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This isn't a simulated universe per se, but in a similar fashion, there is an entity "in" this universe (let's call it the "Processor" to keep the computer analogy). This Processor "simulates" the entire universe. In other words, it computes the laws of physics and applies them to the world and thus updates every object (or field; I'll probably ask a separate question about exactly what the Processor needs to update to update everything). To update "everything", the Processor needs to know all information about everything in this universe at all times.

This poses two problems:

  1. It creates a preferred frame of reference (the Processor's frame) and thus we can define "absolute simultaneity" simply as "two events that happen at the same time according to the processor"

  2. Information can travel faster than the speed of light. The Processor knows what happened because it "made" it happen

(I don't think this breaks quantum physics because, assuming the processor can generate random numbers, it can introduce non-deterministic physics through them)

Do these problems break the logical consistency of the world or are they not real problems because "inside" the universe to every entity it still "seems" that the laws of relativity are intact? If they do, can I make a small change to my setup to remove this inconsistency, or is relativity fundamentally mutually exclusive to "simulated" universes?

(I have a possible fix: to have each particle have its "own" processor, keeping information localized. But that doesn't really fit in with the magic system I'm creating, and poses the issue of particles vs waves vs fields etc.)

EDIT:

Editing to clarify what I mean by "the frame of the processor." This is not the frame that the processor experiences, but the one that it calculates. Here is the model by which it operates: It runs the calculations on the current state of the universe, figures out the values needed for the next state of the universe, and then updates those values. I'm calling each such calculation a "Frame." It doesn't matter if the processor takes longer on one frame than the next in its own time, because the simulation time is independent of the processor time. The processor could pause for a thousand years in its own time and the simulation wouldn't be able to detect that.

The universal frame is instead the "frame number," or the "time coordinate" that the processor uses in its own calculations. Let's say there are two values (it doesn't matter what they are, just that they are actual values that exist in the universe. Can be the value of a field at two points, for instance). The Processor updates both of them in the same frame. Thus, from the "universal frame," they are simultaneous events.

EDIT 2: It was wrong of me to state that the Processor exists "in" this universe. I think it's best to model it as something that exists outside of it but can be accessed from inside it.

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    $\begingroup$ I mean such a Processor is just straight up magic that could never exist and breaks very basic laws. Such as you would need the entire matter of the universe to build it. So idk why you are concerned about Relativity here if we have broken much more basic stuff as a prerequisite. $\endgroup$
    – ErikHall
    Jul 12, 2023 at 20:17
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    $\begingroup$ This is . . . not how a simulation works. The two problems listed mght emerge only if the simulation is extremely badly designed. The frame of reference of the processor is completely irrelevant for the simulated objects; and there is no relationship between the time of the processor and the simulated spacetime. $\endgroup$
    – AlexP
    Jul 12, 2023 at 22:40
  • $\begingroup$ You have a god that has the power to affect everything in the universe at the same time and you're wondering if the perception of anything inside the universe can affect the god? I'm having trouble not voting to close this question as needing (a lot) more focus. Your god sets the rules for the universe and you set the rules for your god. I'm having (a lot) of trouble understanding why you're experiencing a conundrum. It's as if you think the known rules of the universe bind the apparently-not-all-powerful god. Also... $\endgroup$
    – JBH
    Jul 13, 2023 at 3:15
  • $\begingroup$ ... An interesting discussion of the concept of an infinite universe is that you can draw a cube around any finite space within that universe and within that finite cube is a deterministic amount of energy and energy states. There are only a finite amount of energy and number of energy states that can exist within that finite cube... which means the cube replicates within the infinite universe. My point? Most of the universe is nothing more than multiple instances of a finite number of unique instances of space, seriously reducing the computational load of your god. $\endgroup$
    – JBH
    Jul 13, 2023 at 3:19
  • $\begingroup$ @ErikHall "It's already magic so why worry about realism" defeats the entire purpose of worldbuilding. It doesn't matter if the laws of physics that apply to the processor aren't the real laws of physics, only that the laws of physics that apply to the universe it's simulating are the real laws of physics. $\endgroup$ Jul 13, 2023 at 10:37

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The "laws of physics" as we know it apply only within the simulation, not outside of it. It matters little that a simulation of a bouncing ball is actually 10 IEEE-754 floating point numbers rendered as bundles of electrons on RAM gates. What matters is that the model within the simulation behaves according to the expected laws. Thus it doesn't matter if the processor itself has a frame of reference in the outside world; this does not affect the inside frames of reference.

Likewise, most simulations have their own definition of time. They need not follow the exact flow of time of the outside processor. This is a good thing, as we often want to model things that are blazing fast (such as quantum mechanical interactions) or astonishingly slow (like galactic collisions).

There is a class of simulations which do care about real time. These are simulations that interact directly with the outside world. These would need to update in "real time," from the perspective of an outside observer. To do this, you may need to encode the simulation state carefully to make sure that "spooky action at a distance" (quantum entanglement) can resolve "fast enough."

I would recommend Greg Egan's book Permutation City for an introduction into what would have to be done to successfully model large physical systems like human minds. It can almost be treated as a novel-length textbook on how such simulations would have to be developed.

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  • $\begingroup$ By the Processor's frame of reference, I do not mean the frame of reference it experiences but rather the frame of refrence that it imposes upon the simulated universe because of calculating. Basically, the variable 't' that it uses to simulate the universe. I have edited the question what I meant.. Thanks nonetheless, and for the book recommendation $\endgroup$ Jul 13, 2023 at 10:41
  • $\begingroup$ @TheInfiniteOne If it is a imposed frame of reference, one can define a frame that is "preferred" in the sense of "this is the one we do our calculations in," but not one that is "preferred" in the sense of "the calculations yield different results in this frame than they do in other frames." There would be some preference terms of things like rounding errors, but that's outside of physics -- physics has no rounding errors. $\endgroup$
    – Cort Ammon
    Jul 13, 2023 at 18:22
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It's fine. The principle of relativity means that you can use any reference frame you like, not that you must use every reference frame. Since all frames are equivalent, calculations in any one frame will correctly model everything the world, including the behavior of systems that happen to be moving relative to that frame.

General relativity doesn't change that. Quantum mechanics probably doesn't change it either, although how quantum mechanics and general covariance interact isn't well understood. The undetectable preferred frame is a hidden variable. From the perspective of people in the simulation, it may as well not exist, since you've arranged things so that they can't detect it by any experiment.

A bigger problem with simulating this universe inside itself is that there are probably fundamental limits on how much storage a computer can have (from the Bekenstein entropy bound) and how long it can run (because of heat death), and that would preclude a simulation as complicated as the real world. But I don't think there's any fundamental logical problem with the idea of unlimited computing power.

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  • $\begingroup$ Will it break relativity if the people in the experiment could query the processor and find out about "absolute simultaneity?" I suppose that's FTL and makes it possible for information to travel into the past from the perspective of the people inside the universe. (As for storage limits and stuff, I think it's best to have this Processor actually exist outside the universe in some universe with different laws of physics, or perhaps simply more storage space) $\endgroup$ Jul 13, 2023 at 10:45
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Real rules don't matter

Let's give an example of a simulator: https://xkcd.com/505/

In this strip we can see a guy in an infinite desert simulating the universe with stones. It takes incredibly long to create each 'frame' of the universe. But the important thing is, it doesn't matter how quick the guy updates the frames. In 'real time' the frame takes infinity to set. But inside the simulation nothing seems to be amiss. They have no concept of outside, nor are bound to the rules of outside.

You can break the rules of the universe just as easily in the simulation as you build them. It's a simulation. Just like we 'simulate' war or city builders on our computers. The important part is that the real world rules have no influence on the simulation, except to make the simulation possible.

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  • $\begingroup$ I agree that the frame of the "simulating" universe does not affect that of the "simulated" universe. But rather, by simulating this universe in frames (like my processor, and the desert guy), we have assigned an "absolute" time coordinate to every event in the simulated universe (the frame number). That's what I meant by it "breaking the relativity of simultaneity" $\endgroup$ Jul 13, 2023 at 10:58
  • $\begingroup$ The point of this whole system is to attempt to design a "hard" magic system where mages write scripts that the processor executes. So the simulated universe CAN interact with the processor. Thus, information can "travel faster than light" for the simulated universe. Maybe an event happens in alpha centauri, and I write a script by which the processor tells me when that event is happened as soon as the processor computes it having happened $\endgroup$ Jul 13, 2023 at 11:00
  • $\begingroup$ @TheInfiniteOne then I actually still feel like I miss the problem. I understand what you say, but as it's a simulation it doesn't need to uphold the laws of the real physical universe. That would mean that you can change data in the processing or storage that instantly changes something far away. Like the change that the supermassive black hole at the center of our galaxy is a supermassive banana. It makes no matter that it breaks the perceived rules, as it's actually simulated rules that are actively being rewritten. I feel it's changing the rules and then wondering if they're broken. $\endgroup$
    – Trioxidane
    Jul 13, 2023 at 12:24
  • $\begingroup$ I want to keep the simulated universe approximately the same as our universe in terms of physical laws. Maybe some laws can be broken, like the second law of thermodynamics, but that doesn't mean I let all laws be broken. In particular, I don't want to introduce time travel paradoxes into the system. The solution is either throw relativity out or have the processor (or another program that runs on it) intelligently check whether an action it computes breaks relativity and then forbid that action (for instance, not having the script return an answer until 4 years have passed) $\endgroup$ Jul 13, 2023 at 13:57
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    $\begingroup$ I guess it's impossible to keep the universe have all the laws of physics AND have magic (ie people inside the universe making the processor do something that it otherwise wouldn't have). Since the current state deterministically (- quantum) produces the next one, the only magic that produces a state that's also valid according to the laws of physics is changing the result of wave function collapses (which COULD maybe be the basis of a magic system by itself, but not what I'm looking for) $\endgroup$ Jul 13, 2023 at 14:00
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No

  • Someone outside of the universe knowing information that can not be known inside the universe does not break anything, as long as the professor just observes and does not change things based on this knowledge (otherwise any simulation of anything at all would not work).
  • The professors frame of reference is no frame of reference in the context of physics, since its not even inside the universe, has no velocity, defined point of origin etc.

However

You DO break quantum physics, knowing all about everything and making exact predictions based on that is incompatible with it. So your simulated universe is not one where the laws quantum physics are valid (though the laws of that universe might still be close enough so that nobody notices).

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  • $\begingroup$ Quantum uncertainty can simply be modeled by random number generation, which the Processor has access to $\endgroup$ Jul 13, 2023 at 14:05

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