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A Cartesian space expands from a zero-point within it but a polar space doesn’t. If one blows up a balloon, its surface expands everywhere at once, not from a point on the surface. The physics conclusion that space is expanding “everywhere at once, not from a fixed point in it, suggests that any simulation of it is polar not Cartesian. If the earth was flat then Cartesian coordinates would work but it turned out to be a sphere surface so we use longitudes and latitudes instead, which are polar coordinates. The north and south poles define the axis around which the earth rotates.

The nature of a circle is that its start point is arbitrary so any point can begin it. The axis chosen to turn a circle into a sphere is also arbitrary – rotating a circle on any axis through its center creates the same sphere, so the poles of the generated sphere are also arbitrary – any opposite circle nodes could be poles of the sphere (Figure 2.4). The same logic applies to a hypersphere, so if our space is a three-dimensional surface generated by rotation, how it happens is arbitrary.

Now add that this all occurs on a network. We know that our space is isotropic or uniform in all directions. If space was an object like the earth, it might rotate a certain way but it isn’t a physical “thing” as there is no physical ether. Space as a polar simulation raises the question of what rotations generate it? The quantum network seems to do what quantum reality always does – take every option – but how could it do this?

If the sphere in Figure 2.4 came from fixed network rotations, it would have fixed poles, which is asymmetric. Every line is a connection on a network, so the poles would have more connections as shown in Figure 2.4 and the result wouldn’t be a uniform space. Computer science however reveals that a network can easily alter its links, as our cell phone networks routinely change their connections to improve efficiency as the load changes. If the quantum network does the same, each node can locally configure its own links as if it were an axis pole. In other words, if control is distributed, each node can “paint” its own polar coordinates, setting its connections as if it were a rotation axis. This approach doesn’t allow an objective view of space but as will be seen, our world has no need for that because as Einstein concluded, every object in our universe “has its own space”.

A network that distributes control lets every node choose its neighbors as if it were the center of all space. Each gets a slightly different view but that doesn’t matter because every view is equivalent. Each node of space decides itself which nodes are neighbors, just as a web designer can decide which pages a web page links to. In a distributed network, polar coordinates allow a relative space where every node is the center of its own frame of reference.

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Cartesian space is so deeply ingrained in western thought that one might think it is the only way to describe a space but it isn’t so. Euclid derived Cartesian coordinates by extending a point to a line, extending the line to a plane and then extending the plane to a volume. But instead of using straight lines, one can extend a point using rotations to derive polar coordinates.

Given a network, one can rotate a point to create a circle and then repeat. The first circle defines one-dimension, as every node has two neighbors giving left and right directions and the distance between two points is the number of link connections (Figure 2.3). The network architecture, or how the nodes connect, defines distance and direction as a node directly linked to another is “near” while another many links away is “far”. The advantage of a circular dimension is that it is finite not potentially infinite and it does not have its zero point on itself.

So just as Euclid did for a line, the circle in Figure 2.3 can be rotated at right angles to give a two-dimensional sphere (Figure 2.4).

A “Flatlander” confined to this surface would see a space that is:

1. Finite. Has finite number of points.

2. Unbounded. Moving in any direction never ends.

3. Has no center. No point on the sphere surface is the center.

4. Approximately flat. If the sphere is large enough.

5. Simply connected. A mathematical term that means any loop on it can shrink to a point.

In other words, this surface performs just like our space but with only two dimensions.

Now just as rotating a circle gives a sphere with a two-dimensional surface, so rotating a sphere gives a hypersphere with a surface of three dimensions (Figure 2.5).

A hypersphere is what you get by rotating a sphere just as a sphere is what you get by rotating a circle and in mathematics, a hypersphere surface has three dimensions just as a sphere surface has two. Centuries earlier, the mathematician Riemann speculated that our space was a hypersphere surface because such a surface is unbounded, simply connected and three-dimensional just as our space is. The logic is even more convincing today, when Einstein argues that space curves like a surface and cosmology says it expands everywhere at once like a balloon surface. Logically, our 3D space could easily be a surface in a four-dimensional bulk:

“When it comes to the visible universe the situation could be subtle. The three-dimensional volume of space might be the surface area of a four dimensional volume” (Barrow, 2007) p180

Davies makes the case even more clearly:

“… the shape of space resembles a three-dimensional version of the surface of a sphere, which is called a hypersphere.” (P. Davies, 2006) p45

If our space is a hypersphere surface within a four-dimensional quantum network, why then does space appear flat not curved? The simple answer is that the surface of a hypersphere bubble that has expanded for over 14 billion years would seem flat to us.

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Berners-Lee called a scalable system one whose performance doesn’t degrade as it expands however big it gets because growth increases demand and supply in tandem, so the system can grow forever (Berners-Lee, 2000). He designed the World Wide Web to be scalable and the Internet also began this way, as every new Internet Service Provider (ISP) increases both the demand and the processing to handle it. A scalable network has to distribute control but when the Internet began, pundits expected its lack of central control to result in chaos. It didn’t collapse and the reason turned out to be because it had no central control. Computer science discovered that an infinity anywhere in a centralized network crashes it but distributed networks carry on despite a local crash – they degrade but don’t collapse. Our brain neural network distributes control for the same reasons (Whitworth, 2008).

The performance of our space hasn’t changed much over time, even after expanding for billions of years, so if space isn’t nothing, it must be a scalable system. If our virtual space expands like the Internet, then adding nodes must increase both supply and demand, suggesting that space has local limits. The evidence agrees as:

“…recent observations favor cosmological models in which there are fundamental upper bounds on both the information content and information processing rate.” (Paul Davies, 2004) p13.

We call the upper limit of what space can hold a black hole. It is in effect the bandwidth of space.

In general, space as a scalable network suggests distributed control.

In contrast, Cartesian coordinates require:

1. A predefined maximum size: Cartesian coordinate memory allocation requires a predefined size, so a point stored as (2,9,8) in a 9-unit cube must be stored as (002,009,008) in a 999-unit cube, and so takes up more memory.

2. A zero-point origin: A (0,0,0) point that is the absolute center of space.

A Cartesian space needs a predefined maximum size but our space has expanded for billions of years with no end in sight. If our space was Cartesian, its maximum size would have to be defined before the first event, to avoid a Y2K problem. Our Y2K problem arose because old computers stored years as two digits to save memory, so 1949 was stored as “49”. The problem was that the year 2000 would be stored as “00” that was used for the year 1900. Changing all our databases to four-digit years meant that any programs accessing them might crash if not modified. That our space is still expanding without upgrade suggests that it can’t be a Cartesian virtual space.

A Cartesian space also requires an origin point from which to expand. Since Hubble showed that every star and galaxy is receding from us, a Cartesian space implies that our Earth is that origin! Planet earth only began recently, so it can’t be the Universe’s origin. Our space is expanding with no absolute center so it can’t be Cartesian.

In general, Cartesian coordinates work for small spaces but not for an expanding space as ours is.

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That space is a “something” raises the question What does it do? It seems strange to talk of what space “does” but modern simulations of it do just that:

“…we think of empty spacetime as some immaterial substance, consisting of a very large number of minute, structureless pieces, and if we let these … interact with one another according to simple rules … they will spontaneously arrange themselves into a whole that in many ways looks like the observed universe.” (Ambjorn et al., 2008) p25.

For the purposes of geometry, Euclid gave our space a structure many years ago as follows. First, he imagined a point with no dimensions. Then he extended that point continuously to create a line, that was again extended at right angles to give a plane, that was again extended to give a cube. This defined a Cartesian space with three orthogonal dimensions, where every point was represented by three real number coordinates (x, y, z).

War-gamers don’t use Euclid’s space because squares only allow four directions to attack an enemy but divide their maps into hexagons instead, to give more interaction directions. In general, a space requires:

1. Dimensions. That define the degrees of freedom needed to create it.

2. Locations. That define when two objects are “in the same place” and so interact.

3. Directions. That define the number of ways a point can interact with its neighbors.

Simulating space as a network isn’t a new idea, e.g. in Wilson’s networks a node is a volume of space and in Penrose’s spin networks a node is a point event with two inputs and an output (Penrose, 1972). All these models, including loop quantum gravity (Smolin, 2001), cellular automata (Wolfram, 2002) and lattice simulations (Case, Rajan, & Shende, 2001) map nodes to a Cartesian space, so they all encounter the problem of scalability.

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Does space itself exist? This question has concerned the greatest minds of physics. Simply put:

If every matter object in the universe disappeared, would space still be there?

Newton saw space as the canvas upon which God painted, so it would still exist even without objects. In contrast Leibniz considered a substance without properties unthinkable so to him space was based on object relations, just as a meter was defined as the distance between two marks on a platinum-iridium bar in Paris. If objects only move with respect to each other, he concluded that without matter there would be no space.

Newton’s reply to Leibniz was a hanging bucket of water that spun around (Figure 2.2). First the bucket spins, not the water, then the water also spins and presses up against the side to make a concave surface. If the water spins with respect to another object, what is it? It can’t be the bucket, because when it initially spins relative to the water the surface is flat, and when later it is concave, the bucket and the water spin at the same speed. In a universe where all movement is relative, a spinning bucket should be indistinguishable from one that is still. If an ice skater spins in a stadium his arms splay out by the spin. One could see this as relative movement, as the stadium spinning round the skater, but why then do the skater’s arms splay? He concluded that the skater really is spinning in space (Greene, 2004) p32.

This seemed to settle the matter until Einstein showed that objects actually do move relative to each other. Mach then resurrected Leibniz’s idea, arguing that the water in Newton’s bucket rotated with respect to all the matter of the universe. In a truly empty universe, Newton’s bucket would stay flat and a spinning skater’s arms would not splay, but this isn’t testable as one can’t empty the universe. This resort to speculation reflects how disturbing some physicists find the idea of a space that is:

“…substantial enough to provide the ultimate absolute benchmark for motion.” (Greene, 2004) p37

How then could a virtual space handle object interactions? There are two options:

1. Centralized. Give each particle an absolute position then compare all positions every cycle and if any are equal, then a collision has occurred. To the inhabitants of this virtual reality, space would indeed be truly nothing and potentially continuous. Yet as the particles increase the interactions grow geometrically, as each point must be compared to every other point every cycle. For a simulation the size of our universe, the processing required is unimaginable.

2. Distributed. Let each point of space be a node with a pre-allocated processing capacity. Now a collision is when a node gets more processing than it can handle. To the inhabitants of this virtual reality, space isn’t continuous and does exist apart from the objects in it. This tactic seems wasteful as empty space is allocated null processing but has the advantage that expanding the system also adds more processing.

Reverse engineering prefers the distributed option because the processing is finite. It implies that a point of empty space can show a dot or “nothing”, just like a screen point, where showing nothing is null processing. This means that if every object in our space disappeared, it would still exist, just as a screen still exists even if no image is shown, supporting the current verdict of physics that:

“space-time is a something” (Greene, 2004) p75

Empty space as null processing is neither the passive canvas of Newton nor the nothing of Leibniz because null processing is something not nothing and it is active not passive.

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Continuum problems have plagued physics since Zeno’s paradoxes two thousand years ago (Mazur, 2008):

1. If a tortoise running from a hare sequentially occupies infinite points of space, how can the hare catch it? Every time it gets to where the tortoise was, the tortoise has moved a little further on; OR

2. If space-time is not infinitely divisible, there must be an instant when the arrow from a bow is in a fixed unmoving position. If so, how can many such instants beget movement?

To deny the first paradox exposes one to the second and vice-versa. Zeno’s paradoxes resurface today as infinities in field equations, e.g. an electron as a dimensionless point has infinite mass and charge density unless one assumes other dimensions as string theory does. Physics handles the infinities of quantum field theory by the mathematical trick of renormalization, that makes the infinities of field theory go away by requiring particles to interact via other particles in Yang-Mills interactions. Dirac described this tactic as follows:

“Sensible mathematics involves neglecting a quantity when it turns out to be small – not neglecting it just because it is infinitely great and you do not want it!”

Feynman was even blunter:

“No matter how clever the word, it is what I call a dippy process! … I suspect that renormalization is not mathematically legitimate.”

Renormalization pulls physical reality from the quantum hat although continuity is a mathematical convenience not a proven empirical reality:

“… although we habitually assume that there is a continuum of points of space and time this is just an assumption that is … convenient … There is no deep reason to believe that space and time are continuous, rather than discrete…” (Barrow, 2007) p57

Quantum realism concludes that space isn’t continuous because a digital reality has no half pixels and time isn’t continuous because it has no half cycles. Processing by definition chooses from a finite set that doesn’t allow infinite values. It then answers Zeno’s questions as follows:

There is indeed an instant when the arrow is in a fixed, unmoving position but there is still movement as another quantum cycle generates the next physical state. Equally the hare cannot get closer to the turtle forever as there is a minimum pixel distance that can’t be divided, so the hare catches the turtle.

Denying the infinitely small avoids the infinitely large. A digital world of irreducible pixels and indivisible ticks makes the infinities of continuity disappear, like ghosts in the day. Reality as a series of frames strung together, as in a movie, resolves the paradoxes that continuity cannot.

Our space breaks down at the order of Planck length because it is discontinuous. To study the very small needs short wavelength light that is high energy light, but putting too much energy into a space gives a black hole that hides information from us. If you probe the black hole with more energy, it expands its horizon to reveal no more, so nothing below the Planck length can be known. Planck length and time are the irreducible limits of our reality.

This predicts what current physics doesn’t, that repeatedly dividing our space gives a pixel that can’t be split and repeatedly dividing our time gives a cycle that can’t be paused. Just as closely inspecting a TV screen reveals only irreducible dots, closely inspecting our space reveals irreducible Planck lengths. If physical reality is a screen image, the Planck limits are its resolution and refresh rate, so the pixel size of physical reality is 10-33 meters and its refresh rate is 1043 times per second.

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This section considers how a quantum network spreading quantum processing could connect to simulate our space:

QR2.2.1   Continuum Problems

QR2.2.2   Is Space Nothing?

QR2.2.3   A Cartesian Space

QR2.2.4   Scalability

QR2.2.5   A Polar Space

QR2.2.6   Polar Coordinates

QR2.2.7   The Density of Space

QR2.2.8   Quantum Space

QR2.2.9   Electromagnetism

QR2.2.10 Creating Directions

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To truly copy physical reality, one must know what it actually is in the first place. It is clear that a photo of me isn’t me, nor is a movie of me, nor is a biological clone of me. But if physical events are created by quantum processing, as quantum theory implies, can we copy the quantum processing? If quantum processing creates physical reality, to really duplicate a physical event one must copy the quantum processing behind it.

Unfortunately, the quantum no-cloning theorem explicitly excludes this, stating that it is impossible to create an identical copy of a quantum state because to “know” a quantum state is to collapse and so destroy it. Hence talk of uploading and downloading universes, minds or ourselves has no basis in quantum theory or information theory. It is all just wishful thinking.

A key corollary is that the quantum network proposed can’t use static storage because it is impossible to store quantum activity in any way by the quantum no-cloning theorem. The quantum network acts in a way that doesn’t have the luxury of static storage. Like a star that constantly shines, quantum processing is constant activity without pause. Cell-phone and Internet networks use buffers to handle overloads but a quantum network can’t use memory of any sort to store what it does. Computers and cell-phones save and reload physical states but quantum computers can’t store or reload quantum states. Quantum theory doesn’t allow RAM, ROM or buffers of any sort.

By this logic, McCabe’s argument that physical reality can’t come from information based on physical reality doesn’t apply to quantum reality. Classical processing needs a physical context to exist but quantum processing doesn’t depend in any way on physical reality. The original quantum reality just is what it is.

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Information theory clarifies why a physical world can’t output itself, because that would require a context specified in advance based on physical states that are not yet defined. As McCabe concludes:

“All our digital simulations need an interpretive context to define what represents what. All these contexts derive from the physical world. Hence the physical world cannot also be the output of such a simulation.” (McCabe, 2005).

The same physical world can’t be both processor and output but can one part save and reload another? Could we save and reload physical reality as we do information? To save a matter scene as we do a game scene requires a data structure that existed before the scene did, so it can’t be based on matter. To save a game requires a pre-defined data structure, so if a new game version changes that, old saves don’t work! To reload a universe would likewise require a known data structure else the result would be nonsense, just as reloading a WordPerfect file into Word gives gibberish because Word doesn’t know WordPerfect’s “interpretive context”, as McCabe argues.

Imagine our universe frozen in a static state at a moment in time, as innumerable physical states that have no information at all in themselves. Information requires an observer to decode it but who could “read” it? Not us, as we would be frozen too! A frozen world without an observer would be as empty of information as this page is without a reader. To save and reload a physical universe one must define its data structure and exist outside it!

When we store movies in file to replay later, we need an agreed format like mp3. To play the file, we also need something to dynamically play it, like a laptop or projector, so without a projector to play it, there is no movie. Likewise, a computer plugged into a power source is needed to run a program file. So even if one could save the universe as static data, what “projector” using what power source could reload and run it? Information stored as a static file always needs a dynamic system to reload into.

Trans-humanists take the mind to exist entirely as information encoded in the physical brain, so expect that we will soon be able to upload the mind and download it to a new, younger, body and so live forever. However even if we could make a perfect physical copy of a brain at a moment, that is no better than taking a photo in a movie theater and taking a photo of a movie doesn’t “store” it, as one frame is not a movie. Even many photos taken and replayed in sequence doesn’t “resurrect” the person, any more than playing a movie of a dead person resurrects them. Recording a physical scene and replaying it as a hologram may emulate a dead relative but it doesn’t recreate them. The viewing experience would be real but the “person” viewed wouldn’t experience life as an observer. Information based on physical states still needs an observer, so one has to copy the observer as well. In the same way, saving a multi-player online game doesn’t save the other people playing it because they aren’t “in” the game. Chapter 6 returns to the issue of the need for an observer in more detail.

Since genes are information, why not copy genes to create a biological copy of ourselves? This can be done but nature already does it, as identical twins are from copies of the same original cell. Yet the result is twins that are two different people not the same person. A clone of me doesn’t make another me but another person. Even if that copy of “me” has experiences, it still isn’t me if I don’t experience what the clone does.

Something is missing in the reloading reality idea and it is the quantum reality behind physical events. If that is what “runs” physical reality, the question reduces to whether quantum processing can be saved and reloaded.

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Quantum realism proposes that the quantum network can be understood in terms of information theory but not in terms of how we implement information theory physically.

Modern information theory began with Shannon and Weaver, who defined information as the power to the base two of the number of choice options (Shannon & Weaver, 1949). By this definition, a choice between two physical options is one bit of information because two is two to the power of one, and a choice between four options is two bits because four is two to the power of two. By this logic, two to the power of eight, or 256 is 8 bits or one byte. Equally a choice of one option, which is no choice at all, is zero bits. Processing was then defined as changing information, i.e. the event of making a new choice.

Hence while the choice between two states is one bit, according to information theory a physical state in itself has no information at all because it is just one way. A book “contains” information but has zero information in itself because, being physical, it is fixed in one way. This may seem wrong but it isn’t, as hieroglyphics no-one can decipher do indeed contain no information. A book only gives information when a reader decodes it and that depends entirely on the decoding context, so reading every 10th letter of a book, as in a secret code, gives a different message with different information.

The amount of information “in” a physical state depends on the assumed number of physical states it was chosen from. One electronic pulse sent down a wire can represent one bit, or it can be one byte as ASCII “1”, or as the first word in a dictionary, say Aardvark, can represent many bytes. It is because the information in a physical message depends on the decoding context that data compression can store the same data in a smaller signal, using more efficient encoding. If information was a physical thing, data compression couldn’t pack the same data into a physically smaller signal!In general, the information in a physical signal is undefined until a reader decodes it. Only when sender and receiver agree on the encoding-decoding context can they exchange information.

It follows that information only emerges from a physical state when an observer is added. The same applies to information in a book or database – the states in themselves contain no information at all until read. If one writes a book in English say, that language is the encoding context that allows communication. The receiver can only extract the information the sender put in if they know the encoding context.

If processing is defined as creating information, writing a book is processing, as one can write it in many ways, and reading a book is also processing, as one can read in many ways, but the physical book itself, being just one way and no other, is empty of information. Information stored as physical states doesn’t exist without a reader to decode it by a series of dynamic events. By Shannon and Weaver’s definition, processing is the dynamic means by which static information is encoded and decoded so the information in a physical book literally doesn’t exist until an observer decodes it.

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