What is the computational-hypothesis?
The computational-hypothesis is an information theory of physics. The physical processes are a result of processing information.
It's not just an essay or mere speculation. We will derive formalized mathematical results that expand on some of the most important discoveries of the 20th century, and provide new predictions, such as the possibility of faster than light travel and communication.
The phenomena of slowing-down of clocks due to velocity and presence of mass, the very notion of mass and the speed of light, as well as relativistic mass increase is explained, and Einstein's formulas are found to be a special case.
The notion of mass and the speed of light are taken for granted in today's physics. We will derive the need for them to exist. Do you know of any other theory that starts with nothing but a concept of information, and derives (what is currently considered) the elementary notions of mass and speed of light? Einstein postulated the constancy of speed of light, we will derive it as a special case.
Only the information theory will be used to do the aforementioned. There is no notion of light, mass, gravity, or relativity to begin with at all. This alone should give a pause. If this is possible, then the computational-hypothesis may be a better explanation for the physical reality. Simpler is better, and even better if it delivers. It's the Occam's razor cutting to the chase.
The true nature of what Einstein called 'time dilation' is shown to be a special case of a simple and paradox-free framework. Substantial faster than light speeds are possible under some circumstances, although not on or near Earth or other large masses.
The concept of information is a generic one in the computational-hypothesis, i.e. no assumption is made about how it's represented, stored or processed.
The computational-hypothesis lays the foundation for the view of reality as information-based. The explanation of nature of light, the nature of mass and slowing-down of clocks is chosen to show the formalization of it. The quantum nature of reality is forthcoming in the same framework. The goal is to establish the foundation of formal information theory of physics and to show a proof of concept.
I hope that such results, obtained (as far as today's physics is concerned) "out of thin air" and formalized without the use of existing physics will serve as an initial validation, and as a starting point for a more comprehensive research.
The idea
The idea is that every fundamental entity (called an 'object') in the Universe has information that defines it at every moment. Each object computes the information that comes from all the objects in the Universe, which drives the reality we see. It's all about the speed of processing (computing) this information.
It turns out the processing of information slows down when moving or when near other objects. Here are analogies to help visualize why is this so:
If you move in a fast train, looking out of the window, some details are blurry, because there is too much information to process at the same time.
If you look at the big city from a distance, you don't see much, but when you get closer there is lots more of information to process all at once.
When there is more information than can be processed, it gets processed slower. It doesn't matter the mechanism of processing, or how is information represented. A computer with too much information to process will slow down. Time did not slow down, only the processing of information did. The premise is that, at the very fundamental level, the mass is computational.
This is an alternative to Einstein's relativity, not a critique of it. We will deduce Einstein's postulate (the constancy of speed of light), alongside the generic transformation of local clock speeds (aka 'time dilation' of special and general relativity), of which Einstein's formulas are a special case.
First steps to the computational-hypothesis
The building blocks (or the fundamental entities) of reality are computational in nature. We call such building blocks 'objects' (we will later deduce a notion of object to correspond to rest mass). An object has its own information, and can share it with other objects. It can process information. The result of processing information is the new information, and it causes the physical change (that we observe).
The objects exist in three dimensional space, and their number is finite. An object occupies some amount of space. Object processes information by computation, which is deterministic, meaning the same input always produces the same output.
The analogy here is that of a computer. A computer has information of its own that it can share with other computers. It can process it, and that makes new information. This new information causes change, for example robots performing work, which then affects the information of all computers. That's why we call it the computational-hypothesis.
Processing information takes a bit of time, otherwise everything would unravel in an instant. For this reason, the storage for information in an object must be limited. If it weren't, an object could amass infinite amount of information. This information would then take infinity to process.
Note that we're not talking about what exactly is the storage. Or how is information processed. If the Universe is computational in nature, those questions (good as they are) can be answered later. Without even knowing all that, we can deduce a lot, just by using basic tenets of information processing.
Information in the computational-hypothesis
When information is processed in an object, there must be at least three components to it. One is the very definition of an object. The second one is the previous state of processing. The third one is the current state of processing. Let's think about why this should be so.
If information is all there is, then 'an object' is information. An object is defined by its information. We call this a definition-information, or just 'definition'.
An object needs to know as much about the definition-information from all objects (including itself) as possible. Without knowing about the Universe, you can't interact with it. We call this knowledge about the Universe a state information. Plainly put, it's the state of the world, as seen by an object. It is this information that is processed to create change.
An object must keep track not only of the present state, but of the past too. Why? Without at least two states, the Universe would be stateless. If it were stateless, then there would be no memory of any kind. We know it's not like that. So we'll have the previous state and current state, to account for the past and present.
You can think that object is surrounded by a symmetrical cloud of its own information, where every sphere around an object has the object's definition spread on it that's available instantly (see Summary or the paper for why this is so). So at any object's location, there is information from other objects that's available to it, always. That's why we call it available-information. State information is then a 'snapshot' of available-information than an object can process.
Processing of previous and current state, put together in computation, creates new definition-information. By this act, an object is changed. For example, you see an object starting to move when it was at rest just a second ago. That change happened because the information (describing an object) was replaced with the new and different one. Before the new snapshot of the Universe is taken into the current state, it is squirreled away into previous state for the next computation.
Here is most of this in a simple picture on the right:
This describes a simple stateful machine. A Universe is a finite collection of stateful machines.
Slowing down of clocks
Object processes information, and this change of information is reflected elsewhere. So an object looks like it has a 'cloud' of information around it that changes in time.
When object is moving, it's visiting more locations in the same period of time (than if it's at-rest). This means more information to process (and consequently slower processing!). This is the cause of what Einstein called 'velocity time-dilation'.
Closer to other objects, there is more information per unit of volume, and so there are more changes. This too, means more information to process (and again, slower processing!). This is the cause of what Einstein called 'gravitational time-dilation'.
The above simplistic description can give you an idea why clocks slow-down when moving or when close to other objects. And more importantly, why there is a single root cause of slowing-down. If there is more information per unit of time, the processing of it slows down. This is the sole reason for the phenomenon Einstein called 'time dilation', whichever variety. Time itself did not slow down. Only processing of information slowed down. We will provide exact equations for this slowing-down. They reduce to Einstein's in special (but important) cases, such as near Earth.
We'll formalize all these intuitive conclusions and derive equations that can be reduced to Einstein's (in special cases). We will only deal with familiar concepts of processing information, and nothing else. That approach is simple and makes sense, don't you think? Because of that, no paradoxes will come about.
A preview of the central equation
If you are on pins and needles to find out what is the central equation derived in the computational-hypothesis, here it is:
This equation describes the speed of information processing of any object. This speed determines if object's physical processes (including a clock-tick) slow down or speed up. When that speed of processing reaches zero, an object cannot accelerate any more and has reached its maximum relative speed (relative to all other objects). The above equation says that speed limit depends on locale, and locale means masses, distances and speeds of other objects. It's not that simple to say what the speed limit is, except for the simplest of cases (such as near Earth for example). This speed equals to 186,000 miles/s near (and relative to) Earth (or other large masses), or for very small masses. However, a macroscopic object away from celestial bodies can accelerate to much higher speeds.
In above equation:
t1 and t2 are perceived-times (times measured by a same clock) in two different locales.
s is a constant (a reciprocal value of the minimum speed limit, also known as the 'speed of light').
vj1 are speeds of all objects in the Universe (relative to a clock) at time t1.
vj2 are speeds of all objects in the Universe (relative to a clock) at time t2.
fj1 are influences of all objects in the Universe at time t1. Basically influence of an object is higher if it is closer and has higher mass. Sum of all influences on an object is always exactly 1. Earth and Sun are a dominant influence on all of us and all our equipment. Most faraway objects have an influence of practically zero.
fj2 are influences of all objects in the Universe at time t2.
When you're near Earth, the above equation is reduced to a familiar Einstein's time-dilation formula featuring (1-v2/c2)-0.5 factor (aka gamma factor). When applied to distances, this same equation is reduced to a familiar gravitational time-dilation formula (featuring factor (1-2GM/Rc2)-0.5)). We get this without any concept of light or gravity, without geometry and without relativity (and without aether if you're curious). We also deduce the notion of local speed limit (i.e. speed of light).
We use a term of 'perceived-dilation' and 'perceived-time' because time itself doesn't change. Also, the perceived-dilation is not symmetrical, and it depends on a locale. The perceived-dilation is simply slowing down of information processing, and this eliminates paradoxes of mutual slowing-down.
There is only a single cause of perceived-dilation and above equation is the central result of the computational-hypothesis.
Einstein's equations (for what he calls 'time-dilation') are special cases of above equation, both for Special and General relativity. The 'Math' section of this web site will derive the above equation and show how Einstein's formulas become a special case of it. Read more if you're intrigued.