If mass is a wave, what is it a wave in? Space itself. We can call it curvature, but I think it is more helpful to think of it as the density of space itself, which is to say, it is a change in the distance between two points. It is very difficult to think in terms of distance itself being variable, because in order to make comparisons, you must make comparisons against an imaginary "flat" space, either in terms of curvature or density. This change in distance is why it looks more like sin(ln(x)) than sin(x), because x, that is, the distance, isn't flat; all the mass around it is simultaneously changing the distances involved.
All mass in this framework has this property, but not all mass is identical. There are, broadly, two kinds of relevant mass; composite mass, which is to say, something like a proton, made up of even more smaller pieces; and unified mass, like an electron, which is only a single wave. Composite mass has more interesting properties than unified mass, most specifically that the sum of the waves can have multiple points in a given stretch of space where the magnitude of the wave is at zero, or close to it. Why does this matter? Because zeroes are where interesting things happen.
When space is becoming denser as you get closer - that is, when the sine wave has a positive value - it becomes an apparently attractive force. When it is becoming less dense - when the sine wave has a negative value - it becomes an apparently repulsive force. This is the same principle as relativity - indeed, this model is a relativistic model, although I may often, for purposes of conveying ideas, talk as if it weren't. Let's talk about relativity for a moment.
In relativity, the variable density of spacetime is often called "curvature". I'm sure you have seen the bowl-shaped model of gravity; this often confuses people because it feels like the orientation of gravity changes from pulling towards mass, to pulling "down" in the bowl. Curvature, while mathematically elegant, is also misleading. The important thing about the bowl shape isn't that things fall down into the bowl, it is that the bowl has greater surface area than a flat circle. If you were to draw, say, triangles of a given size, you could draw more triangles on a bowl than a circle. So how does gravity in relativity really work? Well, to understand, think of a spaceship orbiting the planet.
Because space is getting denser as you get closer to the origin of the wave - the planet, in this case - we arrive at an interesting situation in which the near side of the spaceship is traversing more space than the far side, if it were to go in a straight line. Because the entire ship is traveling the same speed, this can't be the case - they must traverse the same amount of space. But the same amount of space, in this case, is "shorter", relative to an imaginary flat space, on one side than the other. This pulls the ship towards the planet.
But wait, you say, that makes sense when the spaceship is orbiting, but why do things fall when they aren't moving? The answer is that they are moving - through time. It is exactly the same behavior, it's just really hard for most people to think in four dimensional terms, so it is easier to think in terms of the spaceship orbiting, and then intuit that movement through time provokes a similar effect. We'll discuss this in more detail in the chapter on time.
Attractive forces and repulsive forces both use the same principle - the near side and far side exhibit different distances. This has some really interesting characteristics that I won't go into detail about here, but a thought experiment for you to consider is to think about what this means for, for example, the moon. What if the moon had its own rotation? What would happen, as the rotation is going "faster" on one side than the other?
Back to zeroes. There are, broadly, two types of zeroes to consider. When the sine wave is rising, and when it is falling. When it is rising, the nearer side of the zero is repulsive, and the far side is attractive. Everything will tend to fall into the zero boundary and probably oscillate slightly, but generally stay there. The other kind of zero, when the sine wave is falling, has an attractive force on the near side, and a repulsive force on the far. Things will tend to fall away from this zero boundary. One boundary is stable, one is unstable. I think of these as spheres of stable orbit, and spheres of unstable orbit. Really it is the stable orbits that are most interesting, because matter will tend to congregate there. Like electrons.
Now, without a discussion of time, I can't really give a full explanation of behavior here, and the explanation I have in mind for time is still later, but let's try anyways.
First, I am going to assume that electrons are antimatter. This gets into the time thing, for reasons physicists should already know, but we're going to tiptoe past that for now. All this means for our current purposes is that electrons are repulsive where protons are attractive, and vice versa - their sine waves are upside down. So at the distance from a proton at which electrons occupy a stable orbit, the electron's own wave is repulsive; the electron is in a stable orbit, but the proton is in an unstable one. Since the proton is so much bigger than the electron this doesn't end up matter much for the proton for our purposes here, but it matters a lot for other electrons - the orbit gets a lot less stable when occupied by an electron. Future electrons that happen to fall into our proton's orbit will be in a much less tenable position, at least as long as there is only one proton there. If there are two, we get an interesting new effect: There are now two stable orbits, because each proton's stable zone will be originating from a different point. Imagine two spheres which largely overlap; more, they reinforce, because the attractive force further out from the nucleus of the atom is that much stronger. Thus, we can now fit two electrons there. Technically, four; for now, imagine the extra two occupy opposing positions on the far sides of the spheres, which while not quite accurate, is good enough for now.
As we add more protons, the overlapping spheres get more and more complex, and eventually we reach a point where some of the spheres aren't quite stable without more electrons in the nearer spheres pushing outward. This corresponds to metals, in the periodic table. As we continue to add more protons this happens again, then again, each time corresponding to another group of metals.
What about neutrons? Well, this gets into time again. We'll discuss them in that chapter. For now, imagine an electron is suspended in a proton, which is a composite particle made up of smaller particles and thus has room. Again, not quite accurate, but close enough for now. This electron, with its wave canceling out part of the proton's wave, makes for an orbit that isn't strong enough to support an electron - and again, this isn't accurate, but is close enough to move forward.
I think you can see how a simple sin(ln(x))/x^2 could get us to a fairly simple atom at this point. Left unaddressed are the smaller particle which make up the proton; we'll discuss quarks, and leptons other than electrons, in a later chapter. For now, let's see what happens when we run the universe in fast forward in this model, because it is illustrative of how the model works on a larger scale.
I'm sure you have heard of black holes. They still exist in this model, and have largely the same behavior - with one critical difference. The attractive force that forms them, gravity, isn't alone. Farther out from the origin than gravity is another repulsive force, which we call a number of names; I'll call it the cosmological constant, because that's what Einstein called it.
In conventional physics, I believe the current consensus is that the cosmological constant is just that - a constant. In this model, however, it is a force like gravity, or rather, just another part of the same wave of which gravity is one part. Our repulsive force is really far away right now, but the stronger gravity gets, remembering that gravity is density of space, the closer, from an outside perspective, that repulsive force gets, because gravity increasing means there is a greater and greater distance between the origin and a given flat-space point. And the stronger gravity gets, because that repulsive force is part of the same wave, the stronger that force gets.
Eventually, if you fast forward through a black hole swallowing matter, the repulsive force gets so strong, nothing else can get in, not even light. We get a white hole. We'll discuss the mechanics of white holes later, but for now, it is enough to make one observation: The white hole looks like a really, really big electron (or a positron, it's regular matter counterpart).
Which is the pattern of the whole; made up of smaller pieces, all following a simple rule, sin(ln(x)). We'll come back to this idea a few times, fleshing out the universe a little more each time. But this should begin to give an idea of what the model looks like.
For now, I'm going to turn to a part of the model that I think works exceptionally well; the translation of energy into mass. This model only really has spacetime; there's no mass, there's no energy, just variations in the density of spacetime. Light is a variation in the density of spacetime; mass is a variation in the density of spacetime; even kinetic energy is a variation in the density of spacetime, which I'll get to in more detail in a bit. But let's use light as an example. Light is a moving variation in the density of spacetime, and specifically, it is an "update" to the mass wave itself, as its origin moves, and that change propagates away. Concentrate enough light in an area, and the increased (or decreased) density of spacetime creates a microscopic region of space which is, in effect, a tiny black (or white) hole, an area of spacetime in which light either can't enter - a white hole - or can't escape - a black hole. Either is self-sustaining, once created; a white hole, I think, will end up being antimatter at the scales we are considering, and a black hole will end up being matter. There's some stuff involving time here, relating to why zero-density white holes are probably self-sustaining as opposed to evaporating, but this is an area I won't return to here, because I don't understand my conceptualization well enough to translate it into language. I might understand it well enough to explain in a few years, assuming I don't drop it out of the model entirely.
In relativity, the variable density of spacetime is often called "curvature". I'm sure you have seen the bowl-shaped model of gravity; this often confuses people because it feels like the orientation of gravity changes from pulling towards mass, to pulling "down" in the bowl. Curvature, while mathematically elegant, is also misleading. The important thing about the bowl shape isn't that things fall down into the bowl, it is that the bowl has greater surface area than a flat circle. If you were to draw, say, triangles of a given size, you could draw more triangles on a bowl than a circle. So how does gravity in relativity really work? Well, to understand, think of a spaceship orbiting the planet.
Because space is getting denser as you get closer to the origin of the wave - the planet, in this case - we arrive at an interesting situation in which the near side of the spaceship is traversing more space than the far side, if it were to go in a straight line. Because the entire ship is traveling the same speed, this can't be the case - they must traverse the same amount of space. But the same amount of space, in this case, is "shorter", relative to an imaginary flat space, on one side than the other. This pulls the ship towards the planet.
But wait, you say, that makes sense when the spaceship is orbiting, but why do things fall when they aren't moving? The answer is that they are moving - through time. It is exactly the same behavior, it's just really hard for most people to think in four dimensional terms, so it is easier to think in terms of the spaceship orbiting, and then intuit that movement through time provokes a similar effect. We'll discuss this in more detail in the chapter on time.
Attractive forces and repulsive forces both use the same principle - the near side and far side exhibit different distances. This has some really interesting characteristics that I won't go into detail about here, but a thought experiment for you to consider is to think about what this means for, for example, the moon. What if the moon had its own rotation? What would happen, as the rotation is going "faster" on one side than the other?
Back to zeroes. There are, broadly, two types of zeroes to consider. When the sine wave is rising, and when it is falling. When it is rising, the nearer side of the zero is repulsive, and the far side is attractive. Everything will tend to fall into the zero boundary and probably oscillate slightly, but generally stay there. The other kind of zero, when the sine wave is falling, has an attractive force on the near side, and a repulsive force on the far. Things will tend to fall away from this zero boundary. One boundary is stable, one is unstable. I think of these as spheres of stable orbit, and spheres of unstable orbit. Really it is the stable orbits that are most interesting, because matter will tend to congregate there. Like electrons.
Now, without a discussion of time, I can't really give a full explanation of behavior here, and the explanation I have in mind for time is still later, but let's try anyways.
First, I am going to assume that electrons are antimatter. This gets into the time thing, for reasons physicists should already know, but we're going to tiptoe past that for now. All this means for our current purposes is that electrons are repulsive where protons are attractive, and vice versa - their sine waves are upside down. So at the distance from a proton at which electrons occupy a stable orbit, the electron's own wave is repulsive; the electron is in a stable orbit, but the proton is in an unstable one. Since the proton is so much bigger than the electron this doesn't end up matter much for the proton for our purposes here, but it matters a lot for other electrons - the orbit gets a lot less stable when occupied by an electron. Future electrons that happen to fall into our proton's orbit will be in a much less tenable position, at least as long as there is only one proton there. If there are two, we get an interesting new effect: There are now two stable orbits, because each proton's stable zone will be originating from a different point. Imagine two spheres which largely overlap; more, they reinforce, because the attractive force further out from the nucleus of the atom is that much stronger. Thus, we can now fit two electrons there. Technically, four; for now, imagine the extra two occupy opposing positions on the far sides of the spheres, which while not quite accurate, is good enough for now.
As we add more protons, the overlapping spheres get more and more complex, and eventually we reach a point where some of the spheres aren't quite stable without more electrons in the nearer spheres pushing outward. This corresponds to metals, in the periodic table. As we continue to add more protons this happens again, then again, each time corresponding to another group of metals.
What about neutrons? Well, this gets into time again. We'll discuss them in that chapter. For now, imagine an electron is suspended in a proton, which is a composite particle made up of smaller particles and thus has room. Again, not quite accurate, but close enough for now. This electron, with its wave canceling out part of the proton's wave, makes for an orbit that isn't strong enough to support an electron - and again, this isn't accurate, but is close enough to move forward.
I think you can see how a simple sin(ln(x))/x^2 could get us to a fairly simple atom at this point. Left unaddressed are the smaller particle which make up the proton; we'll discuss quarks, and leptons other than electrons, in a later chapter. For now, let's see what happens when we run the universe in fast forward in this model, because it is illustrative of how the model works on a larger scale.
I'm sure you have heard of black holes. They still exist in this model, and have largely the same behavior - with one critical difference. The attractive force that forms them, gravity, isn't alone. Farther out from the origin than gravity is another repulsive force, which we call a number of names; I'll call it the cosmological constant, because that's what Einstein called it.
In conventional physics, I believe the current consensus is that the cosmological constant is just that - a constant. In this model, however, it is a force like gravity, or rather, just another part of the same wave of which gravity is one part. Our repulsive force is really far away right now, but the stronger gravity gets, remembering that gravity is density of space, the closer, from an outside perspective, that repulsive force gets, because gravity increasing means there is a greater and greater distance between the origin and a given flat-space point. And the stronger gravity gets, because that repulsive force is part of the same wave, the stronger that force gets.
Eventually, if you fast forward through a black hole swallowing matter, the repulsive force gets so strong, nothing else can get in, not even light. We get a white hole. We'll discuss the mechanics of white holes later, but for now, it is enough to make one observation: The white hole looks like a really, really big electron (or a positron, it's regular matter counterpart).
Which is the pattern of the whole; made up of smaller pieces, all following a simple rule, sin(ln(x)). We'll come back to this idea a few times, fleshing out the universe a little more each time. But this should begin to give an idea of what the model looks like.
For now, I'm going to turn to a part of the model that I think works exceptionally well; the translation of energy into mass. This model only really has spacetime; there's no mass, there's no energy, just variations in the density of spacetime. Light is a variation in the density of spacetime; mass is a variation in the density of spacetime; even kinetic energy is a variation in the density of spacetime, which I'll get to in more detail in a bit. But let's use light as an example. Light is a moving variation in the density of spacetime, and specifically, it is an "update" to the mass wave itself, as its origin moves, and that change propagates away. Concentrate enough light in an area, and the increased (or decreased) density of spacetime creates a microscopic region of space which is, in effect, a tiny black (or white) hole, an area of spacetime in which light either can't enter - a white hole - or can't escape - a black hole. Either is self-sustaining, once created; a white hole, I think, will end up being antimatter at the scales we are considering, and a black hole will end up being matter. There's some stuff involving time here, relating to why zero-density white holes are probably self-sustaining as opposed to evaporating, but this is an area I won't return to here, because I don't understand my conceptualization well enough to translate it into language. I might understand it well enough to explain in a few years, assuming I don't drop it out of the model entirely.
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