2026-09-04
Turning on and off acceleration as a projection of higher splitting
Application
Could acceleration not arise anew, but simply be included as one of the projections of a more complete motion? Observations of active galactic nuclei show that the same astrophysical system is capable of switching between radiative and kinetic regimes [1]. In the latter case, radio jets are formed, in which matter is accelerated to relativistic velocities; when the regime switches, this channel weakens or disappears. In this note, we consider these observations as possible indirect confirmation of the hypothesis of a switchable acceleration projection.
Earlier, in the seminal work [2], it was shown that the observed accelerated motion can be represented as a projection of a set of uniform higher phases. The mathematical theorem proves the possibility of such a representation, but does not in itself establish that nature actually uses this mechanism. Therefore, processes in which acceleration does not act continuously, but appears and disappears along with the switching of the state of the same physical system, are of particular interest.
1. Activity That Turns On and Off
The cores of most galaxies contain supermassive black holes. The black hole itself doesn't literally turn on and off: the state of the surrounding accretion flow—the matter falling toward the central object—changes. When highly active, such a system can release enormous energy both in the form of electromagnetic radiation and through directed streams of relativistic matter called radio jets.
Astronomical observations show that the activity of galactic nuclei is episodic. Nuclei with changing spectral patterns, relic radio structures, ionization echoes of a former bright state, and traces of several successive jet activations have been detected. These phenomena span very different time scales:
\[\tag{1} \tau_{\mathrm{CL}}\sim 1-10\, \text{years}, \qquad \tau_{\mathrm{ion}}\sim10^4-10^6\, \text{years}, \qquad \tau_{\mathrm{radio}}\sim10^6-10^8\, \text{years}. \] Most significant for this work is the observed switching between two activity modes. In the radiative mode, the energy manifests itself primarily as radiation and ionization cones of the surrounding gas. In the kinetic mode, a significant portion of the manifestation is associated with radio jets, momentum transfer, and acceleration of matter. Thus, the same complete system allows for at least two different modes of external manifestation:
\[\tag{2} \text{active core} \quad\longrightarrow\quad \begin{cases} \text{radiative mode},\\ \text{kinetic acceleration mode}. \end{cases} \] 2. Standard Physical Explanation
In modern astrophysics, the change in mode is associated with a change in the accretion rate, accretion disk instabilities, magnetic field restructuring, depletion of available matter, and subsequent resumption of its influx. The feedback of radiation and jets on the surrounding gas can also influence subsequent stages of activity. These mechanisms describe the immediate physical conditions near the black hole and do not require the introduction of additional spaces.
The interpretation proposed below does not deny the processes listed. It raises another question: why does the overall motion even allow for division into different observable channels, and why can the channel associated with the acceleration of matter become dominant and then be suppressed? In the concept of multilevel splitting, standard astrophysical causes can act as the observable switching mechanism, while the geometry of the splittings describes a more general principle of organization of the overall state.
3. Acceleration as a Result of Projection
Let the highest-level state consist of mutually orthogonal idempotent channels:
\[\tag{3} J_N(t)= \sum_{\boldsymbol{\sigma}} E_{\boldsymbol{\sigma}} e^{i\phi_{\boldsymbol{\sigma}}(t)}, \qquad E_{\boldsymbol{\sigma}}E_{\boldsymbol{\tau}} =\delta_{\boldsymbol{\sigma}\boldsymbol{\tau}}E_{\boldsymbol{\sigma}}. \] At the highest level, all unrolled phases can move uniformly:
\[\tag{4} \phi_{\boldsymbol{\sigma}}(t) =\omega_{\boldsymbol{\sigma}}t+phi_{\boldsymbol{\sigma}0}, \qquad \dot\phi_{\boldsymbol{\sigma}}=\omega_{\boldsymbol{\sigma}}=\operatorname{const}, \qquad \ddot\phi_{\boldsymbol{\sigma}}=0. \] The observer sees not individual higher phases, but their reduction into a single parameter of external motion:
\[\tag{5} b(t)=\mathcal B[J_N(t)], \qquad v(t)=c\sin\!\bigl(\pi b(t)\bigr). \] After differentiation, the observed acceleration appears:
\[\tag{6} \boxed{ A(t)=\frac{dv}{dt} =\pi c\cos\!\bigl(\pi b(t)\bigr)\dot b(t). } \] Therefore, the zero second derivative of each higher phase does not require zero acceleration of its overall projection. Acceleration appears at the lower level due to a change in the relationship between the overall state and the observed motion parameter.
4. Split Acceleration Channel
Consider the simplest additional splitting into two mutually orthogonal channels:
\[\tag{7} E_0+E_A=1, \qquad E_0E_A=0, \qquad E_0^2=E_0, \qquad E_A^2=E_A. \] Here \(E_0\) denotes the channel that does not create a change in the observed velocity, and \(E_A\) denotes the channel capable of creating acceleration after projection. The full state has the form
\[\tag{8} J_{\mathrm{full}}(t) =E_0J_0(t)+E_AJ_A(t). \] The full state itself does not necessarily appear or disappear. The degree of manifestation of its accelerating channel in the projection visible to the observer changes. We introduce a dimensionless coefficient of such manifestation \(q(t)\):
\[\tag{9} b(t)=b_0+q(t)b_A(t), \qquad 0\le q(t)\le1. \] Its derivative is
\[\tag{10} \dot b(t)=\dot q(t)b_A(t)+q(t)\dot b_A(t). \] If on some interval \(q=0\) and \(\dot q=0\), the accelerating channel does not manifest itself, and at constant \(b_0\), the observed acceleration is zero. If \(q\ne0\), the change in \(b_A\) is included in the observed motion. During the switching itself, an additional contribution is also made by \(\dot q\). Therefore, the "on" and "off" states can be written in an idealized form:
\[\tag{11} \boxed{ q=0\, \Longrightarrow\, A_{\mathrm{obs}}=0, \qquad q\ne0\, \Longrightarrow\, A_{\mathrm{obs}}\ne0. } \] In a real system, "off" should not necessarily mean the absolute disappearance of any acceleration, but rather the suppression of a given channel below the level at which it determines the main observable behavior.
5. What does the channel itself include?
If the coefficient \(q(t)\) is introduced arbitrarily, then the cause of the switching remains outside the model. The multi-level construction allows us to take the next step: consider \(q(t)\) as a projection of an even deeper splitting,
\[\tag{12} q(t)=\mathcal Q[J_{N+1}(t)]. \] Then the change in the observed regime itself turns out to be the result of a higher motion. At the N+1 level, the phases can still be uniform, but their projection controls the availability of the N-level channel:
[tag{13} \boxed{ \begin{gathered} \text{uniform phase of the higher splitting}\\ \Downarrow\\ \text{change in projection }q(t)\\ \Downarrow\\ \text{switching on or off the acceleration channel}\\ \Downarrow\\ \text{observed acceleration of matter}. \end{gathered} } \] This creates a hierarchical picture: the acceleration of a lower level is determined by the projection of a higher level, and the switching of this projection is determined by the state of the next splitting. This is consistent with the general principle that each new level reveals the internal structure of the previous one without creating a new, complete norm.
6. Two Active Core Modes in Split Geometry
For the active core, we introduce two mutually orthogonal channels:
\[\tag{14} J_{\mathrm{AGN}} =E_{\mathrm{rad}}J_{\mathrm{rad}} +E_{\mathrm{kin}}J_{\mathrm{kin}}, \qquad E_{\mathrm{rad}}E_{\mathrm{kin}}=0, \qquad E_{\mathrm{rad}}+E_{\mathrm{kin}}=1. \] The first channel corresponds predominantly to the electromagnetic manifestation of activity, the second to the kinetic transfer of energy and momentum with the formation of relativistic jets. With a unit norm for each branch, the full algebraic norm is preserved:
\[\tag{15} J_{\mathrm{AGN}}\overline{J_{\mathrm{AGN}}} =E_{\mathrm{rad}}+E_{\mathrm{kin}}=1. \] This equality refers to the geometric norm of the state and does not in itself imply constancy of the measured nuclear power: the influx of matter and the energy available to the system can vary. However, it expresses the main structural principle—both observed regimes belong to a single full state and can be considered not as independent processes, but as mutually complementary modes of its manifestation.
In this interpretation, the strengthening of the radio jet signifies the opening of the kinetic projection, in which the acceleration of matter is particularly clearly manifested. The weakening or disappearance of the jet corresponds to the suppression of this projection and the redistribution of the observed activity into other channels:
\[\tag{16} \text{radiative projection} \quad\rightleftarrows\quad \text{kinetic projection of acceleration}. \] 7. What exactly do the observations confirm?
Astronomical data confirm several facts essential to the hypothesis under consideration. First, one physical system indeed allows for qualitatively differentmentation modes. Secondly, the relativistic acceleration channel can strengthen, weaken, and be reactivated. Thirdly, a previously switched-off mode retains information about itself in the form of relic radio structures and ionization echoes. The observed state therefore does not exhaust the entire history of the system.
These data can be viewed as indirect confirmation of the physical possibility of a switchable acceleration channel: acceleration in the same system need not be continuously manifested, but can be switched on and off along with changes in its internal mode.
However, observations do not yet prove that the switching is caused by idempotent splitting, that the higher phases move uniformly, or that the jet acceleration is merely a projection. Standard accretion and magnetohydrodynamic models also describe regime switching. Therefore, it is correct to speak of confirmation of one qualitative consequence of the hypothesis, but not of proof of its entire geometric mechanism.
8. Possible Quantitative Verification
To move from a qualitative match to a physical verification, the model must predict the relationship between the observed channels before processing specific data. Since the total power of the core can change with accretion, it is more convenient to consider not absolute powers, but their relative fractions:
\[\tag{17} \eta_{\mathrm{rad}} =\frac{P_{\mathrm{rad}}}{P_{\mathrm{full}}}, \qquad \eta_{\mathrm{kin}} =\frac{P_{\mathrm{kin}}}{P_{\mathrm{full}}}. \] For the simplest two-channel state, an approximate ratio is expected:
\[\tag{18} \boxed{ \eta_{\mathrm{rad}}(t)+\eta_{\mathrm{kin}}(t)\approx1. } \] This equality itself is not yet unique enough. A stronger test would be a pre-determined phase relationship between the radiation enhancement, the appearance of a jet, and the subsequent relic trail. If a single switching law can describe several active nuclei without individually selecting all the coefficients, this will be an argument in favor of a specific projection geometry.
The following observational features of a future test can be formulated: reproducible complementarity of relative powers; A certain delay between regime changes; preservation of phase information in successive jet episodes; the ability to predict the subsequent manifestation of another channel based on the state of one channel.
Conclusion
Active galactic nuclei provide a natural example of a system in which the relativistic acceleration of matter manifests itself not continuously, but as part of a switchable kinetic regime. Within the framework of multilevel splitting, this allows for the interpretation of acceleration as a separate channel of the projection of the total state. When the corresponding projection is unfolded, jets and acceleration of matter are observed; when it is suppressed, activity manifests itself primarily in a different manner.
\[\tag{19} \boxed{ \begin{gathered} \text{full state of the system}\\ \Downarrow\\ \text{redistribution between projections}\\ \Downarrow\\ \text{switching on or off the kinetic channel}\\ \Downarrow\\ \text{appearance or disappearance of the observed acceleration}. \end{gathered} } \] Thus, astrophysical observations can be considered indirect confirmation of an important qualitative consequence of the hypothesis: the acceleration channel in a single physical system is indeed capable of being switched on and off. But the projection nature of this switching remains a hypothesis until a quantitative relationship is derived from the splitting geometry that distinguishes its predictions from standard accretion models.
References
- A.V. Moiseev, A. Arshinova, A.A. Smirnova. Archaeology of the Activity of Galactic Nuclei, Uspekhi Fizicheskikh Nauk, 2026.
- Acceleration as a projection of the uniform motion of higher splittings. Website.
- A.V. Moiseev, A. Arshinova, A.A. Smirnova. Archaeology of Galactic Nuclei Activity, arXiv:2603.19459.
- YouTube. It turns out that giant black holes can turn "On" and "Off" — a popular science review of observations.