What we call physics is really two distinct practices; physicists themselves only think of one as "physics", I think in large part because the other part has fallen so far behind. There is mathematics - what physicists think of as physics - and philosophy.
It is pretty common today for physicists to have no idea what the math means. Partly this is because the math had gotten insanely complex, and partly because the math is more useful and so gets more attention - and also, the philosophy is hard. If you've ever taken basic physics coursework, you may be familiar with the "click", the moment the math suddenly makes sense. As the mathematics get increasingly complex, the click gets harder and harder to achieve. Hell, it wasn't until I started studying quantum physics that I understood what a partial derivative meant, and I worked with them in my coursework in college without issue - I just didn't worry about what it meant, because I didn't need to know.
Physics thus has developed a near-spiritual nature; understanding is generally limited to a superficial high-level view, or to a narrow-focused low-level view (mathematics), and the high level and the low level view don't have much bridging them. I've seen PhD physicists who get basic relativity wrong (for example, by thinking velocity, rather than acceleration, is responsible for twin paradox situations); this isn't because they don't know the math, and if you point out that they need to integrate the equation they're using they'll figure out what you meant pretty quickly, but rather because the explanations attached to the mathematics frequently get key details wrong in subtle ways.
Physics thus has developed a near-spiritual nature; understanding is generally limited to a superficial high-level view, or to a narrow-focused low-level view (mathematics), and the high level and the low level view don't have much bridging them. I've seen PhD physicists who get basic relativity wrong (for example, by thinking velocity, rather than acceleration, is responsible for twin paradox situations); this isn't because they don't know the math, and if you point out that they need to integrate the equation they're using they'll figure out what you meant pretty quickly, but rather because the explanations attached to the mathematics frequently get key details wrong in subtle ways.
I think this is pretty much the routine attitude in physics today, fostered by an attitude that seems increasingly prevalent that the universe doesn't work by human logic, and it may be unreasonable to expect humans to be able to make sense of it.
I think this view is wrong.
But the philosophy remains a hard problem. This is yet another attempt to create a philosophy of physics. It is a crackpot's attempt - it is heavily influenced by my own, to put it mildly, unconventional ideas about physics. I have a grand unified field theory here - sin(ln(x))/x^2. It's probably wrong, but the point isn't actually to get it right, the point is to get it right enough to convey a view of physics, a philosophy of physics, that I think may be helpful.
The Copernican Principle says, basically, that we aren't special, and the place we occupy in the universe isn't special either. Modern physics says we are, or rather that we do - specifically, it holds that the scale, the size, we happen to occupy holds a special place in the universe, exactly some multiple of the fundamental, special size.
This is a natural outcome of quantum physics, the most successful theory of physics since the last one. At its core is the belief in the quantum, the fundamental unit of energy. So, being arrogant enough to think I could figure out something better, I started on it. It's been a hobby since I was seven or eight, although until a couple of years ago, the ideas had too many problems. Over the last couple of years, I have had surprising-to-me success in resolving these problems, and I suddenly have a philosophical framework for physics that appears to maybe work.
Why is this important? I mean, strictly speaking, the mathematics works. It works really, really well, even if we have no idea what any of it means, and even without knowing what any of it means we've made surprising progress over the last century. It staggers me that we continue to make progress. So why does it matter?
I think it matters because philosophy gives direction to mathematics. A century ago, people made progress in physics through thought experiments; you could advance the field just by thinking carefully about it; Einstein invented the concepts of relativity, and only then set about inventing the math to describe it. That doesn't seem to be the case anymore.
So here is a radically different perspective on physics, diverging, like most crackpots, around the time of Einstein. Unlike many, I think he was right. I just don't think he took his ideas quite far enough. Specifically, I think relativity extends to scale, which is to say, large objects have the same relationships to each other as small objects have to each other. I think physics can be described purely in terms of size.
I'd say the Copernican Principle is the zeroeth law of physics. We aren't special. We don't occupy a special place in the universe. Quantum physics gives us a special place. There was an alternative - many alternatives, actually - at the time, being developed by Johannes Rhydberg. Modern physicists are probably most familiar with Rhydberg through the concept of Rhydberg Atoms, which are atoms which obey the rules Rhydberg was attempting to create; as far as I can tell, he gave up on the idea when quantum physics solved the problem. In an alternate universe in which he finished his work, I think physics would look very, very different.
The problem he was trying to solve was that of light emission; specifically, the previous models didn't describe why electrons in a given atom in a given configuration only emitted certain wavelengths of light, and suggested, in fact, that they should emit all the wavelengths of light, which also happened to be an infinite amount of energy. It was, at the time, a serious problem.
Quantum Physics solved the problem by asserting that energy had a minimum value, and that it only came in multiples of this value. Mathematically, this worked out really well, and the rest is history.
Rhydberg's solution was to suggest that light was emitted in the frequency of the resonant frequency of the electron in that configuration. As far as his work went, it worked. Unfortunately, the mathematics was really, really hard, and the problem was solved in quantum physics shortly after he had figured it out for the simplest case, a hydrogen atom.
I think he was right. And also, I think quantum physics, or at least the mathematics of it, were right. There's a concept in mathematics called isomorphy; it means, approximately, that two things are at a fundamental level the same, even if they are structured differently. I think quantum physics is isomorphic to Rhydberg's unfinished work. I'll talk more about this later, like much of this.
Fundamentally, the problem in this enterprise is that a working philosophy that addresses both relativistic and quantum scales can't just tinker around the edges; either the macroscopic philosophy has to give in it's entirety, or the microscopic, or both. I think microscopic philosophy is the one that has to give the most, and I have to not only conceptualize what, for example, a quark is in this new model, but also to be able to explain that to you, the reader. This is, given the totality of the extent to which everything is getting subtly redefined, a problem, not just in terms of explaining it, but organizing the explanation to minimize things that are obviously wrong with the explanation at each step. An explanation of neutrons requires a new understanding of what "time" in physics refers to; do I start with time? Time in turn requires an understanding of what motion now means, and motion, in turn, requires understanding what mass now means.
At each step, there are lots of dependencies left hanging, each of which is going to be a big "But what about..." for you, the reader. I am acutely aware I don't get infinite lassitude on this point; if at any point I leave too many things hanging, unexplained, I'm going to lose your interest. So the chapter on mass can't be complete; I can't really explain neutrons purely in terms of the mechanics described there. Every chapter is going to be incomplete, even the last one; I don't know everything. My ultimate goal isn't to explain the universe, to answer every question, because I don't know the questions to answer. My goal is to provide a framework; ultimately, if you're not comfortable thinking in terms of the framework, if you aren't willing to try to figure out an answer for yourself, none of this will be of any use to you.
Discussing my crackpot grand unified field equation - which basically amounts toreplacing G in General Relativity with sin(ln(x)), although I think since it is a tensor it is more complicated than I am making it sound - the exact equation doesn't matter too much. This framework is designed around the requirements I used to develop that equation, the equation is entirely secondary to those requirements.
The requirements aren't complicated. First, the equation must be relativistic - in particular, it must pertain to the shape of spacetime, rather than to additional phenomena. Second, it must describe a recursive or fractal geometry. And third, the geometry should reflect an alternating series of attractive and repulsive phases.
There are reasons for all three requirements, of course. The first is necessary for compatibility with relativity itself. The second is necessary to comply with Copernican non-specialness. And the third requirement is necessary to ensure that the spacetime metric is conserved - the conservation law which I believe exists beneath all conservation laws, whose symmetry is, I believe, on the axis of scale itself. As above, so below.
My earliest version, as a teenager, was literally just an infinite nested series of forces with alternating polarity and an ever-increasing rate of decay. Later I realized this simplified to a sine wave with a decaying period and amplitude, and had something like sin(1/x^2), which works great, but only for x<1.
Sin(ln(x)) has stuck with me since I discovered it, in large part owing to it's possibly coincidental characteristic shape looking an awful lot like the characteristic shape of the strong (and weak) nuclear force, the force I think we, from our perspective, have the most insight into, seeing the fullest range of. Gravity is a good second contender, but I don't have the skill to tease out what the shape of gravity would look like without dark matter being used to fill in the apparent holes.
The important thing here isn't the equation, it is the requirements, because they, not the equation, are what this approach to understanding physics is based upon. Everything here works regardless of the actual equation, so long as the requirements themselves are a valid description of the universe. I think they are.
I'd say the Copernican Principle is the zeroeth law of physics. We aren't special. We don't occupy a special place in the universe. Quantum physics gives us a special place. There was an alternative - many alternatives, actually - at the time, being developed by Johannes Rhydberg. Modern physicists are probably most familiar with Rhydberg through the concept of Rhydberg Atoms, which are atoms which obey the rules Rhydberg was attempting to create; as far as I can tell, he gave up on the idea when quantum physics solved the problem. In an alternate universe in which he finished his work, I think physics would look very, very different.
The problem he was trying to solve was that of light emission; specifically, the previous models didn't describe why electrons in a given atom in a given configuration only emitted certain wavelengths of light, and suggested, in fact, that they should emit all the wavelengths of light, which also happened to be an infinite amount of energy. It was, at the time, a serious problem.
Quantum Physics solved the problem by asserting that energy had a minimum value, and that it only came in multiples of this value. Mathematically, this worked out really well, and the rest is history.
Rhydberg's solution was to suggest that light was emitted in the frequency of the resonant frequency of the electron in that configuration. As far as his work went, it worked. Unfortunately, the mathematics was really, really hard, and the problem was solved in quantum physics shortly after he had figured it out for the simplest case, a hydrogen atom.
I think he was right. And also, I think quantum physics, or at least the mathematics of it, were right. There's a concept in mathematics called isomorphy; it means, approximately, that two things are at a fundamental level the same, even if they are structured differently. I think quantum physics is isomorphic to Rhydberg's unfinished work. I'll talk more about this later, like much of this.
Fundamentally, the problem in this enterprise is that a working philosophy that addresses both relativistic and quantum scales can't just tinker around the edges; either the macroscopic philosophy has to give in it's entirety, or the microscopic, or both. I think microscopic philosophy is the one that has to give the most, and I have to not only conceptualize what, for example, a quark is in this new model, but also to be able to explain that to you, the reader. This is, given the totality of the extent to which everything is getting subtly redefined, a problem, not just in terms of explaining it, but organizing the explanation to minimize things that are obviously wrong with the explanation at each step. An explanation of neutrons requires a new understanding of what "time" in physics refers to; do I start with time? Time in turn requires an understanding of what motion now means, and motion, in turn, requires understanding what mass now means.
At each step, there are lots of dependencies left hanging, each of which is going to be a big "But what about..." for you, the reader. I am acutely aware I don't get infinite lassitude on this point; if at any point I leave too many things hanging, unexplained, I'm going to lose your interest. So the chapter on mass can't be complete; I can't really explain neutrons purely in terms of the mechanics described there. Every chapter is going to be incomplete, even the last one; I don't know everything. My ultimate goal isn't to explain the universe, to answer every question, because I don't know the questions to answer. My goal is to provide a framework; ultimately, if you're not comfortable thinking in terms of the framework, if you aren't willing to try to figure out an answer for yourself, none of this will be of any use to you.
Discussing my crackpot grand unified field equation - which basically amounts toreplacing G in General Relativity with sin(ln(x)), although I think since it is a tensor it is more complicated than I am making it sound - the exact equation doesn't matter too much. This framework is designed around the requirements I used to develop that equation, the equation is entirely secondary to those requirements.
The requirements aren't complicated. First, the equation must be relativistic - in particular, it must pertain to the shape of spacetime, rather than to additional phenomena. Second, it must describe a recursive or fractal geometry. And third, the geometry should reflect an alternating series of attractive and repulsive phases.
There are reasons for all three requirements, of course. The first is necessary for compatibility with relativity itself. The second is necessary to comply with Copernican non-specialness. And the third requirement is necessary to ensure that the spacetime metric is conserved - the conservation law which I believe exists beneath all conservation laws, whose symmetry is, I believe, on the axis of scale itself. As above, so below.
My earliest version, as a teenager, was literally just an infinite nested series of forces with alternating polarity and an ever-increasing rate of decay. Later I realized this simplified to a sine wave with a decaying period and amplitude, and had something like sin(1/x^2), which works great, but only for x<1.
Sin(ln(x)) has stuck with me since I discovered it, in large part owing to it's possibly coincidental characteristic shape looking an awful lot like the characteristic shape of the strong (and weak) nuclear force, the force I think we, from our perspective, have the most insight into, seeing the fullest range of. Gravity is a good second contender, but I don't have the skill to tease out what the shape of gravity would look like without dark matter being used to fill in the apparent holes.
The important thing here isn't the equation, it is the requirements, because they, not the equation, are what this approach to understanding physics is based upon. Everything here works regardless of the actual equation, so long as the requirements themselves are a valid description of the universe. I think they are.
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