The simulation hypothesi.., p.17
The Simulation Hypothesis, page 17
For example, in a simple simulation of a fractal process that runs for, say, 1,000 steps, each step could be thought of as one iteration of the program. Typically, computers have a clock-speed that defines the maximum speed at which operations of computation can be performed. In reality, all measurements of time on this processor are multiples of this clock-speed.
When simulating the population of fruit flies or another species in a computer program, each “step” is assumed to be the reproduction cycle (assuming the species reproduces in regular intervals, which many do, yearly).
For example, a 1.7-gigahertz processor can perform 1.7 billion cycles per second. When speaking about processors, this is the maximum frequency at which a single processor can perform operations. Today’s computers and smartphones typically have multiple processors (or multiple cores, as they are called).
One thing to keep in mind is that the operations in the clock-speed of a processor are low-level operations. Usually when video game developers write code for a video game or simulation, we write it in a high-level language like java or C#, which gets compiled down to bytecode, which then gets run on top of a virtual machine. One line of code at a high level might translate into hundreds of lower-level operations.
So, what happens in video games or online role-playing games where multiple people are logged in to different computers with different processing speeds?
In these games, there is an idea of a universal “server” time—and operations are logged against this universal time so that the order of operations can be determined. While simultaneity might be tough to measure, multiplayer simulations do a lot of work to be sure that order of operations is respected. Basically, if I swing my sword against your player first, theoretically this needs to be recorded as part of our “fight.”
As discussed earlier, relativity and the speed of electromagnetic signals tell us that this may not be absolutely correct, given that renderings are happening on different machines separated by signals that must cross the Internet. So there may need to be some form of conflict resolution when dealing with multiple players or processes that are distributed. The basic rule of thumb is that simulations in the video game world do the best they can to maintain an order of operations, even if we cannot guarantee simultaneity at a physical level.
Given the response time of humans, preserving simultaneity among multiple players isn’t really a problem for today’s video games, but if there were two AIs competing with each other, with millisecond response times, determining who struck first would become a very important (and, according to Einstein, an impossible) task.
Quantized Space and Time Are Interrelated
Time inside video games is quantized, based on the steps of the simulation, which is some multiple of the processing time of basic operations in the CPU (or GPU). So, is there some idea of quantized time in the physical world around us? If there is, this would be a big hint that we may be inside a simulation, which attempts to use computation as a structure of the universe and would require a discrete clock-speed.
Thomas Campbell goes a step further in My Big TOE, showing that if the speed of light is constant and we can assume a quantization of space, we can actually calculate the minimum quantum of time in our physical universe.
If PMR (what he refers to as physical matter reality, or what we are calling the Great Simulation) consisted of a certain number of indivisible units (quantized space or what he calls 3D pixels), we could calculate those units theoretically as long as c, the speed of light, is fixed.
Campbell asserts that if there was a virtual space that really defined our 3D reality, it would be like the virtual space we use inside computer programs and simulations. Every object would have a 3D representation within this space—typically (x, y, z) coordinates—and a fourth coordinate for time, t. If the speed of light is fixed, and the smallest possible pixel is fixed, then the minimum quantum of time would be defined by light traversing the smallest pixel.
While the quantization of space has been accepted by many physicists, the quantization of time is a relatively new concept, but it must be implied by modern notions of space-time as one indivisible unit. “We've long suspected that space-time had to be quantized,” says Steven B. Giddings, a theorist at the University of California at Santa Barbara.37
Calculating Quantized Time and Space
Back to Campbell’s calculations. He defines DELTA t as a value representing the smallest time increment possible (which would be the clock-speed of the simulation)—let’s just call it T for simplicity in our equations. You could then divide c (the speed of light) by DELTA t (T) and get the smallest increment of space (the smallest length, or L) and vice versa. Campbell defines the equation:
L = c * (T)
Of course, you could define it by dividing the minimum space by the speed of light and get the minimum time as well.
L / c = (T)
Using the Planck length, which physicists now generally acknowledge as the smallest possible measurable distance of length in our 3D reality, the value T in our equation comes out to a very small number, which is essentially how scientists have come up with the Planck time constant.
Since we know the Planck length, dividing it by the speed of light, c, gives us a value that has been defined as the Planck time:
A Planck time unit is the time required for light to travel a distance of 1 Planck length in a vacuum, which is a time interval of approximately 5.39 × 10 −44 sec.38
Physicists are quick to point out that the Planck time is currently just a mathematical equation—there is not yet conclusive evidence to show that time is or isn’t quantized. However, given the relationship between space and time, the fact that there is a minimum length below which measurement of space becomes meaningless, it’s more than possible that the length of time it takes light to traverse this “minimum” distance may be a lower bound on our ability to measure.
William G. Tifft, a professor of astronomy at the University of Arizona, says that his research on measuring light from stars that is red-shifted seems to suggest that the light comes in the form of multiples of some value and that seems to suggest that there could be a minimum quantum of time just like there is a minimum quantum of space.
As we saw earlier, all computer simulations rely on some time clock to control the simulation, and if we are really in a simulation, there should be some evidence of this. If quantized time proves to be correct, that lends even more credence to the idea that there is a clock-speed and minimum distance in the 3D world around us.
Traversing Space Time Instantly in a Simulation
It’s important to note that the speed of light is seen as a constraint when we are traversing space-time as we know it. This doesn’t mean that it is a physical constraint—just that it is a constraint of our physical reality—or the physics engine that our simulated world is using.
If our 3D reality is actually a simulation, then what we think of as physical space and time are really virtual constructs. In a virtual world, the speed of actions is constrained by the virtual clock and the physics engine that runs the game. Since all simulations run on some form of computation, the pixels of time and space inside the simulation are typically some multiple of the underlying clock-speed and underlying bits that can keep track of information.
If we are in a simulation, then it may be possible to get around the constraints of Einstein’s special theory of relativity by moving around in the simulation instantly. These are speculative areas, but as we look at each of these three areas, we’ll see that the simulation hypothesis gives us some interesting insights on how instantaneous communication (and perhaps travel) might be possible—by not going through the virtual space, or virtual pixels, in the simulation. These three areas are:
Teleportation
Wormholes
Quantum Entanglement
Traversing Space-Time No. 1: Teleportation
A great example of teleportation is the virtual world called Second Life. In it, your character can walk from one part of the virtual world to another, which will be relatively slow. The character can also fly—in this case the virtual distance traveled is the same, but the speed is much quicker. To get from one plot of land to another will always be so many virtual units (pixels or other units of distance). This is the basic physics engine of the virtual world.
However, in Second Life, as in many other modern video games that have a virtual 3D space that is large, you can also “teleport” your character from one part of the world to another. In this mechanism, your character instantly de-renders from one part of the virtual world and re-renders in another part of the virtual world. It can take no time at all, no matter how “far away” the second plot of land is from the first plot of land in the virtual space. If we think of a 3D virtual world as having x, y, z coordinates, then teleporting would be a matter of setting new x, y, z coordinates without having to go through the points in between.
In the original Star Trek television series, teleporting was introduced as a matter of economy. If the crew could start in the starship Enterprise one instant and be on the planet in the next instant, the television production team wouldn’t have to create visual effects of a shuttle flying from the ship to the planet’s atmosphere and landing. In some ways, teleporting in video games is also for economy—though it’s more for economy of time. In Star Trek, teleporting was limited to relatively close distances—you couldn’t teleport to another planet in another solar system for example—but in a virtual world or video game the point of teleportation is to be able to get to any other part of the world instantly.
If we are able to develop some kind of teleportation, this might be further evidence that a physics engine governs our physical world.
Traversing Space Time No. 2: Wormholes
The second concept, which is closer to the video game idea of teleporting, is the concept of an Einstein–Rosen bridge, better known as a wormhole.
The idea was spawned from Einstein’s general theory of relativity. Austrian physicist Ludwig Flamm proposed in 1916 that if black holes existed per Einstein’s theory, then so called “white holes” could also exist.39 In 1935, Einstein and fellow physicist Nathan Rosen put together their own paper on this idea of “bridges,” and they became known as Einstein–Rosen bridges more formally. The term wormhole wasn’t coined until 1957 by the ubiquitous John Wheeler.
As shown in Figure 26, a wormhole would allow matter to go into one point in space-time and come out at a different point in space-time. The idea was that if there was a gravitational singularity of significant mass, it could create a tear in space-time.
Wormholes theoretically allowed for transformation of information and of matter at speeds much faster than the speed of light, assuming you were to measure the total distance between the two ends of the wormhole. However, this doesn’t mean that the actual spacecraft or information being transmitted is moving through 3D space-time at faster than the speed of light. It just pops out of ordinary space-time and back in at the appropriate “other point.” From the inertial point of view of the “traveler,” travel would be at ordinary speeds.
The problem with wormholes may not be that they don’t exist but that they are too small to be practical. Some wormholes are thought to be microscopic. While this wouldn’t prevent sending information through, it would prevent spacecraft from making it through. A bigger problem may be that wormholes are not generally thought to be stable for long. A wormhole might exist only for a small period of time—too short of an interval for us to be able to detect it or put it to use.
Even more complicated is the fact that the only phenomenon that can produce a wormhole (even a theoretical one) is a black hole. Anyone trying to go through a black hole, which is caused by gravity so strong that even light cannot escape, is likely to be crushed in the singularity instantly.
Figure 26: Wormholes allow for going from point A to point B directly without traversing the space in between.40
There are a few scientists who believe that quantum entanglement could be the key to finding and figuring out how wormholes work. Juan Maldacena at the Institute for Advanced Study and Leonard Susskind at Stanford have theorized that wormholes are like quantum entanglement at a macro level, linking two points in space together just as two quantum particles can be linked together.41
If wormholes are real, and we can link together two points in space-time without having to go through the intervening distance, this would be even more evidence of the simulation hypothesis and would be analogous to the teleporting in video games like Second Life.
Traversing Space-Time No. 3: Quantum Entanglement
We are used to having to traverse physical space (or the pixels that make up physical space), but since most of our travel has been on Earth, the distances haven’t been prohibitive. If our 3D physical reality consists of pixels spread out virtually, and if we were to traverse all the pixels of this virtual universe, it would take us an unbelievably long time to get to any place interesting outside of our own solar system—even if we were to travel at the speed of light.
The nearest star system, Alpha Centauri, is 4.5 light years away, and the Milky Way galaxy is approximately 100,000 light years across. Of course, with time dilation, traversing this distance might seem to take less time, but we wouldn’t be able to get back to the same point.
This brings us to the idea of quantum entanglement. This is when two particles become “entangled,” meaning it is theoretically possible from the state of one particle to guess the state of the corresponding entangled particle instantaneously, even if it is far away. Einstein called this “spooky action at a distance” but it has been shown to be a real phenomenon.
Quantum entanglement seems to have the capacity for instantaneous communication across light years—which means that information would go from one part of our world to another faster than the speed of light. While physicists admit that quantum entanglement exists and is being used in applications like quantum cryptography, there is still plenty of debate about whether two entangled particles actually constitutes sending information from place A to B faster than the speed of light.
No one knows exactly how or why quantum entanglement works. We’ll explore this idea and quantum computing in more detail in Chapter 11, Skeptics and Believers: Evidence of Computation, but once again the simulation hypothesis provides us with a model from the world of video games that may be relevant in explaining the previously unexplainable.
If two pixels are co-related on a computer screen, then both physical pixels would be getting their value from the same point in memory. If we change the memory value (let’s say its RGB value from red to green), then both pixels should change on the screen from red to blue. If we decide that a particular pixel should no longer get its value from that memory location, then the pixels are theoretically un-entangled!
Pixels, Quanta, Space-Time, Wormholes, and the Simulation Hypothesis
The whole idea that space-time as we know it is not a continuous spectrum but consists of small discrete parts provides not just a powerful analogy to how video games and computers work but may reveal much about the structure of our physical universe. Though all of our video games to date have simulated a 3D world in 2D (on computer screens), that is starting to change, and there is no reason that pixels couldn’t exist in three dimensions, as evidenced by 3D printers.
Such a “virtual space” would be consistent with the simulation hypothesis—that we live in a pixelated world with an underlying computation engine. The fact that c, the speed of light, is constant is an odd fact that shows that our physical world may consist of electromagnetic underpinnings—not unlike a rendered video game. The fact that there is minimal distance below which we may not be able to measure, the Planck length, lends further credence to the idea that we live in a pixelated, digital world.
Moreover, along with this minimum distance, the suggestion that we may have a minimum quantum of time, referred to as the Planck time, also points to a digital rather than an analog world. This minimum time quantum can be deduced from the time it takes photons traveling at the speed of light to traverse the Planck length. This is analogous to the idea of having a clock that runs in a simulation, which is produced by and shares information via electromagnetic waves.
While there are no clear answers to the questions raised here, the idea of a wormhole is itself intriguing and suggests, along with quantum entanglement, that there are ways to get around the physical limitations of the speed of light in our physical reality. Quantum entanglement is completely unexplainable given our current models of physical reality.
If any of these methods can be used to get around the speed of light, then this suggests very strongly there is something outside of space-time.
If there is something outside of space-time, then that which looks like physical reality to us starts to resemble a virtual world inside something bigger. Video games and science fiction continue to provide the best metaphors for how this might work, and the simulation hypothesis gives us a better model for the structure of our world.
In the next part of this book, we’ll leave the physics behind and travel down the road of a different model of the universe that also posits that the physical world is not all that exists. We’ll look at Eastern mystics, who have long suggested that the physical world is a kind of illusion, and we’ll examine Western religious traditions and other unexplainable phenomena, showing that the simulation hypothesis may be the only theory that can connect all of these ideas together into a single, coherent model of reality.
Part III
