Spacetime Curvature Inside a Stationary Volume Completely Enclosed by a Near-Light-Speed Energy Shell: The Börekci Energy Field Apparatus, the Redesigned Börekci Metric and Antimatter Production

Hasan Börekci

HB ZECHMANN Medical R&D, Manisa Technopark, Celal Bayar University Area, Manisa, Türkiye

ORCID: 0000-0001-9137-6342 • Correspondence: hborekci@hotmail.com.tr

Originality and AI-use statement. This experimental apparatus, the theory and the parts of the system are entirely the original work of Dr. H. Börekci; however, artificial intelligence was used for all mathematical calculations and background information. Scientific responsibility for the content rests with the author. A patent application has been filed with TÜRKPATENT for the Börekci Energy Field antimatter production system. An earlier version of this research programme is deposited as a preprint on Research Square [1].

Abstract

This work describes an experimental apparatus designed to test whether a measurable gravitational time dilation arises inside a stationary volume completely enclosed, from top to bottom, by an electromagnetic energy shell flowing at near-light speed. The apparatus is built beneath a mountain and comprises, from the outside inwards: a single continuous snail-spiral channel of Ø1 m borosilicate vacuum tube — reaching 24 m diameter at the equator and narrowing to 4 m at both ends, with 12 descending plus 12 adjacent ascending turns and a total path length of 1,280 m; a cylindrical borosilicate electromagnet of 24 m inner diameter, 24 m height and 2 m wall, externally wound — since calculation shows that 10 T in copper would require 0.65 GW and is impossible, the main winding is Nb₃Sn superconducting and the dense outer copper serves only as trim and quench protection; inside the bore, a coaxial rotating tungsten-steel sleeve (R = 11 m, wall 0.5 m, height 20 m, 10.78 kt) spins at a rim speed of 100 m/s to produce spacetime dragging; a 16 m diameter evacuated outer capsule with multilayer walls whose inner surface is covered with positron traps; and an elliptical inner capsule of 12 m pole-to-pole separation holding a biological payload at 1 atm. Two W-Re electrodes, positioned above the upper pole and below the lower pole, rotate in the same sense, left to right, at 3500 rpm; both electrodes additionally vibrate at 100 Hz. A 25 MV arc and a simultaneous 20 kV circular laser create an energy shell that completely surrounds the inner capsule from top to bottom for 24 hours, proton injection is absent in this version.

A redesigned Börekci metric is introduced and its four contributing terms are computed separately. The 10,857 m³ bore stores 346 GJ at 10 T (fringing factor 0.8), giving Φ_field/c² = 3.57×10⁻³⁴ — 3.6 times v13. The co-rotating electrodes carry a net angular momentum J_net = 27.78 kg m² s⁻¹ and produce a Lense-Thirring term Ω_LT = 1.91×10⁻²⁸ rad s⁻¹ at r = 6 m; an intermediate version of this work used counter-rotating electrodes, but calculation showed that this configuration cancels the gravitomagnetic dipole exactly, and the design was reverted to co-rotation. Weighted by the Olson-Guarino active-mass factor, the flow term gives Φ_flow/c² = 4.00×10⁻⁴⁶, and the 100 Hz vibration of the two electrodes produces a strain between h = 5.3×10⁻⁴⁵ (in phase) and 3.2×10⁻⁴⁰ (anti-phase) depending on their phase relationship. The rotating sleeve carries J = 1.19×10¹⁰ kg m² s⁻¹ and produces a frame-dragging rate of Ω_LT = 3.44×10⁻²⁰ rad s⁻¹ — 176,000 times the earlier shuttle concept; its 53.9 GJ of rotational kinetic energy contributes Φ_sleeve/c² = 5.57×10⁻³⁵, 13.5% of the total on its own. In total, standard weak-field general relativity (ξ = 1) gives Φ_B/c² = 4.13×10⁻³⁴ and measurability requires ξ ≥ 2.42×10¹⁵ — the strongest configuration of the entire programme. This constitutes the falsifiable core of the author's hypothesis.

Three critical findings are reported: producing 10 T with copper alone would require 0.65 GW and is impossible, making a superconducting main winding mandatory; the removal of proton injection reduces the antimatter yield to 22–88 pg but does not eliminate the neutron source, as W(γ,n) photoneutrons from 25 MeV bremsstrahlung still produce ~3.5×10¹³ n/s and the shielding requirement stands; and the ferromagnetic sleeve, by virtue of its axial symmetry, experiences no net force and no eddy braking while rotating in the uniform axial field — the 134 kN incompatibility of the spiral-shuttle geometry vanishes in this architecture. The work further computes a 24-hour positron yield of 22–88 pg via the Bethe-Heitler channel alone, a W(γ,n) photoneutron flux of approximately 3.5×10¹³ s⁻¹ with the corresponding shielding requirement, an energy consumption of 148 MWh, and a complete profit-and-loss account. Literature supporting the hypothesis and literature opposing it are presented separately and in full, ξ is defined as the experimental arbiter of the claim, and a low-cost analogue-horizon pre-experiment is proposed before the large apparatus is built.

Keywords: spacetime curvature; time dilation; gravitoelectromagnetism; Lense-Thirring; energy shell; antimatter; positron; Börekci metric; analogue gravity

1. Introduction

General relativity describes gravity not as a force but as the curvature of spacetime geometry. In this framework an object does not attract the objects around it; it curves the spacetime around it, and objects moving within that curvature follow their geodesics. Much as a person standing in the middle of a sloping road is drawn downhill, it is the geometry rather than the object itself that is decisive. In the Einstein field equations the source is not rest mass alone but the entire stress-energy tensor: energy density, momentum flux, pressure and stress components each contribute separately to the geometry.

This observation raises a natural question. If flowing energy also sources geometry, could completely enclosing a stationary volume in a dense energy shell moving at near-light speed render the spacetime inside that volume measurably different from the spacetime outside? The existing literature contains validated formulae for the spacetime curvature of moving bodies and for the curvature around stationary masses; but there is no validated formulation addressing specifically the curvature inside a stationary volume that is completely enclosed by a near-light-speed energy shell. This gap is the rationale for the Börekci metric introduced below.

This paper describes a complete apparatus designed to test that question experimentally, specifies every component and the operating protocol in detail, computes all relevant quantities, presents the supporting and the opposing literature separately, and reduces the claim to a single falsifiable parameter. The author holds that a significant curvature will arise inside the inner capsule; standard physics predicts a result close to zero. Throughout the paper these two positions are presented in separately marked boxes and are never conflated. The final arbiter is the experiment to be built.

2. Theoretical Framework

2.1 Spacetime as a quantum energy field

In classical intuition the vacuum is a passive stage containing nothing. Quantum field theory inverts this picture: the vacuum is the ground state of all fields, a medium filled with zero-point energy in which virtual particle pairs continuously appear and disappear. This picture was experimentally confirmed through the force Casimir predicted in 1948 and later measured in the laboratory [2, 3]. The vacuum is, like a soup, filled with virtual particles and fluctuating fields.

The most striking quantitative evidence for the same picture lies in the origin of the mass of matter. Only about one per cent of a proton's mass comes from the Higgs-derived masses of its constituent quarks; the remaining ninety-nine per cent is the binding energy of the strong field that holds them together. Lattice quantum chromodynamics calculations have produced hadron masses from first principles on exactly this basis [4, 5]. Mass is therefore primarily a property of field energy rather than of particles; and by E = mc² this energy sources gravity.

Author's position: What we call spacetime is a quantum energy field enveloping the particles of every atom, the stars and the entire universe. That the fundamental quarks constituting an atom account for only one per cent of its mass, with the remaining ninety-nine per cent being the work of this field, shows that spacetime is not a passive stage but an active and material medium. Stars and atoms are born within this field. Such a medium cannot be expected to remain unaffected by a dense energy flow passing through it at near-light speed.

2.2 The spacetime ocean model

The conceptual model proposed by the author is as follows: the whole of spacetime is like an ocean. Very massive objects such as black holes sink into this ocean under their weight; objects moving at near-light speed carry forward the ocean water adjacent to the volume they occupy. This is the intuitive counterpart of the phenomenon known in general relativity as gravitomagnetism or frame dragging.

The theoretical basis of this analogy is sound. In the weak-field limit the Einstein equations reduce to a structure formally identical to Maxwell's equations: mass density sources a gravitoelectric field and mass current sources a gravitomagnetic field [6]. The dragging of inertial frames around a rotating mass is the Lense-Thirring effect and has been confirmed by two independent space experiments: the nodal precession of the LAGEOS satellites [7] and the gyroscope precession measured by Gravity Probe B [8]. That energy currents source geometry is therefore not an analogy but a measured fact. What is in question is its magnitude in this apparatus.

2.3 The falling ring analogy

The author's second analogy is this: when a hollow ring falls into water at high speed, the water at the centre of the ring is abruptly driven in the direction opposite to the ring's fall. The belt electromagnet added to the system is expected to accelerate the curvature of the quantum field at its centre in a similar way.

Hydrodynamically this is correct and follows from the continuity equation: the volume swept by the descending ring must be displaced, and the path of least resistance is through the centre of the ring. The gravitational counterpart, however, is constrained by the shell theorem. Inside a spherically symmetric shell the gravitational force is exactly zero while the potential is not: inside, Φ = −GM/R. This is an important and constructive distinction for this apparatus — measuring force inside the energy shell is meaningless, whereas measuring the potential (and hence the time dilation) is in principle meaningful. The primary observable of the experiment is therefore time dilation.

2.4 The divided water volume and the decoupling hypothesis

Author's position: Imagine a rectangular volume filled with water. Divide that volume exactly in half with a dense material. When you agitate the water in one half, does the water in the other half move? Of course it does not; it stays completely still. It is true that you cannot divide spacetime with dense matter. But we are not dividing spacetime with dense matter — we are dividing it with a non-dense energy field flowing at near-light speed. When this separation occurs, the spacetime inside the inner capsule — that is, the quantum energy field — may not behave as it does in the spacetime from which it has been separated. Its effect on the spacetime inside the inner capsule must be substantial.

This argument constitutes the central hypothesis of the paper and contains an explicitly testable prediction. Where the analogy holds and where it does not is examined in detail in Section 9.3; here only the formal statement of the hypothesis is given: if the energy shell partially or completely decouples the quantum field of the inner volume from the outer field, then the metric inside may depart from the outer metric by far more than the standard calculation predicts. The magnitude of that departure is measured by the parameter ξ defined in Section 3.

Brief note — what standard physics says: In general relativity there is no known mechanism for 'shielding' the spacetime metric by any arrangement of matter or energy. Electromagnetic fields shield electric fields, but the stress-energy tensor that sources gravity cannot itself be shielded; on the contrary, the energy of the shielding agent is added to the source. No experiment to date has observed gravitational shielding, and equivalence-principle tests constrain such effects at the 10⁻¹³ level [9, 10]. The author's decoupling hypothesis is therefore not a prediction of the existing theory but a claim beyond it, and it is treated as such in this paper.

3. The Redesigned Börekci Metric

3.1 Why a new formulation is needed

The existing validated formulae cover three cases: the curvature around a stationary mass (Schwarzschild), the curvature around a rotating mass (Kerr, and Lense-Thirring in the weak field), and the proper time of a moving observer (special-relativistic time dilation). In addition, the exact Einstein-Maxwell solutions of Bonnor and Melvin give, at the level of principle, how static magnetic field energy curves spacetime [11, 12, 13].

None of these corresponds exactly to the question posed here: when a stationary volume is completely enclosed from top to bottom by an energy shell moving at near-light speed, what is the metric inside that volume? Weak-field superposition can be applied to this situation and is applied below; but it does not encode the topological completeness of the enclosure, the antiparallel structure of the flow, or any possible decoupling effect. The Börekci metric is proposed as a framework that sums all known contributions explicitly and confines the unknown possible contribution to a single measurable parameter.

3.2 Structure of the metric

In isotropic coordinates and weak-field form:

Here Φ_B is the total effective potential and A_g the gravitomagnetic vector potential. The total potential is written as the sum of four contributions multiplied by ξ:

The complete formulation of the metric, with all terms written out explicitly, is given below:

Written out: the line element is ds² = −(1 + 2Φ_B/c²)c²dt² − (4/c)(A_g·dx)dt + (1 − 2Φ_B/c²)(dx² + dy² + dz²). The total potential is Φ_B = ξ(Ω,γ,β)·[Φ_field + Φ_flow + Φ_rot + Φ_vib], where the terms are respectively Φ_field = −(G/c²R)(B²/2μ₀)V_eff, Φ_flow = −(G/c²R)Σᵢ(1+βᵢ²)γᵢNᵢmᵢc², Φ_rot = −(G/c²R)Iω² and Φ_vib = −(G/c²R)mA²ω_v². The gravitomagnetic vector potential is A_g = −(G/2c²)(J_net × r)/r³ with J_net = L_upper + L_lower = 2Iω. The decoupling factor is defined as ξ = 1 + κΩⁿ(γβ)^m, where Ω is the ratio to 4π of the enclosed solid angle.

3.3 Definition of the terms

The first term comes from the magnetic field energy stored by the belt electromagnet and is the dominant term:

The second term weights the energy of the flowing particles by the Olson-Guarino active gravitational mass factor. Olson and Guarino showed that the active gravitational mass of a moving body exceeds its rest value by a factor (1+β²)γ [14]:

The third term is the frame dragging arising from the net angular momentum of the rotating electrodes. An intermediate version of this work tested counter-rotation of the two electrodes, but calculation showed that this configuration cancels the net angular momentum, and hence the gravitomagnetic dipole at the centre, exactly. The design was therefore reverted to co-rotation:

The fourth term is the gravitational-wave contribution from the time-varying mass distribution produced by the vibration of the upper electrode.

3.4 The parameter ξ: the falsifiable core of the hypothesis

ξ is defined as a function of the completeness of the enclosure Ω, the Lorentz factor γ of the flow and its speed β:

Here Ω is the ratio to 4π of the solid angle by which the energy shell encloses the inner capsule; in this apparatus, neglecting the region occupied by the electrode mounts, Ω ≈ 0.97. The quantities κ, n and m are unknown and are not derived from any field theory in this paper. Standard physics predicts κ = 0 and hence ξ = 1. The author's hypothesis is ξ ≫ 1. This reduces the entire claim to a single measurable number and renders the experiment falsifiable.

The experiment is the arbiter: the value of ξ will be settled not by argument but by measurement. A 24-hour comparison of the inner and outer optical clock pair gives ξ directly: ξ = (Δτ/τ)_measured / (Δτ/τ)_GR. Standard physics predicts ξ = 1 while the author expects ξ ≫ 1; the experiment will decide which prediction is correct.

4. Materials and Methods: Complete Description of the System and Its Operation

This section describes the apparatus component by component from the outside inwards, then gives the operating protocol step by step. The overall view is presented in Fig. 1.

4.1 Site

The experiment is carried out in an underground chamber beneath a large mountain with its entrance sealed. The rock overburden serves three functions: it attenuates cosmic-ray background and muon flux; it provides a thermally stable environment with annual temperature variation below 0.1 K; and it isolates the facility from anthropogenic seismic noise. The sealed entrance is also a safety requirement, since a high neutron flux arises during operation as computed in Section 5.7.

4.2 The cylindrical electromagnet and the rotating tungsten-steel sleeve

Outermost, replacing the belt magnet and the spiral channel of earlier versions, is a cylindrical structure: a hollow borosilicate cylinder of 24 m inner diameter, 24 m height and 2 m wall thickness. Its exterior is densely wound and the whole assembly forms an electromagnet frame.

Geometry contradiction in the source text — reported: the design text states in the same sentence both an inner half-diameter of 24 m and an inner diameter of 12 m. Since the 16 m outer capsule cannot fit a 12 m bore, and all earlier versions of the programme use the 24 m envelope, this paper adopts INNER DIAMETER = 24 m and takes the height (unspecified in the text) as 24 m so as to cover the capsule fully.

Critical engineering finding 1 — 10 T in copper is impossible: for a cylindrical solenoid B = μ₀nI, so 10 T requires a surface current of 7.96×10⁶ A/m. At a continuous current density of 2 A/mm² this means a copper build 3.98 m thick dissipating 0.65 GW — beyond any cooling. The realistic continuous ceiling for copper is ~1.5 T, itself costing 88 MW. The main winding is therefore Nb₃Sn SUPERCONDUCTING (10 T, lossless, cryogenics ~6 MW); the dense outer copper winding of the design text is assigned the trim and quench-protection role.

At 10 T the 10,857 m³ bore stores E = 346 GJ with a fringing factor of 0.8 for end effects. This is 3.6 times the 96.6 GJ of v13/v15 and raises the field term to Φ_field/c² = 3.57×10⁻³⁴.

4.2.1 The rotating tungsten-steel sleeve

Inside the bore, coaxial with the cylinder and surrounding the outer capsule, is a rotating tungsten-steel sleeve — the engineering realisation of the design text's 'moving tungsten-steel structure for spacetime dragging'. Since its dimensions are not given in the text, the following parameters are selected and justified: radius 11 m, wall 0.5 m, height 20 m, mass 10.78 kt (ρ = 15,600 kg/m³ W-steel composite). The sleeve is levitated on magnetic bearings and spun to a rim speed of 100 m/s (86.8 rpm); the hoop stress ρv² = 156 MPa lies safely below the yield of the steel backing layer.

Key compatibility finding: in the spiral-channel intermediate version, a ferromagnetic body in the 10 T field was calculated to suffer an uncontrolled 134 kN force, and the iron shuttle was rejected. The rotating sleeve solves this by GEOMETRY: a body that is coaxial and axially symmetric keeps its magnetisation CONSTANT in its own frame while rotating in a uniform axial B — no net force arises and no eddy-current braking occurs. The steel component moreover concentrates flux in the bore through its saturation magnetisation (a bonus of up to ~+1 T, conservatively excluded from the calculation). Ferromagnetic material is fatal in the wrong geometry and useful in the right one.

The gravitomagnetic value of the sleeve is the strongest term of the apparatus: its angular momentum J = mR²ω = 1.19×10¹⁰ kg m² s⁻¹ produces a frame-dragging rate Ω_LT = 2GJ/(c²r³) = 3.44×10⁻²⁰ rad s⁻¹ at r = 8 m — 176,000 times the earlier tungsten shuttle. Its rotational kinetic energy of 53.9 GJ contributes Φ_sleeve/c² = 5.57×10⁻³⁵, 13.5% of the total on its own; for the first time the mass-transport term reaches the same order as the field term.

4.3 The outer capsule

Inside the magnet is a spherical outer capsule of 16 m diameter and 150 tonnes, evacuated to 0 atm. The wall layers from the outside inwards are:

• 150 cm of thermally and electrically insulating SiC-SiC
• 50 cm of circulating water cooling
• 90 cm of tungsten-steel composite forming the inner surface

The inner surface of the outer capsule is almost entirely covered with high-quality SUKRO positron capture traps. These traps are connected to the structure that delivers positrons to the antimatter facility at CERN. In addition, four precision cameras positioned in four directions between the two capsules, inside the outer capsule, record continuously.

4.4 The inner capsule

At the centre of the outer capsule is the elliptical inner capsule of 90 tonnes. Its two poles are pointed and it stands upright at the centre of the large capsule; the pole-to-pole separation is 12 m. Its interior holds only normal terrestrial air at 1 atm, a 9 kg pig wearing a protective suit, and one precision camera.

The wall of the inner capsule comprises, from the outside inwards:

• 90 cm of SiC-SiC that permits neither electricity nor photons to pass
• 90 cm of additional tungsten-steel wall
• 100 cm of lead-clad layer
• A 30 cm water-filled circulating cooling gap facing the interior

This multilayer structure protects the inner volume from the electric current and from the photon flux of the laser; the inner volume remains exposed only to gravitational influence. This is critical to the design logic of the experiment: electromagnetic effects are shielded, so any departure observed in the inner clock must be geometric rather than electromagnetic in origin.

4.5 Electrode system, rotation and vibration

Outside the inner capsule, above its upper pole and below its lower pole, are solid circular electrical terminals of W-Re alloy, each 10 cm in diameter and 20 cm thick. The upper terminal is the negative pole and the lower the positive. Both electrodes rotate at 3500 rpm in the same sense, from left to right. Both electrodes additionally vibrate 100 times per second.

The purpose of these circular motions is to further amplify the wave-generating property that electrons already possess in their motion, thereby promoting greater curvature of the spacetime quantum field inside the inner capsule. The design is inspired by the work of Maier and colleagues, who imaged the quantum motion of single electrons tunnelling through an energy barrier using scanning tunnelling microscopy with attosecond time resolution [15]. That work established that position and time evolution cannot both be determined with arbitrary precision, identified isolated electron tunnelling transients shorter than 1 fs, and found that the electrons respond to the laser field with a delay of about 500 attoseconds. This demonstrates that electron wave packets are mechanically drivable.

Design change and its rationale: an intermediate version of this work tested counter-rotation of the two electrodes. However, the calculation in Section 5.2 showed that counter-rotation cancels the net angular momentum exactly and destroys the gravitomagnetic dipole at the centre. Rather than enhancing frame dragging, that configuration eliminated it entirely; it was therefore abandoned and the design reverted to co-rotation. This is a concrete instance of a calculation directly correcting a design.

4.6 Laser system

Above the upper W-Re negative terminal there is a 10 cm diameter circular laser firing head that generates a laser current encircling the inner capsule. From this head a 20 kV laser current is applied so as to surround the inner capsule completely from top to bottom, confined between the outer and inner capsules. The laser flows parallel to and nested with the electron arc in the same direction; it contributes to increasing the speed of the electrons and supports positron formation.

4.7 Sleeve drive system (proton injection removed)

The proton injection of earlier versions is absent from this architecture; the energy shell consists solely of the downward electron arc and its accompanying laser. The two consequences are quantified in Sections 5.7 and 5.6: antimatter production falls to the Bethe-Heitler channel alone, and the neutron source shifts from (p,n) to W(γ,n) photoneutrons. The sleeve is driven on the induction principle by circumferential stator windings embedded in the cylinder wall; magnetic bearings provide contactless levitation, and in vacuum there is no friction loss. The standing losses are bearing control and stator copper (~2 MW drive budget).

4.8 Observation system

Four precision cameras positioned in four directions between the two capsules and one precision camera inside the inner capsule record continuously. The rationale for these cameras and their relation to the observer effect are discussed in detail in Section 9.4.

4.9 Operating protocol

• Step 1 — Preparation. The outer capsule is evacuated to 0 atm; the inner capsule is filled with terrestrial air at 1 atm and the biological payload is installed. All water circulation loops are started. The five cameras begin recording.
• Step 2 — Energising the magnet. The Nb₃Sn main winding is ramped to establish B = 10 T axial field in the bore; uniformity is trimmed with the copper winding and field stability is verified.
• Step 3 — Electrode motion. Both W-Re electrodes are brought to 1500 rpm in the same sense; the 100 Hz vibration of the upper electrode is started.
• Step 4 — Firing. One minute after the magnet begins operating, the electric arc and the laser are fired simultaneously. The arc is driven at 25 MV, initially at 50–200 μA and subsequently in the 0.5–2 mA range. The laser operates at 20 kV.
• Step 5 — Sleeve spin-up. The tungsten-steel sleeve is levitated on its magnetic bearings and brought to a rim speed of 100 m/s (86.8 rpm) by the stator windings; imbalance vibration is verified below 10 μm.
• Step 6 — Continuous operation. The system runs uninterrupted for 24 hours. The inner and outer optical clocks are compared continuously; positron trap counts are recorded; temperature, neutron flux and structural displacement are monitored.
• Step 7 — Shutdown and cool-down. The arc and laser are switched off and the magnet is ramped down. A cool-down period is observed because of activation; access to the capsules is by remote handling only.
• Step 8 — Analysis. ξ = (Δτ/τ)_measured / (Δτ/τ)_GR is computed; positron counts and activation products are measured.

5. Calculations

5.1 The cylindrical magnet and the rotating sleeve

Two qualitative gains of this architecture: (1) the mass-transport term reaches the same order as the field term for the first time — the 53.9 GJ of rotational energy of the 10.78 kt sleeve supplies 13.5% of the total potential on its own. (2) The incompatibility of ferromagnetic material with the 10 T field is resolved by GEOMETRY rather than by material substitution: in coaxial axially-symmetric rotation the magnetisation is constant in the body frame, so no net force and no eddy braking arise.

5.2 Rotating electrodes — co-rotation at 3500 rpm

Taking the density of the W-Re alloy as 19,300 kg m⁻³, a disc 10 cm in diameter and 20 cm thick has a volume of 1.571 L and a mass of 30.32 kg. For a solid cylinder the moment of inertia is I = ½mr² = 0.03790 kg m². A speed of 3500 rpm corresponds to ω = 366.52 rad s⁻¹, giving an angular momentum per electrode of L = Iω = 13.889 kg m² s⁻¹.

Brief note: co-rotation is a definite improvement over counter-rotation — it yields a non-zero rather than a zero gravitomagnetic dipole, and 3500 rpm increases J_net by a factor of 2.33 relative to 1500 rpm. But the magnitude changes no scales: Φ_rot/c² = 5.26×10⁻⁴² is 5×10⁻⁸ of the field term and does not alter the total in any way. The real cost of the selected 3500 rpm is an engineering one: the risk of electrode surface erosion under 24 hours of continuous arcing is markedly higher than at 1500 rpm, and a spare electrode set together with an intermediate maintenance window is required (see Section 5.6).

5.3 Vibration contribution

The 100 Hz vibration of both electrodes, at an assumed amplitude of 100 μm, produces a peak acceleration of a = Aω² = 39.5 m s⁻² (about 4.0 g). The peak force required per electrode is F = ma = 1.20 kN, a value achievable with piezoelectric or hydraulic actuators. The gravitational-wave strain is computed from the quadrupole moment of the time-varying mass distribution:

Two electrodes vibrating together create a qualitatively new situation relative to a single one: the result depends critically on the phase relationship between the two vibrations. The gravitational contribution of the vibration is therefore entirely negligible. The vibration does, however, have a real and valuable engineering function: by continuously displacing the arc attachment point it prevents hot-spot formation and consequent melting on the electrode surface. This is a critical contribution to 24-hour continuous operation.

5.4 Particle kinematics

Evaluating the quadrupole moment Q_zz = 2mz² for electrode positions z = ±z₀ + A·sin(ω_v·t) yields two distinct regimes. Under in-phase vibration the +12z₀A term of the upper electrode and the −12z₀A term of the lower cancel exactly, leaving only the second-order term of order A². Under anti-phase vibration these linear terms instead add.

Design recommendation — the second correction from calculation: the vibrations of the two electrodes should be driven in anti-phase (breathing mode, so that both approach the inner capsule simultaneously and recede simultaneously). This produces a quadrupole strain 6.0×10⁴ times larger than in-phase driving. The finding is the exact counterpart of the counter-rotation versus co-rotation analysis — but with the opposite sense: co-rotation wins for rotation, whereas anti-phase wins for vibration. If driven in phase, the linear quadrupole terms cancel in a manner analogous to the cancellation of net angular momentum under counter-rotation.

Brief note: this factor of 6×10⁴ is relative and changes nothing in absolute terms. Even in the best case h = 3.16×10⁻⁴⁰ lies 3.2×10¹⁸ below the LIGO detection threshold of h ~ 10⁻²¹, and the potential contribution of the vibration, Φ_vib/c² = 1.24×10⁻⁴⁶, is 10⁻¹² of the field term. The choice of phase is not a gravitational gain but a cost-free design improvement; its real value is that both electrodes displace their arc attachment points, limiting surface erosion over 24 hours of operation.

The axial 10 T field ties the electrons to the field lines in tight 0.85 cm helices; the arc thereby flows as a thin, stable shell around the inner capsule. With the proton component removed the shell is single-species; the antiparallel configuration of Tolman, Ehrenfest and Podolsky is not realised in this architecture (see the note in §6.2).

5.5 Total potential and the ξ threshold

Brief note — the prediction of standard physics: the total above is the result that weak-field general relativity gives for the v16 apparatus, and it corresponds to Δτ/τ ≈ 4.1×10⁻³⁴ — the highest of all versions of the programme (4.1 times v13). The resolution of the best optical clocks is of order 10⁻¹⁸ [17, 18]; the gap has narrowed to 15.4 orders of magnitude but has not closed. The notable structural change is that the total is no longer single-term: the mass transport of the sleeve takes a 13.5% share, of the same order as the field term for the first time.

Author's position: This calculation is the result the existing formulae give. But I believe that in a volume completely enclosed by an energy shell at near-light speed, spacetime may enter a regime in which the Lorentz factor can be considerably different, just as it is for moving electrons. The existing formulae compute the curvature of moving bodies; there is no validated formula that computes the curvature inside an enclosed stationary volume. That gap does not mean the result of the calculation is definitive.

The experiment is the arbiter: measurability requires ξ ≥ 2.42×10¹⁵ — the least severe requirement of any version. This shows plainly how numerically ambitious the hypothesis is, and at the same time makes it fully testable. When the inner and outer clocks are compared, ξ will be read directly; if the result is ξ = 1 the hypothesis is falsified, and if ξ ≫ 1 one of the most important findings in the history of physics will have been obtained.

5.6 Thermal and radiation tolerance: can it run for 24 hours?

Thermal loads in v16 come in three items: (1) the Nb₃Sn main winding is lossless; its cryogenic plant draws ~6 MW (346 GJ store, ~8× the ITER class). (2) Sleeve drive: stator copper loss plus magnetic-bearing control, ~2 MW; owing to its axial symmetry the sleeve takes no eddy braking from the main field, and there is no friction in vacuum. (3) Arc + laser + auxiliaries ~1.2 MW. Total ~9.2 MW. The arc analysis below is unchanged.

The arc power is 25 MV × 2 mA = 50 kW, all of which ultimately becomes heat. To carry this load in the 50 cm circulating water layer of the outer capsule with a temperature rise of ΔT = 20 K requires a flow rate of ṁ = P/(c_p ΔT) = 0.60 kg s⁻¹, or 2.2 tonnes per hour. This is readily achievable at industrial scale; thermally, 24-hour operation is unproblematic.

There are three radiation loads. The first is the bremsstrahlung produced by 25 MeV electrons on tungsten; the 90 cm tungsten-steel and 100 cm lead layers of the inner capsule attenuate this adequately. The second is gamma emission from activation products, which requires a post-run cool-down period. The third and most serious is the neutron flux.

Critical safety warning: the W(γ,n) photoneutron reactions driven by 25 MeV bremsstrahlung on tungsten produce approximately 3.5×10¹³ neutrons per second. Neutrons are not effectively stopped by lead or tungsten; a moderator and an absorber are required. IN ADDITION to the existing 30 cm water layer, approximately 1 m of polyethylene and boron carbide (B₄C) is mandatory. Furthermore, because of structural activation a post-run cool-down period must be observed and access to the capsules must be by remote handling only. This is a component absent from the current design whose addition is obligatory.

As regards electrode durability, the melting point of the W-Re alloy is about 3400 °C. Surface erosion under continuous arcing is the limiting factor for 24-hour operation. Since the selected 3500 rpm raises this risk, the continuous displacement of the arc attachment point by the 100 Hz vibration on both electrodes becomes critical; having the vibration on both terminals limits erosion simultaneously at cathode and anode and is a marked improvement over the earlier single-terminal design. A spare electrode pair and an intermediate maintenance window must be planned for 24-hour operation; alternatively the rotation speed may be reduced to 1500 rpm, which lowers Φ_rot from 5.26×10⁻⁴² to 9.66×10⁻⁴³ without altering the total result.

5.7 Antimatter production

Antimatter does form between the two capsules, but only as positrons and, in v16, through a single channel. The antiproton threshold is 5.6 GeV, far above 25 MV; and with proton injection removed, the (p,n)/(p,2n) β⁺ channel of earlier versions is also absent.

5.7.1 Electron channel — Bethe-Heitler pair production

Over 24 hours the arc current in the 0.5–2 mA range carries between 2.70×10²⁰ and 1.08×10²¹ electrons. Assuming a positron yield of about 9×10⁻⁵ for a thin-target geometry, the production is 2.43×10¹⁶ to 9.71×10¹⁶ positrons, that is 22–88 pg.

5.7.2 The removed proton channel

The (p,n)/(p,2n) → β⁺ channel, which contributed 49–491 pg in earlier versions, disappears with the removal of proton injection. The lost yield should be weighed against the gained simplicity: the proton line, the injector, most of the tungsten-target activation and the PET-isotope inventory leave the design.

The positrons produced are captured by the SUKRO traps on the inner surface of the outer capsule. Positron accumulation and storage techniques in Penning-Malmberg type traps are mature [19, 20]; the quantities produced in this apparatus are compatible with existing laboratory scales.

5.8 Energy cost and profit-and-loss account

Note on economic honesty: the widely quoted price of US$62.5 trillion per gram of antimatter is not a market price but an estimate of the production cost with existing accelerators. At picogram scale there is no buyer market and this item should not be counted as genuine revenue. The real value of the positrons produced is scientific rather than commercial. The marginal profit table also excludes capital cost: the underground facility, the large-scale 10 T magnet system and the multilayer capsules require an investment in the range of US$500 million to US$2 billion. On the assumption of US$5 million revenue per run, this capital is recovered over 101 to 405 runs. The system is marginally profitable but, in capital terms, an investment that returns only over the long term.

6. Support for the Hypothesis in the Literature

This section presents separately the work that supports the hypothesis that a significant curvature may arise inside the inner capsule. The opposing literature is treated in Section 7.

6.1 Energy currents genuinely source geometry — confirmed

Gravitoelectromagnetism predicts that in the weak-field limit mass currents produce a gravitomagnetic field [6]. This prediction has been confirmed by two independent space experiments: the measurement of the nodal shift of the LAGEOS and LAGEOS-2 satellites agreed with the general-relativistic prediction to within about 10% [7]; and Gravity Probe B measured frame dragging directly with four superconducting gyroscopes [8]. This is experimental evidence that flowing energy curves geometry and supports the basic assumption of this apparatus.

6.2 The gravity of light depends on orientation — Tolman-Ehrenfest-Podolsky

In 1931 Tolman, Ehrenfest and Podolsky showed that the gravitational effect of light beams depends on their relative orientation: two parallel light beams do not attract one another, whereas the interaction between antiparallel beams is non-zero [16]. In this apparatus the proton flow is downward and the electron flow upward — that is, exactly the antiparallel configuration is realised. This shows that the design selects a theoretically privileged arrangement.

6.3 The active gravitational mass of a moving body increases — Olson-Guarino

Olson and Guarino derived that the active gravitational mass of a moving body exceeds its rest value by a factor (1+β²)γ [14]. For the electrons in this apparatus the factor is 99.8; that is, each electron behaves as a gravitational source roughly one hundred times stronger than at rest. This is included explicitly in the calculation in Section 5.5.

6.4 Time dilation at high γ is experimentally confirmed — Bailey et al.

Bailey and colleagues measured the time dilation of muons circulating at γ = 29.33 in the CERN muon storage ring to an accuracy of 0.1% [21]. This is the closest experimental analogue to this apparatus: high-γ charged particles on a circular orbit with confirmed relativistic effects. The γ = 49.92 of the electrons in this apparatus is of the same order.

6.5 Magnetic field energy curves spacetime — exact solutions

Bonnor's solution for static magnetic fields in general relativity [11] and Melvin's pure magnetic geon solution [12] show, not as a weak-field approximation but exactly, that magnetic field energy curves spacetime. Thorne proved the absolute stability of the Melvin universe [13]. This guarantees that the 96.6 GJ of field energy in the apparatus is, at the level of principle, a genuine geometric source.

6.6 Gravity has become measurable at the millimetre scale

Westphal, Hepach, Pfaff and Aspelmeyer measured the gravitational coupling of 90 mg gold spheres directly with a torsion balance [22]. Bothwell and colleagues resolved the gravitational redshift across a millimetre-scale atomic sample [17]. This progress in measurement technology shows that the path toward bringing the effects produced by the apparatus closer to the threshold of measurability is open.

6.7 Electron wave packets are mechanically drivable

The attosecond-resolution scanning tunnelling microscopy work of Maier and colleagues showed that the quantum motion of single electrons during tunnelling can be imaged directly and that the electrons respond to the laser field with a delay of about 500 attoseconds [15]. This is direct evidence that electron wave packets are sensitive to external mechanical and optical driving, and it constitutes the physical rationale for the rotation and vibration imparted to the electrodes.

6.8 Analogue gravity: moving energy field plus horizon

The analogue gravity community works on precisely the idea of a 'horizon within a moving medium'. Following Unruh's founding proposal [23], Steinhauer observed analogue Hawking radiation and its quantum entanglement in a Bose-Einstein condensate [24, 25]; Weinfurtner and colleagues measured stimulated Hawking radiation in water waves [26]; and Barceló, Liberati and Visser provided the comprehensive review of the field [27]. The central finding of this programme is that a moving medium can create causally separated regions for the excitations within it. This belongs directly to the same conceptual family as the author's decoupling hypothesis.

Author's position: Read together, the eight headings above establish separately confirmed facts — that near-light-speed energy flows affect neighbouring spacetime, that the antiparallel flow configuration is privileged, that the active gravitational mass of moving sources increases, and that moving media can create causal decoupling. I believe that when these phenomena are applied together and in a complete enclosure geometry, they will produce an effect far greater than the linear sum of their individual contributions. The existing formulae were not designed to compute this composite situation.

6.9 Unresolved observational anomalies at the highest energies

Observational evidence that the Standard Model is incomplete at the highest energies is not confined to the cosmological scale; concrete events recorded at neutrino observatories also exist and deserve separate presentation here.

In 2006 and 2014 the ANITA balloon experiment recorded two upward-going air showers emerging from the Earth at exit angles of about 27° and 35° and corresponding to an energy of roughly 0.6 EeV [34]. Under conservative extrapolations of Standard Model interactions no particle is known that can propagate through the Earth with probability greater than 10⁻⁶ at these energies and exit angles. For nearly twenty years neither beyond-Standard-Model proposals (sterile neutrinos, R-parity violating supersymmetry, boosted dark matter) nor mundane explanations such as subsurface reflection have gained community acceptance, and the independent search by the Pierre Auger Observatory returned a null result [35].

Similarly, the event KM3-230213A recorded by the KM3NeT/ARCA telescope on 13 February 2023 and reported in Nature in 2025 is the most energetic neutrino observed to date [36]. The measured muon energy is 120 (+110/−60) PeV, and assuming an astrophysical E⁻² flux the inferred neutrino energy is about 220 PeV (90% confidence interval 72 PeV to 2.6 EeV; coordinates RA = 94.3°, Dec = −7.8°). The event was identified as a single muon that crossed the entire detector, inducing signals in more than a third of its active sensors. The real puzzle is not the energy itself: IceCube, with a substantially larger effective area and a considerably longer exposure, has reported no neutrino above 10 PeV, which under the assumption of a diffuse isotropic origin yields a 3.5σ discrepancy, and 2.5σ–3σ in joint fits including the null observations of other experiments [37]. This has introduced sterile-neutrino and non-standard-interaction interpretations into the literature.

Brief note — the function of these anomalies in this paper is limited, and that limit must be stated explicitly: they are anomalies of particle physics and astrophysics. They concern source populations, propagation through the Earth, neutrino-nucleon cross-sections and a possible sterile sector. They bear no direct relation to the engineered decoupling of spacetime, to measurable artificial curvature, or to the claim ξ ≫ 1, and no such connection is asserted here. Their sole function is to show that in the highest-energy regime there exist documented, peer-reviewed and still-open cases in which the current theoretical framework does not fully match observation. This supports observationally the argument about theoretical incompleteness developed in Section 9.5; it does not constitute evidence for the specific hypothesis of this paper.

7. The Position of Standard Physics Against the Hypothesis

Scientific honesty requires that the literature opposing the hypothesis also be presented in full. This section serves that purpose.

7.1 — The gravity of light beams is weak and forms no horizon. Olum and Everett examined in detail the gravitational effects of light beams and energy flows and showed that such configurations produce practically unmeasurable effects. This is the most serious direct argument against this hypothesis and is not disregarded here.

7.2 — Gravitational shielding has never been observed. Equivalence-principle tests constrain composition-dependent gravitational deviations at the 10⁻¹³ level [9]. There is no experimental evidence that any arrangement of matter or fields shields gravity, and the structure of general relativity does not admit such a mechanism.

7.3 — No anomaly has been seen in electromagnetically isolated clocks. Optical clocks operate at the 10⁻¹⁸ level [17, 18] and are routinely run inside strong magnetic fields, vacuum chambers and cryogenic shields. To date no unpredicted deviation in clock rate caused by electromagnetic isolation has been observed.

7.4 — The energy budget does not close the scales. The energy required for a measurable time dilation is sixteen orders of magnitude above what is stored in this apparatus. This is not a gap that can be closed by engineering improvements.

These four objections constitute the scientific position against the hypothesis and are not held to be invalid by the author. The author's position is not that these objections are wrong, but that the enclosed geometry may differ from the situations from which they were derived, and that this can be determined only by experiment.

8. Proposal for a Low-Cost Analogue-Horizon Pre-Experiment

Before building the large apparatus, the most realistic way to test the claim ξ ≫ 1 is a small-scale pre-experiment aimed at the analogue gravity community. The proposal is as follows: in a Bose-Einstein condensate or an optical medium, an inner region enclosed by a moving energy front is created, and the extent to which the excitations in the inner region decouple from the outer region is measured.

This pre-experiment can be published independently under a neutral designation — for example 'phenomenological decoupling parameter Ω' — and constitutes a critical credibility step while funding is being sought for the large apparatus. The relevant communities are the groups of Leonhardt, Faccio and Steinhauer.

9. Discussion

9.1 Does the energy shell fully separate the quantum field of the inner capsule from the outer field?

This is the central question of the paper, and the honest answer is that within standard quantum field theory and general relativity no decoupling is expected. Electromagnetic fields shield electric fields because free charges in a conductor produce a counter-field. For the stress-energy tensor that sources gravity there is no such counter-source; negative energy density is unknown at macroscopic scale. Moreover, the energy of the shielding agent is itself added to the source — the energy shell is itself a gravitational source.

The analogue gravity programme does, however, offer a genuine nuance. In a moving medium, causally separated regions can arise for the excitations of that medium [23, 24, 27]. But what decouples there is not spacetime itself but the effective metric seen by the waves in the medium. This distinction is critical: analogue horizons alter not the real spacetime geometry of the inner region but the effective geometry perceived by the phonons or photons of that medium. An atomic clock inside the inner capsule is not an excitation of a medium but a physical system moving in real spacetime.

Author's position: If the decoupling is complete, curvature can be expected, and in that case the Planck-energy requirement does not apply. For the Planck energy is the scale required to curve spacetime from nothing; what is at issue in a decoupled region is the interruption of the continuity of the existing geometry. Decoupling is a problem of topology, not of energy.

Brief note: This distinction is not theoretically supported. In general relativity the metric is the solution of the field equations together with continuity conditions; whatever the source distribution, the metric and its first derivatives are continuous across a matter distribution (the Israel junction conditions). Producing 'topological decoupling' requires violations of energy conditions that known forms of matter do not provide. This has not been proven impossible; but neither is it a prediction of the existing theory.

9.2 Is the Planck energy required?

The quantitative answer is this: from Φ/c² = GE/(c⁴R) with R = 8 m, obtaining a time dilation of order 10⁻¹⁸ inside the inner capsule requires E ≈ 10⁻¹⁸ × c⁴R/G ≈ 9.7×10²⁵ J. That is a mass equivalent of roughly 1.1 million tonnes — 2.8×10¹⁵ times the 346 GJ stored in v16. Although the Planck energy (1.96×10⁹ J) is enormous at the single-particle scale, it is small beside the total energy required for macroscopic curvature; the real obstacle is not the Planck scale but the extreme weakness of gravity arising from the denominator c⁴ = 8.1×10³³.

The question should therefore be restated: what is required for measurable curvature by standard mechanisms is not the Planck energy but a total energy of about 10²⁶ J, and this is unreachable with current technology. The author's hypothesis enters at exactly this point: if a decoupling mechanism exists, the curvature is set by geometry rather than by the energy budget, and the energy requirement falls away.

9.3 The divided water volume analogy: where it holds and where it does not

The strength of the analogy is this: a dense partition prevents the agitation in one half from transferring momentum to the other, because the partition absorbs and redistributes that momentum. The author's observation is correct — in a divided volume, one half can be agitated while the other remains still.

The limit of the analogy is this. In the water example the partition is a solid medium capable of carrying the momentum of the water; the water wave strikes the partition and transfers its energy to it. In the spacetime case the 'wave' is a metric perturbation, and there is no medium that can absorb it — a metric perturbation passes through everything, because everything is inside the metric. The near-light-speed energy shell is proposed as a non-dense 'partition'; but gravitationally it makes no difference whether something is dense or not, because gravity couples only to stress-energy, and the energy shell is itself a source rather than a barrier.

The experiment is the arbiter: it is clear that this debate cannot be settled theoretically — both sides present coherent arguments. But it is entirely settleable experimentally. When the inner and outer clocks are compared, ξ ≫ 1 will result if decoupling occurs and ξ = 1 if it does not. Measurement will decide whether the analogy is correct.

9.4 The observer effect and the cameras

That the double-slit experiment produces a particle pattern in the presence of an observer and a wave pattern in its absence is the best-known phenomenon of quantum mechanics, and it is the rationale for placing five cameras in this apparatus. The mechanism of this phenomenon must, however, be treated carefully.

What determines the pattern in the double slit is not the presence of a conscious observer but whether which-path information is recorded in the environment. If a photon scatters in such a way as to determine which slit the electron passed through, that information has been transferred to the environment and the interference disappears — even if no one reads that photon. This is the physical process known as decoherence, confirmed in detail experimentally [28]. What is decisive is the physical interaction between system and environment, not the consciousness of an observer.

Three consequences follow for this apparatus. First, the electrons and protons in the energy shell are already moving in a 25 MV arc under intense collisions and radiation; these are already fully decohered classical trajectories, and adding cameras does not change that. Second, because the inner capsule is completely shielded electromagnetically, the outer cameras can acquire no information about any quantum state inside it and therefore cannot affect the quantum state of the inner volume. Third, 100 kV DC was shown to dissipate an unsustainable 115 MW in the copper winding, making sectioned pulsed drive or a superconducting winding mandatory. Fourth, a uniformly energised solenoid was shown to be unable to propel the shuttle, and sectioned travelling-wave excitation was added to the design. Fifth, the intermediate v14 calculation established that an on-tube winding cannot produce the central field, and along-path winding B was added, recovering the 10 T centre. Sixth, producing the 10 T cylindrical field with copper alone was shown to require 0.65 GW, and the main winding was converted to superconductor. Seventh, the ferromagnetic sleeve was shown to experience no net force and no eddy braking in coaxial axially-symmetric rotation, resolving the 134 kN incompatibility of the spiral geometry by geometry itself and raising the mass-transport term to the order of the field term (13.5%). Eighth, the camera inside the inner capsule decoheres its own surroundings, but this is something that already happens in a macroscopic environment — a volume containing 1 atm of air and a 9 kg biological payload is already entirely classical.

Author's position: I think that the placement of the cameras will change the quantum field and the motion inside the energy shell. Observation is part of the system.

Brief note: The cameras genuinely are part of the system and observation genuinely is a physical interaction — on this point the author is right. But the magnitude of the effect is calculable and negligible: passive optical detection does not measurably alter the state of an already decohered plasma. The cameras are valuable for documenting the experiment; they do not provide a mechanism for steering the quantum state.

9.5 Faster-than-light expansion of the universe and the adequacy of the formulae

The phenomenon the author points to is real: sufficiently distant galaxies recede from us at speeds greater than that of light. The reason this does not contradict special relativity is important — special relativity limits the speed of objects moving within space, whereas cosmological expansion is the metric opening of space itself, and no object locally exceeds the speed of light. This is not a deficiency of the existing formulae but, correctly understood, a consistent prediction of them.

The author's broader point, however, is entirely justified and is shared by the physics community. The areas in which current theories are manifestly incomplete are these:

• About 68% of the energy content of the universe is dark energy and 27% dark matter; the nature of neither is known [29, 30].
• There is a discrepancy of order 10¹²⁰ between the theoretical prediction of the cosmological constant and its observed value; this is the largest numerical failure in the history of physics [31].
• General relativity and quantum mechanics have still not been unified; there is no theory of quantum gravity.
• The hierarchy problem does not explain why gravity is 10³⁸ times weaker than the other forces.

Author's position: My answer to those who say that the spacetime of the stationary bodies in this paper will not curve significantly within the energy shell is this: our present formulae appear adequate for calculating many things in our world, but in fact they are not quite adequate. We have much further to go in physics, and many formulae will change as we discover more of the truths of the universe. And of course, when a miniaturised Börekci Energy Field system is built and the spacetime of the inner capsule is measured, the whole truth will emerge.

This objection is methodologically valid and has been vindicated repeatedly in the history of science. But a symmetric caution is also required: that theories are incomplete does not mean that any particular alternative is correct. The known unknowns (dark energy, quantum gravity) appear at specific scales, and at the laboratory scale the correctness of weak-field general relativity has been tested at the 10⁻¹³ level [10]. For the author's hypothesis to be right, an effect never before seen in this well-tested regime must exist. That is possible — but for exactly that reason, measurement is essential.

9.6 Where calculation corrected the design in this work

A concrete design correction emerged during the writing of this paper and is reported here for transparency. This arose in two separate places. The first is rotation: an intermediate version proposed counter-rotation of the two W-Re electrodes. Calculation showed that counter-rotation gives J_net = L_upper + L_lower = 0 and cancels the gravitomagnetic dipole at the centre exactly. That is, the configuration eliminated frame dragging entirely rather than enhancing it. The design was reverted to co-rotation and J_net = 11.905 kg m² s⁻¹ with Ω_LT = 8.19×10⁻²⁹ rad s⁻¹ was recovered. The second is vibration: when the 100 Hz vibration of both electrodes is driven in phase, the terms linear in amplitude in the quadrupole moment cancel exactly, leaving only the term of order A². Switching to anti-phase raises the strain from 5.27×10⁻⁴⁵ to 3.16×10⁻⁴⁰, a factor of 6.0×10⁴. The two findings mirror one another: co-rotation is correct for the rotation, anti-phase for the vibration. Both are concrete instances of a calculation directly improving a design and illustrate the methodological approach of the paper.

10. The Importance of This Work

Thomas Young performed the double-slit experiment while he was a medical student, and he was not a physicist. I too am a general surgeon, a physician. And we physicians who follow in the footsteps of Hippocrates will always go on making more discoveries in the world of physics as well.  From this energy field, from antimatter production to NEW energy, hundreds of innovations and applications for humanity may emerge. In addition, many innovations may be obtained from the in vivo and in vitro biological, physical and chemical experiments to be conducted inside the inner capsule. This is a pre-experimental study. Dr. H. Börekci has filed a patent application for the BÖREKCI ENERGY FIELD antimatter production system. Communication channels are open for the implementation of this system. After the experimental setup is completed, I believe improvements and adjustments can be made to every configuration described in this paper. This experimental apparatus, the theory and the parts of the system are entirely the original work of Dr. H. Börekci; however, artificial intelligence was used for all mathematical calculations and background information.

11. Limitations

• The parameter ξ has no derivation from any field theory; it is a phenomenological placeholder and the values of κ, n and m are unknown.
• The standard calculation gives Φ_B/c² ≈ 10⁻³⁴ and measurability requires ξ ≥ 10¹⁶. This is an extraordinarily large departure to demand.
• Almost the entire total potential comes from the static magnet field; the contribution of the moving energy shell, the distinguishing feature of the apparatus, is at the 10⁻¹² level in the standard calculation.
• The mass and the geometry of the belt magnet are inconsistent (500 tonnes against 8661 tonnes); a design revision is required.
• Neutron shielding is inadequate in the current design; the addition of approximately 1 m of polyethylene and B₄C is mandatory.
• The cylindrical main winding stores 346 GJ and is a superconducting installation ~8 times the ITER class; quench protection and the cryostat integration of the 2 m borosilicate wall require independent engineering verification.
• The geometry contradiction of the source text (inner half-diameter 24 m against inner diameter 12 m) has been resolved by adopting inner diameter = 24 m; the final version of the specification should settle this value.
• Carrying the 10.78 kt sleeve at 100 m/s on magnetic bearings requires an independent rotordynamic analysis for imbalance and gyroscopic loads; the sleeve alone is a manufacturing item of order US$1 billion.
• The selected rotation speed of 3500 rpm raises the risk of electrode surface erosion relative to 1500 rpm; a spare electrode set and an intermediate maintenance window are required for 24-hour operation.
• The antimatter yields are sensitive to assumptions about cross-sections and target thickness; the ranges given are order-of-magnitude estimates.
• The safety of the biological payload over 24 hours, taking neutron and gamma doses into account, requires an independent ethical and dosimetric assessment; this paper does not contain such an assessment.
• The capital cost is in the range of US$500 million to US$2 billion and the facility requires an investment at national scale.

12. Conclusions

This work has described a complete experimental apparatus designed to test whether spacetime curvature arises inside a stationary volume completely enclosed by a near-light-speed energy shell, has specified every component and the operating protocol in detail, has computed all relevant quantities, and has reduced the claim to a single falsifiable parameter.

The redesigned Börekci metric separates four contributing terms explicitly. In the v16 architecture the outermost element is a cylindrical borosilicate electromagnet of 24 m inner diameter and 24 m height; producing 10 T in copper was calculated to require 0.65 GW, so the main winding is Nb₃Sn superconducting (E = 346 GJ, Φ_field/c² = 3.57×10⁻³⁴ — 3.6 times v13). Inside the bore, a coaxial rotating tungsten-steel sleeve of 10.78 kt (R = 11 m, 100 m/s) carries J = 1.19×10¹⁰ kg m² s⁻¹, produces Ω_LT = 3.44×10⁻²⁰ rad s⁻¹, and contributes Φ_sleeve/c² = 5.57×10⁻³⁵ from its 53.9 GJ of rotational energy — the mass-transport term reaches the order of the field term for the first time. The ferromagnetic incompatibility is resolved by the axially-symmetric coaxial rotation geometry. Two W-Re electrodes co-rotating left to right at 3500 rpm carry a net angular momentum J_net = 27.779 kg m² s⁻¹ and contribute Φ_rot/c² = 5.26×10⁻⁴²; the counter-rotating configuration tested during this work was calculated to cancel the net angular momentum exactly, and the design was corrected. The Olson-Guarino weighted flow term is 4.00×10⁻⁴⁶ and the gravitational-wave strain of the 100 Hz vibration of both electrodes remains at 3.16×10⁻⁴⁰ in anti-phase and 5.27×10⁻⁴⁵ in phase. The total for standard physics is Φ_B/c² = 4.13×10⁻³⁴, and measurability requires ξ ≥ 2.42×10¹⁵ — the strongest configuration of the entire programme (4.1 times v13).

The secondary outputs of the apparatus are, by contrast, real and valuable even within standard physics. With the proton channel removed, a 24-hour run is expected to produce 22–88 pg of positrons from Bethe-Heitler pair production alone; antiproton production is impossible because of the 5.6 GeV threshold. The neutron source shifts from (p,n) to W(γ,n) photoneutrons (~3.5×10¹³ s⁻¹) and the shielding requirement stands. A run consumes 221 MWh and generates about US$76,500 in marginal expenditure, against a capital investment of US$500 million to US$2 billion.

The most concrete engineering contribution of this work is that calculation directly corrected the design at seven points. First, the counter-rotating electrode configuration was found to cancel the gravitomagnetic dipole and was replaced by co-rotation. Second, the 100 Hz vibration of the two electrodes was shown to cancel its linear quadrupole terms if driven in phase, and anti-phase (breathing mode) driving was recommended, which increases the strain by a factor of 6.0×10⁴. Third, 100 kV DC was shown to dissipate an unsustainable 115 MW in the copper winding, making sectioned pulsed drive or a superconducting winding mandatory. Fourth, a uniformly energised solenoid was shown to be unable to propel the shuttle, and sectioned travelling-wave excitation was added to the design. Fifth, the intermediate v14 calculation established that an on-tube winding cannot produce the central field, and along-path winding B was added, recovering the 10 T centre. Sixth, producing the 10 T cylindrical field with copper alone was shown to require 0.65 GW, and the main winding was converted to superconductor. Seventh, the ferromagnetic sleeve was shown to experience no net force and no eddy braking in coaxial axially-symmetric rotation, resolving the 134 kN incompatibility of the spiral geometry by geometry itself and raising the mass-transport term to the order of the field term (13.5%). Eighth, the ~3.5×10¹³ s⁻¹ photoneutron flux arising from W(γ,n) reactions was calculated to exceed what the current shielding can handle, and the addition of approximately 1 m of polyethylene and B₄C was found to be mandatory. The mass-geometry inconsistency of the belt magnet has also been reported.

The author's position and the position of standard physics have been presented throughout the paper separately and explicitly marked. Standard physics predicts ξ = 1 and therefore expects an unmeasurable result; the author argues that the enclosed geometry may constitute a regime different from the situations from which the theory was derived and that ξ ≫ 1 may result. These two positions cannot be resolved by theoretical debate. The resolution lies in measurement.

The path this paper therefore proposes is this: before building the full apparatus, the low-cost analogue-horizon pre-experiment defined in Section 8 should be carried out. This experiment can be performed in a single laboratory within six to eighteen months on a budget of US$0.5–2 million and would place the first experimental bound on the scaling behaviour of ξ. A positive result would constitute a strong case for the large apparatus; a negative one would test the hypothesis before an investment of US$500 million is made. In either case the scientific gain is real.

Declarations

Funding: The author received no external funding for this work.

Conflict of interest: The author has filed a patent application (TÜRKPATENT) covering the apparatus described.

Ethics approval: This is a pre-experimental design study; no procedure was performed on any animal or human within the scope of this paper. The use of a biological payload in the apparatus described requires independent ethics committee approval and a detailed dosimetric assessment prior to implementation.

Data availability: All calculations are reproduced step by step in the text; no external dataset was generated or analysed.

Author contribution: H.B. designed the apparatus, the theory and the hypothesis and is responsible for the entire content. The use of artificial intelligence is documented in the statement on the title page.

Preprint: An earlier version of this research programme has been published on Research Square [1].

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Figure

Fig. 1  The complete Börekci Energy Field experimental apparatus. Panel A: facility cross-section — underground siting, the cylindrical electromagnet of 24 m inner diameter × 24 m with its 2 m borosilicate wall (Nb₃Sn superconducting main winding at 10 T, outer copper trim) and the coaxial rotating tungsten-steel sleeve inside the bore (R = 11 m, 10.78 kt, 100 m/s), the 16 m multilayer outer capsule (SiC-SiC 150 cm, water 50 cm, W-steel 90 cm) with SUKRO positron traps on its inner surface, the elliptical inner capsule of 12 m pole-to-pole separation (1 atm, 9 kg biological payload, 1 camera), the counter-streaming energy shell (electron-only, downward in cyan), the W-Re electrodes co-rotating at 3500 rpm and vibrating at 100 Hz, the circular 20 kV laser and the four cameras. Panel B: magnet and sleeve parameters with the v16 term-by-term breakdown of the Börekci metric (Φ_B/c² = 4.13×10⁻³⁴, ξ_min = 2.42×10¹⁵). Panel C: the axial-symmetry compatibility of the sleeve, the antimatter/neutron consequences of removing protons, the power budget and the cost breakdown.