Grand Unified Theory - Taking apart the old
Throw a stone in a lake and watch he waves propagate away from the point of impact. Listen to a distant sound that has traveled to you from its source. Shake a rope and watch the waves travel down the rope. Tune in a distant radio station, the radio waves have traveled outward from the station to you. Watch the waves in the ocean as they travel into the shore.
In short, waves propagate, its their nature to do so, and that is what they invariably do. Maxwell's equations unequivocally demonstrate the fields propagate at light speed. Matter waves, however, remain "stuck" in the matter. Why do they not propagate? What "sticks" them?
An answer to this question was presented by Erwin Schrödinger and Werner Heisenberg at the Copenhagen conventions. The Copenhagen interpretation states that elementary particles are composed of particle-like bundles of waves. These bundles are know as a wave packets. The wave packets move at velocity V. These wave packets are localized (held is place) by the addition of an infinite number of component waves. Each of these component waves has a different wavelength or wave number. An infinite number of waves each with a different wave number is required to hold a wave packet fixed in space.
This argument has two major flaws. It does not describe the path of the quantum transition and an infinite number of real waves cannot exist within a finite universe.
Max Born attempted to side step these problems by stating that the wave packets of matter are only mathematical functions of probability. Only real waves can exist in the real world, therefore an imaginary place of residence, called configuration space, was created for the probability waves. Configuration space contains only functions of kinetic and potential energy. Forces are ignored in configuration space.
-Frank Znidarsic
"Forces of constraint are not an issue. Indeed, the standard Lagrangian formulation ignores them...In such systems, energies reign supreme, and it is no accident that the Hamiltonian and Lagrangian functions assume fundamental roles in a formulation of the theory of quantum mechanics.."
-Grant R. Fowles University of Utah
"In order to obtain such relations that we conjecture to be true, we use the method of abstraction from a Lagrangian field-theory model. In other words, we construct a mathematical theory of the strongly interacting particles, which may or may not have anything to do with reality, find suitable algebraic relations that hold in the model, postulate their validity, and then throw away the model."
-Murray Gell-Mann, one of the fathers of quantum chromodynamics
At its simplest, the Lagrangian is just the kinetic energy of a system T minus its potential energy V.
L = T - V
What I will show is that the Lagrangian, rather than advancing a deep understanding of physics, actually blocked an understanding of the real fields involved. Because Lagrange (and Hamilton) misassigned the fields or operators, and because this formulation has been so successful and authoritative, many generations of physicists have been prevented or diverted from pulling this equation apart.
What do I mean by that? Well, if we take Lagrange at his word, we would seem to have only one field here. In celestial mechanics, the gravitational field causes both the kinetic energy and the potential energy. In quantum mechanics, charge causes both the kinetic energy and the potential.
But let's start with celestial mechanics, since that is where the Lagrangian initially came from. The motions of celestial bodies are gravitational, we are taught, and the potential energy is gravitational potential. That being so, the Lagrangian must have originally been a single field differential. In other words, we are subtracting a field from itself.
Our first question should be, is that even possible? Can you subtract gravity from itself, to get a meaningful energy? Or, to be a bit more precise, can you subtract gravitational potential from gravitational kinetic energy? That would be like subtracting the future from the present, would it not? Potential energy is just energy a body would have, if we let it move; and kinetic energy is energy that same body has after we let it move. So how can we subtract the first from the second?
Another problem is that for Newton, the two energies would have to sum to zero, by definition. This is clear for a single body, and a system is just a sum of all the single bodies in it. Therefore, both the single bodies and the system of bodies must sum to zero, at any one time, and at all times. In fact, Newton actually used this truism to solve other problems. He let potential energy equal kinetic energy, to solve various problems. But here, we are told that potential energy and kinetic energy don't sum to zero, and aren't equal, otherwise the Lagrangian would always be either zero or 2T. A Lagrangian that was always zero would be useless, wouldn't it, as would a Lagrangian that was just 2T.
Many people have told me I am off my rocker, questioning the Lagrangian. They tell me that Newton never summed V and T to zero, and no one else did either. Interesting, since the physics book I now have in my lap says otherwise. In the chapter on Gravity, subchapter on Energy Conservation, we get the problem of an asteroid falling directly to Earth:
"Since gravity is a conservative force, the total mechanical energy remains constant as the asteroid falls toward the Earth. Thus, as the asteroid moves closer to the Earth and U becomes increasingly negative, the kinetic energy K must become increasingly positive so that their sum, U + K, is always zero."
Of course we can see that straight from the equations:
V = -GmM/r
K = GmM/r
If it isn't those energies Lagrange is summing, which energies is it? What other energies does a body have in Celestial Mechanics? The mainstream cannot tell me E/M, since they have told us E/M is negligible in Celestial Mechanics. I will be told a body can have sideways motion, as in an orbit, but since orbits also conserve energy-we are taught-the total kinetic energy must still equal K and still sum to zero with V. Otherwise the body would either be gaining or losing energy all the time, and the orbit wouldn't be stable.
I will be told that mainstream physicists are more interested in applying the Lagrangian and Hamiltonian to quantum physics, as in the Schrodinger equation. OK, but since they have taught us that gravity is negligible at the quantum level, both V and T must come from charge or charge potential, right? In which case we should also have conservation, in which case we should have a sum to zero.
They just forget all this when it comes time to derive the equations, and they let themselves say and write whatever they want.
We can see another problem in this quote from Wiki:
"For example, consider a small frictionless bead traveling in a groove. If one is tracking the bead as a particle, calculation of the motion of the bead using Newtonian mechanics would require solving for the time-varying constraint force required to keep the bead in the groove. For the same problem using Lagrangian mechanics, one looks at the path of the groove and chooses a set of independent generalized coordinates that completely characterize the possible motion of the bead. This choice eliminates the need for the constraint force to enter into the resultant system of equations."
The problem there is that one solves by ignoring forces, looking only at the path. Why is that a problem? Because if you are studying the path and not the forces, you will come to know a lot about the path and nothing about the forces, which is what we see in current physics. The Lagrangian calculates forces by ignoring forces. It goes right around them. If that were just a matter of efficiency, it might be tenable, but we have seen that historically, the Lagrangian and action were chosen to avoid the questions of forces, which physicists were not able to answer. They weren't able to answer them in the 17th century and they aren't able to answer them now. So they misdirect us into equations that “summarize the dynamics of a system” by ignoring the dynamics of a system. Dynamics means forces.
Yes, we are told at Wiki that the Lagrangian is “a function that summarizes the dynamics of a system.” So here is yet another problem. We are then told that T is the kinetic energy of the system. Well, shouldn't the kinetic energy already be a function that summarizes the dynamics of the system? Dynamics means motions caused by forces, so the motion of the particles should be an immediate measure of all the forces on them. In other words, the gravity field should already be causing motion, so there is no reason to add or subtract it from the kinetic energy. Either the gravity field is causing motion, or it isn't. If it is, then it should be included in the kinetic energy. If it isn't, why isn't it?
But physicists have never bothered themselves with these logical questions. Why haven't they? Because they found early on that the Lagrangian worked fairly well in many situations. Like Newton's gravitational equation, it was an equation that they were able to fit to experiments. This is very important to physicists, for obvious reasons. But the fact that the Lagrangian worked meant that the kinetic energy and potential energy did not sum to zero, which meant that the bodies were not in one field only. To express energy as a differential, you must have two energies, which means you must have two fields. One field can't give you two energies at the same time. You cannot get a field differential from one field. As soon as the Lagrangian was found to be non-zero, physicists should have known that celestial mechanics was not gravity only. It had to be two fields in vector opposition.
By the same token, as soon as the Lagrangian was discovered to work in quantum mechanics, the physicists should have known that QM and QED were not E/M only. The non-zero Lagrangian is telling us very clearly that we have two fields. Just as gravitational potential cannot resist gravitational kinetic energy, charge potential cannot resist charge. Charge potential is not charge resistance, it is future charge. You cannot subtract the future from the present in an equation!
This proves once again that gravity is present in a big way at the quantum level, and that E/M forces are a major player on the cosmic scale.
-Miles Mathis
In short, waves propagate, its their nature to do so, and that is what they invariably do. Maxwell's equations unequivocally demonstrate the fields propagate at light speed. Matter waves, however, remain "stuck" in the matter. Why do they not propagate? What "sticks" them?
An answer to this question was presented by Erwin Schrödinger and Werner Heisenberg at the Copenhagen conventions. The Copenhagen interpretation states that elementary particles are composed of particle-like bundles of waves. These bundles are know as a wave packets. The wave packets move at velocity V. These wave packets are localized (held is place) by the addition of an infinite number of component waves. Each of these component waves has a different wavelength or wave number. An infinite number of waves each with a different wave number is required to hold a wave packet fixed in space.
This argument has two major flaws. It does not describe the path of the quantum transition and an infinite number of real waves cannot exist within a finite universe.
Max Born attempted to side step these problems by stating that the wave packets of matter are only mathematical functions of probability. Only real waves can exist in the real world, therefore an imaginary place of residence, called configuration space, was created for the probability waves. Configuration space contains only functions of kinetic and potential energy. Forces are ignored in configuration space.
-Frank Znidarsic
"Forces of constraint are not an issue. Indeed, the standard Lagrangian formulation ignores them...In such systems, energies reign supreme, and it is no accident that the Hamiltonian and Lagrangian functions assume fundamental roles in a formulation of the theory of quantum mechanics.."
-Grant R. Fowles University of Utah
"In order to obtain such relations that we conjecture to be true, we use the method of abstraction from a Lagrangian field-theory model. In other words, we construct a mathematical theory of the strongly interacting particles, which may or may not have anything to do with reality, find suitable algebraic relations that hold in the model, postulate their validity, and then throw away the model."
-Murray Gell-Mann, one of the fathers of quantum chromodynamics
At its simplest, the Lagrangian is just the kinetic energy of a system T minus its potential energy V.
L = T - V
What I will show is that the Lagrangian, rather than advancing a deep understanding of physics, actually blocked an understanding of the real fields involved. Because Lagrange (and Hamilton) misassigned the fields or operators, and because this formulation has been so successful and authoritative, many generations of physicists have been prevented or diverted from pulling this equation apart.
What do I mean by that? Well, if we take Lagrange at his word, we would seem to have only one field here. In celestial mechanics, the gravitational field causes both the kinetic energy and the potential energy. In quantum mechanics, charge causes both the kinetic energy and the potential.
But let's start with celestial mechanics, since that is where the Lagrangian initially came from. The motions of celestial bodies are gravitational, we are taught, and the potential energy is gravitational potential. That being so, the Lagrangian must have originally been a single field differential. In other words, we are subtracting a field from itself.
Our first question should be, is that even possible? Can you subtract gravity from itself, to get a meaningful energy? Or, to be a bit more precise, can you subtract gravitational potential from gravitational kinetic energy? That would be like subtracting the future from the present, would it not? Potential energy is just energy a body would have, if we let it move; and kinetic energy is energy that same body has after we let it move. So how can we subtract the first from the second?
Another problem is that for Newton, the two energies would have to sum to zero, by definition. This is clear for a single body, and a system is just a sum of all the single bodies in it. Therefore, both the single bodies and the system of bodies must sum to zero, at any one time, and at all times. In fact, Newton actually used this truism to solve other problems. He let potential energy equal kinetic energy, to solve various problems. But here, we are told that potential energy and kinetic energy don't sum to zero, and aren't equal, otherwise the Lagrangian would always be either zero or 2T. A Lagrangian that was always zero would be useless, wouldn't it, as would a Lagrangian that was just 2T.
Many people have told me I am off my rocker, questioning the Lagrangian. They tell me that Newton never summed V and T to zero, and no one else did either. Interesting, since the physics book I now have in my lap says otherwise. In the chapter on Gravity, subchapter on Energy Conservation, we get the problem of an asteroid falling directly to Earth:
"Since gravity is a conservative force, the total mechanical energy remains constant as the asteroid falls toward the Earth. Thus, as the asteroid moves closer to the Earth and U becomes increasingly negative, the kinetic energy K must become increasingly positive so that their sum, U + K, is always zero."
Of course we can see that straight from the equations:
V = -GmM/r
K = GmM/r
If it isn't those energies Lagrange is summing, which energies is it? What other energies does a body have in Celestial Mechanics? The mainstream cannot tell me E/M, since they have told us E/M is negligible in Celestial Mechanics. I will be told a body can have sideways motion, as in an orbit, but since orbits also conserve energy-we are taught-the total kinetic energy must still equal K and still sum to zero with V. Otherwise the body would either be gaining or losing energy all the time, and the orbit wouldn't be stable.
I will be told that mainstream physicists are more interested in applying the Lagrangian and Hamiltonian to quantum physics, as in the Schrodinger equation. OK, but since they have taught us that gravity is negligible at the quantum level, both V and T must come from charge or charge potential, right? In which case we should also have conservation, in which case we should have a sum to zero.
They just forget all this when it comes time to derive the equations, and they let themselves say and write whatever they want.
We can see another problem in this quote from Wiki:
"For example, consider a small frictionless bead traveling in a groove. If one is tracking the bead as a particle, calculation of the motion of the bead using Newtonian mechanics would require solving for the time-varying constraint force required to keep the bead in the groove. For the same problem using Lagrangian mechanics, one looks at the path of the groove and chooses a set of independent generalized coordinates that completely characterize the possible motion of the bead. This choice eliminates the need for the constraint force to enter into the resultant system of equations."
The problem there is that one solves by ignoring forces, looking only at the path. Why is that a problem? Because if you are studying the path and not the forces, you will come to know a lot about the path and nothing about the forces, which is what we see in current physics. The Lagrangian calculates forces by ignoring forces. It goes right around them. If that were just a matter of efficiency, it might be tenable, but we have seen that historically, the Lagrangian and action were chosen to avoid the questions of forces, which physicists were not able to answer. They weren't able to answer them in the 17th century and they aren't able to answer them now. So they misdirect us into equations that “summarize the dynamics of a system” by ignoring the dynamics of a system. Dynamics means forces.
Yes, we are told at Wiki that the Lagrangian is “a function that summarizes the dynamics of a system.” So here is yet another problem. We are then told that T is the kinetic energy of the system. Well, shouldn't the kinetic energy already be a function that summarizes the dynamics of the system? Dynamics means motions caused by forces, so the motion of the particles should be an immediate measure of all the forces on them. In other words, the gravity field should already be causing motion, so there is no reason to add or subtract it from the kinetic energy. Either the gravity field is causing motion, or it isn't. If it is, then it should be included in the kinetic energy. If it isn't, why isn't it?
But physicists have never bothered themselves with these logical questions. Why haven't they? Because they found early on that the Lagrangian worked fairly well in many situations. Like Newton's gravitational equation, it was an equation that they were able to fit to experiments. This is very important to physicists, for obvious reasons. But the fact that the Lagrangian worked meant that the kinetic energy and potential energy did not sum to zero, which meant that the bodies were not in one field only. To express energy as a differential, you must have two energies, which means you must have two fields. One field can't give you two energies at the same time. You cannot get a field differential from one field. As soon as the Lagrangian was found to be non-zero, physicists should have known that celestial mechanics was not gravity only. It had to be two fields in vector opposition.
By the same token, as soon as the Lagrangian was discovered to work in quantum mechanics, the physicists should have known that QM and QED were not E/M only. The non-zero Lagrangian is telling us very clearly that we have two fields. Just as gravitational potential cannot resist gravitational kinetic energy, charge potential cannot resist charge. Charge potential is not charge resistance, it is future charge. You cannot subtract the future from the present in an equation!
This proves once again that gravity is present in a big way at the quantum level, and that E/M forces are a major player on the cosmic scale.
-Miles Mathis