The flying fish model:
quantum spinor dynamics
and gravity
Spinor fields are quantum fields that dynamically change in spatial coordinates and their interaction with spacetime creates local variations in the flow of time. Spinor fields obey the Dirac equation. These fields play a key role in quantum transitions in various quantum systems. Spinor fields can lead to the creation of coherent oscillations between different spin states in a spinor Bose-Einstein condensate (BEC) [1]. These oscillations arise due to nonlinear interactions similar to the Josephson effect in superconductors. This phenomenon allows quantum systems to exhibit complex dynamics depending on initial conditions and external magnetic fields. Another relevant study [2] documents the observation of universal dynamics in a spinor Bose gas far from equilibrium. This system describes a complex behavior that can be considered universal for quantum systems in non-equilibrium conditions. This means that under certain conditions these systems can spontaneously transition to new quantum states, which is consistent with the observation of quantum transitions in spinor fields within the model.
The time gradient
The time gradient \(T_s(x)\) represents local variations in the flow of time caused by the dynamics of spinor fields and the system’s entropy. This gradient affects how fast or slow time flows in different parts of the system and is directly related to quantum transitions of spinor fields. The equation is:
\[T_s(x) = T_0 \left( 1 + \alpha_s \langle \overline{\psi}(x) \gamma^0 \psi(x) \rangle + \beta_s S(x) \right)\]
where:
– \(T_0\) is the reference time (time in the absence of quantum transitions),
– \(\alpha_s\) is a parameter determining the impact of spinor field energy density on time,
– \(\langle \overline{\psi}(x) \gamma^0 \psi(x) \rangle\) is the energy density of the spinor field,
– \(S(x)\) is the local entropy of the system,
– \(\beta_s\) is a parameter determining how entropy affects the time gradient [3].
The time gradient \(T_s(x)\) causes changes in spacetime curvature, leading to dynamic feedback between quantum transitions, gravity, and the system’s entropy. These transitions in spinor fields can cause time dilation [6].
Solitons
Solitons are stable, nonlinear quantum structures that arise as solutions to nonlinear equations and serve as stabilizers of spacetime. Besides stabilizing quantum transitions, solitons also act as carriers of quantum information about the state of their surroundings.
\[i \hbar \frac{\partial \psi_{\text{soliton}}(x,t)}{\partial t} = – \frac{\hbar^2}{2m} \nabla^2 \psi_{\text{soliton}} + V(\psi_{\text{soliton}})\]
where \(V(\psi_{\text{soliton}})\) is a nonlinear potential that ensures the stability of solitons [8].
Solitons store quantum information about quantum transitions and spinor fields in their vicinity. This information is transmitted to the rest of the system, ensuring dynamic balance and stability of spatial coordinates. Solitons act as stabilizers of quantum fields, enable stable quantum transitions and store information in dynamical systems [9].
Entropy
In this model, entropy is defined as the entropy of the spinor field, which describes the degree of disorder and quantum transitions in the system. Entropy \(S\) is calculated as the quantum entropy of the spinor field, where \(p_i\) represents the probability that the system is in state \(i\):
\[S = -k_B \sum_i p_i \ln p_i\]
where \(k_B\) is the Boltzmann constant [7].
In this model, higher entropy leads to faster time flow and less spacetime curvature because quantum transitions are more dynamic. Conversely, lower entropy leads to slower time flow and greater spacetime curvature because quantum transitions are less dynamic.
Interactions and principles of the model
Spinor fields represent quantum states of fermions. When these fields undergo quantum transitions, their energy and momentum can affect spacetime by causing changes in its curvature. In this model, quantum transitions of spinors generate a time gradient that modulates time flow depending on the local energy and momentum of the spinor fields. Spin operators do not commute with each other, leading to quantum uncertainties and quantum effects that are transferred into the dynamics of spacetime. Changes caused by the time gradient and quantum transitions do not violate the equivalence principle, as these changes are global and do not create differences between acceleration and gravity at the local level. Solitons described in the model store a finite amount of information in accordance with the holographic principle. Information is distributed throughout the system but never exceeds the limits set by the capacity of spacetime.
At the macroscopic level, these quantum transitions contribute to the formation of a time gradient that describes the flow of time in curved spacetime. This time gradient is the result of the cumulative effect of all quantum transitions in the spinor field. For macroscopic objects, we can define the time gradient as:
\[T_s(r) = T_0 \left( 1 + \alpha_s \frac{M_{\text{spinor}}}{r c^2} \right)\]
where:
– \(T_0\) is the reference time in the absence of quantum transitions,
– \(\alpha_s\) is a parameter dependent on the interaction of spinor fields with spacetime,
– \(M_{\text{spinor}}\) is the total energy contribution from the spinor field,
– \(r\) is the distance from a massive object,
– \(c\) is the speed of light.
This relationship describes the slowing down of time in an object’s gravitational field, as predicted by general relativity, but is also related to quantum dynamics. Changes in the states of the spinor field at the quantum level are transformed into the curvature of spacetime on large scales, which we perceive as gravity. Quantum fluctuations in spinor fields are suppressed by decoherence processes and have a negligible effect on the overall stability of the metric. The time gradient becomes the dominant mechanism. For macroscopic objects, the time gradient will be consistent with the Schwarzschild metric:
\[T_s(r) = \sqrt{1 – \frac{2GM}{r c^2}}\]
where \(M\) is the mass of the object and \(r\) is the distance from the object [7].
Mass is the cumulative result of these elementary interactions between particles and the Higgs field. These interactions contribute to gravitational effects, which are described by the equations of general relativity. In the model, mass is associated with a time gradient arising from quantum transitions in spinor fields:
\[M_{\text{spinor}} = \frac{r c^2}{\alpha_s} \left( \frac{T_s(r)}{T_0} – 1 \right)\]
Precession of spinors in the relativistic context
When time dilation is applied to spinor precession, its observed value changes. Precession \(\theta\) in the particle’s reference frame changes to precession \(\theta’\) from the observer’s inertial frame as per the relation:
\[\theta’ = \frac{\theta}{\gamma}\]
This relation shows that as the object’s speed increases, the observed precession decreases. Time dilation in the gravitational field with potential is adjusted according to the relation:
\[\theta’ = \theta \sqrt{1 – \frac{2\phi}{c^2}}\]
where:
\(\theta\) is the original precession in the absence of a gravitational field, and \(\theta’\) is the adjusted precession in the gravitational field.
Strong gravitational fields can slow down the precession of spinors, manifesting as a reduced precession value. Quantum simulations are an essential tool for testing model predictions [6]. Similarly, it is possible to simulate quantum transitions in spinor fields to observe their effect on the curvature of spacetime.
Summary
This model is based on the idea that quantum transitions in spinor fields create a time gradient. This leads to the emergence of gravitational fields on macroscopic scales, while quantum phenomena are stabilized by solitons and the holographic principle. Experimental simulations and theoretical work, as reported, support this model and show that quantum gravity can be probed through quantum simulations and experiments [12].
Experimental section of the Flying Fish model
The objective of this experiment is to determine whether coherent magnetic oscillations created by three closely spaced harmonic frequencies can accelerate the quantum precession of proton spinor states. If the spinor flip is accelerated to the target frequency, it is thought to induce local gravitational effects similar to those found in weak gravitational fields.
To generate coherent magnetic oscillations, we will use three extremely close harmonic frequencies, which are derived from the fundamental Larmor frequency of protons in the test sample. These selected frequencies are slightly shifted to create low-frequency beat components in the Hz range. The frequencies are:
– First frequency: \( f_1 = 127.740000 \, \text{MHz} \),
– Second frequency: \( f_2 = 127.74000563 \, \text{MHz} \),
– Third frequency: \( f_3 = 127.74001126 \, \text{MHz} \).
These frequencies are chosen to create interference (beat) frequencies that lie within the Hz range, specifically near the target value of 5.63 Hz. The differences between these extremely close frequencies generate low-frequency components that modulate the quantum flipping of spinors.
The interference (beat) frequencies are:
\[f_{\text{beat1}} = f_2 – f_1 = 5.63 \, \text{Hz}, \quad f_{\text{beat2}} = f_3 – f_2 = 5.63 \, \text{Hz}, \quad f_{\text{beat3}} = f_3 – f_1 = 11.26 \, \text{Hz}.\]
These low-frequency beat components are crucial for achieving the desired spinor flipping frequency, enabling quantum transitions in line with the gravitational effects similar to those experienced in Earth’s orbit.
Generating magnetic pulses
**Helmholtz coils** will be used to generate the magnetic oscillations, ensuring a homogeneous magnetic field. The three coils will generate harmonic frequencies \( f_1 \), \( f_2 \), and \( f_3 \), creating coherent magnetic oscillations. The magnetic pulses will be synchronized with a precision of ±0.1 radians. The pulse settings are as follows:
– Pulse duration: 10 microseconds,
– Interval between pulses: 20 microseconds,
– Number of cycles per pulse: 100 cycles per pulse.
By creating interference between the frequencies \( f_1 \), \( f_2 \), and \( f_3 \), low-frequency beat components will be generated, which are critical for achieving the desired spinor flipping frequency. The differences between these frequencies will produce beat frequencies in the Hz range, specifically 5.63 Hz, enabling modulation of spinor flipping and its quantum dynamics. These low-frequency components will be modulated to the target frequency, calculated based on experimental conditions to match the gravitational effects observed in Earth’s orbit (gravitational acceleration approximately 8.7 m/s²).
Sample and environment preparation
The test material will be titanium hydride (TiH₂) or palladium hydride (PdHx), as these materials efficiently bind hydrogen atoms. They contain enough protons for measuring precession. The experiment will be conducted in a cryogenic environment with a temperature below 10 K, ensuring the stability of quantum states and minimizing thermal noise. The sample will be placed at the center of the experimental setup between three Helmholtz coils, which will generate a homogeneous magnetic field.
Proton precession in the system will be measured using NMR spectroscopy. The base precession frequency of protons without applied magnetic waves is given by the Larmor frequency. After applying magnetic pulses, we expect a change in proton precession frequency, indicated by the following equation:
\[\Delta \omega = \omega_{\text{prec}} – \omega_L\]
where \( \omega_{\text{prec}} \) is the reduced precession frequency under the influence of coherent low-frequency oscillations.
Changes in the gravitational field will be monitored using highly sensitive gravimeters placed near the sample. The gravimeters will detect any deviations in the gravitational field caused by the stabilization of spinor states. Flipping the spinor is expected to reduce local gravitational effects. This spinor flipping will be accompanied by a measurable change in proton precession frequency, recorded using NMR spectroscopy.
After the magnetic fields are turned off, the gravitational field returns to its original state, proving that the changes are related to the presence of modulated spinor fields and confirming the connection between quantum spinor rotation and gravitational effects.
Application of the model in a closed chamber
Quantum transitions in spinor fields create a temporal gradient within a closed chamber, which affects how quickly or slowly time flows in different parts of the system. This temporal gradient depends on the energy density of the spinor field and local entropy. Areas with higher energy density experience a slowing of time, while in areas with lower energy density, time flows faster. This phenomenon is analogous to the effect observed in strong gravitational fields, where time flows more slowly near massive objects and more quickly in more distant areas with a weaker gravitational field. In the closed chamber, however, this effect is achieved not through a gravitational field but through dynamic quantum transitions in spinor fields.
To describe the energy changes brought by longitudinal waves into the system, we can use the formula for the energy density of quantum fields, which plays a key role in forming the temporal gradient:
\[\rho(x,t) = \frac{1}{2} \left( \epsilon \left( \frac{\partial \psi}{\partial t} \right)^2 + \frac{1}{\mu} (\nabla \psi)^2 \right)\]
This equation describes how the energy of longitudinal waves changes based on their temporal and spatial propagation. In a system where quantum transitions create longitudinal waves, this energy directly affects local time dilation and contributes to the change in the flow of time. Solitons allow the system to minimize quantum fluctuations that could otherwise destabilize the temporal gradient. In the closed chamber, solitons help maintain balance and stability during quantum transitions, thereby supporting the stable propagation of the temporal gradient throughout the entire system.
\[S_{\text{max}} \leq \frac{k_B A}{4 L_P^2}\]
This relation limits the maximum number of quantum states or transitions the system can host, thus influencing the dynamics of quantum transitions and the formation of longitudinal waves. In the closed chamber, where quantum transitions are limited by the surface area, the holographic principle governs how much quantum information the system can store and transmit.
Experimental realization
To experimentally verify this model, we can design a closed chamber from materials that were used in previous experiments. Magnetic pulses would be used to generate quantum transitions in spinor fields, synchronizing quantum transitions and creating stable longitudinal waves. The experiment should show measurable changes in the flow of time in different parts of the closed chamber. Areas with higher energy density would exhibit slower time flow compared to areas with lower energy density. This effect would be evidence that quantum phenomena on a microscopic level can cause changes in spacetime curvature.
Applications
This experiment could pave the way for technologies to improve and control gravity, enabling new methods of manipulating objects, space applications, or optimizing energy consumption for cargo transportation. The design of the experiment is based on creating stable conditions where accelerated spinor frequencies of nucleons in the experimental material can generate measurable changes in the gravitational field. This field arises exclusively in the material itself, which in further experiments can create a coherent quantum field affecting the internal environment surrounded by a similar device.
The flying fish model represents a new approach to understanding the interplay between spinor fields and the curvature of spacetime. Through experimental verification and further theoretical investigation, this model could provide new insight into the fundamental nature of gravity and open up new possibilities for technological innovation.
Author
Madala Roman I madala@modifiedplanck.com I October, 2024
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