What Happens When Point-Like Particles Interact?

[glengarry]

I'm not sure I understand what you are describing. You're not thinking about the wavefunction on a 3 sphere, are you? The wave function for N particles exists in a space with 3N dimensions, so it doesn't map into the space of spacetime unless you're only talking about one particle.

You must understand this one basic point, or nothing else will make any sense:

Schrodinger equation = Laplace's equation:

http://en.wikipedia.org/wiki/Laplace's_equation

If you do not understand me when I say that all we are looking for is a simple, harmonic standing-wave solution to the Laplace equation (i.e. we can understand this as a pure "eigenstate"), then the entire logical foundation of this entire theory falls apart.

In other words, wavefunctions, qua themselves, have nothing whatever to do with particles. All that a wavefunction does is to tell its infinitesimal spaces how to oscillate. This is easy to observe in the 1 and 2 dimensional cases when we look at harmonically oscillating guitar strings and drumpads. But in order to construct our own 3D universe, it is necessary that we solve this equation for all three dimensions. But the problem here is that we cannot visualize the infinitesimal spaces (tiny volumes in this instance) as extending into another dimension, as with the 1 dimensional case when we see the parts of the wave extending into the second dimension. So, for this oscillating extension to make sense, we have to "bend" the flat 3D space so that it becomes a superficial manifold within a logical fourth dimension.

Now, the "typical" manifestations of the Schrodinger equation are just this very same principle, but only applied to the trajectories of "material points." However, this entire picture is simply the very same thing as the classical, Newtonian model wherein bodies move on simple, parabolic paths through space. The only difference is that it is now the Schrodinger/Laplace equation that governs the movements of particles rather than Newton's classical equations of motion.

It is vital to understand that the only thing that conceptually distinguishes quantum theory from classical kinematics is the idea of harmonically oscillating, space-filling standing waves. If we simply want to "interpret" this notion so that it degenerates back into a kind of "weird" classical model, then that is our right, but we will have ultimately gained nothing from it.

So my project is to get you guys to see the folly in this kind of "interpretive" behaviour, and just start to embrace the utter beauty and simplicity of the things that we call "standing waves." And once we do this, then we can start to realize that anything is possible in terms of coming up with "manifestly believable" models of physical reality. So then, if you can go back and reread what I have already written in terms of the paradigm of "pure waves" rather than "crazily moving particles," then you will be able to start to visualize in your own head what the mathematical object that is known as 'U' is telling you.

 

[glengarry]

This assumption is false. First of all, wave amplitude has a physical meaning in QM, namely probability or particle count if you wish.

The notions of "probability" and of "physical meaning" can only be equated in the most logically tortured of ways. This kind of logical torture is precisely the kind of thing that Einstein spent the entire post-relativity part of his career trying to eradicate. So, you can either join with me and Einstein and whoever else chooses to come along, or you can remain stuck in neutral by "interpreting" the amplitudes of wave equations to be synonymous with levels of chance.

 

[glengarry]

Okay, I now want to dig a little deeper into the reason for turning a flat, bounded harmonically oscillating space into a spherical body. The first point is an easy one: that is simply that we want to think of an interior space in terms a superficial manifold, so that the parts of the wave have room in which to extend.

The other points are related to the possibility of developing a manifestly believable model for a physical universe. I've already discussed the idea that, for a three-dimensional wave, the act of turning it into a sphere will cause distortions in the spatial elements that are nearer to the non-oscillating boundary point, and since there are two dimensions that are getting smaller, the spaces will be compressed in terms of a second order (exponent 2) function. So, this constantly increasing compression will be able to "overcome" the linearly decreasing amplitude, to the point where even those waves with the smallest of amplitudes can be "sensed."

The final point might be the most important, because it is the only way in which we can get all possible forms of standing waves (i.e. any "eigenstates" of the Laplace eqn.) to have a central node (point of zero amplitude) rather than a central antinode (point of maximum amplitude). So, let us consider the simplest standing wave solution that we can imagine, which is a linear, oscillating string that has only a single antinode at its midpoint. Let us now think of how the second law of thermodynamics applies to this situation by way of thinking of "heavy bodies" that are represented as points on this string (not 'of' the string, but 'on' it). Those bodies that are not perfectly situated at the antinode will simply start falling to one side or another. This is obviously not how we understand gravity fields or atomic nuclei to "work."

So what we need to do, then, is to try to find a way to turn the standing wave "inside out" so that the "stable," nodal edges are now situated at a central location. And this is what the "spherical wrapping procedure" is all about. So, once we bend the string back into itself, there will then exist an always stable, central location into which surrounding bodies can fall.

And this is another big reason why the standing wave theories of de Broglie and Schrodinger could never get off of the ground. That is, the simplest (and probably most common) of all such waves is the one that has a central antinode, and there is no way to think of this situation as being applicable to a paradigm of mutual attraction. But by way of turning the boundary of the wave into a central location, there is indeed now a stable point of equilibrium towards which the antinodes of surrounding waveforms can fall.

 

[haael]

The notions of "probability" and of "physical meaning" can only be equated in the most logically tortured of ways. This kind of logical torture is precisely the kind of thing that Einstein spent the entire post-relativity part of his career trying to eradicate. So, you can either join with me and Einstein and whoever else chooses to come along, or you can remain stuck in neutral by "interpreting" the amplitudes of wave equations to be synonymous with levels of chance.

Dear, I don't understand what you are talking about.

You have two parameters: frequency and amplitude. Let's consider a photon. Frequency is it's color, amplitude is the intensity of light. In normal world, these parameters are unrelated. You can have weak red beam, strong read beam, weak blue beam and strong blue beam.
Now you come up with your equation that amplitude is an inverse of frequency. So you can only have strong red beam and weak blue beam. Congratulations, you've just assassinated Quantum Mechanics.

Also, you consider gravitation and space bending. In normal world, the more mass you have, the stronger it attracts, so the stronger space is bent. You made identification of matter waves and space bending, so I guess that this "natural wave equation" holds for gravitation as well. Now, in your theory the more mass (frequency) you have, the smaller amplitude is, and space is more flat. So around a huge mass, space would be almost flat, while vacuum would be enormously curved.

Neither QM nor GR comes from your "theory" as a limit. The assumption that frequency * amplitude = const is just a contradiction.

 

[SpectraCat]

You must understand this one basic point, or nothing else will make any sense:

Schrodinger equation = Laplace's equation:

This is simply wrong as far as I can see. First of all, when you talk about Schodinger's equation, you need to specify the time-dependent (TDSE) or time-independent (TISE) version. When you just say "Schrodinger's equation", it tends to imply the time-dependent version, which is the more general case. The time-independent version does I guess bear some resemblance to the Laplace equation, in that it depends on the Laplacian, but it certainly isn't identical to the TISE. The TISE has the energy eigenvalue and the potential as terms in the equation .. so I guess you could say that the TISE = the Poisson equation, but that would be too broad ... in most cases, the TISE is solved for a bounded potential, in which case the solutions are eigenvalues of the Hamiltonian. If you are talking about the TISE in a region where the potential is zero, fine, but the solutions to that are well known, and they are not solutions to the Laplace equation.

In fact, forget about the math, let's talk physics ... Laplace's equation says that the Laplacian of the function that solves it must be zero ... well, in physics, the Laplacian of the wavefunction is proportional to the kinetic energy of a free particle. For a bound particle, the total energy is related to the curvature of the wavefunction, which is again related to the Laplacian. So, AFAICS, solutions to the Laplace equation simply cannot be solutions to the Schrodinger equation.

Perhaps your idea can still have merit, but you need to explain the physical reason for why you are focusing on the Laplace equation, and treating it as identical to the TISE. Furthermore, you must justify throwing away the other parts of the TISE [i.e. the (V-E)*Psi terms], and show why your results still have physical significance after this step, which seems fairly drastic to me at this point.

 

[glengarry]

Dear, I don't understand what you are talking about.

You have two parameters: frequency and amplitude. Let's consider a photon. Frequency is it's color, amplitude is the intensity of light. In normal world, these parameters are unrelated. You can have weak red beam, strong read beam, weak blue beam and strong blue beam. Now you come up with your equation that amplitude is an inverse of frequency. So you can only have strong red beam and weak blue beam. Congratulations, you've just assassinated Quantum Mechanics.

Okay, thanks for the good criticism. This is exactly the kind of conversation that I was hoping to get into.

First of all, you are talking about a topic related to light signal transmission and reception, which I have not yet begun to get into. That is coming up shortly, with the "theory of signals," which will elucidate the fundamental elements of special relativity. In other words, what you are talking about is the nature of the interactions between elements, whereas I have only given a "natural law" that governs the behaviors of the standing waves that constitute the elements themselves.

If this still doesn't satisfy you, let us think of a counter example. So, in the universe, U, these standing waves can be anything from electrons to the gravity fields that bind together galaxies. Now let us think about what would happen if the frequencies and amplitudes of these two objects were really independent of each other...

You could have an galactic standing wave which oscillates, say, 10^9 times a second and an electron standing wave which oscillates, say, once every 10^9 years. The galaxy, in this case, would be a pure "wall of matter" that extends, perhaps, effectively light years into space and the electron would just resemble a static gravity field so feeble that it could not possibly have any effective existence.

So, you must fully understand that I have merely been setting the ground rules wherein these kinds of bizarre occurrences are simply not possible. The "natural wave postulate" simply guarantees that elemental waves that oscillate very, very fast must necessarily be very, very feeble, and conversely, that waves that are very, very strong must necessarily oscillate very, very slowly--to the point where we think they are just non-dynamic regions of curved space.

Also, you consider gravitation and space bending. In normal world, the more mass you have, the stronger it attracts, so the stronger space is bent. You made identification of matter waves and space bending, so I guess that this "natural wave equation" holds for gravitation as well. Now, in your theory the more mass (frequency) you have, the smaller amplitude is, and space is more flat. So around a huge mass, space would be almost flat, while vacuum would be enormously curved.

Neither QM nor GR comes from your "theory" as a limit. The assumption that frequency * amplitude = const is just a contradiction.

This is quite confusing. But let me say this: the purpose for any foundational theory of physical reality, in my opinion, is to be able to mathematically derive the quality that we call "mass" by way of geometric constructions of pure mathematical space. That is, when we speak of the concept of "mass," we are really just saying that there exists some "thing" that causes the force of gravity.

But the only notion that we have of "things" in the most commonly discussed physical theories come in the forms of mere geometric points. But then, it is always argued that these points are simply the centers of "fields of force" that reach through space and cause attraction to occur. So what I am trying to do is to take this concept of "force field" very seriously by seeing what kind of geometric structure we can give to it. And this is precisely what Einstein did with his general theory of relativity.

However, with Einstein's theory, there was still the problem of the duality between matter and space. With Einstein, matter still came in the form of geometric points, and these are the objects that are supposed to bend the surrounding space. Well, what I came to realize is that, in any n-dimensional space (n=3 in our case), any geometric forms that occupy less than n dimensions cannot be said to be "real." So, any kinds of bodies that consist of 2 or less dimensions simply cannot possibly exist in our universe.

Therefore, the geometric point that lies at the center of any Einsteinian gravity field drops out of the equation, and all that now exists is the bent space itself. This is merely a matter of pure logic. That is, if we are going to talk about the physics of a 3-dimensional universe, then the elements of any such theory must necessarily consist of 3-dimensional bodies.

But the problem with that idea is that modern physicists have always been taught that dealing with geometry is nothing other than Platonic idealism, whereas physicists, at least in the popular imagination, are only supposed to stick to the "facts" as they are given, and to therefore refrain from using their imaginations.

But if physicists are not allowed to resort to constructive geometric techniques, then their sole occupation will always only be charting the trajectories of "material" points through void space, and never will it be to try to develop "manifestly believable" models for the way in which any kind of experience of a 3-dimensional universe is at all possible.

So in the end, theoretical physics finds itself at a standoff. On the one hand, there are "physical realists" who are only interested in applying mathematics to the world as it is experienced. These are the kinds of physicists that use the Schrodinger equation in order to track the trajectories of point particles that are always unpredictably "whizzing around." You can call these people "mathematical physicists." On the other hand, there are people like me and Einstein who are "mathematical idealists" who are only interested in using mathematics as a constructive tool, so as to build models that will depict "believable" ways in which 3-dimensional physical reality is even possible. These people can be understood as "physical mathematicians."

My goal, then, is to try to show you guys that the things that cause so much "flaming" going on between participants in discussions such as these go so much deeper than one person being "right" and the other person being "wrong." In my opinion, if there is every going to be such a thing as a universal theory of physical reality that all human beings will be able to agree upon, then it must necessarily be based upon a purely geo-mathematical construction that can be imaginatively visualized, and it must rely upon only very believable "formal constraints," such as the natural wave postulate and the second law of thermodynamics.

 

[glengarry]

SpectraCat,

Your mathematical reasoning [probably] is technically correct, there is still a conceptual problem that you have failed to address. You see, the only reason that the Schrodinger equation is truly a wavefunction is that its "eigenstates" are simply the various possible standing-waves that can result within a spherically bounded region of space. So, you must realize that when I speak of the Schrodinger equation, I am speaking merely of Schrodinger's equation. That is, I am talking about the specific equation that Erwin Schrodinger himself used in his own studies and not the generalized mathematical formalism that simply takes classical "operations" (such as the Hamiltonian) and then "modernizes" them, so as to conform to the atomic scale.

In fact, you should know that Schrodinger, throughout his entire career, actively campaigned against the use of the wavefunction in this way. He was very much interested in the idea of how space-filling, harmonically oscillating bodies could be used to solve certain problems that had been plaguing theoretical physics. And it is in precisely this spirit that I utilize Schrodinger's equation. Like him, I just want to understand how the dynamically oscillating waveforms themselves can be used within a model of physical reality that allows observers like you and me to have discussions just like these!

I believe that once theoretical physicists seriously start talking about "real" standing waves in conjunction with the Fourier method, then there is absolutely no limit to the problems that they will be able to solve.

 

[haael]

First of all, you are talking about a topic related to light signal transmission and reception

No, it's about certain states existence. In your world, there are no strong beams of blue light, quite contrary to everything I heard for today.

Also, contradictions won't go away as you add more theories and assumptions. The way to deal with contradictions is to relax you assumptions. Your "natural wave" is just plain false, but I see you rather deny QM, GR and all experiments, than drop your idea.

Now let us think about what would happen if the frequencies and amplitudes of these two objects were really independent of each other...

You could have an galactic standing wave which oscillates, say, 10^9 times a second and an electron standing wave which oscillates, say, once every 10^9 years. The galaxy, in this case, would be a pure "wall of matter" that extends, perhaps, effectively light years into space and the electron would just resemble a static gravity field so feeble that it could not possibly have any effective existence.

So what? How does it deny the fact, that frequency and amplitude are unrelated?

Also: electrons can not have that small frequency because of their rest mass. Their minimal frequency is related to Compton wavelength.

So, you must fully understand that I have merely been setting the ground rules wherein these kinds of bizarre occurrences are simply not possible.

I don't understand what you call "bizzare". I also don't understand how this conclusion follows from the previous talk.

This is quite confusing. But let me say this: the purpose for any foundational theory of physical reality, in my opinion, is to be able to mathematically derive the quality that we call "mass" by way of geometric constructions of pure mathematical space. That is, when we speak of the concept of "mass," we are really just saying that there exists some "thing" that causes the force of gravity.

I thought it had already been done with the idea that mass is an eigenvalue of time differential of wavefunction. Yet perhaps you are going to deny it, too.

And you still haven't explain why you think that massive bodies don't bend space and light bodies do.

 

[SpectraCat]

SpectraCat,

Your mathematical reasoning [probably] is technically correct, there is still a conceptual problem that you have failed to address. You see, the only reason that the Schrodinger equation is truly a wavefunction is that its "eigenstates" are simply the various possible standing-waves that can result within a spherically bounded region of space. So, you must realize that when I speak of the Schrodinger equation, I am speaking merely of Schrodinger's equation. That is, I am talking about the specific equation that Erwin Schrodinger himself used in his own studies and not the generalized mathematical formalism that simply takes classical "operations" (such as the Hamiltonian) and then "modernizes" them, so as to conform to the atomic scale.

I frankly have no freaking idea what you are talking about. Please provide the mathematical form of the equation that you are referring to and show explicitly how and why it is "identical to the Laplace equation". Then we can talk about whether or not it has physical significance. Your historical anecdotes about Schrodinger himself do not jibe with what I have read about the man ... do you mind providing a reference for your statements about how he "throughout his entire career, campaigned against the use of his wavefunction in this way"? It is my understanding that he only started thinking that way very late in his career when he was in his mid-seventies.

 

[RUTA]

You must understand this one basic point, or nothing else will make any sense:

Schrodinger equation = Laplace's equation:

http://en.wikipedia.org/wiki/Laplace's_equation

If you do not understand me when I say that all we are looking for is a simple, harmonic standing-wave solution to the Laplace equation (i.e. we can understand this as a pure "eigenstate"), then the entire logical foundation of this entire theory falls apart.

In other words, wavefunctions, qua themselves, have nothing whatever to do with particles. All that a wavefunction does is to tell its infinitesimal spaces how to oscillate. This is easy to observe in the 1 and 2 dimensional cases when we look at harmonically oscillating guitar strings and drumpads. But in order to construct our own 3D universe, it is necessary that we solve this equation for all three dimensions. But the problem here is that we cannot visualize the infinitesimal spaces (tiny volumes in this instance) as extending into another dimension, as with the 1 dimensional case when we see the parts of the wave extending into the second dimension. So, for this oscillating extension to make sense, we have to "bend" the flat 3D space so that it becomes a superficial manifold within a logical fourth dimension.

Now, the "typical" manifestations of the Schrodinger equation are just this very same principle, but only applied to the trajectories of "material points." However, this entire picture is simply the very same thing as the classical, Newtonian model wherein bodies move on simple, parabolic paths through space. The only difference is that it is now the Schrodinger/Laplace equation that governs the movements of particles rather than Newton's classical equations of motion.

It is vital to understand that the only thing that conceptually distinguishes quantum theory from classical kinematics is the idea of harmonically oscillating, space-filling standing waves. If we simply want to "interpret" this notion so that it degenerates back into a kind of "weird" classical model, then that is our right, but we will have ultimately gained nothing from it.

So my project is to get you guys to see the folly in this kind of "interpretive" behaviour, and just start to embrace the utter beauty and simplicity of the things that we call "standing waves." And once we do this, then we can start to realize that anything is possible in terms of coming up with "manifestly believable" models of physical reality. So then, if you can go back and reread what I have already written in terms of the paradigm of "pure waves" rather than "crazily moving particles," then you will be able to start to visualize in your own head what the mathematical object that is known as 'U' is telling you.

I understand solutions to Laplace's eqn on S3 (as opposed to E3). You don't have to equate the solution with displacement in a 4th spatial dimension, it can be ANY scalar quantity (temperature, for example), so that the values of the field can be interpreted easily in 3D. Yes, Schrodinger wrote a paper about this (or was it a short book?). But, the bottom line is, you're not doing QM here. Again, in QM, you solve Schrodinger's eqn (SE) for psi in configuration space where there are three spatial dimensions for each particle involved. The only link between what you are proposing and QM is the time-independent, single particle solution of SE on S3. Interesting, but hardly exhaustive, i.e., pick up an intro textbook on QM and look at all the solutions of SE that you can't reproduce. Thus, you're not doing QM so you would have to show how your approach gives results from QM that are known to work. I doubt that it's possible.

 

[glengarry]

I frankly have no freaking idea what you are talking about. Please provide the mathematical form of the equation that you are referring to and show explicitly how and why it is "identical to the Laplace equation". Then we can talk about whether or not it has physical significance. Your historical anecdotes about Schrodinger himself do not jibe with what I have read about the man ... do you mind providing a reference for your statements about how he "throughout his entire career, campaigned against the use of his wavefunction in this way"? It is my understanding that he only started thinking that way very late in his career when he was in his mid-seventies.

You see, SC, I am already detecting a hint of "flamage" coming from you. But you must understand that the reason for your passion has nothing to do with whether it is me or you who are "right," but rather it has only to do with the things that we are discussing lie at the very heart of all philosophical problems that divide men from one another. In other words, these very same issues have been argued since the dawn of civilization, and these kinds of arguments were most notably captured by the Platonic dialogues.

So, the truth is, the question of whether physical reality "truly" comes in the form of:

1) "actual" waves, or

2) particles whose locations and trajectories can be determined via a formalism that is merely called a wavefunction

...is just the latest, most "sophisticated" incarnation of the age-old conflict that had the "atoms and the void" of Democritus on one side and the "flux" of Heraclitus on the other side.

So, it is my goal to show you that this entire conflict can be avoided by understanding that there needs to be a theory that integrates both of these sides, for the reason that the "atoms and the void" side gives us all of the differences that are manifest in everyday experience while the "flux" side gives us a kind of ontological grounding that allows the differences-as-experienced to be understood in their very possibility.

All that being said, here follows a couple of references that I could find for you on short notice. But I am not saying that these sources should be taken as gospel. I am simply saying that they are in thorough agreement with all of the reading that I have done concerning the history of quantum theory, which is quite a lot. In general, if you want to look into this stuff yourself, you have to pay special attention to the run-up to the 1927 Solvay conference, which effectively established Bohr's Copenhagen interpretation as being the canonical form of the theory of the atom. And it was in this time period that there was much heated debate as regards how to understand the de Broglie-Schrodinger wave theories and the Heisenberg relations as being different aspects of one and the same "meta theory," if you will.

From http://books.google.com/books?id=C8...s constant can be used to describe"&f=false":

Quantum mechanics discovered that Planck's constant can be used to describe the atom, but Planck's constant is about the divisions of energy in a wave. Since Planck's constant works in the quantum model to describe the angular momentum of the electron shells, then there is a wave inside the atom in which the electrons move. Erwin Schrodinger, later in life, discovered this himself. Unfortunately, he envisioned the wave so strongly that he put forth a new theory suggesting that the atom was only a wave. Einstein rejected such a theory and rightly so as who knew better than Einstein that waves move overall at the speed of light but mass does not. However, Schrodinger, the person who invented quantum mechanics into a system that is still used today, believed so fully that a wave existed in the atom other than the type of wave-particle duality of today's matter-wave, but a full atomic wave, that he said in the 1950s:

"Let me say at the outset, that in this discourse, I am opposing not a few special statements of quantum mechanics held today, I am opposing as it were the whole of it, I am opposing its basic views that have been shaped 25 years ago, when Max Born put forward his probability interpretation, which was accepted by almost everybody"

Even in 1926, Schrodinger had argued with Bohr saying, "Surely you realize that the whole idea of quantum jumps is bound to end in nonsense. You claim first of all that if an atom is in a stationary state, the electron revolves periodically but does not emit light, when, according to Maxwell's theory, it must. Next, the electron is said to jump from one orbit to the next and to emit radiation. Is this jump supposed to be gradual or sudden? Why does it not emit a continuous spectrum, as electromagnetic theory demands? And what laws govern its motion during the jump? In other words, the whole idea of quantum jumps is sheer fantasy."

From: http://www.aip.org/history/heisenberg/p09.htm

Not everyone agreed with the new interpretation, or with Born and Heisenberg's statement about future work. Einstein and Schrödinger were among the most notable dissenters. Until the ends of their lives they never fully accepted the Copenhagen doctrine.

 

[glengarry]

I understand solutions to Laplace's eqn on S3 (as opposed to E3). You don't have to equate the solution with displacement in a 4th spatial dimension, it can be ANY scalar quantity (temperature, for example), so that the values of the field can be interpreted easily in 3D.

I will try to give you the reason why E3 spherical harmonics must conform to a 3-sphere in E4 space in the form of a mathematical theorem. Here goes nothing!

Proposition: In order for there to exist the possibility of dynamic translational inter-relations between bodies that take the form of 3-dimensional standing waves, the bodies must conform to the shape of a 3-sphere.

Axiom #1: There exist standing waves that are contained within an arbitrary space, such that the boundaries for each standing wave are mutually exclusive, 2-dimensional spheres.

Problem: We now have a distinction between interior, "material" space and exterior "void" space. But by definition, a void is perfectly devoid of any characteristics. Therefore, inter-relations between the standing waves is not possible, which means that for the possibility of inter-relations between standing waves to exist, they must not exist in a state of mutual exclusivity.

Axiom #2: There exist an arbitrary number of 3-dimensional standing waves that each exist within, and are defined by, the same 2-dimensional boundary.

Problem: Each standing wave will necessarily remain centered at the same location, since this center is determined precisely by the spherical boundary. While there may exist rotational inter-relations, there cannot exist any translational inter-relations (i.e. the centers of bodies cannot move relative to one another).

Solution: Since Axiom #1 is clearly impossible, it must be the case that standing waves exhibit the character of mutual inclusivity in order to avoid the problems inherent in the matter vs. void paradox. And since it is clearly impossible that this mutual inclusivity can take the form of standing waves that have the very same boundary conditions, then there must exist a way for them to be defined by different boundaries, and at the same time, to exist in a state of mutual inclusivity.

We need to first define each standing wave in its own, local 3-dimensional Euclidean space, and then find a way so that each of the waves can be centered at different locations within the same universal space, so as to allow for the possibility of relative translational motion. This can only be effected by way of allowing the defining boundaries and interior spaces of each standing wave to be wholly independent of the selfsame space in which they are to inter-relate. We must therefore consider a point other than the centers of the individual spheres as representing each of their own "origins," and the only symmetrical way to accomplish this is to collapse their 2-dimensional boundaries into singular points. For this operation to ensue, we require the use of a fourth Euclidean dimension. Now, the individual standing waves attain the possibility of translational inter-relations, because the generalized "boundary collapsing procedure" allows for each boundary to be placed at arbitrary locations on a common, 3-spherical, universal manifold.

Conclusion: The proposition in question has been proved.

Yes, Schrodinger wrote a paper about this (or was it a short book?). But, the bottom line is, you're not doing QM here. Again, in QM, you solve Schrodinger's eqn (SE) for psi in configuration space where there are three spatial dimensions for each particle involved. The only link between what you are proposing and QM is the time-independent, single particle solution of SE on S3. Interesting, but hardly exhaustive, i.e., pick up an intro textbook on QM and look at all the solutions of SE that you can't reproduce. Thus, you're not doing QM so you would have to show how your approach gives results from QM that are known to work. I doubt that it's possible.

And I agree with your assessment entirely, which is why we currently find ourselves in the "non-QM / non-physics / non-scientific / non-anything-of-relevance" Philosophy section ;) ! And such is the pattern of my life!

And this is why we need to distinguish the notions of 1) "Quantum Mechanics" as the modern, specialized formalism which merely carries Schrodinger's name, and 2) the more general concept of "Atomic Theory," wherein some of the deepest and most articulate thinkers that have ever existed came together for an all-too brief moment in history and actively tried to "figure out" what we should ultimately be "allowed" to say about the physical reality in which we find ourselves immersed.

So I just repeat myself when I say that the disagreements that we are having here do not arise from whether one or the other of us is "more correct." This is to say that 1) those who tend to have sympathy for the de Broglie /Einstein /Schrodinger /Bohm "picture" version of atomic reality, versus 2) those who align themselves with the Bohr /Heisenberg /Born /Dirac "formalism" version of atomic reality, do not necessarily simply misunderstand each other's positions. This is much rather a profound philosophical disagreement as regards the nature of the kinds of statements that should be accepted as truthful propositions vis-a-vis the scientific community as a whole.

According to modern QM, then, "science" must only ever ultimately reduce to empirical observation and never to a purely objective mathematical "picture," such as the dynamic object, U, that I have been attempting to impress you all with. But what happens when such is the case? It means that our theories say absolutely nothing about any kind of self-subsisting entity that we can call a "universe," but they only rather say things about virtual observers who are running around, conducting experiments, and tallying their results over an infinite number of trials. And here is ultimately all that is said about the modern formalism that you are trying to persuade me to recognize as "valid":

'An observer who conducts the same experiment over an infinite number of trials will, on average, observe the necessary "prediction" of quantum mechanics.'

But when you read into this statement, all it is "really" saying is just:

'For a given experiment, an observer will probably witness the most likely outcome.'

But this is a pure tautology! That is, there is precisely nothing of "interest" that is being asserted here at all!

So, this is why it is important for theoretical physicists to start expanding their minds beyond a framework that leads to nothing other than the equation:

A = A

...so that meaningful propositions can once again be asserted, leading to a renewed spirit in a discipline that has not really made any "interesting" statements of any fundamentally theoretical significance for the major part of an entire century!

And here is where my thinking starts to get really deep. That is, the "real" reason why the standing wave elements need to conform to a spherical form is just that we need to start not from a posture of mere tautology as above, but rather from a posture of logical complementarity:

A = ~B && B = ~A

(where '~' is the complement operator, and '&&' is the logical 'and' operation)

In other words, this just means that for every possible location, A, within the universe, there is a logical complement, B--with the obvious geometric interpretation being that A and B exist as opposing poles of the same spherical manifold. So now, with the inclusion of an essential complementarity/polarity at the most basic theoretical level, there is no longer a possibility that our theories will reduce to statements of sheer identity. That is, for every possible spatial element that we can imagine, there is now a symmetrically opposite element that allows there to be a concept of the opposing forces/tensions that keep our universe vital and whole, saving us from "fretting" over the possibilities of all of those cosmological "disaster scenarios"--i.e. the "big crunch" or "thermodynamic rundown."

I know that this is all very deep, and can all be extraordinarily overwhelming, leading to feelings of exasperation, so I just want you guys to take me as somebody that is capable of "taking you along a path," if that is what you truly want. That is, I have only begun to scratch the surface as far as the overall way of thinking that I have developed over these many years, and all of this thinking about physical reality will only lead you to even deeper questions, such as have been asked by humans since the dawn of civilization. So, if you guys just want to keep your bosses happy so that you can keep your jobs, and remain relatively "sane" in the process, I would advise you to probably forget about this thread.

Hint: This is not about math or physics or philosophy... it is about all of them at the same time!

 

[SpectraCat]

You see, SC, I am already detecting a hint of "flamage" coming from you. But you must understand that the reason for your passion has nothing to do with whether it is me or you who are "right," but rather it has only to do with the things that we are discussing lie at the very heart of all philosophical problems that divide men from one another. In other words, these very same issues have been argued since the dawn of civilization, and these kinds of arguments were most notably captured by the Platonic dialogues.

So, the truth is, the question of whether physical reality "truly" comes in the form of:

1) "actual" waves, or

2) particles whose locations and trajectories can be determined via a formalism that is merely called a wavefunction

...is just the latest, most "sophisticated" incarnation of the age-old conflict that had the "atoms and the void" of Democritus on one side and the "flux" of Heraclitus on the other side.

So, it is my goal to show you that this entire conflict can be avoided by understanding that there needs to be a theory that integrates both of these sides, for the reason that the "atoms and the void" side gives us all of the differences that are manifest in everyday experience while the "flux" side gives us a kind of ontological grounding that allows the differences-as-experienced to be understood in their very possibility.

All that being said, here follows a couple of references that I could find for you on short notice. But I am not saying that these sources should be taken as gospel. I am simply saying that they are in thorough agreement with all of the reading that I have done concerning the history of quantum theory, which is quite a lot. In general, if you want to look into this stuff yourself, you have to pay special attention to the run-up to the 1927 Solvay conference, which effectively established Bohr's Copenhagen interpretation as being the canonical form of the theory of the atom. And it was in this time period that there was much heated debate as regards how to understand the de Broglie-Schrodinger wave theories and the Heisenberg relations as being different aspects of one and the same "meta theory," if you will.

From http://books.google.com/books?id=C8...s constant can be used to describe"&f=false":



From: http://www.aip.org/history/heisenberg/p09.htm

Look, I am following your posts in the hope of learning something new, but that hope is fading fast. I keep asking you for clearly stated, simple mathematical equations, and what I get in return is rambling, discourses that are part qualitative math and part metaphysical musings. I get the sense that you want to communicate something of import, but as yet I have not been able to glean such from your posts. Please back up, slow down, and address the specific questions I am asking of you, rather than brushing them aside in favor of more "big picture" developments of your approach, which I have said I don't follow or accept at a much more basic level.

Let me put it like this, if you can't make your "big idea" clear to me (an academic experimental spectroscopist with a Ph.D. in Chemical Physics and a strong background in non-relativistic QM), then by your own arguments form your earlier posts, how important/relevant/interesting can it be?

 

[glengarry]

I understand you want a "formalism." I don't know how I can be any more "formal" than this:

BEGIN FORMALISM>>>

1) There exists a arbitrary standing wave solution to Laplace's equation in three dimensions.

2) This solution will have an amplitude of 1. Now multiply this amplitude by any arbitrary factor, such that the following relation holds:
amplitude * frequency = universal constant

3) This scaled solution is transformed into a 3-dimensional sphere via an inverse azimuthal equidistant projection.

4) Repeat steps 1-3 as many times as you wish.

5) The resulting object can now be "Fourier summed" so as to result in a composite waveform that we may call "The Universe," or simply: U.

6) Apply the second law of thermodynamics so that the maximum amplitude of U tends to a minimum.

<<<END FORMALISM


RESUME MUSINGS>>>

And SC, as far as all of your credentials are concerned, they really don't add very much weight to your side of the argument. In fact, you have only just exposed your intellectual vulnerabilities, assuming that you focus the majority of your mental energies on the areas in which you are most expert. And I'm not saying this just to be a "jerk." You are the one who brought it up, and I am just responding in kind.

Me, on the other hand, I am just a "phantom." I could be anyone, anywhere. As far as you are concerned, I am just a brain in a vat. Accordingly, that is how I would like this discussion to proceed: brains-in-vats hashing it out, concerning what can "rightfully" be said about the nature of the physical reality that we inhabit. Only mathematics and logic need apply to the discussion.

And now, you accuse me of speaking "metaphysically." Please show one instance of this. But since you brought it up, let me tell you what "metaphysics" really is:

Whenever there exists a physical theory that utilizes techniques such as the application of Hermitian operators to a wavefunction in order to reduce it to a particular quantity (i.e. an "observable"), you have just committed a magical act. That is, these so-called "operators" are nothing other than purely phantasmic "observers" running amok in the middle of what should otherwise be purely quantitative logic. And this is precisely the kind of thing that I would call "qualitative mathematics" in the most egregious sense.

My investigations, on the other hand, have no such elements of, shall we say, "mystical engineering." All I am asking you to do is to solve an equation and then project the results onto the same universal space. Then, simply add a formal constraint (amplitude * frequency = 1). Finally, watch it all work, by letting time fly and applying the second law of thermodynamics. In this scenario, there are no mysterious little observers running around, conducting "ideal" experiments, so that a perfectly ambiguous entity known as a "field of probability amplitudes" will mysteriously "collapse."

The only point that I am trying to make, SC--and I am doing my best to be as forthright as I possibly can--is that the mathematical formalism that goes by the name of "Quantum Mechanics," has precisely zero physical significance. So, let us now just consider the following two statements:

1) There exist people who are called "theoretical physicists"
2) There exist people who make physically meaningful statements

My question, now, is just this: Does statement 1 necessarily imply statement 2? Or vice versa?

And also, I know that it can be problematic in "believing" what I have to say at this point, because I have only merely instantiated a bare mathematical object (the composite waveform, U), with nothing in the way of phenomenological "guidance." In fact, it is only when we are able to "peer into" this object, and get a basic, intuitive understanding for phenomena such as:

1) signal (light) propagation
2) gravity
3) chemical bonding
4) magnetism
5) electrical current
6) the "blackbody" curve
7) atomic spectral lines
8) cosmological redshift

...that the significance of U will really start to hit you, full force! So, all I want you guys to do now is to simply accept the purely logical existence of the dynamic object, U, as I have already laid out. And if you need more help imagining U, then just reduce the dimensionality. In one dimension, all you need to imagine are just harmonically oscillating strings that are formed into circles, such that they all inhabit the same "universal circular space."

And this is all that I really need to do in order to make my point. It is pure mathematics, with precisely zero metaphysical elements allowed. The only reason why I make all of those philosophical and historical points is that our traditions, especially when it comes to the theoretical sciences, tend to be oppressive forces that dictate how we understand our reality, rather than liberating forces that allow us to understand this reality in ever more fundamental and compelling ways.

So, I am honestly very sorry if I am too philosophical for your tastebuds, but I simply take it to be a necessary truth that those who do not develop their understandings of the largest of all "world pictures" will be extremely hard-pressed to leverage their technical skills, so as to be able to develop ideas that are truly significant.

 

[glengarry]

Now I want to make another admission. In addition to having Asperger's syndrome, I am also homeless. Furthermore, I have never graduated college, even though I probably have earned enough credits in my life to qualify as a senior. And I only make these admissions now, since I feel that I have firmly established my skills as a universal/comprehensive thinker, a logical/technical thinker, and a rhetorician.

My problem is that I have always been unable to go along with anyone else's "program," because I have never found anybody's system of thought to be all that compelling. In fact, it is my belief that Western civilization has not seen a complete thinker since Kant. So, my goal, very simply, is just this: using the Critique of Pure Reason as a philosophical touchstone, I want to "update" the Kantian system, so that it will adequately address the most modern of concepts.

In addition, I am interested in pushing Kantian philosophy to the limits by seeing how far we can push our a priori notions, in terms of developing a purely mathematical description of the physical universe. Furthermore, I would like to see how far such a description can be turned into a necessary system of thought; that is, using only the most manifest of all assumptions, I would like to develop a mathematical theorem that proves simply this: If there is something rather than nothing, then this something must exist in such and such a way.

In the biggest picture, I can't get any deeper than this, and it is almost overwhelming to have one's mind occupied in such ways. For, I can think of no better way to eliminate the human brutalities that result from philosophical differences than the creation of a universal system of thought that is anchored by the weight of pure and necessary mathematical reasoning. It is my understanding that [something like] this was Kant's dream, and I just want to do whatever I can in service of this noble idea.

But again, the problem with all of this is that I just can't get myself to go along with any kind of prescribed "way of life." That is, it is important that my body be allowed to roam as freely as my mind. And I don't mean this in the sense of being a world traveler. In fact, just as Kant, I have absolutely no desire to travel. All I want is to be able to go back to my hometown (in Florida) and live out my days in peace. But in order to do this, there will have to be at least one person who is willing to help me to find a stable lifestyle. I can tell you that I do not consume drugs or smoke, and I drink alcohol only occasionally.

The reason that I am homeless is simply that I am psychologically unstable. This does not mean that I am dangerous, it only means that my moods are highly influenced by the thoughts that are running through my mind. That is, if I am in the process of making some kind of exciting connection, I tend to become fairly manic. Otherwise, depression can easily begin to set in.

So, all I know is that I need help if I am do be able to find a decent life for myself. You must understand that there is really no such thing as "mental health" for indigent adults such as myself. The only thing that exists is to be given a prescription for a powerful pharmaceutical after a mere five or ten minute sit-down session with some kind of overworked county-employed psychiatrist. To these people, you are only either bipolar or schizophrenic, and the "treatments" for these two diseases are much the same. And if one is not willing to take the medicine as prescribed, then one is simply labeled "non compliant," and is therefore "beyond being helped."

It is very obvious to me that I have Asperger's syndrome, but this kind of diagnosis is simply not available to me. And I don't really need "treatment" for it, because, after all, I am in my mid-30's, and I have been able to get along fine enough as it is. If only I can find some way to receive sociological support, in the form of having a room in which to live and a group of peers who are interested in the same things that interest me, then I cannot ask for anything more.

 

[glengarry]

This is the first instance that I have seen in which a prominent theoretical physicist has used a description that perfectly matches my own understanding of the natural order. The essential quote is at the bottom in bold.

From Imagery in Scientific Thought, Arthur I. Miller, p. 145:

Heisenberg expressed his sharp opinion of Schrodinger's wave mechanics in the 8 June 1926 letter to Pauli quoted from in the epigraph to this section. And, as Heisenberg wrote in his 1926 paper "Many-body problem and resonance in quantum mechanics," it was for "expediency" in calculations that he used Schrodinger's wave functions. In this paper Heisenberg exploited the mathematical equivalence of the two theories with the caveat that Schrodinger's "intuitive pictures [anschauliche Bilder]" should not be imposed on the quantum theory. For, continued Heisenberg, as Schrodinger himself had written, such pictures led to conceptual difficulties in treating many-body problems. Schrodinger's reason was that both theories used formulas from classical mechanics that considered atomic objects to be point particles, but this was "no longer permissible" because atomic objects were "actually extended states of vibration that penetrate into one another" (1926a).

Until yesterday, I was not aware that Schrodinger was an advocate for the idea of standing wave mutual inclusivity. I don't know how far he tried to take this idea, but it is always rebuffed by the "Heisenbergians" by saying things like "matter cannot consist of actual wavepackets, because wavepackets diffuse/expand." And this is precisely why we must think of standing waves in terms of modes of oscillation of the universal manifold itself. That is, the only thing that can be gained by thinking of spatially segregated standing waves is the existence of a duality between "material space" (inside the standing wave boundaries) and "void space" (outside of all boundaries).

 

[SpectraCat]

I understand you want a "formalism." I don't know how I can be any more "formal" than this:

BEGIN FORMALISM>>>

1) There exists a arbitrary standing wave solution to Laplace's equation in three dimensions.

2) This solution will have an amplitude of 1. Now multiply this amplitude by any arbitrary factor, such that the following relation holds:
amplitude * frequency = universal constant

3) This scaled solution is transformed into a 3-dimensional sphere via an inverse azimuthal equidistant projection.

4) Repeat steps 1-3 as many times as you wish.

5) The resulting object can now be "Fourier summed" so as to result in a composite waveform that we may call "The Universe," or simply: U.

6) Apply the second law of thermodynamics so that the maximum amplitude of U tends to a minimum.

<<<END FORMALISM


RESUME MUSINGS>>>

And SC, as far as all of your credentials are concerned, they really don't add very much weight to your side of the argument. In fact, you have only just exposed your intellectual vulnerabilities, assuming that you focus the majority of your mental energies on the areas in which you are most expert. And I'm not saying this just to be a "jerk." You are the one who brought it up, and I am just responding in kind.

Me, on the other hand, I am just a "phantom." I could be anyone, anywhere. As far as you are concerned, I am just a brain in a vat. Accordingly, that is how I would like this discussion to proceed: brains-in-vats hashing it out, concerning what can "rightfully" be said about the nature of the physical reality that we inhabit. Only mathematics and logic need apply to the discussion.

And now, you accuse me of speaking "metaphysically." Please show one instance of this. But since you brought it up, let me tell you what "metaphysics" really is:

Whenever there exists a physical theory that utilizes techniques such as the application of Hermitian operators to a wavefunction in order to reduce it to a particular quantity (i.e. an "observable"), you have just committed a magical act. That is, these so-called "operators" are nothing other than purely phantasmic "observers" running amok in the middle of what should otherwise be purely quantitative logic. And this is precisely the kind of thing that I would call "qualitative mathematics" in the most egregious sense.

My investigations, on the other hand, have no such elements of, shall we say, "mystical engineering." All I am asking you to do is to solve an equation and then project the results onto the same universal space. Then, simply add a formal constraint (amplitude * frequency = 1). Finally, watch it all work, by letting time fly and applying the second law of thermodynamics. In this scenario, there are no mysterious little observers running around, conducting "ideal" experiments, so that a perfectly ambiguous entity known as a "field of probability amplitudes" will mysteriously "collapse."

The only point that I am trying to make, SC--and I am doing my best to be as forthright as I possibly can--is that the mathematical formalism that goes by the name of "Quantum Mechanics," has precisely zero physical significance. So, let us now just consider the following two statements:

1) There exist people who are called "theoretical physicists"
2) There exist people who make physically meaningful statements

My question, now, is just this: Does statement 1 necessarily imply statement 2? Or vice versa?

And also, I know that it can be problematic in "believing" what I have to say at this point, because I have only merely instantiated a bare mathematical object (the composite waveform, U), with nothing in the way of phenomenological "guidance." In fact, it is only when we are able to "peer into" this object, and get a basic, intuitive understanding for phenomena such as:

1) signal (light) propagation
2) gravity
3) chemical bonding
4) magnetism
5) electrical current
6) the "blackbody" curve
7) atomic spectral lines
8) cosmological redshift

...that the significance of U will really start to hit you, full force! So, all I want you guys to do now is to simply accept the purely logical existence of the dynamic object, U, as I have already laid out. And if you need more help imagining U, then just reduce the dimensionality. In one dimension, all you need to imagine are just harmonically oscillating strings that are formed into circles, such that they all inhabit the same "universal circular space."

And this is all that I really need to do in order to make my point. It is pure mathematics, with precisely zero metaphysical elements allowed. The only reason why I make all of those philosophical and historical points is that our traditions, especially when it comes to the theoretical sciences, tend to be oppressive forces that dictate how we understand our reality, rather than liberating forces that allow us to understand this reality in ever more fundamental and compelling ways.

So, I am honestly very sorry if I am too philosophical for your tastebuds, but I simply take it to be a necessary truth that those who do not develop their understandings of the largest of all "world pictures" will be extremely hard-pressed to leverage their technical skills, so as to be able to develop ideas that are truly significant.

*Sigh* ... there you go again with the Laplace equation .. it is clear that you think I am fairly stupid, so why don't you go with that, and explain to me in simple terms (as I have asked repeatedly), what the Laplace equation has to do with the Schrodinger equation. Many posts ago, I gave you a fairly detailed accounting of why I thought that was incorrect, and you have never addressed those points. Now you are trying to get me to accept a formalism based entirely around solutions to the Laplace equation. Can't you guess what my response to that will be?

Second, you never (in my view) successfully refuted haael's objection that frequency and amplitude are independent free variables, and thus not subject to the constraint: frequency*amplitude=constant, that you have placed on them in point 2 of your formalism. I read your phenomenological rejection of his point, and frankly it made little sense to me. You seem to be equating large amplitude with large mass, at least from your examples, but the wavelength of massive bodies tends to *decrease* with mass, which by your own formalism would require that the amplitude would decrease as well. So it would appear that your formalism already has a built-in contradiction.

Basically, your whole framework is far too fuzzy for me to understand, and I need you to lay it out in more concrete terms. So please, as I have asked, start with point 1 of your formalism and explain to me what the Laplace equation has to do with the Schrodinger equation, beyond the fact that they are both second order differential equations.

 

[glengarry]

I'm not going to keep going around in circles with you, SC... life is too short for that. The simple fact here is that we come from profoundly different perspectives. My perspective is simply the creative possibilities that are inherent in mathematical construction. It is in this sense that my style of thinking precedes any formalism. That is, once my constructions become sufficiently "solid" to stand on their own terms for the forseeable future, then we can start talking about developing a system of symbolics that can represent them.

But you are merely interested in constructions that are already so well established that their symbolic representations have already been around for quite some time. However, I am simply taking off from the "stream of consciousness" that was begun when Schrodinger established the fact that three-dimensional standing waves should somehow have something to do with any fundamental theory of physical reality.

He simply did not agree with the idea that a solution to a wavefunction should come to mean anything other than harmonically oscillating three-dimensional forms. So, when you come at me with the demand that I show you how these particular mathematical objects that we call standing waves have some kind of connection to the entire way of thinking that is given by the name "Quantum Mechanics" (i.e. determining the expectation values of infinite applications of Hermitian operators to a field of values), then there is simply no possible way for us to effectively communicate, and the entire thread thus becomes muddied.

Simply put: If you cannot accept the mathematical existence of the composite waveform known as U (as previously outlined), then my conversation with you is at an end.

 

[rewebster]

My main concern with theoretical physics is with 'scare quotey' language just like this. On the one hand, we want to use (i.e. be inspired by) certain images that are related to our every day experiences (e.g. watching an apple fall from a tree).

But when pressed, the typical theoretical physicist will say that these are only analogies, and that the formalism is the thing that really counts. What I want is to come up with an idea of theoretical physics that no longer plays such games.

Can anyone help me?

What you're looking for is a theory of everything that's correct...

 

[glengarry]

What you're looking for is a theory of everything that's correct...

No, I've gotten beyond that idea. What I think I have come up with is a general mathematical context (i.e. harmonic standing waves, "Riemannization", Fourier summation, minimization of maximum amplitude) that is capable of inspiring the most imaginative mathematical minds to start working towards the idea of theoretical physics as a discipline that requires the positive proof inherent in mathematical theorems rather than the merely negative style of proof that is inherent in Popper's falsifiability doctrine.

But in order to begin the process of inspiring people, I need to describe how the various phenomena (I have already mentioned them in a previous post) can be understood as "believable" possibilities from within this context. This means that people are going to have to give me a break about giving them "wildly successful" predictions about phenomenon X, Y, or Z (this is the language of QM which can supposedly predict everything, but yet describe nothing).

I mean, I really do want to get into the details, but I want to feel like I am doing something collaborative rather than simply trying to bang something into people's heads that they might not be ready to hear.

 

[rewebster]

No, I've gotten beyond that idea. What I think I have come up with is a general mathematical context (i.e. harmonic standing waves, "Riemannization", Fourier summation, minimization of maximum amplitude) that is capable of inspiring the most imaginative mathematical minds to start working towards the idea of theoretical physics as a discipline that requires the positive proof inherent in mathematical theorems rather than the merely negative style of proof that is inherent in Popper's falsifiability doctrine.

But in order to begin the process of inspiring people, I need to describe how the various phenomena (I have already mentioned them in a previous post) can be understood as "believable" possibilities from within this context. This means that people are going to have to give me a break about giving them "wildly successful" predictions about phenomenon X, Y, or Z (this is the language of QM which can supposedly predict everything, but yet describe nothing).

I mean, I really do want to get into the details, but I want to feel like I am doing something collaborative rather than simply trying to bang something into people's heads that they might not be ready to hear.

so, it sounds like you (think you) have a 'end product', but you don't have all/any of the 'details' to establish it

 

[glengarry]

so, it sounds like you (think you) have a 'end product', but you don't have all/any of the 'details' to establish it

No, I think that I have a mathematical context through which interesting questions can be asked and answered. I think I have just enough details to get certain talented mathematicians to start thinking in terms of mutually inclusive, harmonically oscillating geometric entities that are constantly trying to find positions of equilibrium from within the context of a Fourier summed universal spatial manifold.

I'd love to hear what you think about all of this...

 

[rewebster]

No, I think that I have a mathematical context through which interesting questions can be asked and answered. I think I have just enough details to get certain talented mathematicians to start thinking in terms of mutually inclusive, harmonically oscillating geometric entities that are constantly trying to find positions of equilibrium from within the context of a Fourier summed universal spatial manifold.

I'd love to hear what you think about all of this...

I think, or was wondering really, if you think you've got 'part' of it, why hasn't it fallen into place for you?

It still sounds like you're missing 'parts'; and, if its your own idea, then you may not have the right parts in place yet, or the right parts to begin with---

There's a whole lot of papers out there that are basically conjectures.

If you're at a point where there's a problem, then you may not be on the right path. If you're at a point where things seem to fit, but then you don't have the next step, my suggestion is to submit it for publication.

 

[magpies]

I am psychologically unstable. This does not mean that I am dangerous, it only means that my moods are highly influenced by the thoughts that are running through my mind. That is, if I am in the process of making some kind of exciting connection, I tend to become fairly manic. Otherwise, depression can easily begin to set in.

This is the problem you should be working on brother. Not how to solve math problems...

 

[glengarry]

This is the problem you should be working on brother. Not how to solve math problems...

How, exactly, am I supposed to "work on" my own mind? I am my mind! Thinking about the universe is precisely how I cope with my mental issues...

 

[glengarry]

I think, or was wondering really, if you think you've got 'part' of it, why hasn't it fallen into place for you?

It still sounds like you're missing 'parts'; and, if its your own idea, then you may not have the right parts in place yet, or the right parts to begin with---

This has nothing to do with typical articles that are submitted for publication in academic journals. This rather has everything to do with rethinking our understanding of theoretical physics as a formalism that merely predicts certain phenomena--so that it can instead be built upon a robust mathematical system that will allow believable ontological models to be constructed.

My idea is much better understood as a paradigm shift rather than a simple equation (or set of equations) that can be "solved" in order to attain a specific result. This latter version is how the academic establishment currently understands the nature of theoretical physics.

I don't want any fame from this. I just want to be recognized as having an ability that has value within the world at large, so that I can find a place within society that can lead to a happy and fulfilling life. I am simply not capable of compromising my intellectual or moral standards so that I can live a typical consumerist kind of life.

We have to understand that the mathematics involved within my idea verges on infinite complexity. We are talking about solving partial differential equations, morphing them into spherical shapes, "Fourier summing" them together, and finding out how they will reach equilibrium.

The "bleeding edge" of mathematics, however, has only just recently come into a proof of the Poincare conjecture, which merely describes the way in which individual three-dimensional manifolds can be morphed into spheres. And if you look into Perelman's three papers, I feel pretty confident that you will agree that the mathematics involved with making any kind of statement about three-dimensional manifolds is something entirely different than what the typical theoretical physicist imagines mathematics to be.

So what I am trying to do is to redefine theoretical physics as nothing other than interactive differential geometry, which, to put it mildly, will find extraordinary resistance by the powers that be in the academic physics establishment. I think that people will start to become interested when I get into detail about the various phenomena (esp. the electromagnetic and optical phenomena) that can be intuitively understood from within the context of the mathematical object, U.

Also, it is important to understand that my online efforts are only a tiny fraction of my total energy expenditure in getting my ideas out in the open. I currently live on and around the UCLA campus, and I have been making myself very well known by way of holding signs around campus so that people will get interested in what I have to say. My current sign says:

Thesis: "The axioms of quantum mechanics are logically absurd." Einstein thought so, and so do I!

I get very different responses from the different kinds of people that I talk to. The "know it all" physics undergrads and grad students tend to respond the most negatively to me, since my ideas only push their understandings into theoretical irrelevancy. But I really don't care about what they have to say, because they are typically too prejudiced to open their minds to another way of thinking about physical theory.

My best responses are from those who are interested in philosophy or math, and preferably both at the same time. I have had some very good conversations with both kinds of students, some of whom became visibly excited by the concept of theoretical physics that I describe to them.

But the "holy grail," as far as I am concerned, is to get the attention of one of the smartest people in the world, Terence Tao, who is a mathematician at UCLA. What I am trying to do is to create a kind of general buzz around campus that there is a person (me) who has exciting things in store for the future of theoretical physics, and that Mr. Tao would be a perfect person to provide an expert opinion on the nature of the mathematical object (U) that I have in mind.

That is, he specializes in partial differential equations and in Fourier analysis (among other subjects), and he is also well versed with issues in differential geometry. If I can just get him to contemplate the possibilities that are inherent within U, I feel that he would be inspired to comment on it in his blog, thus conferring instantaneous legitimacy (at least in the eyes of mathematicians) to this new idea of what theoretical physics can be.

I know this all sounds ridiculous coming from an anonymous, disembodied voice on the internet, but if I were to talk to you face-to-face, I promise you that you would feel differently about all of this. I am slowly but surely building up a real world following, and they should be filtering into this forum to see how I handle myself with you guys, even if they don't take part in the conversation. So, to all of my potential interlocutors, you should be aware of the possibility that all of this can very well lead to something fairly significant, and that your ability to make a well-considered point can have a real impact on the future course of theoretical physics.

At the moment, I am highly eager to get into the special relativity (i.e. signal propagation) aspects of the model, but I have no interest in doing this unless I can feel a positive vibe coming from you guys. Indeed, I want this to be a collaborative effort (just like Terence has collaborative "polymath" projects on his blog), so that we can provide legitimacy to the idea that the openness of the WWW is truly a force for good for humanity rather than simply a place to waste a few hours every day.

 

[magpies]

Ok I'll bite what would you want us to do to help you? <-- keep in mind I am lazy and have my own projects.

 

[rewebster]

glengarry--from your post #96---if you haven't already, create a facebook page and put your writings on it (and allow comments)----

--see where it goes from there, that is, if (or maybe, since) you don't want to see if it will be accepted for publication at a journal.

--I think you're allowed to put personal writings on your own PF blog also---but I'd ask or find out first for sure...

 

[pbnjeff]

glengarry, maybe instead of standing on Bruin Walk you should just go to the MS building if you really want to talk to Terence Tao?

 

[GeorgCantor]

So much hay is made out of the fact that quantum theory—and its associated experiments—violates the principle of local causality, as canonically developed by the classical (Newtonian) and relativistic (Einsteinian) models. But no one ever really asks about what these models are 'truly' saying about physical reality. That is, in all of these theories, it is axiomatically assumed that material bodies, in the elemental sense, come in the forms of geometric points. But there is a major difference between the following two ideas:

1) points as the solutions to linear, analytical equations
2) points as 'really existing' physical objects

In fact, it is my thesis that the desire to satisfy idea #1—at least within the community of mainstream academic physics—has always overshadowed the question that idea #2 is constantly begging. And this question is:

"If the form of physical bodies, in the most elementary sense, is not that of the geometric point, then what is it?"

Mental constructs of ....(fill in the blank with "1D strings", "loops", "mathematics", "bits", or something else)

But before we even demand from ourselves a [hypothetical] answer to this question, let us return to the original question: How is local causality possible?

That is, we will assume the existence of two elementary bodies that come in the form of geometric points, and for the sake of simplicity, we will consider a one-dimensional space. Now, just like those 'cars approaching each other from opposite directions' questions, we will consider our particles, A and B, to be involved in the same kind of collision course.

So A and B are now approaching each other with some arbitrary relative speed (it makes no difference what the individual velocities might be in a given frame of reference). So, A and B get closer and closer until something happens. My question is simply this:

"What is the nature of this 'something' when we say that two physical bodies, in the form of points, have 'interacted'?"

And I ask this because of this difficulty: the only way that we can say that two points are not different is when they are, in fact, the same point. So here are the choices that we have left:

1) The two points are not interacting precisely because they are different—i.e. there is some amount of space between them.
2) It is senseless to say that interaction exists precisely because there is only a single point in existence.

Anybody have any comments about this difficulty?

This is a philosophical question and will reflect the underlying philosophy of the poster.