What Zitterbewegung is

Quantum Zitterbewegung is chaotic motion of small particles in vacuum due to quantum fluctuations of it. In dense aether model it's an analogy of Brownian motion of polen grains within water, which are kept in motion with thermal fluctuations of water molecules. But Zittebewegung doesn't cease down even at absolute zero temperature and as such it's closely related to so-called Zero Point Energy.

Another difference of Zitterbewegung from Brownian motion is, the quantum motion isn't constrained to changes of location (i.e. vector waves or fields) - but also density, that is the density fluctuations of vacuum change energy density of particles (scalar waves or fields). This is where the things become interesting for me, because this mode of fluctuations can be source of energy, scalar beams and antigravity effects.

From dense aether model follows that if we constrain particle in motion across space, it will start to fluctuate in temporal dimension, i.e. its scalar fluctuations become prominent. This routinely happens with electrons constrained within graphene, superconductors and topological insulators - but also with electrons constrained in motion with charged capacitors and bucking magnets which are often utilized in overunity and antigravity experiments. Such an electrons have increased tendency to interract with density fluctuations of vacuum and they can be dragged with them, thus violating momentum and inertia conservation laws.

Welcome to Zitter Institute

The Zitter Institute is an International Working Group created in 2023, whose primary objective is the promotion and evolution of Zitter Models of the electron’s dynamics.

Let me add something about the theory of circular motion.

From the principle of least action applied to circular motion, the Cauchy-Riemann conditions are easily deduced, and hence the harmony of functions. And since quantum mechanics operates with complex numbers, it is expected that the action is the length of the phase path (latitude) on a seven-dimensional sphere.

Let

S=∫φ(t)dt
Then a variation of the action

δ∫φ(t)dt=0
leads to the differential equation

d²φ/dt²=0
which entails
ω=dφ/dt=const
Next, let the motion of the circle be set in evolution so that the radius of the circle is related to the evolutionary parameter of time t by dependence

at=log(ρ)

V_r=dρ/dt=aρ

V_r=a(x∂x + y∂y)

In turn,

ω=dφ/dt=V_τ/ρ=b

V_τ=b(y∂x - x∂y)

Thus, due to the correspondence of the algebra of complex numbers and the resulting algebra of linear vector fields, we have

1= x∂x + y∂y

i = y∂x - x∂y

v = a + bi = c

If each point of the plane serves as the center of a rotating circle, then each point corresponds to a local algebra of vector fields isomorphic to the field of complex numbers. In this case, only conformal transformations of the plane preserve local algebras of vector fields, which in turn induce analytic transformations of the complex plane.

Follow the link below
Article Applications of the local algebras of vector fields to the m...

Quote from bayak

Let me add something about the theory of circular motion.

From the principle of least action applied to circular motion, the Cauchy-Riemann conditions are easily deduced, and hence the harmony of functions. And since quantum mechanics operates with complex numbers, it is expected that the action is the length of the phase path (latitude) on a seven-dimensional sphere.

Let

S=∫φ(t)dt
Then a variation of the action

δ∫φ(t)dt=0
leads to the differential equation

d²φ/dt²=0
which entails
ω=dφ/dt=const
Next, let the motion of the circle be set in evolution so that the radius of the circle is related to the evolutionary parameter of time t by dependence

at=log(ρ)

V_r=dρ/dt=aρ

V_r=a(x∂x + y∂y)

In turn,

ω=dφ/dt=V_τ/ρ=b

V_τ=b(y∂x - x∂y)

Thus, due to the correspondence of the algebra of complex numbers and the resulting algebra of linear vector fields, we have

1= x∂x + y∂y

i = y∂x - x∂y

v = a + bi = c

If each point of the plane serves as the center of a rotating circle, then each point corresponds to a local algebra of vector fields isomorphic to the field of complex numbers. In this case, only conformal transformations of the plane preserve local algebras of vector fields, which in turn induce analytic transformations of the complex plane.

Follow the link below
Article Applications of the local algebras of vector fields to the m...

Display More

Off topic, but how do you edit your equations here? I usually am using MS Word and I find that difficult. I'm too lazy to do my own research and just want suggestions. I guess I could use ChatGPT

Useful link

Gaugeless Maxwell's equations and the Zitterbewegung electron model are related to Cauchy-Riemann conditions:

from Maxwell's Equations and Occam's Razor

The equation ∂G = 0 can be seen as an extension in four dimensions of the Cauchy-Riemann conditions for analytic functions of a complex (two dimensional) variable [15,18]. In [18] Hestenes writes: “Members of this audience will recognize ∂²ψ₀ = 0 as a generalization of the Cauchy–Riemann equations to space–time, so we can expect it to have a rich variety of solutions. The problem is to pick out those solutions with physical significance.”

Quote from bayak

Let me add something about the theory of circular motion.

From the principle of least action applied to circular motion, the Cauchy-Riemann conditions are easily deduced, and hence the harmony of functions. And since quantum mechanics operates with complex numbers, it is expected that the action is the length of the phase path (latitude) on a seven-dimensional sphere.

From the article I referred to, it follows that the generalized Cauchy-Riemann conditions are a condition for preserving a local Clifford algebra isomorphic to the Dirac algebra. However, physics is not algebra, physics is the principle of least action, so the main thing is the geometric-dynamic interpretation of the action.

Quote from bayak

From the article I referred to, it follows that the generalized Cauchy-Riemann conditions are a condition for preserving a local Clifford algebra isomorphic to the Dirac algebra. However, physics is not algebra, physics is the principle of least action, so the main thing is the geometric-dynamic interpretation of the action.

correct, but in natural units the Action is dimensionless and is related to the Zitterbewegung phase (dimensionless value) and Aharonov-Bhom equations, not to its time integral

Quote from bayak

From the article I referred to, it follows that the generalized Cauchy-Riemann conditions are a condition for preserving a local Clifford algebra isomorphic to the Dirac algebra. However, physics is not algebra, physics is the principle of least action, so the main thing is the geometric-dynamic interpretation of the action.

Physics is not mathematics. Physics is the principle of the absoluteness of the motion of matter, therefore the main thing is the material-energetic mathematical interpretation of the motion of matter.

Quote from bayak

Useful link

Θανκς, θατ ηελψ.

Quote from Aleksandr Nikitin

Physics is not mathematics. Physics is the principle of the absoluteness of the motion of matter, therefore the main thing is the material-energetic mathematical interpretation of the motion of matter.

Physics is not buzzwords strung together meaninglessly.

Quote from gio06

correct, but in natural units the Action is dimensionless and is related to the Zitterbewegung phase (dimensionless value) and Aharonov-Bhom equations, not to its time integral

You're right, I wrote something stupid. In fact, this action is a phase, so the integrand should be the rate of change of the phase (Lagrangian), not the phase.

S=∫ω(t)dt

Quote from Aleksandr Nikitin

Physics is not mathematics. Physics is the principle of the absoluteness of the motion of matter, therefore the main thing is the material-energetic mathematical interpretation of the motion of matter.

From a philosophical point of view, this is true, but from the point of view of physics, mathematics is important and not philosophy.

My philosophy

Thanks for posting our mini-conference, here are more of this type: http://th.if.uj.edu.pl/~dudaj/QMFNoT

Here is this direct confirmation of electron zitterbewegung/de Broglie clock: for ~81MeV electrons distance between ticks agree with silicon crystal lattice - they observe increased absorption: https://link.springer.com/article/10.1007/s10701-008-9225-1

For those still in doubt, this is exactly the same mechanism as in neutrino oscillations: https://en.wikipedia.org/wiki/…pagation_and_interference

Update: Evolving field configuration in agreement with electron properties, and mechanisms of clock propulsion: https://community.wolfram.com/groups/-/m/t/3398814

Update: Recording from 2nd Zitterbewegung miniconference:

Quote from bayak

From a philosophical point of view, this is true, but from the point of view of physics, mathematics is important and not philosophy.

My philosophy

Your book is called "Mathematical Notes on the Nature of Things", and not "The physical nature of things described by means of mathematics"

The fundamental error of modern science lies in the mathematization of physics. In order to solve the problem of cold nuclear fusion, it is necessary to put physics in the main place:

Physics is the King!

Mathematics is the Queen!

If someone is interested in learning about the origin of the Dirac algebra, then I can report that the Lie algebras of the Dirac algebra are isomorphic to the algebra of tangent vector fields to the hyperspheres of an 8-dimensional space with a neutral metric, and the hypersphere is isomorphic to the space S³xR⁴

bayak what do you think about the Dirac electron deep levels ( and the its possible Lenr involvement ) as presented by Paillet and Meulenberg ?

deep dirac levels - Google Suche

Quote from bayak

If someone is interested in learning about the origin of the Dirac algebra, then I can report that the Lie algebras of the Dirac algebra are isomorphic to the algebra of tangent vector fields to the hyperspheres of an 8-dimensional space with a neutral metric, and the hypersphere is isomorphic to the space S³xR⁴

These solutions are criticized due to the lack of strict mathematical validity. Personally, I believe that the non-relativistic approach has not yet exhausted itself. I mean the generalized Schrödinger equation from the article