I would say that the computer and program need to be included in the simulation. They are a part of the universe, therefore in order to have a perfect simulation they have to be included (Keep in mind, that it should be introduced into the simulation only after a finite amount of time, since it wasn't there at the start.)

As to booting it from an off state, I think the simulation should be kept on stand-by. Sooner or later, random pair-creation in our universe should create an electron, which should start  current, which in turn starts the simuation. The computer and program in the simulation should be kept in a similar condition, waiting for a random pair-creation inside the simulation to start 

If the computer is part of the universe then it should be included as it will play a role as well.

If you don't want to keep it in simulation you will have to keep it outside our universe.

Thank you Allard and Bhushan,

"As to booting it from an off state, I think the simulation should be kept on stand-by."

Allard, -- please notice I said a totally off-state,  not just an off-state.  

If you include computer inside a simulation there would be problem of infinity because the computer inside a simulation would have computer as well and this will go on.

As we have limited energy in our universe its not possible to capture this much of information.

Gaurav, there you run into a fundamental problem. Considering that a lot of things in the universe are a result of random events, what constitutes 'a simulation of the universe'? Would that be a simulation that is based on the same physical laws, but where the events are again random (and therefore may work out differently from our own universe), or would it be a simulation where you insure that exactly the same events take place as in our own universe?

It's old question, it has to with the theory of systems, auto-reference and Godel theorem. It's such a long story that the best I can do now is pointing you to a good reference to start with: Gödel, Escher, Bach by D. Hofstadter. 

I am not too impressed by all the Gödel stuff really, and I could not make much of the Hofstadter book. I think this is a problem of our confusion of tokens and types in the realm of causal relations. The logic chaps tended not to get their hands dirty with actual instances of causal relations.

I do not think you can simulate the universe on a computer, nor would one want to but the issue of laws being 'within' the universe remains interesting. As I understand it the only legitimate sort of physics is an account of the world in terms of token instances of causal relation. Those tokens can 'stem from' each other in a causal sense. To have a predictive theory we have to infer from these token relations, types of causal disposition that the tokens are instances of operation of. These we can call rules or laws. But types of disposition do not in themselves have any causal relations so they do not 'stem from' anything. They are not causes, or effects. They are, in Leibniz's terms 'sufficient reasons'. A universe is the acting out of token instances of operation of its sufficient reasons. Reasons cannot be within or outside their universe because, as types, they have no relations at all. They are only ever 'here' as their tokens of operation, which constitute the universe. They do not need to have 'been there in advance' because only tokens are there in advance of other tokens.

I think it would depend on what you constitute as a "simulation of the universe".  I think some computability issues would come up pretty fast if you want to have a simulation that simulates undecidable problems within the universe (since you will of course need to simulate mathematicians too and the possible decidable languages a programmer could choose to write).   I think a lot of problems do occur if one were to invoke computation to meet the demand of ultimately determining how to halt an undecidable problem (which in itself is undecidable).  You would need an oracle to tell you when to make that determination (keep in mind there is an infinite number of these undecidable problems out there to encounter).

If we are talking about simulation as in planets and bodies in space, I'd say sure!

Simulation of the Universe if possible,requires a computer with a power  reminding  the "Laplace's demon". this issue interconnected  firmly with a "Deterministic" or "causal" approach to the natural phenomena, which states if someone (or Demon) knows the coordinates and energy-momentum of ( initial data) all ingredient of Universe (particles,fields etc)  then due to mechanical laws the past and future of the world can be predicted (i.e. simulated). However this idea withdrawn after establishment of Quantum mechanics notions about "determinism" and "causality" and introduction of "Uncertainty" and " indeterminism". Consequently  for writing the "program" codes for such a computer we have to implement the laws of the physical world for a real simulation that do not allow us the absolute determination of "world state" evolution. Moreover there is a strict limit on the volume of the "bits" to download all information in the Universe, recently it has been calculated to be about 10120 bits and appears in a close relation with Entropy of the world. For more insight review this link :  http://focus.aps.org/story/v9/st27. Finally with impossibility of such a computer and program, talking about the details will not be logical.

Yes, there is just one computer to simulate perfect precisely the whole Universe, It is nothing other than the "Universe" itself.

I am hugely impressed by the interest and quality of thought put into answers here. 

Thank you Peter Breuer.  Yours is a truly clear, succinct, brilliant and helpful response.  Thank you again.

My reason for originally asking this question, is surely, Peter Breuer's summing up does actually apply.  And The Actual Universe is restricted by Turing.  This is why I believe Physical Theorists must eventually face this problem and confront it, rather than ignore it.  As I see it, acceptance of Turing, as part of physical theory, would lead the way and guide us towards the fundamental foundations of Physical Law. 

Can you have a universe simulator which can predict what you going to do in an hour? That will be non-causal and thus even if a computer simulates universe it cannot do it faster than the reality itself else the simulation can be contradicted by the conscious entities.On the other hand a simulator may predict multi-option/multi-path. Given a starting point the number of options will grow so rapidly that the simulation will be meaningless. 

A third kind of simulation is, which is allowed to go wrong and refine itself using the new data. The goal of such simulator is to be better than a wild guess. This can be done. Can this simulator simulate itself? Yes it can because the information it has to predict about itself is fuzzier than what it actually does.

Part of the problem is that the "shape" (geometry and topology) of the universe is not currently know. It may be finite or infinite as well as closed or open, so there are 4 fundamental possibilities. Also it is important to note that this shape includes time, as space-time is at least a 4 dimensional manifold (which may or may not have a boundary). A simulation of the universe would not run as a function of time, since the universe as an object contains all space and time. Well contains is not really the right word, more like it is a particular geometry and topology of some number of dimensions. It would not make sense to simulate the space and physical laws of the universe as a function of time. It would be equivalent to simulating the shape of time and the physical laws as a function of space. Entropy creates the illusion that the future does not exist yet when in reality the universe by definition contains all of space-time. If the computer simulating the universe was not contained with that universe then it would not exist in space-time (or at least not the same topology, geometry connectivity, etc...). My brain is starting to hurt, so I'll leave it at that.

There are two theorems to confirm that you can't realize simulating a computer by this computer.

1) A Turing machine  T1 can't determine itself haft, so it can't simulatie itself.

2) Godel Second Uncompleteness Theorem says that a system T1 must be confirmed by a system  T2 larger than  T1 .

So there is not a limit to simulate T1,T2......

I agree with most of people here. In fact, if the Universe is a giant analogical/quantum/discrete/biological computer (and, no doubt, with many other attributes...) - then it might simulate itself simultaneously in many ways. We will never know if we are a part of one of these simulations, or what we are seeing is the basic computer - I mean, the basic universe. We don't know if there is something like the Basic Universe. In fact, I don't know if the simulation chain is well founded or not. Maybe we are living in an Universe U, which runs as simulation in an Universe V, which runs as simulation in an universe W, and so on, and the chain is also infinite in this backward direction too.

Dear Jonathan,

I rely on the Gödel stuff, which is an exact mathematical theorem rather than any "token" stuff, although interesting in itself is not of comparable in rigour.

Since building a computer simulation of the universe imparts building a computer simulation of itself (the computer) the selfreference is already manifest and Gödel's theorem looms.

Supporting the references to Gödel, one might hence reformulate the question (whether a computer can simulate itself): Are we as living beings subjected to Gödel's incompleteness theorem? (Ladik and Seel 1986).

There is no way we can avoid Gödel!

I think conservation rules such as charge, energy, etc. are firstly considered.

Actually conservation rules are always at the level of transaction and not whole universe because the concept of single universe state does not exist as there is no universal time. So the bigger problem is the causality and free will.

I fully agree with Peter Breuer's first answer. The only problem with it that I see is that a Turing Machine is not a computer, but rather a computer program. The original question actually carefully distinguishes between computer and computer program.

A computer in any realistic kind of sense is always finite, and can never contain an encoding of the entire universe, simply for a lack of capacity.

It could. however, contain a finite program that could simulate the universe given the appropriate input. Although it could never get this input in our universe, the program could still be there. So it would in some sense contain the laws that rule the universe and the ways in which to apply them on a given encoding of the universe.

One problem that such a program might run into: computer input is discrete, while the universe might contain non-discrete quantities that cannot be quantisized; for example exact distances. Then the finite encoding could not even potentially exist as already single "bits" could be infinite. I am not an expert on this.

Summing up, I think it is impossible for the universe to contain a computer that can simulate it, and it is improbable that it can contain a program that potentially could simulate it.