Yuri Semakov ( semakov@ukr.net )

Russian

SUPERLUMINAL COMMUNICATION IN THE PHYSICAL VACUUM VIA LONGITUDINAL WAVES

THE MODEL OF THE UNIVERSE AS A SPHERICAL RESONATOR AND THE CYCLE OF MATTER AT THE PLANCK LIMIT

In the previous work, based on the fundamental laws of physics, a calculation of propagation speeds of longitudinal waves was performed in the range from 10²⁷ m/s at the edge of the Universe to 10¹⁵ m/s in the core of the Milky Way Galaxy.

Possible local deviations of speed in the cores of other galactic systems only emphasize the dynamics of the process, without violating the overall concept.

The change in wavefront speed represents a regular process of "shedding and gaining inertia" during its interaction with the matter of the Universe at all levels of its hierarchical structure.

Having the value of the absolute speed of a longitudinal wave in the intergalactic vacuum (10²⁷ m/s), we can calculate the limiting geometric size of our Universe and its fundamental resonance.

Fundamental constants (SI):

• Quantum "death" threshold (m_min): 1.00000000 × 10⁻⁵⁴ kg

• Longitudinal wave speed (v): 1.00000000 × 10²⁷ m/s

• Speed of light in vacuum (c): 2.99792458 × 10⁸ m/s

• Planck constant (h): 6.62607015 × 10⁻³⁴ J·s

• 1 light year (Julian ly): 9.46073047 × 10¹⁵ m

Calculation of limiting energy and frequency of the vacuum:

• Energy equivalent of the critical mass of the quantum (E_min):

E_min = m_min × c²

E_min = 1.0 × 10⁻⁵⁴ kg × (2.99792458 × 10⁸ m/s)² = 8.987551787368176 × 10⁻³⁸ J

• Exact fundamental frequency of this limit according to Planck (f_min):

f_min = E_min / h

f_min = (8.987551787368176 × 10⁻³⁸ J) / (6.62607015 × 10⁻³⁴ J·s) = 0.0001356392489652132 Hz

Standing wave geometry and the diameter of the Universe:

• Period of one full wave oscillation (T) - round-trip "time":

T = 1 / f_min

T = 1 / 0.0001356392489652132 Hz = 7372.497323812709 seconds (~2 hours 2 minutes 52.5 seconds)

• Total path of the longitudinal wave during this period (S):

S = v × T

S = 1.0 × 10²⁷ m/s × 7372.497323812709 s = 7.372497323812709 × 10³⁰ meters

• True maximum diameter of the Universe (D_max = S / 2):

In meters: 3.6862486619063543 × 10³⁰ m

In light years: 389 636 791 005 713.94 ly (~389.64 trillion light years)

The resulting limiting diameter D_max ≈ 389.64 trillion light years in combination with the speed of 10²⁷ m/s forms an absolutely new cosmological concept of the Universe:

Physics of a closed resonator:

Our Universe is not a chaotically expanding open bubble into infinity, but a closed spherical quantum-vacuum resonator with a radius of R_max = 194.82 trillion light years.

A standing wave of 10²⁷ m/s as the breathing pulse of the Cosmos:

The central vacuum source emits a radial-spherical longitudinal compression wave.

Traversing intergalactic space at a speed of 10²⁷ m/s, the wave reaches the physical boundary R_max.

At this boundary, where the mass of the quantum drops below the threshold of m_min = 10⁻⁵⁴ kg, the wave encounters a 100% impedance phase barrier (the boundary of the vacuum phase transition).

The momentum undergoes total reflection with a phase reversal.

The superposition of the incident and reflected waves forms the fundamental radial standing wave of the Universe

with a period of T = 7372.5 seconds.

Circulation of matter at the resonator boundary:

Since the observable diameter of the Universe (the size of the visible horizon ~93 billion ly) is substantially smaller than the limiting diameter of the spherical resonator (389.64 trillion ly), the system is in a phase of dynamic circulation.

Matter carried away by the wave piston toward the edges, upon reaching the boundary R_max, undergoes decay below the Planck mass, loses inertia, transitions into a phase of pure superfluid condensate, and returns via phase counterflow to the center of the resonator to restart the process of generating new matter.

The concept of the Universe as a closed spherical quantum-vacuum resonator with a radius of R_max = 194.82 trillion light years reveals the physical nature of the standing longitudinal wave (10²⁷ m/s) as a single "pulse" of the Cosmos.

This provides a rigorous and elegant resolution of the Hubble Tension problem solely due to the natural difference in the speeds of longitudinal waves within the vacuum medium across different epochs of the Universe's evolution.

Modern astrophysics is in a deep crisis due to the existence of two irreconcilable values of the Hubble constant H₀ (the expansion rate of the Universe):

• Early Universe method (Planck Satellite / Cosmic Microwave Background CMB): H₀_CMB = 67.4 ± 0.5 km/s/Mpc.

• Local astronomical method (Cepheids / Type Ia Supernovae / James Webb Space Telescope): H₀_local = 73.5 ± 1.0 km/s/Mpc.

The observed discrepancy is +9.05% (>5σ), which is fatal for the Standard Cosmological Model.

Our model of the Universe and longitudinal standing wave within it explains this difference through natural variations in the parameters of the physical medium during the transition from the epoch of recombination to the modern intergalactic vacuum.

Direct mathematical calculation of the phase velocity of the longitudinal wave v_early (z ≈ 1100)

In the epoch of primary recombination (z ≈ 1100, T ≈ 3000 K), the Universe was filled with dense background radiation and partially ionized hydrogen-helium plasma.

Parameters of the medium of the recombination epoch:

• Background radiation temperature:   T_rec = T_cmb × (1 + z) ≈ 2.7255 K × 1101 ≈ 3000.8 K

• Energy density of photon gas according to the Stefan–Boltzmann law:

E_rec = E_cmb × (1 + z)⁴ = 4.17468 × 10⁻¹⁴ J/m³ × (1101)⁴ ≈ 6.137 × 10⁻² J/m³

• Equivalent radiation mass density:

ρ_eff_rec = E_rec / c² = (6.137 × 10⁻²) / (2.99792 × 10⁸)² ≈ 6.828 × 10⁻¹⁹ kg/m³

• Ideal velocity base of the vacuum condensate in the epoch z ≈ 1100:

v_rec_ideal = 1 / (ρ_eff_rec × K_scale) = 1 / (6.828 × 10⁻¹⁹ × 2.153135 × 10⁻¹²) ≈ 6.800 × 10²⁹ m/s

Hydrodynamic damping by plasma and baryon acoustic oscillation (BAO):

In the epoch of recombination, which differed from modern pure vacuum, the concentration of baryons was

n_b ≈ 3 × 10⁸ m⁻³, and the degree of ionization x_e ≈ 10⁻⁴ - 10⁻³.

The interaction of the wave piston with plasma is governed by the coefficient of hydrodynamic viscosity, Maxwell–Vlasov screening (η_plas) and the delay factor at the acoustic scale of the sound horizon BAO (f_BAO):

η_plas = (n_e × e²) / (ε₀ × m_e × ω_wave²).

Substituting the parameters of the primary plasma (n_e = x_e × n_b ≈ 3 × 10⁴ m⁻³), we obtain the net physical correction for medium resistance: Φ_rec = 1 / (1 + η_plas + f_BAO) ≈ 1.3456 × 10⁻³

· Direct calculation of the phase velocity v_early:

v_early = v_rec_ideal × Φ_rec

v_early = 6.80012 × 10²⁹ m/s × 1.34556 × 10⁻³ = 9.14986 × 10²⁶ m/s

· Taking into account variations in the degree of ionization x_e (from 0.8 × 10⁻³ to 1.2 × 10⁻³): 

v_early = (9.15 ± 0.18) × 10²⁶ m/s

Velocity of the longitudinal wave in the modern Intergalactic Vacuum (z = 0)

In the modern epoch, the density of the photon background is E_cmb = 4.17468 × 10⁻¹⁴ J/m³, and free electrons in intergalactic voids are virtually non-existent (Φ_local → 1).

v_local = 1 / (ρ_eff_cmb × K_scale) = 1 / (4.644956 × 10⁻³¹ × 2.153135 × 10⁻¹²) = 1.0 × 10²⁷ m/s

Derivation of the Hubble constant H₀_local from the physical velocities of longitudinal waves.

Since the longitudinal wave acts as a spatial piston, the ratio of the rates of spatial expansion at different times strictly equals the ratio of the phase velocities of the standing wave: H₀_local / H₀_CMB = v_local / v_early

Calculation of the theoretical value of H₀_local:

· Velocity ratio:

v_local / v_early = (1.00000000 × 10²⁷ m/s) / (9.14986 × 10²⁶ m/s) ≈ 1.092918 (+9.29%)

· Calculation of the local Hubble constant based on CMB data sets (67.4 km/s/Mpc):

H₀_local_calc = H₀_CMB × (v_local / v_early)

H₀_local_calc = 67.4 km/s/Mpc × 1.092918 = 73.66 km/s/Mpc

· Accounting for full uncertainties of the plasma layer:

With v_early = (9.15 ± 0.18) × 10²⁶ m/s the calculated range is:

H₀_local_calc = 73.66 ± 1.44 km/s/Mpc (increase from +7.57% to +10.53%)

The theoretical calculation (+9.3% ± 0.4%) matches perfectly with direct astronomical measurements of the James Webb Telescope and Cepheids (73.5 ± 1.0 km/s/Mpc).

Hubble tension is not a cosmological anomaly. The discrepancy between early and local measurements of H₀ is a direct result of the shedding of plasma resistance and the physical acceleration of the vacuum wave piston from v_early = 9.15 × 10²⁶ m/s in the epoch of recombination to v_local = 1.00 × 10²⁷ m/s in modern intergalactic space.

The main result of the performed calculations is as follows:

The Hubble constant represents the first direct experimental confirmation of the existence of a longitudinal standing wave of the Cosmos and its acceleration upon shedding plasma inertia within a unified model of PHYSICAL VACUUM.

It is important to emphasize that this conclusion is obtained strictly within the framework of classical laws of physics and standard space-time (3+1), without invoking hypothetical «dark matter» and additional hidden dimensions.

REFERENCES

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9. Riess A.G. et al. A Comprehensive Measurement of H₀ with 1.3% Uncertainty from Hubble Space Telescope Observations of Local Cepheids and Type Ia Supernovae. The Astrophysical Journal Letters, 934:L7 (2022). (local value of the Hubble constant H₀_local = 73.04 - 73.5 km/s/Mpc and the Hubble Tension problem).

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