Take, for example, such a concept as a minimum flow, that is, a gradient vector field, the level surfaces of which are the minimum surfaces. Then the globally minimal flow, evolving to an absolutely minimal state, could be compared with a quantum vacuum, and the locally minimal flow could be compared with fields and particles. At the same time, it is clear that it is necessary to correctly choose the space in which this minimum flow moves.
The structure wave concept defines thus generates the quantum vacuum:
The successive amplitude values of a suitable structure wave period (that can have a billion digits, yet all must yield amplitude 9) can be reiterated as pulses describing any gradient field with the required local minima/maxima while the flow is translated as the continuation of the period that may be thought as a vector.
The structure wave concept defines thus generates the quantum vacuum:
The successive amplitude values of a suitable structure wave period (that can have a billion digits, yet all must yield amplitude 9) can be reiterated as pulses describing any gradient field with the required local minima/maxima while the flow is translated as the continuation of the period that may be thought as a vector.
This subject has a links with the following math. fields , therefore it is possible that the quantum vacuum have analogies in mathematics
Equations
- Dirac
- Klein–Gordon
- Pauli
- Rydberg
- Schrödinger
Formulations
- Heisenberg
- Interaction
- Matrix mechanics
- Path integral formulation
- Phase space
- Schrödinger
Other
- Quantum
- algebra
- calculus
- differential
- stochastic
- geometry
- group
- Q-analog
Maged Gumaan Bin-Saad,
Everything that you have listed can be attributed to the mathematical apparatus that is used to describe the quantum vacuum, and I meant the analogy between a mathematical phenomenon and a physical phenomenon. In other words, I am looking for a mathematical object (for example, an evolving vector field of a seven-dimensional sphere), which for its description requires the same mathematical apparatus as a quantum vacuum.
Quantum vacuum is related to physics, not to mathematics, which is only modeling the Nature using its abstract language; This way, mathematics can model also the quantum vacuum, if its physical properties will be understood enough to get modelled by mathematics. That's it.
Structure wave theory shows how mathematics as a structurally active language based on the release of structure waves is converted into physics.
I agree! But the reality is that science does not understand how the atom works. And without this it is impossible to understand the structure of space.
Victor P. Revenko,
And if we move from the opposite, first establish the structure of space, and then deal with the work of the atom. In my mathematical constructions, I proceed from the fact that matter moves on the surface of a seven-dimensional sphere, so I look for a solution for vacuum at the intersection of two quadratic harmonic functions in 8-dimensional Euclidean space, where one harmonic function is a quadratic interval of 8-dimensional Euclidean space, and the second is a quadratic interval of an 8-dimensional space with a neutral metric. In this case, at the intersection of the level surfaces of these functions, a Clifford torus S3xS3 is formed, and if the radius of the hypersphere of the 8-dimensional Euclidean space has a certain dependence on the evolutionary parameter, then in the process of evolution, the radius of one of the spheres of the Clifford torus will increase, and the other will decrease. As a result, we have a 3-dimensional Euclidean space, as a subspace of Minkowski space, which is hidden in its compact image S3xS1. Other local solutions (including those describing the work of an atom) in the form of a pair of harmonic functions must satisfy this global (vacuum) solution.
See the classics of the XYIII-XIX centuries, the XX century is hopelessly lost. First you need to understand physics, and then choose a mathematical method! I can tell you that you are looking in the wrong direction. Only taking into account the presence of the medium (ether) can explain how field forces (electromagnetism, gravity, etc.) work, as well as the propagation of light.
Matter in motion presupposes a medium (ether), and the question of the space in which this medium moves requires separate consideration. I touch on this issue in my works and sometimes raise it publicly, for example, here https://www.physicsforums.com/threads/geometry-of-matrix-dirac-algebra.994329/
Anatolij K. Prykarpatski,
Do you think we don't understand enough quantum vacuum to model it? But we know something, for example, that the quantum vacuum has the symmetries of both the Dirac algebra and the gauge transformation group, and that the vacuum is not stable, since it can generate particles under perturbation. Isn't that enough?
Hi, Igor, can you develop your arguments in more concrete analytical reasonings with clear inferences subject to the question "How to eat this, and what does it mean, if any?"
With warm regards,
sincerely,
A.
Anatolij K. Prykarpatski,
You are asking me to express my thoughts in the analytical language of mathematics. Well, I'll try to do it without formulas. I understand perfectly well that physics is the principle of least action, so my main method is to generalize the principle of least action. At the same time, I understand that in the case of physics, the generalization must be specific (adequate to reality), therefore the generalized principle of least action is an integral variational equation that delivers the minimum flows (vector fields of velocities of matter particles) on the seven-dimensional sphere. Locally, the acceleration field of the minimum flow satisfies the Laplace differential equation in 8-dimensional Euclidean space, which delivers harmonic functions, but since we consider flows on a sphere, we need to take a pair of harmonic functions, one of which is a quadratic function of the metric interval of Euclidean space, and the other is arbitrary ... The intersection of the level surfaces of a pair of harmonic functions is a 6-dimensional compact subspace of the 7-sphere and determines the local geometry of the flow. In the case of a vacuum (globally minimal) flow, this is the geometry of the Clifford torus, and for locally minimal flows this issue has not yet been studied. Something like this.
Igor.
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