Experimental Spacetime Distortion: Generating Gravitational Waves in the Laboratory

This paper discusses our observations of gravitational wave generation through the rapid formation of high-energy density fields created by electrically driven spark gaps. Leveraging laser interferometry, this research investigates whether spacetime distortions are produced within the spark-gap plasma. The results indicate fringe movement correlated with spark power, distance from the laser, spark/laser orientation, and pulse repetition frequency, suggesting a possible spacetime distortion effect and the propagation of gravitational waves. We also address a number of strategies that we employed to mitigate causes of interference fringe displacement that may not be attributed to gravitational waves. These results could have profound implications for gravitational wave research, propulsion technologies, communications, biomedical applications, and even fusion reaction stabilization, among many other potential applications. The concept of a “gwavelets” phased array is proposed as a novel approach to constructively interfere gravitational waves to shape and manipulate them. Experimental results and potential technological implications are discussed.

Introduction

Work in high-energy physics suggests that extreme energy densities may induce measurable spacetime distortions [1], [2]. This paper explores a unique approach: utilizing high-voltage spark gaps to create rapid, localized, high energy densities capable of producing gravitational wave-like disturbances. If confirmed, this research would open new avenues in propulsion, energy manipulation, and extended electrodynamics. The use of electrically driven spark gaps presents a novel, scalable means of producing high-energy densities, with immediate experimental results obtained via laser interferometry.

Theoretical Background

Our hypothesis is that rapidly formed high-energy density fields within a spark gap can induce small but measurable space-time distortions. By analyzing Einstein’s field equations [3] in the context of the energy density generated in spark plasmas, we explore the feasibility of generating gravitational waves. Preliminary calculations indicate that energy densities within spark gaps may approach those required to produce such distortions on a nanometer scale.

(1) $$\begin{array}{r}{R}_{\mu \nu }-\frac{1}{2}R{g}_{\mu \nu }=\frac{8\pi G}{c^4}{T}_{\mu \nu }\end{array}$$

where

R_μν – the Ricci curvature tensor, which represents how much spacetime is curved due to the presence of mass and energy in a particular direction. It is derived from the Riemann curvature tensor by contracting indices.

R – the Ricci scalar, a scalar quantity that represents the degree of curvature of spacetime. It is the trace of the Ricci tensor, obtained by contracting R_μν with the metric tensor g^μν:

(2) $$\begin{array}{r}R=g_{\mu \nu }{R}_{\mu \nu }\end{array}$$

where

g_μν – the metric tensor, which defines the geometry of spacetime. It specifies the distance between nearby points and encodes the gravitational field.

T_μν – the stress-energy tensor, representing the distribution and flow of energy and momentum in spacetime. It encapsulates the density of matter, energy, and momentum as well as the pressures and stresses acting within the matter fields.

G – the gravitational constant, a fundamental constant of nature, with an approximate value of 6.674 × 10₋₁₁ Nm²/kg².

C – the speed of light in vacuum, another fundamental constant, approximately 3.00 × 10⁸ m/s.

The Einstein field equations describe how the geometry of spacetime (curvature) is influenced by the energy and momentum of matter and radiation present. They are the foundation of general relativity and play a central role in understanding gravitational phenomena.

Since the key to initiating spacetime curvature is based on the magnitude of the energy density [4], we sought a form and structure of energy that would maximize this. Furthermore, we postulate that the rapid formation of the spark plasma can induce gravitational waves that propagate out from its center. This proposition is supported in work on gravitomagnetism and other theoretical investigations into the creation of gravitational waves [5]–[11].

A spark initiated by a high electromagnetic field was the foundational structure that we chose. As such, we could model such a spark as a cylinder of a particular radius and length. This model allows us to calculate the energy density within the spark, assuming that we know the distribution of energy across its volume.

As illustrated in Fig. 1, the spark is represented as a cylinder with radius r = 0.25 mm and length l = 2.5 mm. The energy density u within the spark volume can be calculated as:

Fig. 1. Illustration of the spark modeled as a cylindrical volume with radius r = 0.25 mm and length l = 3.5 mm.

(3) $$\begin{array}{r}u\left(t\right)=\frac{U(t)}{V}\end{array}$$

where

U(t) – the total input of energy that varies in time in the spark

V – the volume of the cylinder

We can further define the following:

(4) $$\begin{array}{r}U\left(t\right)=P\left(t\right)\tau =v\left(t\right)i(t)\tau \end{array}$$

where

v(t) – the voltage

i(t) – the current, and τ is the pulse length

The volume V is given by:

(5) $$\begin{array}{r}V=\pi r^{2}l\end{array}$$

So, we can say:

(6) $$\begin{array}{r}u\left(t\right)=\frac{v\left(t\right)i(t)\tau }{\pi r^{2}l}\end{array}$$

Assuming an input energy U (obtained from the spark setup), the energy density u can be determined by substituting U and V into the formula above. This energy density plays a crucial role in estimating the gravitational influence of the spark as well as potential spacetime distortions in our experiment. Given this geometry, we are able to achieve energy densities in the order of 10¹¹ or 10¹² J/m³. Drake suggests that several unusual phenomena occur within plasmas formed by energy densities in this range [1].

We also must consider the impact of a rapid change in energy density as the spark is formed, that is,

(7) $$\begin{array}{r}\frac{du}{dt}=\frac{\tau }{\pi r^{2}l}\frac{d}{dt}v\left(t\right)i(t)\end{array}$$

which describes the power density in relation to instantaneous power, as illustrated in Fig. 2. We postulate that a strong, time-varying energy density induces gravitational waves, as has been observed by LIGO in cosmological phenomena [12]. This is supported by Kiefer and Ludwig [13] as they suggest that a time-varying change in the quadrupole moment induces gravitational waves. We further suggest that changes in the relative position of the energy with respect to time can also induce gravitational waves. The inspiral, merger, and ringdown stages in the black hole mergers observed by LIGO are empirical examples of gravitational wave production by this process [14].

Fig. 2. Variation of the energy density within the spark plasma with respect to time.

Experimental Setup and Methodology

A block diagram of the spark gap system is shown in Fig. 4. In it, the output of a signal generator is amplified to the power level required to drive a transformer. This transformer provides the voltage required to break down the air and produce a spark. The transformer is capable of producing potentials of around 400,000 V across the tips. The spark gap tips are tungsten rods filed down to points of about 0.5 mm. As Fig. 3 shows, the position of the tips can be adjusted for different spark lengths (or gap distances). While the gap distance, in combination with the properties of the surrounding gas, can determine the spark formation rate, the signal generator can control the frequency once the minimum distance and voltage are established.

Fig. 4. Block diagram of the spark gap system for experimentation.

Fig. 3. Example of a plasma formed by the spark gap by the ESD experimental setup.

We utilized a Michelson interferometer arranged in a common path configuration, with both a 532 nm laser and a 650 nm laser to measure fringe movement caused by potential spacetime distortions in the spark plasma. The use of two different wavelengths allowed us to determine whether the fringe movement was dependent upon wavelength. This allowed us to eliminate fringe movement mechanisms other than that caused by gravitational waves. The mirrors were set about 150 mm away from the splitter, with the screen about 500 mm away. The spark gap was placed halfway between one of the mirrored arms, as shown in Fig. 5.

Fig. 5. Block diagram the interferometer test structure.

Interferometry Analysis

The interferometer setup was optimized to detect nanometer fringe shifts. Fringe movements were recorded and analyzed across various input power levels and with the spark at various distances away from the laser. Video analysis was performed to quantify frame-by-frame fringe shifts relative to baseline measurements. This allowed us to track fringe displacements in relation to a wavelength for the particular laser used.

The gravitational wave strain (h) is a dimensionless quantity that represents the fractional change in the distance between two points in spacetime due to a passing gravitational wave [12]. In an interferometer, h relates to the change in the optical path length (∆L) as:

(8) $$\begin{array}{r}h=\frac{\mathrm{\Delta }L}{L}\end{array}$$

where

h – the gravitational wave strain

∆L – the change in the optical path length caused by spacetime distortion

L – the original optical path length of the interferometer In our specific situation, L = 725-mm

Gravitational waves cause differential stretching and compression of spacetime along the interferometer arms, resulting in a measurable change in ∆L. The strain h quantifies this relative change. In the absence of changes to the index of refraction, this strain represents the fractional change in the optical path length due to the influence of spacetime distortions and is also considered to be the magnitude of the gravitational wave at the point.

Working Hypothesis

Given the radial distribution of the energy within the spark, we suggest that it is strongest at the center and creates a spacetime contraction from the center. Following the formalism set out by Alcubierre [15] and the expression he derived for the energy density based upon his “top hat” shaping function given as

(9) $$\begin{array}{r}{T}_{00}=-\frac{c^4}{8\pi G}\frac{v_s^2}{4}{\left(\frac{df}{dr}\right)}^2\end{array}$$

Now, if we introduce a shaping function that has the following form:

(10) $$\begin{array}{r}f\left(r\right)=-a{e}^{-\beta {(r-r_0)}^2}\end{array}$$

Having a derivative with respect to r as:

(11) $$\begin{array}{r}\frac{df(r)}{dr}=2\alpha \beta (r-r_0)e^{-\beta {(r-r_0)}^2}\end{array}$$

This gives a new expression for the energy density:

(12) $$\begin{array}{r}{T}_{00}=-\frac{c^4}{2\pi G}{v}_s^2{\alpha }^2{\beta }^2(r-r_0{)}^2{e}^{-2\beta {(r-r_0)}^2}\end{array}$$

In our case v_s is defined as the displacement of the fringe divided by the duration of the spark pulse. Fig. 6 shows an example of the change in optical path length due to space-time compression at the center of the spark.

Fig. 6. Illustration of an increase in the optical path length of a laser passing through the region of the spark that undergoes compression at the center outward.

Others have worked to show that the magnitude of the energy density required to produce spacetime curvature, or “warp bubbles,” as described by Alcubierre, was indeed not as great as suggested [16], [17], but also not negative [18].

Furthermore, we suggest that gravitational waves are induced by the rapid change in energy density.

Experimental Results

In order to perform analysis of the fringe movement we needed to extract time series data from the video of the interferometer screen. A rate of 30 frames per second was adequate for the camera to capture displacements that occur with a spark pulse rate of no faster than approximately five pulses per second. Each frame was captured and rotated to provide vertical fringe lines, a threshold was applied to remove extraneous influences, and the pixels were summed vertically and smoothed. Fig. 7 shows an example of the processing of one such frame for the 532 nm wavelength laser test, and Fig. 8 shows the same for the 650-nm wavelength. The movement of the peaks is tracked and compared against a basis frame where there is no fringe movement. The displacement is calculated as the average difference of the peak positions when the spark is on versus when it is off. The difference in the peak is the wavelength of the laser and thus allows us to determine the scale factor for the number of pixels per nanometer. We can calculate the fringe movement induced by the spark for various distances and orientations in nanometers. Fig. 9 shows an example of the displacement of a 650 nm fringe under the influence of a spark.

Fig. 7. Interferometer fringe analysis steps for 532 nm laser test.

Fig. 8. Interferometer fringe analysis steps for 650 nm laser test.

Fig. 9. Example of the analysis of the fringe movement for the 650 nm interferometer test.

We considered all possible mechanisms that could explain the movement of the fringes. These mechanisms informed the experimental procedures we employed so that we could mitigate them or eliminate them as a cause. The mechanisms we considered were the following:

• Mechanical and acoustic vibrations are initiated by the formation of the spark.

• Shock waves are produced by the pressure of rapid spark formation.

• Changes in the index of refraction within or around the spark, which could change the optical path length.

• Intense electromagnetic pulse or electrostatic discharge that affects the optical path.

• Compression of a small region of spacetime at the center of the spark and propagating outward as a gravitational result of $du/dt$.

The strategies used to mitigate or eliminate all non-spacetime distortion mechanisms for fringe movement were:

• We placed our testbed on a vibration resistant platform. We also observed that the spark did not cause movement of the fringe lines when placed well away from the laser, even though it remained on the platform and remained in operation.

• The fringe movement effect was nonexistent if the spark was at a distance of 20 mm or more from the laser. The orientation of the spark in relation to the laser did not impact the response. A pressure wave would travel farther in the air and depend on the orientation.

• We oriented the spark at 0° and 90° to the laser beam. This did not impact the magnitude of the fringe movement with respect to the distance of the spark from the laser. Snell’s law suggests that there would be a significant difference [19]. In addition, we measured interferometer fringe displacement using lasers at 532 nm and 650 nm wavelengths. If the index of refraction was at play, then the magnitude of the displacement would be different for the different wavelengths.

• Electrostatic discharge or electromagnetic pulses can indirectly affect the length of the optical path by changing the local index of refraction, called the Pockel effect [20]. The strategy we cited above would account for this.

The parameters we were able to adjust in our measurements were (1) spark gap distance, (2) spark input power, which ostensibly affected the spark pulse length and rate and thus the energy density, (3) the distance between the spark and the laser, and finally (4) the orientation of the spark with the laser beam. The following set of graphs shows the results of these tests. Observations include:

• The movement of the filament matched the frequency of repetition of the spark, and the displacement increased with input power.

• The displacement of the filament was not affected by the orientation of the spark but decreased with distance from the spark.

Fig. 10 shows the magnitude of the fringe displacement versus the distance from the 650 nm laser center and a 5 mm gap width. The magnitude peaked around 140 mm and fell in a 1/r² fashion. The direction of displacement was always in the direction of increase in optical path length although it did ring as it settled back down after the pulse ended. Note that the orientation of the spark to the laser did not significantly affect the result. Fig. 11 is the same test with the 532 nm laser. In this case, the displacement peak was also around 140 nm in the direction of increased L.

Fig. 10. 650 nm laser interferometer fringe displacement versus distance of the spark from the laser given 0° and 90° orientation with 5 mm spark gap.

Fig. 11. 532 nm laser interferometer fringe displacement versus distance of the spark from the laser given 0° and 90° orientation with 5 mm spark gap.

Decreasing the spark gap width served to decrease the spark duration, thus increasing the repetition rate, while at the same time increasing the energy density for the same input power level due to the decreased volume of the spark. Figs. 12 and 13 show slightly higher maximum fringe displacement values while having the same behavior as before with respect to distance and orientation.

Fig. 12. 650-nm laser interferometer fringe displacement versus distance of the spark from the laser given 0° and 90° orientation with 2.5-mm spark gap.

Fig. 13. 532 nm laser interferometer fringe displacement versus distance of the spark from the laser given 0° and 90° orientations with 2.5 mm spark gap.

Adjusting the input power levels and the gap widths, we were able to isolate different energy density values of 1.4 and 2.4 GJ/m³. The displacements shown in Figs. 14 and 15 show their dependence on the energy density in a way that we would expect for space-time distortion. The spark/laser orientation of both 0° and 90° gave similar results.

Fig. 14. Energy density versus fringe displacement for 90° orientation.

Fig. 15. Energy density versus fringe displacement for 0° orientation.

Discussion

Our findings suggest that rapidly forming high-energy sparks can produce gravitational wave-like effects. Given the lack of significant vibrational, shockwave, or refractive-index influences, the observed fringe movement is attributed to space-time distortions.

Summary of Observations

In our experimental setup, using a spark gap to explore potential spacetime distortions, we have systematically documented and analyzed the following key observations:

• Fringe Movement in Interferometer: The interferometer consistently shows fringe movement synchronized with the spark formation. The magnitude and frequency of the fringe movement scales proportionally with the power applied to the spark gap and aligns with the frequency of the spark formation. This indicates a change in the optical path length (OPL) near the spark region.

• Orientation Independence: The fringe movement is unaffected by the orientation of the spark gap relative to the laser beam. Both perpendicular and parallel orientations produce the same fringe movement magnitude and pattern. This orientation independence suggests that traditional refractive index changes, which are typically angle-dependent, may not be the primary mechanism responsible for the observed fringe shift.

• Effect of Laser Wavelength: The fringe movement characteristics remain consistent across different laser wavelengths (532 nm and 650 nm). This wavelength independence is inconsistent with traditional refractive index changes, which would result in chromatic dispersion. This suggests that the observed effect may be wavelength-independent and possibly due to spacetime distortion or gravitational wave effects. Furthermore, if there was a change in the index of refraction, then the velocity of the fringe displacement would be: where v₀ is the velocity in the air n is the index of refraction in some other medium. So then and likewise: which gives: This is the ratio of the difference in the displacement values during the 532 nm laser test and the 650 nm laser test that we should expect to see if the index of refraction is being changed by the spark. This should be particularly evident when the laser passes directly through the spark region. Instead, these values are nearly identical.

(13) $$\begin{array}{r}{v}_d=\frac{v_0}{n}\end{array}$$

(14) $$\begin{array}{r}\mathrm{\Delta }{x}_{532}=\frac{v_0}{n_{532}}\mathrm{\Delta }t\end{array}$$

(15) $$\begin{array}{r}\mathrm{\Delta }{x}_{650}=\frac{v_0}{n_{650}}\mathrm{\Delta }t\end{array}$$

(16) $$\begin{array}{r}\frac{\mathrm{\Delta }{x}_{532}}{\mathrm{\Delta }{x}_{650}}=\frac{\frac{v_0}{n_{532}}\mathrm{\Delta }t}{\frac{v_0}{n_{650}}\mathrm{\Delta }t}=\frac{n_{650}}{n_{532}}=\mathrm{1.22.}\end{array}$$

• Lack of Chromatic Dispersion: Introducing white light near the spark produces no observable chromatic dispersion or rainbow-like effect within the plasma region. A true refractive index change would likely cause dispersion as different wavelengths of light refract differently. The absence of dispersion further supports the hypothesis that the observed fringe movement is not due to traditional refractive index change.

• Distance Dependence: The magnitude of the fringe movement decreases with increasing distance from the spark, dropping off completely around 20 mm. This drop-off is symmetrical on both sides of the laser beam. The symmetry and distance dependence suggest a localized effect originating from the spark region, potentially indicating a spherical or radial field effect such as a gravitational wave.

• Series Configuration of Spark Gaps: When multiple spark gaps are placed in series, the fringe movement appears to be additive, with each spark contributing to the overall displacement. This additive nature hints at a cumulative or constructive interference mechanism, consistent with the concept of an array of “gwavelets” combining to form a larger, coherent spacetime distortion pattern.

• Helium Environment: Replacing air with helium in the experimental setup does not eliminate the fringe movement. In fact, the effect becomes more pronounced, and the spark forms more easily in helium at lower energy levels. This suggests that traditional refractive index changes are not the primary cause, as these would behave differently in helium compared to air.

• Power Scaling: Increasing the input power to the spark gap proportionally increases both the fringe movement and the frequency of spark formation. This behavior supports the idea that the effect is related to energy density in the spark region, consistent with the hypothesis of spacetime distortion. Furthermore, the rise time of the spark pulse was approximately 1/10 of the pulse width, so then we can estimate the power density as The pulse formation time was related to the input power and dependent upon the gap length. For the 2.5 mm gap, the power density was as high as 1 × 10¹¹W/m³, and when the gap was 5 mm the power density was as high as 8 × 10¹⁰W/m³.

(17) $$\begin{array}{r}p=\frac{du}{dt}=\frac{\mathrm{\Delta }u}{\mathrm{\Delta }t}\end{array}$$

• Energy Density: As shown in (11), the energy density is dependent upon the velocity of the distortion. Our maximum observed displacements are between 140 nm and 160 nm in periods of 0.17 and 0.23 seconds for the gap widths of 5 mm and 2.5 mm, respectively. Calculated velocities then are in the range of 650 nm/s to 850 nm/s. These relatively slow displacement velocities serve to reduce the required energy density for the shaping function we assumed.

On the basis of these observations, the spark gap experiment is proving that it is producing an effect that cannot be solely attributed to traditional refractive index changes, shock waves, or electrostatic interactions. The consistency of the fringe movement across orientations, the lack of chromatic dispersion, and the persistence of the effect in different spark/laser orientations suggest that the observed behavior may involve space-time distortion or gravitational wave generation. The observed additivity of the effect with multiple spark gaps further suggests the potential for a phased array of ‘gwavelets’ to produce controlled and steerable gravitational wave patterns. Fig. 16 shows a diagram of the concept of a phased gwavelet array. Here, sixteen spark-gap elements are arranged in a 4 × 4 configuration, creating a beam at the center. If this hypothesis is accurate, it would have profound implications for both physics and engineering, particularly in gravitational wave research, spacetime manipulation, and advanced propulsion applications.

Fig. 16. Conceptual diagram of a 4 × 4 gwavelet array driven by amplitude, phase, and frequency to create shaped and steerable gravity waves.

Potential Applications

If confirmed, this technology could revolutionize propulsion, particularly for spacecraft, by generating directional thrust through controlled gravitational wave emissions. Additionally, phased spark gap arrays could be applied to stabilize fusion reactions or study gravitational wave properties at a laboratory scale [21]. Fig. 17 shows a conceptual illustration of a set of gwavelet arrays used to compress both space and time in the region around deuterium and tritium atoms to stabilize the reaction time, as well as in the way that gravity is responsible for the stability of the fusion reaction within the Sun.

Fig. 17. Conceptual illustration of gwavelet arrays used to confine and stabilize fusion reactions.

In addition, if we consider the time compression that would occur within the region, it would be possible to increase the relative reaction time for chemicals and biological processes. The impact on the medical field would be substantial. Fig. 18 is an illustration of this.

Fig. 18. Conceptual illustration of gwavelet arrays used to create a time-stasis in order to relatively slow down or speed up reactions in biological applications.

Since we showed that we could modulate the spark formation timing artificially with a signal generator and that the gwavelets travel finite distances due to their power density $du/dt$, then a communication system could be created that could propagate in multiple media.

Conclusion

Our experimental results suggest that spacetime distortion is induced at the center of a spark plasma that has a sufficiently high energy density, in excess of 1 GJ/m³. Interferometer fringe displacements of up to 160 nm were observed under proper conditions, which were associated with an increase in optical path length. After other potential factors that could contribute to fringe displacements, such as vibrations, shock waves, and index of refraction change were mitigated, we conclude that minor gravitational lensing occurs at the center of the spark, causing the laser path to be distorted.

Additional experiments to increase the energy density, either in a vacuum or in other gases, will be carried out to further expand on the results produced here. In addition, the author is investigating optimal frequencies for maximizing space-time distortion effects, as well as the additional influence of rotational fields.