Is it physically possible that we may one day simulate the entire universe with every single particle, field and law of physics factored in? Can n number of particles (say the number of particles that make up my computer) represent what happens with "more than n particles" without neglecting, generalizing or rounding up anything. If so, would it be possible for the beings in the simulated universe to know about it?
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6I'm not an expert, but I'm pretty sure there is a recursion problem that says no. If we wanted to simulate every particle in the universe, that would include the computer itself. So the computer has to simulate a particle of the computer which is simulating a particle of the computer which is simulating... and so on. – tpg2114 Feb 01 '15 at 21:03
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Related: http://physics.stackexchange.com/q/8895/2451 , http://physics.stackexchange.com/q/110854/2451 and links therein. – Qmechanic Feb 01 '15 at 21:05
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Not to mention it is impossible to know everything about a given particle so such a simulation would not have the initial conditions needed to be correct. – tpg2114 Feb 01 '15 at 21:05
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1Yeah Heisenberg uncertainty limits everyone – Mithoron Feb 01 '15 at 21:10
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Then wouldn't this also mean we can never have a theory of everything? Or am I just comparing apples and oranges? – user71361 Feb 01 '15 at 21:11
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@user71361 I don't know that that's a correct conclusion but that might need to be a separate question. For example, we can easily write down an exact mathematical equation which has no known solution and would require infinite computational resources to "solve exactly." But that equation could still be a theory of everything. Although again, this is all just me speculating since it's outside of anything I study. – tpg2114 Feb 01 '15 at 21:14
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the Universe is a simulation. It's just that we're not running it. – Hot Licks Feb 01 '15 at 23:16
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@tpg2114 The infinite recursion is not an obstacle, given the way the question is stated. See my comment to the first answer, and my own answer. This might apply even if you see the universe as discrete, as you suggest. – babou Feb 02 '15 at 02:46
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5I'm voting to close this question as off-topic because it is asking for a prediction of the future and not physics. – Kyle Kanos Feb 02 '15 at 03:22
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@babou That could be, again I'm not an expert. But I know there are proofs in the cryptography world that it would require more energy to break encryption over a certainly length (not huge) than exists in the entire universe throughout it's existence. If we couldn't even break a X-bit encryption due to energy constraints, it seems very unlikely we could ever simulate every part of the universe. Recursion aside. – tpg2114 Feb 02 '15 at 10:56
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@KyleKanos Actually there can be some physics in this question. It can be understood as asking for arguments why this might or might not be possible. My own input is mostly to see some implications. and to reject arguments that are non-conclusive as given. I do not see why there should not be clean answers to such a question, given the current state of the art in physics. I was quite careful not to mislead anyone with my very partial answer, which was downvoted nevertheless, without comment. So much for the maturity of some users. – babou Feb 03 '15 at 01:54
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@babou: It starts off with, "Is it conceivable..." this is asking for pure speculation. There could be some physics in that, but it seems to me that those were covered in the links Qmechanic links. – Kyle Kanos Feb 03 '15 at 01:59
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@KyleKanos I think it's entirely clear that it's asking about whether there are physical limitations that would prevent it, not about what humans can conceive. (I've edited to change the wording.) – N. Virgo Dec 22 '15 at 11:55
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@nathaniel: I don't think it changed the fact that it is still asking for opinions, most especially with the last question. – Kyle Kanos Dec 22 '15 at 12:18
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@Kyle Kanos Delete the question and move on with your life if it still keeps you awake at nights please. I feel bad for you. I don't have a physics degree and I didn't know keeping this site strictly mathematical was your sole purpose in life. I was just curious about something and I got my answer. You can get rid of it and breathe easier. – user71361 Dec 26 '15 at 21:45
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@user71361: This site is not my sole purpose in life, but something I do to entertain myself and most certainly doesn't keep me awake at night. Don't feel bad for someone who's happy doing what he's doing. – Kyle Kanos Dec 26 '15 at 22:14
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I am assuming that you do want a simulation of the whole universe and not just a theory of everything.
Your question should be decomposed into two questions.
The first is really a mathematical question: Can a part (the simulator) simulate the whole ?
Given a positive answer to the first question, the second is whether the mathematical structures thus identified can be used to describe the universe.
To be true, I am mostly incompetent on both accounts, and I am only trying to make sense of the question, not stating too fast that it is impossible. So please do not take this as an answer (who would have one?) but rather as speculation on how an answer the question could make sense.
A part that simulate the whole means that somehow you can define a structure preserving bijection between the part and the whole. I am not quite sure I am correct, but this reminds me of the self-similarity and fractal structures ... To be checked with someone more competent than myself in fractals. Then the question would be whether a fractal structure is compatible with what we know of the universe. Building a bijection between an infinite set and an infinite subpart of that set is quite common. Can it be done in a way that preserves the laws describing the universe?
But such a bijection is possible only if the universe is infinite, and then the simulator would have to be infinite too.
Another constraint might be that the simulator should be a localized fragment of the whole, rather than spread uniformly (as you would have with a mapping of integers on the multiples of some integer $p$, these multiples playing the role of the simulator. But then, I am not sure how "localized fragment" should be defined meaningfully. This is why I was inclined to consider fractal structures, rather than more general structures that are isomorphic to some of their subparts.
But I have to leave it to more advanced physicists than I to tell whether that can be compatible with what we know of the physics of the universe.
babou
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Of course not, you would have to also simulate the simulation, etc. ad infinitum.
To address one of the OP's comments: no, this does not mean we can never have a theory of everything. A theory of everything is a theory that can describe every type of fundamental particle and interaction; there is nothing in this definition that says you have to simulate the entire universe if you have one!
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2You negative answer is unwarranted without further arguments to sustain it. An infinite structure can be in structure preserving bijection with one of its parts. You would have an infinite recursion, as you suggest, but that does not preclude the existence of such a simulator. The question does not say that the simulator should be finite (see my own answer). – babou Feb 02 '15 at 02:37
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1It seems to imply finiteness to you apparently, not to me. How do you know that the universe fragment that you call your computer is finite? Is it? It certainly has finite dimensions that we can perceive. But how good an instrument is our perception? – babou Feb 02 '15 at 03:06
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Adding to what @babou is saying, infinite recursion is "weird", but certainly not a contradiction (or at least cannot in general be proven to be one): most mathematicians accept axioms of infinity, for example, i.e. the logical consistency of asserting the fact of existence of the natural numbers as one entity. One can state a philosphical position that one is unwilling to accept actual infinities in the physical world, in which case your argument shows that an everything simulation tells against this position.The World is weird enough that I don't feel confident taking on such a position. – Selene Routley Feb 02 '15 at 07:37
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To address both of your specious comments: You can only conceivably simulate the universe inside the simulation if fundamental laws are scale (which implies conformally) invariant. This is known to be false; in e.g. string theory the length scale is set by the string length. – Feb 02 '15 at 19:20
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@alexarvanitakis, the scale invariance is not obviously necessary. Could you explain why you think it is? (Laws of chemical reactions in atmosphere are not scale invariant, yet we can model those chemical reactions by a computer that fits in a box. And even if there is typical length scale in some theory, it does not mean it is a fundamental law.) – Ján Lalinský Feb 03 '15 at 08:15
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Is it concievable that we may one day simulate the entire universe with every single particle
Who should type the properties of every single particle into the computer? Even if the calculation power were available (which it aint) there is nobody who would live the time to make the input.
But more seriously, Stephen Wolfram has some good recitals on Youtube about the universe possibly beeing a cellular automaton, which means that it would take the whole universe to simulate the whole universe (because no simplifications can be made if you want to trace every particle).
The next problem would be that the quantum world is rather probabilistic than deterministic.
Yukterez
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Just to speculate. Is it not reasonable to imagine starting our simulation with a rather simple singularity and let things work their way following the given laws of nature. As in big bang. Rather than collecting the current data of the universe and running the simulation from there on. – user71361 Feb 02 '15 at 00:36
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you inevitably come to the point where you have to run all the present particles, this happens when your simulation reaches the present. Even if you start simple at the big bang and end up complicated in the future the simulation as a whole won't become any simpler, just larger because you don't only run $t$ from $t_{Now}$ to $t_{End}$ but from $0$ to $t_{End}$ where $t_{Now}$ is inbetween. – Yukterez Feb 02 '15 at 02:59
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I think the only way to simulate the universe as a whole is to create a whole exact duplicate universe. – Yukterez Feb 02 '15 at 03:06
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A computer made up of n (finite) particles will not be able to simulate all the states of a larger system. This is known as the Pigeon hole principle.
If the simulator is made up of an infinite number of particles, it may be possible. But it would have to already exist; it would be impossible to construct.
Consider: Connect the output of the simulator to an LED such that "yes" = LED ON and "no" = LED OFF. Query the simulator on whether the LED will be OFF when it renders output. What will happen? The simulator will violate its own prediction when it renders output either way.
Beings inside the simulation should be able to know that they are in a simulation. Information always leaks.
user66309
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