"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 the construction of some advanced civilisation - not as improbable as it might appear! In fact, it would be surprisingly simple to create intelligent life:

"Hydrogen is a light, odourless gas, which, given enough time, turns into people."
- Edward R.Harrison, Cosmologist

How practical would it be to make a universe of your own, a universe capable of sustaining life? If you want to know how to make your own universe in a laboratory, MIT's Edward Farhi, Alan Guth, and Jemal Guven have produced a recipe. It basically involves compressing a 10-kilogram sphere of mass to an extremely high density. The ball would implode usually forming just a black hole. Occasionally, though, it would branch off by quantum tunnelling to create a baby universe hidden inside the black hole. This branch could grow to a large size without interfering with the laboratory (see this New Scientist article).

It sounds so easy! Well, maybe not easy, but it would be well within the ability of a advanced civilisation. Just think of the technological progress of human civilisation over the last thousand years and consider where we might be in a million years (assuming we don't blow each other up). In fact - if the universe is already teeming with life as some suggest - the technology might well be in existence already, somewhere "out there".

Edward R. Harrison, a cosmologist at the University of Massachusetts has proposed an ingenious theory explaining the proliferation of universes which may be amenable to the development of intelligent life (see this Smithsonian article). He assumes that if sufficiently advanced civilisations had the capability to create universes then some of those universes would be of a form conducive to intelligent life evolving within them. Those inhabitants of the new baby universe will eventually evolve to become sufficiently advanced to create baby universes of their own, and so on. Universes unfit for habitation would lack intelligent life and would not be able to reproduce, so we end up with a form of "natural selection" producing a series of universes containing life.

The Simulation Argument

But maybe there is a simpler way to create your own "universe", a method which utilises our extraordinary advances in computer technology. In an imaginative paper entitled The Simulation Argument, Oxford University philosopher Nick Bostrom has presented an argument that it is quite possible we are living in a computer simulation similar to that depicted in the film The Matrix. Though the world feels "real" to us, we might be merely logic states in an advanced computer.

It's very hard (if not impossible) to disprove this "Matrix" theory (see the "Brain-in-a-Vat" Argument). This is because our notion of "reality" is so loosely defined: our human sensory inputs form the easily-fooled last link in the chain of our cognition, but we rely on those senses to define the nature of all our reality. Forget Gödel's Theorem and the Heisenberg Uncertainty Principle: the Brain-in-a-Vat argument tells us everything we need to know about the limitations of science, mathematics, and our possible knowledge of the universe. Put simply, we can never know anything for certain. We might be living in the Matrix, or be a brain-in-a-vat with all our sensory inputs being faked, and we would have absolutely no way of knowing. David Deutsch says: "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). As a result, Deutsch finds the idea 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).

As Gordon McCabe says in his paper Universe Creation on a Computer, "Bostrom's computer simulation does not have empirically testable predictions", in other words it is impossible to prove false. This objection is based on the principle that 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 Simulation Argument is ambitious in that it takes this idea one step further. It doesn't just say "We might be in the Matrix", it 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 the Matrix.

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 in the Matrix right now!

In fact, the future human race could easily create Matrices 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 Matrix 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 the Matrix.

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."

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). It would spoil your fun a bit, but you would effectively have no choice. You would have to rein in your omnipotent freedom a bit 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.)

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 - 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 time because all of spacetime can be viewed as being laid-out as an unchanging four-dimensional block:

For more information about block time, 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 time 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".

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 asks the question "Does a simulation really need to be run?". He seems to be arguing that a description of a simulated universe which is just stored on a simulator computer does not have to be computed (rendered graphically). He argues: "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. 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."

In this respect, Tegmark seems to be arguing that a simulated universe would have a block universe structure, with no moving "now". I don't agree with this. As I suggested earlier, the structure of a simulated universe recreates the moving "now" and seems to give new life to the tensed theory of time. Indeed, the tensed theory would seem to be a likely contender for the nature of time within a simulation: 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 would not 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: any simulation would have to be run.

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 - see here). 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?

I don't believe the Rietdijk-Putnam Argument kills the tensed theory of time, but it does show how the tensed theory has to be modified to accommodate special relativity. 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, 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" (see here). We can still have a "now", but it will be represented in proper time for a particular observer. For example, you might say "The time is now 10 o'clock" - that's a statement of the "now" in your personal, proper time. 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.

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):

When we have this analogy we find that this concept of proper time for a specific observer once again ties in very nicely with the idea of a simulated universe, because in order to produce a view of the simulation on a simulating computer screen we would have to specify the position of our computer's viewport within the simulation. In that way, we are indeed specifying a particular "now" for a particular observer, and we would take the proper time of that particular observer to represent time in our simulation:

Note that "reality" as perceived by each observer could be subtly 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, only "existing" as a mathematical model). We have different "realities" - and different "nows" - for each observer. In fact, this is the most efficient method of simulation: reality is created "on demand" only after an observer position is defined.

This principle is called point-presentism. For more information read James Harrington's paper which describes point-presentism in depth and presents a general review of time theories (see here).

Lee Smolin describes a similar observer position-dependent interpretation of quantum theory called relational quantum mechanics in his book Three Roads to Quantum Gravity: "Could there be a different kind of quantum theory, one in which the quantum states refer explicitly to the domain seen be some observer? Such a theory would be different from conventional quantum theory. It would in a sense 'relativize' that theory, in the sense that it would make the quantum theory depend more explicitly on the location of the observer inside the universe" - see Carlo Rovelli's arXiv paper on Relational Quantum Mechanics.

It is also interesting to consider the ideas of James Hartle who describes an Information Gathering and Utilising (IGU) system (a human, basically) embedded in 4D spacetime: "The present is not a moment of time in the sense of a spacelike surface in spacetime. Rather there is a localized notion of present at each point along an IGUs' world line." - see this New Scientist article or James Hartle's paper The Physics of 'Now'.

The Holographic Principle

It has been discovered that the amount of information (i.e., entropy) trapped in a black hole is proportional to the area of the horizon of that black hole. This is because when an object falls into a black hole, from the point of view of a distant observer the object slows down and gets frozen near the event horizon (as described in this New Scientist article). So everything just piles up on the horizon, and all the information contained within the black hole is spread on its surface. This result can be extended to any region of space, and is called the Bekenstein bound. This is a surprising result as we would expect the amount of information contained within a region of space to be proportional to the volume of that space, not the area of its boundary.

Gerard 't Hooft has proposed an interpretation of this result which treats the horizon of a black hole (or the surface of any region) like a computer screen. Each pixel can be on or off, which means it encodes one bit of information about the contained region (each pixel is incredibly small - just two Planck lengths square). Hence, the total amount of information contained within the region is equal to the total number of pixels in the computer screen. This is called the holographic principle (see Jacob Bekenstein's Scientific American article Information in the Holographic Universe).

What this means is that whenever we examine a region of space, we can never be certain if we are not just viewing a highly-advanced, phenomenally high resolution TV screen! The information we would receive would be exactly the same! As Lee Smolin says in his book Three Roads to Quantum Gravity: "The point is that there is no way for the observer to tell if they were interacting with The Thing itself, or merely its image" (see diagram below).

As Jacob Bekenstein says in his aforementioned Scientific American article: "The holographic principle contends that an analogue of this visual magic applies to the full physical description of any system occupying a 3D region: it proposes that another physical theory defined only on the 2D boundary of the region completely describes the 3D physics."

The parallel with a two-dimensional CGI rendering of reality by a computer graphics viewport (described in the section immediately above) is uncanny!

In physical reality - as in CGI rendering - information is only used to create the mathematical "virtual" structure: that structure only becomes "reality" when it is transformed via a rendering process. Reality is then defined as a continuous rendering process through space, converting virtual information into hard reality at each point. As Lee Smolin goes on to say: "We are mistaken to think that the world consists of Things that occupy regions of space. Instead, all that there exists in the world are Screens, on which the world is represented".

As Lee Smolin concludes: "The holographic principle is the kind of idea one hopes to run into just as one is turning the corner to a new universe."

Time Dilation: The "Glitch"?

The previous example has shown how reality in a simulation could be generated on a per-individual basis (in a process reminiscent of rendering in a computer graphics system). In a universe without any absolute positional axes, the role of the observer is crucial: everything is calculated relative to the inertial frame of reference (the viewport) of the computer-simulated observer.

As one of the key factors in the rendering process, the speed of light would be one of those properties calculated relative to your inertial frame (viewport). The result of this would be in accordance with special relativity: the speed of light is the same as measured in all inertial frames. The benefit of this approach is that it produces a quality, undistorted image of the simulation, even if your inertial frame is travelling extremely fast within the simulated universe ("According to the principle of general covariance, a theory must give the same results not matter how you move its coordinate system around in the universe" - quote taken from the Cosmic Universe page).

Nick Bostrom has suggested that tell-tale programming flaws in a simulated universe could expose the truth about the simulation to the simulated beings: "Déjà vu is a sign of a glitch in the Matrix ... One person, for instance, told me that he could see flickering pixels when he looked in his bathroom mirror" (see here). John Barrow has continued this theme suggesting that we might expect to see occasional glitches and small drifts in the supposed constants and laws of Nature over time (see here). Might not the distortion of time dilation (time passes at different speeds in different inertial frames) be considered a glitch? It's not such an obvious "bug" as a missing pixel, but then you wouldn't expect to see something so shoddy as a missing pixel in such a sophisticated simulation. Time dilation would seem to be an inevitable consequence of having a rendered reality which is generated relative to each observer - I don't see how any simulator could avoid this flaw. Even in present day simulations such as The Sims we would still confront the distortion of time dilation if the animated characters could travel at speeds approaching the speed of light within that simulated world.

So time dilation emerges as an unavoidable "glitch" for any simulation. However, if the simulators set the speed of light to a constant, extremely high value then it would be an unnoticeable flaw for the majority of the inhabitants of the simulated universe who would only be capable of travelling at relatively low speed. We see precisely this constant, extremely high speed of light in our own universe.

As John Barrow has said: "The flaws of Nature are as important as the laws of Nature for our understanding of true reality."

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!)

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