Tuesday, November 2, 2010

Smallest of the Small

Disclaimer: This article is merely intended to be a speculative thought experiment, and shouldn't be mistaken for an actual research paper (in case using Wikipedia as my primary reference didn't already make that clear).

Throughout history, speculation on the fundamental building blocks of matter have been rampant within scientific curiosity. As early as 350-450 BCE, it was believed that all matter was made up of building blocks of four basic elements, Earth, Air, Fire, and Water. It was speculated that all matter could be broken down into these constituent 'elements'. Even today, though they may be a lot more elements listed on the periodic table, the idea is essentially unchanged. Matter consists of massive groups of molecules, which is subsequently made up of varying types of atoms (elements), which in turn consist of neutrons, elections, and protons, which are further subdivided into even more sub-subatomic particles, for example quarks and other types of leptons.

As of current understanding, quarks and leptons are the most elementary form of fermion (traditional matter) particles known. For a particle to truly have no substructure, it must be considered to be the most fundamental particle, the one from which all other matter is built.

It is only natural to ask the question, are these the most fundamental particles or do they have substructure? Quarks are not identical after all, they have different masses, charges, so is it not unreasonable to concluded they might be composed of yet smaller blocks? There have been many ideas on the existence of 'preons', particles considered to be building blocks of quarks. For our purposes here, we are going to indeed make the assumption that quarks do indeed have a yet-undefined substructure. Furthermore, what ever this substructure is, let's assume that it can furthermore broken into an n-particle limit, that is, subdivided and subdivided to a finite level of substructure. The question then becomes, what is the last level? What is the smallest of the small?

We are going to step into a thought experiment, and assume this fundamental particle exists, which we will simply refer to as Particle X. What can we infer about this particle? Assuming that it exists, a few properties seem to be logical extensions of it: 1) All of the particles are identical but unique; 2) They are infinitesimally small, most likely on the order of Planck Length; 3) They exist for only infinitesimal periods in time;

That is, the smallest particle would also be related to the smallest units of time, size, mass, as well as being zero-dimensional. Zero-dimensional you say? I know that can be hard to imagine, given that we normally experience a three dimensional physical universe. If it helps, here's how I visualize N-dimensions (borrowed heavily from arrays in my main vocation, with is computer science). First, imagine a single point, alone, in a vast void. Since there exists no other points, there's no reference with which to differentiate it from another, therefore if we were to try and give coordinates for it, there wouldn't be any. This is the 0th dimension. Now, imagine that we take an infinite number of those points and arrange them in a line. Now, we can refer to a specific point by giving a single coordinate, X if you like, it's position in the line. Using a single coordinate to reference it's position, this is the 1st dimension. Now, imagine that we take an infinite number of those lines and lay them parallel to each other, forming a plane. To refer to a specific point, we need two coordinates, the line it's on (Y), and the particle in that line (X). This is the 2nd dimension. Then, we take take an infinite number of these planes and stack them on top of one another, creating a cube of sorts, using a third coordinate (Z) to reference a single point, basically three dimensions. Then, we could take an infinite number of of these “cubes” and lay them “besides” each other, now using a 4th coordinate to differentiate between the various cubes, creating a forth spatial dimension, and continuing so on in that fashion for any number of dimensions we want.

Of course, an obvious contraction seems to rouse it's head. We assume that all of the particles would have to be identical, since, if two fundamental particles were different, it would imply that they have a substructure which differentiates them, and we've already said that our particle X is the last level. But if they are all identical, how could they possibly come together to form different higher level particles? That is, they would have to be both identical and unique, which doesn't seem correct.

There are two other aspects of Particle X that haven't been considered yet, namely it's location, and it's motion, or amount of energy. Gauge bosons are currently considered elementary bosons, or units of energy. There may in fact also be a fundamental unit of energy, in essence, possibly even grand unification energy, in analogy with the fundamental particle. Here is the basic model as I'm envisioning it: all fundamental particles are physically identical, for each particle is an associated unit of a unique amount of energy. It is the differing amount of energy which separates different particles. This is where we tie in another necessary smallest, size. What I propose is that the energy level of each particle is dependent on it's location in space-time, and vice versa. My speculation is that there could be a one-to-one relationship between a particle's location in time and space, and the amount of energy it has. This relationship isn't all that much of a stretch. An object will move in a vacuum so long as it has kinetic energy and nothing to interfere with that motion. If something collides with it, or slows it motion, its kinetic energy will lessen and become potential energy.

Consider the Big Bang. We might now think of it as an element of Particle X, with the highest possible energy level (the first location). As time went on, the energy level decreased. This corresponded to the initial expansion of the universe. For a useful analogy, think of cell division. The first Particle X's energy level decreased, creating more particle's out of one, whose level decayed into new particles, and so on. Each new 'generation' is associated with a unique instant in time. The individual energy level of each Particle X is different. That is, each moment of time is 'frozen' where each particle has a unique energy level. But if we were to examine a particle from our point of view, it would appear as though the energy of it was changing over time. The change in time however is relative, if we were to examine two particles, we would notice a consistent change in their energy over time (it should be decreasing), however the two particles would also have a different energy due to their location in space. The difference in the spacial component of their energy would remain the same (assuming they were stationary with respect to one another), relative to their change in temporal energy. So as the universe moves forward in time, the energy decreases, but stays the same relative to other particles in that instant.

So the property that differentiates one particle from another is it's location, and subsequently it's energy. If that were the case, what would allow groups of this particle to differentiate substructures or high structure particles that they form? Since the only property unique to the particle is its location or energy, let's infer that is the property we seek. In essence, it's possible that the differentiating factor is the difference in the collective energy of one group of Particle X's compared to another group. Since the difference in the energy level of two particles stays the same relative to one another over time, this would allow higher level particles to exist, over time. As an analogy, imagine we could take the average of the energy level of a group of Particle X. A certain group of particles may have a mean energy level, different from the mean energy level of another group of particles. For example, one mean may correspond to an 'up' quark, whereas another mean may correspond to a 'down' quark. Given this model, it is possible that all sub atomic particles develop in this way, which is how the most basic substructures are formed.

Another analogy for the location-energy relationship is that of electrons in an atom. It thought that the distance an electron is from the nucleus of an atom is directly dependent on it's energy level (see Electron Shells). That is, the more energy it has, the further from the nucleus it exists. It has also been conjectured, if not proven, that electrons may jump orbits without even moving through the space in between, which alone has spectacular implications.

So let's continue to extend this idea to our Particle X. The 'nucleus' in this case would be the center/beginning of the universe in space time, the big bang. The particles are like the electrons moving around it. Though in this case, it seems it may be more logical to have the situation reversed. The big bang was a massive amount of energy, so in order for particles further from it to have higher energy, it seems like we would be violating the law of conservation of energy. So instead let's reverse it: units of the particle have higher energy as we wind the 'universe's film' (like a movie film) backwards to the big bang, which was a single unit of the particle with the total amount of energy in the universe. Then as the universe expanded, the energy was divided among newly formed particles, which would still be continuing today. But to what end?

The ultimate fate of the universe would then seem to depend on these particles, whether or not the universe eventually contracts or expands indefinitely. Three outcomes are theorized, either 1) the universe doesn't stop expanding, and eventually the thermodynamic energy is equally divided in the universe (heat death); 2) The universe eventually contracts back to a single point; 3) The universe stops expanding but doesn't contract. It may be simply that the “evening out” of fundamental energy as I've describe here works out be the heat death described in the model.

So what happens when I move my hand though the air? Or more precisely, when any sort of body moves through space? In the model as I've described it, every Particle X should have a unique, fixed energy level. Over time, it appears to us that the particle's energy is changing, but staying the same relative to its spacial position. So how does something move, in standard kinematics, given this model? Imagine a ball being thrown, and let's pretend that we have an ultimate high resolution camera with which can take a photo down to the level of Particle X once every Planck second. If we were to analyze each photo, what would see happening to the energy level of each Particle X in the ball, as well as the air it is displacing? First, lets just consider the front end of the ball, without the air. Would our fundamental particle still be present in a vacuum? I would have to venture a “yes” guess, at the very least in the form of virtual particles. Indeed, the fundamental Particle X should permeate all of existence, there shouldn't be anywhere which can exist without it at a corresponding energy level. So either way, with the air or not, the particles in the ball should be displacing other particles just the same.

The balls moves through the air, but the particles can't move though one another. Obviously the particles in the air molecules are be displaced by the particles in the ball's molecules. Since location is depended on energy level, by changing the ball's location, the energy level of its particles must also be changing as a result of the movement. The Particle X's of the ball would either give up or accept energy depending on the direction of the motion (spatially, away from the universe origin point), but of course the precise energy level would always be decreasing, unless the ball was moving backwards in time. Energy level in the ball's particles are thus being swapped particle by particle with the energy of the air molecules it's moving through. Thus, any movement can be generalized as a particle by particle swapping this of fundamental energy among various Particle X's. This could also explain why there is a universal 'curtain' speed limit, for example if a Particle X took such an amount of time to swap an amount of energy with it's neighboring particle (in order to move), perhaps at the speed of light is the fastest this swapping could occur.

Keeping in mind that the preceding argument was all just a speculative thought experiment, if any of it were real, might it be at all useful to us? Assuming this idea is correct, at least in principle it could be useful, but the actual engineering would be extraordinarily complex, if at all possible. The idea is to create a device capable of artificially changing the energy of a group of these particles. With enough energy, we would be able to move an object to any point in space-time, instantly. We wouldn't actually be moving faster then light, in terms of classical mechanics, the mass was motionless the whole time, but rather it is more like a leap, much like the electron jumping orbits, without going through the space in between. Sound like a useful form of transportation? Additionally, we would be able to change the molecular structure of matter at a fundamental level, the ultimate recycling, since the substructure of a complex particle is just the differencing energy level. Whether or not the technology could practically exist to change the energy level of the particle is unknown, but there would be no shortage of applications. We change the energy of a particle all the time by simply moving an object, so what we want to be able to do is the opposite.

Though it also raises the question, if we could artificially change the location of a mass by changing its energy, what would happen to the mass (particles) that are already in the position where we placed the mass? We know that the total amount of energy is constant, so the most logical conclusion seems to be that, for instance, the energy needed to be added to a mass to move it would be directly subtracted from the energy of the place we are relocating it. Since location is dependent on that energy, whatever was previously occupying that point in space time would then take the place of the original object we wanted to move, in effect they would be swapped, without disturbing anything in between. For an example, imagine two cubes, A and B. We know the relative difference in the energy between them, so we know how much energy needs to be added to (or subtracted from) A to give it the location of B. When we apply it, the cubes would swap places, with the A cube taking the place of the B cube, and vice versa.

In conclusion, the 'fundamental particle' we have conjectured may actually be something already conceived, superstrings. Likewise, the energy level we have attributed to our particle may be the vibration of these strings, which is driven by what we have come to call grand unification energy. Let me reiterate, this is all just speculation. There is no experimental evidence for my ideas at the present time, though I feel this is a truly fascinating topic to explore. I've done my best to properly infer my conclusions logically, and hope you enjoyed my take on it. By all means, feel free to leave a comment and share your own thoughts as well.