"An unwillingness to admit the possibility that mankind can have any rivals in intellectual power occurs as much amongst intellectual people as amongst others: they have more to lose." - Alan Turing

Are We Living in the Matrix?

This page examines the theory that our universe is in fact a simulated universe which is running on a massively powerful computer programmed by some advanced civilisation. Though the world feels "real" to us, we might be merely logic states in an advanced computer. As improbable as this might sound, the theory has gained a lot of attention recently due to a similar idea in the film The Matrix, and the idea is even attracting the attention of several physicists.

However, as we shall now see, the particular situation depicted in The Matrix would seem to be a very unlikely description of our reality:

1) The "Brain-in-a-Vat" Scenario

The idea that we might be living in a simulated world is so fascinating because it is impossible to disprove the theory that we are living in a simulated universe. In order to see how difficult it is to disprove, consider the Brain-in-a-Vat Argument. The Brain-in-a-Vat Argument considers the situation whereby a person's brain has been removed from their body and is floating in a life-sustaining fluid. The brain is connected by wires to a computer which provides the brain with exactly the same impulses as the brain would normally receive, the computer effectively creating a "virtual reality". The person with the disembodied brain would continue to have perfectly normal conscious experiences without these being related to objects or events in the real world. It would be impossible for the person to discover the reality of their simulated world.

This is the basic premise behind the movie The Matrix in which Keanu Reeves's character was kept in a coma in a vat while the aliens' computer fed him false sensory information (fortunately for Keanu Reeves, the aliens did not remove his brain!). The simulated world created inside Reeves's head was called the Matrix, and for Reeves it was indistinguishable from normal reality.

While it might certainly be the case that the reality I feel is just a "dream state" and I am actually a brain-in-a-vat, I feel that would be very unlikely. I can think of no reason why a "Grand Simulator" would behave in that way. This is because the only person able to experience the excitement of the elaborate virtual reality world would be the person whose brain is in the vat: the simulator would not experience anything. So why bother to go to all the trouble of inputting an elaborate virtual reality world into the head of some poor unknowing person? What could possibly be your motive?

In the movie The Matrix the motive of the simulators was explained by claiming that the humans in the vat were being used as batteries (to power the aliens' machines). But if that was the case, why did the aliens need to go to all that trouble of creating that virtual reality world in the heads of their human captives? Couldn't the aliens simply just have kept their human captives in a drug-induced coma while extracting the energy from them? Why bother with creating the Matrix world?

2) The "Universe-in-a-Computer" Scenario

However, there is another model of our world as a computer simulation which does not requirement the confinement of some poor soul floating in a vat! Instead, the possible type of computer-simulated universe which will be suggested here is one in which our entire universe is contained within the computer of an advanced simulation (i.e., there is no need for our universe to have its own "Keanu Reeves" floating in a vat somewhere). In this case, the "particles" of our universe would be represented by "bits" inside the alien computer. This is now a similar scenario to the computer game The Sims in which all the simulated characters and the entire simulated world is contained within the simulating computer.

The motivation of the simulators in creating this simulated world is now much clearer: the world could be viewed and experienced on the computer for entertainment purposes, just as we currently enjoying playing so-called God games such as The Sims.

David Deutsch finds the simulated universe hypothesis highly distasteful: "It entails giving up on explanation in science. It is in the very nature of computational universality that if we and our world were composed of software, we should have no means of understanding the real physics - the physics underlying the hardware of the Great Simulator itself. Of course, no one can prove that we are not software. Like all conspiracy theories, this one is untestable. But if we are to adopt the methodology of believing such theories, we may as well save ourselves the trouble of all that algebra and all those experiments, and go back to explaining the world in terms of the sex lives of Greek gods." (quote taken from David Deutsch's paper It from Qubit). And many scientists have criticised the idea on that very basis that if it is untestable (unfalsifiable): if a theory can never be proved wrong then it should not be regarded as scientific. However, Brian Whitworth in his paper The Physical World as a Virtual Reality makes the point that the existing orthodox view of the physics establishment is equally unfalsifiable: "The theory that the world is is an objective reality is just as unprovable as the theory that it is a virtual reality. It is inconsistent to dismiss a new theory because it is unprovable when the accepted theory is in exactly the same boat."

The General Uncertainty Principle

This idea that if we would never be able to tell if we were living in a simulated universe would appear to have profound implications for science. We would never be able to tell if our observations were real, or merely simulated. This result can be summed-up simply in one statement which I'm calling the General Uncertainty Principle: We can never know anything for certain.

David Deutsch appeared well-aware of this drastic implication when he said: "From the point of view of science it's a catastrophic idea, the purpose of science is to understand reality. If we're living in a virtual reality we are forever barred from understanding nature." (quote taken from here).

Many scientists believe the simulated universe theory should be rejected because it fails Occam's Razor which suggests that the simpler of two theories should be preferred (if the two theories give the same predictions). On this basis, the simulated universe theory should be rejected because it gives precisely the same predictions of what we would experience if the universe was not being simulated (hence, there is no need to introduce the extra complication of the simulated universe theory).

But this type of objection matters not one jot. The unavoidable truth still remains: if we were living in a simulated universe, we would never be able to detect it.

This General Uncertainty Principle ("We can never know anything for certain") reflects an all-encompassing uncertainty about every aspect of our world. This all-inclusive nature of the principle means it has must enclose the existing uncertainty principles such as Gödel's Theorem (described on the Mathematical Universe page), and the Heisenberg Uncertainty Principle from quantum mechanics (described on the Quantum Mechanics: An Introduction page). The General Uncertainty Principle represents a much wider uncertainty about absolutely everything in existence!

(The General Uncertainty Principle is a consequence of external world skepticism).

The Simulation Argument

The Simulation Argument presented by Oxford University philosopher Nick Bostrom is ambitious in that it that it does not stop by merely suggesting that we might be living in a simulated universe, it argues that we probably are living in a simulated universe! The argument uses evidence gathered from the world around us (about the rapid growth of our computer technology) and solid scientific reasoning to show that a rational scientific person has to take seriously the possibility that we are already living in a computer simulation.

The basic principle behind this theory is that the human civilisation will one day have access to sufficient computing power capable of running simulations of their ancestors (us!). Maybe in a few thousand years in the future we might actually make a re-appearance (as Sims) in those advanced simulations. That doesn't sound too far-fetched, does it? But what if it is the case that human civilisation has, in fact, already reached that advanced state and is already running those simulations? That would mean we are living in a simulated world right now!

In fact, the future human race could easily create simulations containing astronomical numbers of simulated beings (this has the ring of truth to it: when you run The Sims there's only one of you, but the program contains thousands of Sims). There is therefore a possibility that the number of conscious, simulated humans will one day become very much larger than the number of real humans.

The Simulation Argument then goes one step further by stating that with the number of simulated humans inevitably outnumbering real humans, the computer simulation scenario is actually the most probable situation (unless you think the human race is going to become extinct pretty soon, or we're going to get bored with The Sims and start playing Tetris again - both of which seem quite unlikely).

To sum up, the Simulation Argument is a rigorously-presented argument which means that a rational, scientific person considering the extraordinary recent increase in computing power available to us, now has to treat seriously the possibility that we are already living in computer simulation.

The Monkey Universe (Revisited)

On the page entitled Is the Universe a Computer? we imagined how the universe could be created by a million monkeys randomly typing into a typewriter for ten hours a day. We concluded that the probability of a monkey typing the information which defines the universe would be infinitely small. However, if the same monkeys type onto a computer instead then there would be a much higher probability that one monkey might type the short computer program which could produce our universe (a short computer program can generate tremendously complex structures, such as intricate fractals).

However, if we now entertain the possibility that the universe could be generated by some intelligent entity (some "Grand Computer Programmer") then we find we can interpret this result differently. We had previously assumed that the short program which produced the universe was generated by a random process (a monkey). However, we can now consider an alternative scenario that the program is short because a simple, short program would be easier for our Grand Programmer to write, and would be a more compact and elegant solution for producing a complex universe. A short, elegant program would be the result of good software design.

John Barrow describes this well in his book "Impossibility": "Just as the most expert computer programmer is the one who can write the shortest program to effect a particular task, so we might expect the Architect of the ultimate program that we call the laws of nature to be elegantly economical on logic and raw materials. It is a common tendency to think that it would be a hallmark of the universe's profundity if it were unfathomably complicated, but this is a strange prejudice. This view is motivated by the idea that the Creator needs to be superhuman - and what better way to assert that superiority than by incomprehensibility? But why should that be so? Anyone can explain how to assemble a model aircraft in 500 pages of instructions; it is not so easy to do it in 10 lines. Profound simplicity is far more impressive than profound complexity."

But ... surely there's "nothing outside the universe"?

On the Cosmic Universe page we stated that there was "nothing outside the universe" (which was called the "first principle of cosmology" by Lee Smolin in his book Three Roads to Quantum Gravity). We then saw how this simple maxim led to important conclusions such as the principle of relativity. However, we now seem to be suggesting that our universe might be a simulation on a computer contained within an external, simulator universe. So in that case, there is something outside the universe. In fact, there's another universe outside our universe! So was it wrong to say that there's "nothing outside the universe"? Is our simple maxim wrong?

Well, we came to the conclusion that there's "nothing outside the universe" by examining the behaviour of the universe and realising that the universe behaves in a self-contained manner which needed no external axes of position or time. Hence, what we really should have concluded was that the universe needs nothing outside the universe - which is a different thing to saying that there is definitely nothing outside the universe.

This is an important distinction as it would be possible to create a simulated universe which, to its inhabitants, would appear to need nothing outside of that universe. David Deutsch realises this in his book The Fabric of Reality when he writes: "The rendered environment would also have to be such that no explanations of anything inside would ever require one to postulate an outside. The environment, in other words, would have to be self-contained as regards explanations." Indeed, this is probably the most likely form of simulated environment as it would deceive the inhabitants into thinking that their environment was not simulated. In other words, they would think there's "nothing outside the universe" when, in fact, there was a whole simulator universe outside of their universe!

The Need for Constraints

Purely from a practical point of view, it would prove essential to impose some constraints on the abilities of your Sims. This is to avoid logical inconsistencies which would have a calamitous effect on your computer simulation. For example, if you allowed your Sims to travel back in time you would have to deal with "killing your own grandfather"-type paradoxes. There would be nothing to stop you programming time travel functionality into your simulation. You have complete freedom in that respect: you're effectively omnipotent in what you can allow. But "with great power comes great responsibility" (as Spiderman would say). You would need to constrain such behaviour or the resultant logically-inconsistent scenarios could bring down your entire simulation.

In order to clarify the dangers, let's imagine the situation of going back in time (say, from the year 2007 back to the year 1950) and killing your father before you are born. Once you have committed the murder, the simulation would need to determine the implications of the event. For example, if the simulation wants to display the situation in the year 1970, say, it will have to consider the effect of that murder back in 1950. The problem is that the implications of the paradoxical murder can never be established in a satisfactory and unambiguous form.

Because of the sequential nature of computer programming, in order to calculate the effect of the murder we could break down the required computer simulation processing into four steps:

a) Initially, a "father" object is created and, in time, the father object produces a "son" object (function father_constructor() is called to construct a father object (object-oriented programming) and that function in turn calls the son_constructor() function to construct the son object).

b) The effect of creating the son object has a calamitous effect on the father object (as the son goes back in time and kills the father). So function son_constructor() calls the father destructor.

c) When the father is killed, he cannot produce his son. So function father_destructor() calls the son destructor (the son is never constructed).

d) If the son is never produced then there is now nothing to kill the father. So function son_destructor() calls the father constructor.

Here are the four resultant functions:

If you consider the functions you will see that each function will call the next in a cyclic manner:

A => B => C => D => A => B => C ...

The sequence never terminates. In the computer simulation, this will manifest itself as an infinite loop. This will crash the entire computer simulation! To see the simulation running (trapped in an infinite loop), click the button below:

(To view the actual JavaScript code used in this simulation, see patricide.js)

In order to avoid these practical problems, you would unfortunately feel the need to impose a constraint on your Sims to prevent time travel behaviour: something along the lines of Stephen Hawking's chronology protection conjecture, or imposing an upper speed limit on light (see below). It would spoil your fun a bit, but you would effectively have no choice. You would have to rein in your omnipotent freedom slightly and apply some constraints to your simulation (ensuring logical inconsistencies are impossible). Constraints would be necessary to produce a quality universe capable of interesting, complex interactions (some of the more complex processes might even arrogantly describe themselves as "life"!). It's all reminiscent of the way we have to impose laws on society or else we would just be left with a useless, anarchic mess (which even the criminals would find undesirable!).

(This need to apply constraints to a completely unconstrained environment (in order to produce a tenable universe) has important ramifications for the "anything goes" interpretation of the Anthropic Principle. See "And now ... the Ultiverse!" in the page on The Anthropic Principle.)

Is a Simulation actually "Real"?

There are some important questions we could ask about the reality of a computer simulation. For example, are objects within the simulation just as "real" as everyday objects outside the simulation? So is a computer simulation actually a "real" environment?

These are difficult concepts, but some things are clear. Firstly, the simulation has to run on a physical computer. If the simulation is not being run on any computer then surely it cannot be said to "exist", and so the objects within the simulation could never be said to be "real". So now we're seeing the first links between the reality of the external environment and the reality of the simulated environment: the reality of the simulation is dependent on the reality of the computer.

We could then ask what exactly are objects in a computer simulation? For example, if there is an (apparently solid) desk in a computer simulation, what is it made out of? Well again, clearly, the element in the computer simulation is dependent on a real object in the physical computer: objects are described by combinations of binary "bits" in the computer's registers and memory. In many ways, the role of bits in a computer simulation is analogous to the role of atoms in the physically real world.

But, you might argue, bits are not actually real atoms, so it is mistaken to suggest a universe based on bits could ever be as real as one based on atoms. Well, if you examine computer bits at the most fundamental detail you in fact discover that they are indeed made of atoms, atoms composing the computer registers and memory units. So computer "bits" are just as real as atoms because bits are made of real atoms.

So, I would argue, that a computer simulated universe has just the same ontological status (i.e., reality status) as our normal universe. This is a surprising result, but David Deutsch comes to the same conclusion in his book "The Fabric of Reality": "The simulated universe passes the test for reality because the calculations to create it are physical processes within the computer, and the computer is an ordinary physical object, and perfectly real."

It is now possible to simulate another computer on your PC by creating a virtual machine (see image above). When you use the virtual machine window on your PC it feels like you are operating a completely different PC. This is because the virtual PC is a completely self-contained unit, with no indication that it is actually a simulation contained within a larger computer - just how a simulated universe would feel. However, all calculations in the virtual PC are actually being performed on the external, simulating PC. So the "virtual" PC is actually just as real as the simulating PC.

A universe on a memory stick: Does a simulation really need to be run?

In the section "Implications for the Simulation Argument" on page 17 of his Mathematical Universe paper, Max Tegmark suggests that a computer-simulated universe could be held on a memory stick: "If the computer need only describe and not compute the history, then the complete description would probably fit on a single memory stick, and no CPU power would be required."

On the basis of the previous discussion of the reality of a computer simulation, I would agree that this computer simulation on a memory stick could be considered "real" as it is being stored on a physically real memory stick: the simulation therefore "exists". However, Tegmark then goes one step further and suggests that we could do without the memory stick altogether: "It would appear absurd that the existence of this memory stick would have any impact whatsoever on whether the multiverse it describes exists for real." However, I would disagree with Tegmark about this on the basis of the previous discussion about the reality of a computer simulation. Without the memory stick, the simulation could not be said to "exist" - the simulation would not be "real". As we have just discussed, the reality of the simulated environment depends on the reality of the computer. (This idea of Tegmark that mathematics has some form of independent reality of its own is considered on the Mathematical Universe page. Basically I disagree with him.)

By suggesting that a computer-simulated universe could be held on a memory stick, Tegmark seems to be arguing that a simulated universe would have a block universe structure, with no moving "now". While this is possible, in the next section I will suggest that it is more likely that a simulated universe would be designed with a moving "now". After all, why waste resources (computer memory) retaining full, detailed descriptions of the entire past and future when only the present needs to be calculated, stored, and rendered on your computer display (I would imagine this is how most conventional simulations - such as The Sims - are coded). Tegmark's "memory stick" containing full descriptions of past and future would simply not be required, and so could not be said to exist. All that would exist would be the "now", represented by the computer's current rendering of the simulation. Thus it could be said that only the "now" has any form of reality in that it is currently being represented - as states in a microprocessor - in our physical world.

Also, I would suggest that a simulation that is not "played" would be very boring for the simulators. Consider a reel of movie film: each frame of the film describes a single moment in time, so the entire celluloid reel could be considered a "block universe" (each moment being equally real). However, just to hold the reel in your hand would be very boring: it would only be interesting if it was played-back through a projector, and the movie viewed as intended. The process of playing-back the movie essentially recreates the moving "now" (the current position in the projected movie). So I disagree with Tegmark: it is more likely that a simulation would be run. In the next section we will see that this gives new life to the tensed theory of time.

Spacetime in a Simulation

Relativity and quantum mechanics are the two most fundamental and important theories known to physics, and, as such, any theory that suggests we might be living in a computer simulation would have to provide an explanation for their presence. However, both of these theories are problematic for computer simulation theories because they would both appear to be totally unrelated and unnecessary for any simulation of human behaviour (I bet the programmers of The Sims, for example, don't bother coding-in relativistic or quantum mechanical features). The next couple of sections considers relativity and quantum mechanics in a simulation, starting with a discussion about time.

There are two dominant - and incompatible - theories of time: the tensed theory, and the tenseless theory. The tensed theory of time most resembles the popularly-held view of time. The tensed theory requires there to be a present moment (the "now"), and a distinction between an event in the past, present, and future (an event in the past was real, an event in the present is real, and an event in the future will be real). Notice that the "now" moves. This apparent movement of the "now" is an essential feature of the tensed theory of time.

However, the Cosmic Universe page showed how the Wheeler-DeWitt equation suggested a universe in which all of time is laid-out (just as the space dimension is laid-out), and there is no moving "now". All times are equally real: as there is no special "now", there is no distinction between past and future. This forms the tenseless theory of time. The apparent flow of time is considered to be just an illusion of human perception due to the asymmetry of the time dimension: we can remember the past, but we cannot remember the future. This then gives the illusion of a flow of time with the unknown future becoming the fixed past. For more details on this, see the Arrow of Time page.

Most physicists would favour the tenseless theory as the most accurate representation of time. It is also called block universe because all of spacetime can be viewed as being laid-out as an unchanging four-dimensional block:

For a clear explanation of the block universe, see this excellent Scientific American article by Paul Davies.

Another objection to the moving "now" is related to a question which has puzzled philosophers: "How fast does time flow?". If the "now" moves then it must move with respect to some time reference. So is it moving with respect to itself? Surely not. To say "Time moves at the rate of one second per second" is meaningless. Rather, the rate of time flow would have to be measured with respect to some secondary, external time reference. Throughout the page on The Cosmic Universe it was stressed that there was no clock outside the universe, so there could not be any such external time reference.

So the absence of any time reference external to the universe is another argument in favour of the block universe model, and against the moving "now" model. However, now we are considering a simulated universe we discover that we can postulate a time reference external to our universe: we finally have that "clock outside the universe"! This could be pictured as the master clock of the microprocessor performing the simulation.

This answers the question "How fast does time pass?" (at least, in the simulated universe). Time passes at 5 simulated seconds (as experienced by the simulated beings) per 15 actual seconds (as experienced by the simulators - the simulators are watching the football in slow motion). It's as if the simulators are watching frames of a movie, and they can control how fast the movie is played.

So the structure of a simulated universe recreates the moving "now" and seems to give new life to the tensed theory of time.

The precise value for the "now" (which is set by the simulator) now becomes a crucial free parameter which has similarities with the parameters which are said to be set in The Anthropic Principle. If the simulator sets a value too close to the start of the universe (say, 500 million years) then the resultant universe might be rather featureless and lacking in life. It would seem far more likely that he turns the dial to the 21st century at which point he finds the simulated beings starting to discuss the possibility that they might be living in a computer simulation, and figuring-out the secrets of the simulation. How fascinating that would be!

Does this lead to infinite regression?

However, we're not out of the woods yet. The question now arises "How fast does time pass in the simulator universe?". Do we have to propose a secondary simulator universe outside of the simulator universe in order to provide us with yet another time reference - a simulation within a simulation? Surely that would lead to infinite regression: an infinite series of simulations within simulations. This is certainly problematic for the idea of the universe being a computer simulation.

This problem with infinite regression was realised by the 13th century theologian Thomas Aquinas because it essentially represents the question "Who created God?" (God, in this case, being represented by the "Grand Programmer"). The answer to that question only poses another question: "Who created the person who created God?", and so on, thus resulting in infinite regression.

This question was considered in the Wired article God is the Machine: "Any large computer these days can emulate a computer of some other design. You have Dell computers running Amigas. The Amigas, could, if anyone wanted them to, run Commodores. There is no end to how many nested worlds can be built. If smaller worlds have smaller worlds running within them, however, there has to be a platform that runs the first among them. If the universe is a computer, where is it running?" While this problem of infinite regression does not necessarily mean that we are not living in a computer simulation, it does mean that it cannot be the whole story: it does not explain the origin of the "Grand Programmer".

Relativity in a Simulation

Another objection to the tensed theory has been raised on the basis that it is incompatible with special relativity (see the Rietdijk-Putnam Argument). Special relativity says that the rate at which time passes can be different for each individual, dependent on their relative motion (due to time dilation). Hence there is no such thing as a global time - one clock for every person in the universe. But if there is no global time, how can there be a single "now" for the entire universe? With the tensed theory so dependent on the principle of the "now", how can the tensed theory survive relativity? The function of the "now" in the tensed theory is to turn the unreal future into something real. However, observer-dependency in special relativity means that some events are in the present for some observers (i.e., real) but still in the future for other observers (i.e., unreal). How can an event be both real and unreal?

So the tensed theory of time - which I have suggested is a likely model of time in a computer-simulated universe - is once again being challenged. How can it survive?

Well, the computer simulation idea can provide a solution to this problem. This is because is order to generate a view of the simulation on a simulating computer screen we would have to specify the position of our "observer" within the simulation. So we don't need a single "now" for the entire universe (as the Rietdijk-Putnam Argument suggests) - we only need a "now" for our particular observer position.

We can understand the concept of the "observer" in a computer simulation by the analogy with the rendering process in computer graphics. Rendering is the process of producing a two-dimensional image on a rectangular viewport (essentially, the computer screen) from a three-dimensional mathematical model (see here). Once a precise observer position (and time) is defined, the scene can be rendered:

We should not be concerned about the lack of a global time: the only time with any physical significance is local time - the time as experienced by a particular (specified) individual. It doesn't matter if you are in bed getting woken by your alarm clock, or in a spaceship travelling at near the speed of light, your personal local time (or, more correctly, proper time) is the only time with any relevance to you, the only real measurement of time in the universe. Once we understand that the only time is proper time, "most of the interpretative problems of special relativity drop away" (quoted from here). You can still retain the concepts of past, present, and future, but they are specific to a particular observer - they should no longer be regarded as global for the entire universe.

So each observer has a specified position AND time. These combine to produce a unique worldview for that particular observer, which is realised by the computer graphics rendering process.

So each observer has a different "reality" worldview. Reality as perceived by each observer could be different in that the time-ordering of events could be different for each observer due to special relativity. Some events are in the present for some observers (i.e., real) but still in the future for other observers (i.e., unreal). We have different "realities" for each observer. In fact, this is the most efficient method of simulation: reality is created "on demand" for each observer only after an observer position and time has been specified.

Programming Spacetime in a Simulation

This method of rendering a view of a simulation is effectively the same as taking an "observation" of the simulation (the simulators would use this method to "observe" the events occurring in the simulation). So the process of rendering a view should employ exactly the same method as a simulated observer (a human, for example) embedded in the simulation would use. And this is indeed the case: if I make an observation of the world around me then I have a specified position in the universe and I am making that observation at a particular specified time. Those time and position values combine to give me my unique worldview.

But it's not just human observers which have their own, unique worldview within the simulation: every element of the simulation, right down to the smallest particles (electrons, say) must have their own worldviews (the worldview of the human observer is then the cumulative total of all those tiny worldviews). And those worldviews must operate in exactly the same way as the human observer. So this gives us an insight into how spacetime is structured at the smallest scales, and how it would need to be programmed in a simulation.

(Important Note: This is not the orthodox view of spacetime, it is just a suggestion for the most likely implementation of an accurate simulation of spacetime (which would incorporate general relativity) in a game like The Sims for example. However, for the simulated beings, this suggested spacetime structure would be completely indistinguishable from the orthodox model of spacetime. For a description of the orthodox model of spacetime, see The Hole Argument).

So that is how "time" would work for each particle in the simulation. But spacetime is composed of both "space" and "time", so how would we handle "space" in the simulation? We intuitively think of objects moving around in Newtonian absolute space, with reference to a background substrate. And, indeed, this is how most computer graphics applications are programmed: plotting the positions of objects with respect to absolute Cartesian axes (see the diagram below). But if we are going to accurately model space then we must do so without reference to any background substrate as there is no such thing as absolute space: "There are no absolute axes of reference for space or time outside the universe" (see the Cosmic Universe page). So in the absence of any absolute global time or position for the simulation, both time and position must be relative. So instead of defining our particles with respect to a background coordinate system, we would have to define our particles' positions with respect to the position of other particles in the simulation:

"Space" then emerges as a result of the positional relationships between the particles - it does not exist as a separate entity in its own right. If you removed all the particles from the universe you would not be left with "space" - there would just be "nothing".

So now we can describe how spacetime could be represented in a computer simulation. Each particle would have to maintain its own personal "proper" time, and it would have to store its position relative to every other particle in the simulation:

(This resultant network structure is similar to a spin network which is believed to represent the fundamental structure of spacetime (see Lee Smolin's Scientific American article Atoms of Space and Time) in that the geometry of both techniques is purely relative and they are fully background independent).

As far as rendering this simulation is concerned, we can see that the "time" property for each particle is really only a numeric value used for "filtering" purposes, i.e., the simulator selects a certain value for "now" and only those particles which possess that value as their time property (and are positioned in the rendering viewport) would be rendered. All other particles without that value for their time property would be filtered-out (otherwise the rendered image would be a mess of all particles). This ties-in with John Wheeler's quote: "Time is nature's way of keeping everything from happening at once".

As far as programming this spacetime structure is concerned, we could use an object-oriented approach in which the objects are the individual particles (in this case, electrons). The dynamic properties which each individual electron would have to store would be its proper time and its relative position (its distance to all other particles). The remaining static properties (such as electric charge) would be inherited from a generic "electron" class and those fixed values would apply to all electrons:

Now, when we want to instantiate an individual electron, we define it to be an object of the "electron" class. It then inherits values for electric charge and mass from the class definition, but its values for time and position have to be set for each individual electron:

As Brian Whitworth says in his paper The Physical World as a Virtual Reality when comparing particle physics to object-oriented programming: "In computing terms, objects can be 'instances' of a general class. Likewise every photon in the universe is exactly identical to every other photon, as is every electron, quark, etc."

Quantum Mechanics in a Simulation

The question has been asked "What purpose would be served by simulating events at the quantum mechanical level?" For example, in his book Quantum Reality, Nick Herbert wonders what is the point of quantum non-locality (for a discussion of quantum non-locality, see the page on Quantum Entanglement): "If all the world's phenomena are strictly local, what need is there to support local phenomena with a non-local fabric? Here we confront an alien design sense bizarre by human standards: the world seems strangely overbuilt."

I was one of the contributors to a highly-speculative discussion on this topic which considered if quantum mechanics might be an artifact of the underlying simulating computer system - see here. However, the most surprising similarity between quantum mechanics and computer simulation technology is revealed when we consider computer graphics rendering techniques, considered next:

The CGI Universe

We are all aware of the tremendous advances which have been made in computer generated imaging (CGI) over the last few decades. Astounding photorealistic images are now commonplace in movies such as The Matrix. It would be very important to generate the highest-quality visuals in any computer-simulated reality (in order to fool the participants). The most accurate rendering algorithm is ray tracing.

Ray tracing works - as its name suggests - by tracing individual rays of light emitted from light sources as those rays bounce off reflective surfaces. Ray tracing is especially useful for generating photorealistic images involving multiple reflections or shadows. Ray tracing is the only way to achieve perfect photorealism, and would therefore be the chosen method in any potential computer-simulated universe: "Implementing the rendering equation gives true photorealism, as the equation describes every physical effect of light flow." - see here.

You might imagine that ray tracing would work by tracing all possible rays from a light source to the eye (or computer viewport), taking into account any reflections of those rays off any intermediate objects:

However, it transpires that this is a very inefficient way to generate an image - you would have to generate lots of rays which never reach the eye (the computer viewport) and so never appear in the final image (these "wasted rays" are shown on the image above). As Wikipedia says: "Following rays in reverse is many orders of magnitude more efficient at building up the visual information than would be a genuine simulation of all possible light interactions in the scene, since the overwhelming majority of light rays from a given light source do not wind up providing significant light to the viewer's eye." - see here. It is actually far more efficient to trace rays backwards from the eye, and to see if those rays eventually finish at a light source. In this way, no rays are "wasted":

As in the example considered above, "Relativity in a Simulation", reality is created "on demand" only after an observer position is defined. This is the most efficient way of generating a simulation.

It so happens that we can now start to see parallels between these efficient methods of generating reality and the method by which reality is created in quantum mechanics. In the double-slit experiment, for example, a particle appears to take all possible paths before it hits the screen (the double-slit experiment is explained on the page Quantum Mechanics: An Introduction), including passing through both slits at once! (Also see the Feynman sum-over-paths: "Fast moving subatomic particles travel from point A to point B not by a single path but by all possible paths").

This could be considered the equivalent to the inefficient ray tracing method in which rays are traced along all possible paths from the light source to the eye. However, in quantum mechanics we find that once an observation is made (i.e., once the particle hits the screen) then it appears clear that the particle only passed through one slit. It is though the act of defining an observation position (placing the screen) forced the past history of the particle to take only a single route through a single slit. It is as if the history of the particle is then defined backwards in time along its path once the observation position is defined.

We can now see the similarity between this process and the efficient ray tracing method by which rays are traced backwards from the eye to the light source. It will always be more efficient to generate reality by waiting until an observer position is defined, rather than modelling all possible eventualities. Hence, one of the interpretations of quantum mechanics is consistent with the idea that our reality might, indeed, be simulated!

These ideas are based on the consistent histories interpretation of quantum mechanics. This approach says that the result of a quantum observation (say, a particle hitting the screen in the double-slit experiment) is used to determine the past history of that particle. Hence, there is an element of "changing the past to fit the present". For example, in the delayed-choice double-slit experiment, once the particle hits the screen the past history of that particle is selected as one in which the particle passed through the slit that was not blocked. (The equivalent of the "wasted rays" in the ray tracing example could then be considered to correspond to parallel universes in the many-worlds interpretation of quantum mechanics which never become real).

This idea is also considered by Brian Whitworth in his paper The Physical World as a Virtual Reality: "In an online virtual world, the entire world is not calculated onscreen at once. The computer, for practical reasons, only calculates what the viewer chooses to view after they choose to view it, i.e., screen calculations are as required. If what we call reality is a multi-dimensional spacetime interface, it would likewise be expected to be calculated only on demand. The virtual reality viewer would then be no more aware of this than a virtual game player is, as everywhere they looked the world would 'exist'."

For more about this idea of "retrocausality", including a description of the delayed-choice double-slit experiment, see this New Scientist article, or Stephen Hawking's paper Cosmology from the Top Down which considers retrocausality at the cosmological level: "The histories of the universe depend on what is being measured, contrary to the usual idea that the universe has an objective, observer-independent history".

But that's not all ...

It is now an established fact that matter can be broken down into individual atoms and fundamental particles. But might space itself possess a similar "atomic" structure? One of the current frontrunners for a "theory of everything" - loop quantum gravity - asserts that space is composed of discrete elements. In other words, space is not infinitely divisible, but instead it is composed of incredibly small units of volume (the smallest is a cubic Planck length: 10^-99cm³) which cannot be broken-down into smaller elements.

According to loop quantum gravity, structures known as spin networks describe the relationships between these discrete elementary objects. In a spin network, the volume element is represented by a dot, or node, and the lines between the nodes show how the elements are connected together (see the section "Visualizing Quantum States of Volume" in Lee Smolin's Scientific American article Atoms of Space and Time). In other words, the position of each unit of space is defined in terms of the positions of the units which surround it (rather than relative to some absolute axes):

At this point we can now see a parallel between the discrete nature of space and the computer graphics technique of forming objects out of small polygons (such "volumetric pixels" are called voxels in computer graphics terminology). Our current technique for creating voxels has remarkable similarities with the relational nature of spacetime: "Voxels themselves typically do not contain their position in space (their coordinates) - but rather, it is inferred based on their position relative to other voxels (i.e. their position in the data structure that makes up a single volume image)" - quoted from the Wikipedia entry on voxels here. I'll admit when I read that, my jaw dropped! We're creating spin networks artificially without realising it!! Is that just a coincidence? Voxels do appear to be the hot new thing in computer graphics - we've already made voxel galaxies at the San Diego Supercomputer Center (SDSC). Also see the ENZO cosmology simulation code at the SDSC, designed to do simulations of cosmological structure formation.

At high resolutions, the voxels become so small as to be completely visually undetectable (as is the case with discrete volumes of space). Might these elements of discrete space be a form of voxel in an advanced rendering system? Are we living in a universe simulation created by an advanced civilisation's equivalent of the SDSC? At the very least, our own attempts to generate realities of our own seem to be taking us down the same path by which our actual reality is created, and that's fascinating.

Of course, this is all probably just a coincidence. But there again ...

The Big Brother Universe

But do we have any evidence that we are living in a computer simulation? Is it just a coincidence that our current popular pastimes - such as watching reality shows like Big Brother and playing God games such as The Sims or the latest astonishing game called Spore - are aimed at producing environments identical to the one in which we find ourselves? Why should that be? It doesn't have to be that way. We love to watch these participants carry out their (often boring!) daily activities, contained within a carefully controlled, closed environment.

There's no reason why these forms of entertainment should be so popular, but the fact of their popularity and their increasing sophistication does seem to provide circumstantial evidence that maybe 500 to 1,000 years from now we would ourselves be interested in creating simulations of the environment we now inhabit. And that, in turn, might be viewed as providing evidence-of-a-kind that we are, indeed, already participants that ultimate game of Big Brother.

Some tactics have been suggested to ensure we remain participants in any such universe simulation: "You should care less about others ... expect to and try more to participate in pivotal events, be more entertaining and praiseworthy" (see here) - surprisingly similar to the tactics likely to avoid eviction from the Big Brother house!

Russell Brand and me on Big Brother's Big Mouth.

Here are some insights about the Big Brother environment:

• If our universe is a simulation, then the Big Brother house would be a simulation within a simulation. On eviction from the house, the contestant returns to the higher-level simulation. Similarly, if you were woken (evicted) from a particularly vivid dream you would return to the higher-level reality. By analogy, if our universe really is a simulation then maybe when we are evicted (die) we move to the higher-level reality - maybe this could give some solace to those who believe in some form of existence after death! (See this thread on the Big Brother forum).
• Contestants on the show frequently behave unnaturally, aware that they are being watched. In physics we know you cannot make an observation without distorting the experiment. The only way to avoid this would be if the contestants were unaware they were being observed (in a recent reality show, Space Cadets, the participants were completely unaware they were on a show). This would provide an explanation for why we would not be informed if we inhabited a simulation.
• The UK version of the show has a concept of an "Evil" Big Brother who stirs things up within the house to increase the entertainment value. If our universe is simulated then maybe that would provide an explanation for natural disasters and other challenges - they're designed to increase the entertainment value for those viewing the simulation (see the illustration below! Also see this article in which a video game character complains about his hard life, being used for the entertainment of his simulator).

Maybe we should modify Edward R. Harrison's "natural selection" universe theory (described at the top of this page) in which only universes conducive to intelligent life would predominate. Instead we should say that only those universes which support intelligent life which is interested in creating Big Brother-style simulations would predominate.

Wouldn't it be ironic if now by taking a look at ourselves, and our own behaviour, we may indeed - as Stephen Hawking famously said - finally get to "know the mind of God"?

(Footnote: The "Space Cadets" experiment was due to be terminated if the participants figured-out the secret of the hoax. So maybe we shouldn't be trying too hard to uncover these secrets!)

"There is a theory which states that if ever anybody discovers exactly what the universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable. There is another theory which states that this has already happened." - Douglas Adams

Back to the main page

Comments

Comments are now closed on this page.