulated automata deals with this issue all the time: the need to get information from a system faster than you actually can. They have a very powerful term to describe what you need for your mad scientist approach to work: quiescence. A quiescent object is one that is not in the process of changing shape, or firing neurons, or anything. It just sits there, and lets you tear it apart atom by atom.
Unfortunately, quiescence is not a trait associated with humans. Once you start nibbling at their fingers with your nanomachines, electrical signals race up to the brain letting it know there is a problem. By the time you dismantle the brain and plumb it's secrets, it has already changed its state (likely reflecting the trauma of a limb dissolving before its eyes). There's no known way to back it out and find out what that brain was like before the nanos arrived on scene. The information you need to predict the universe-that-was is literally destroyed by the mere act of trying to measure it. All you can do is predict the behavior of a universe as it is torn apart by nanomachines, atom by atom.
Down the rabbit hole
So how far could this go? Can you possible measure the state of the universe without disrupting it? What if your measurement devices were really really tiny and could pass through matter?
The limits to this approach are written into quantum physics. Heisenberg uncertainty raises its ugly head. By the rules of quantum mechanics, the better you know the position of a particle, the worst your best estimate of its velocity can be, because the mere act of interacting with it classically changes the system's state unpredictably. Unless we invent an entirely-new never-seen-before, never-imagined-before way of measuring quantum mechanical systems, any chaotic system that finds a quantum mechanical state as part of its essence will be forever unpredictable, simply because we cannot measure it.
So where does this lead us
We have a few ways out of this predicament
- QM is only a model. We could find new discoveries that invalidate QM, and possibly give us an opening to build our simulator. Who knows! It happens in science all the time!
- Stochastic modeling. There are things you can do to capture some characteristics of a chaotic system stochastically. While they cannot predict the future, they may be able to at least give you some information you can use to shape it.
- Holography and entanglement. You mentioned holography, so it makes sense that this falls at the bottom of the rabbit hole.
Holography is not a simulation. It merely states that information we think as 3-dimensional can be encoded in a 2 dimensional boundary. It doesn't do simulation, it just stores information. However, what it does do is suggest that the world as we know it could be stored in a much smaller object (indeed, an object of lower dimensionality). As that information evolved, it would look like a simulation, but it isn't traditionally considered one - more like an ant farm.
So you could play a game here. Split everything we have into entangled pairs of particles (handwaving here, GREATLY). Move one of those entangled particles into one of these 2 dimensional holographic representations of our world. By the laws of physics, this structure would continue to evolve the same way it would in 3-space. However, I don't call it a simulation because simulations usually represent things with data -- this structure is actually working on real things, as real as you or I.
If you never interacted across the boundary of your 3space and their holographic 2space, you'd never know the difference. Both worlds would evolve identically. In fact, if you did it right, you might not even be able to tell which world you are in, which sure sounds an awful lot like the Matrix.
However, this is not a simulation. Let's say we look into our holographic crystal ball and see something. This is a "classical observation," which means we had effects at the quantum level on the holographic world. Because we are entangled with it, that means we would see quantum effects in our world too, which are consistent. The mere act of trying to use this crystal ball to see the future would literally cause that future to occur, just like Novikov's Self-consistency principle does for wormholes.
Smoking the Hookah with the Caterpillar
So where could this go? What if we step aside from the boring laws of physics and talk literary prose. If we want the hologram to model our real world, it's going to have to actually model it. This means neither side gets to know which side is the hologram, and which side is the real. Otherwise, they'll evolve differently.
So picture the world from the perspective of a scientist in either world. The hologram would have a very natural appearance: it would look like a mirror. After all, in both points of view, it has to look like a 2d object. Now let's assume the universe was symmetric, so we can see a difference - the mirror world mirrors left and right. That's all we know.
At first, scientists were fascinated with this quantum mirror. You could reach up and touch it, and feel your own hand pushed against by the interactions with the mirror universe, ensuring information does not travel from one universe to the other. You could try to punch yourself in the face, but you find quickly that you simply hit your mirror's fist as you both raise a punch at the same time.
Eventually the novelty dies. Over time, without the excitement, a darker side takes over. Which one of us is real? ponder citizens, staring at their perfect reflection. Troubled citizens begin having nightmares of staring into the mirror, to suddenly find their mirror self smile, and walk off without them. Fear of being the holographic copy, rather than being "real" ripple through society. Finally, the government closes viewing of the holographic mirror. There's no reason to cause such upset, especially since the physics claims no new information can come across the mirror.
Eventually things calm down enough that the government can release their iron grip on the mirror. Most of the citizenry has forgotten it existed, and it's expensive to keep people away from a device that the people don't really want to go visit in the first place. A subculture of mirror-gazers develop, calling it akin to meditation. Indeed many of them show the positive signs associated with meditation. It just might be meditation, and nothing more.
One evening, a young man walks along the mirror after his daily ritual of shadowboxing across space and time. The other gazers have already gone away. While everyone knows the physics say the mirror cannot do anything to you, hearsay and anecdote of strange flickering sensations felt by those near the mirror when the sun is down have been enough to cause the gazers to keep a distance from the mirror at night. There's no point in doing something which would disrupt the meditative enlightenment they seek.
But the dark is cloying. This man had visited the mirror during twilight several times before. The shadowboxing was the same. Every time he used force on the mirror, it used force right back, light or dark. But somehow it did feel different. Maybe it was just because there was no one there to watch him.
He unwrapped his handwraps, and an odd feeling spread across him, arising deep from in his soul. He shivered, but the feeling persisted. He looked into the mirror and it looked into him. The mirror looked into him, and he looked into it.
Raising his hand to the surface of the mirror, he drew a line so gently that he would not have thought his hands still had such softness left in them. As he stroked the mirror and it stroked him, ripples formed on the mirror. The universe on the other side bent and stretched like ripples across a glassy pond. The hand in the mirror bent and stretched along with them. Perhaps his hand did as well, but when he drew his attention back to his own hand, both it and the mirror were once again smooth and unaffected.
He looked into the mirror and it looked into him. The mirror looked into him, and he looked into it. Perhaps another night he would softly touch the mirror, and let it softly touch him. He turns around and walked away from his dual to retire for the night.
This little scene may bear the pungent smell of a Hookah loaded with a few too many substances, but it does show something at least tangentially related to reality. If you want the simulation to reflect your world, it must be a perfect match. Unleashing anything which was not captured properly by the hologram creating process would disrupt the entanglement, potentially forever.
Science would take great care to not let this happen. Every bit of physics would be accounted for in making this holographic simulation/mirror. However, to date, no one has truly found a scientific way to plumb the soul. There may simply not be a way for science to do so. There may be things in the soul which can truly reach across the perfect holographic mirror and entangle with their partner in ways not predicted by the physics.
This would not be something that is seen openly. It would be something that is so deep set inside the soul that science never gets a chance to quantify it. It would be something you can't dig out by force, only through time and patience.
What would it feel like to have something so primal open up from deep in your soul? What would it be like when the firm barrier of the mirror is plied or shattered? It would certainly have to reflect on your soul when you did so. Something would ply or shatter within. Symmetry does seem to play a part in such things.
And, in the words of Forrest Gump, "That's all I have to say about that."
Thank you for reading the ramblings of a mind. I leave with a music video for your viewing pleasure: Shatter Me by Lindsey Stirling (feat. Lzzy Hale)