Debunks Reality Denial Curvature Experiments

Testing Laser-over-Water Experiments

Laser-over-water experiments are among the most popular attempts to test whether Earth curves. The appeal is obvious. Water appears flat, a laser appears straight, and a distant target gives an apparently simple yes-or-no result: put the laser a known height above the water, put a target the same height several miles away, and see where the beam arrives. If Earth curves, the argument goes, the surface should “drop away” and the laser should strike far above the original height—or perhaps be blocked altogether. If it still arrives at the same height, the water must be flat.

The basic intuition is good. Controlled optical surveying really can test curvature. The problem is that most internet versions are not controlled optical-surveying experiments. They combine a ray-path problem, a spherical-geometry problem, a beam-propagation problem, a near-surface atmospheric-refraction problem, a water-level problem, and a metrology problem, then treat the result as though a handheld laser were an infinitely thin perfectly horizontal mathematical line. It is not.

The same surface that makes these experiments attractive—long, unobstructed water—is also one of the worst environments for uncontrolled optical refraction. Temperature gradients immediately above lakes, canals, bays, salt flats, and ice can bend near-horizontal rays significantly. Meanwhile, real laser beams diverge, wander, scintillate, and form finite spots. Tiny angular pointing errors become feet or tens of feet after several miles. The physical beam observed on a distant target is therefore not automatically the geometric axis that left the emitter.

The decisive issue: a laser experiment does not test curvature merely because a laser crosses water. It tests curvature only if the experiment independently establishes the emitter and receiver heights, the laser’s initial direction, the beam axis rather than its halo, the water or datum geometry, and the atmospheric refractive conditions well enough that the competing models make distinguishable numerical predictions. If the unexplained optical uncertainty is larger than the predicted curvature signal, the experiment has measured the atmosphere and alignment—not Earth’s shape.

Laser safety: do not reproduce long-range outdoor laser tests casually. The FDA warns that direct exposure to higher-class lasers can injure eyes, and the FAA states that aiming a laser at an aircraft is a federal crime in the United States.[1][2] A serious experiment should use compliant equipment, controlled beam paths, appropriate permissions, professional laser-safety practice, and procedures that prevent illumination of people, vehicles, boats, wildlife, and navigable airspace. High power is not a substitute for good metrology.

Contents

1. What Is a Laser-over-Water Experiment Trying to Test?

The intended test is usually straightforward. Choose two points separated by several miles across a lake, canal, reservoir, bay, or other large water body. Put a laser emitter at a known height above the water at the first point. Put a target, camera, or detector at the far point. If the water surface is curved, then a straight optical path should behave differently than it would above an infinite plane.

That is a legitimate idea. The difficulty lies in defining exactly what the competing predictions are.

On a flat plane, a perfectly level laser placed 6 feet above the plane remains 6 feet above that plane everywhere if “level” means parallel to the plane. On a spherical Earth, a laser initially horizontal relative to local gravity is tangent to the local level surface. The surface then curves away beneath the tangent. If nothing obstructs the beam, its height above the curved surface increases with distance.

But a second observer several miles away does not share the first observer’s local horizontal. Their vertical direction points toward Earth’s center from a different location. Therefore “6 feet above the water” at the far station is not on the same Euclidean horizontal plane as “6 feet above the water” at the emitter.

This is the core geometrical signal an experiment is trying to measure.

However, the physical beam is not necessarily launched tangent to the local equipotential surface. A spirit level can be misadjusted. A tripod can settle. The laser housing may not be aligned with its mechanical base. The water surface may move. The target height may be estimated incorrectly. Most importantly, atmospheric refractive index can vary with height and curve the laser path.

The experimental question is therefore not simply “Did I see the laser?” It is: Where was the beam’s central axis predicted to intersect a surveyed target under the measured atmospheric conditions, with what uncertainty?

2. The Correct Spherical Geometry

For a spherical approximation with radius R, the surface departure below a tangent line after horizontal distance d is approximately:

y ≈ d² / (2R)

for distances small compared with Earth’s radius.

Using Earth’s radius, this yields the familiar short-distance approximation of roughly eight inches per mile squared. The approximation is geometrically useful, but it answers a specific question: how far below the emitter’s local tangent plane is the spherical surface?

It does not automatically answer whether the beam is visible at a receiver, because the beam may intersect Earth before reaching the receiver if launched too low, the receiver itself is elevated, the beam may be tilted, and the atmosphere may refract it.

For exact calculations, one can work in an Earth-centered coordinate system. Let the emitter be located at radius R + he. Let the receiver be separated by central angle θ and located at radius R + hr. The straight chord or ray from one point can then be compared with the Earth surface along the route.

Professional geodesy uses still more accurate ellipsoidal and gravitational reference surfaces when necessary. NOAA’s National Geodetic Survey treats level surfaces as equipotential surfaces in Earth’s gravity field rather than as infinite planes.[3]

For most internet experiments, the spherical approximation is not the limiting source of uncertainty. The far larger uncertainties are usually the beam path and endpoint heights.

3. Equal Height at Both Ends Does Not Imply Equal Ray Height in Between

This point causes repeated confusion.

Suppose two stations are each precisely 10 feet above the same ideal spherical sea-level surface. They are several miles apart. Those two points do not lie on one global horizontal plane tangent to Earth. Their local horizontal planes are rotated relative to each other.

A perfectly straight line connecting the two 10-foot points is a chord-like sight line. Depending on the separation and heights, that line may intersect the Earth or water surface between them. If it does, mutual direct visibility is impossible without refraction or additional elevation.

Conversely, a laser launched horizontally from the first 10-foot station follows the local tangent direction, not the straight line joining equal-height points. Its height above the curved surface increases with distance—if the surface does not intercept the beam first because the emitter itself has a finite horizon.

Thus there are at least two different experiments:

These are not the same geometry. Many online tests aim the laser until it is visible on the far target, then later describe the beam as “level.” Once the operator has adjusted azimuth and elevation to acquire the receiver, the beam direction is no longer an independent measurement of level.

A test becomes circular if the laser is manually tilted until it reaches a desired height and that arrival height is then used to prove the water is flat.

4. Tangent Drop Versus Line-of-Sight Obstruction

The tangent-drop formula is often misused in laser discussions in the same way it is misused in long-distance photography.

At 10 miles, the spherical surface lies roughly 66.7 feet below a tangent plane originating at the emitter’s surface point. That does not mean a laser 6 feet above the water will arrive 72.7 feet above the water at the far shore.

Why not? Because a laser 6 feet above the water has a geometric horizon only a few miles away. A horizontally launched tangent ray can clear the curved surface, but the relevant tangent point is associated with the elevated emitter geometry rather than simply adding emitter height to the tangent-drop rule in an informal way. Exact line-of-sight geometry should be used.

Similarly, if one asks whether two 6-foot stations can see one another, the proper calculation uses the horizon distance from both ends. If their separation exceeds the sum of those horizon distances, a straight unrefracted line connecting them passes through the sphere.

The key distinction is:

surface drop below one tangent ≠ amount hidden from an elevated line of sight

Any experiment that reports “X feet of missing curvature” should specify which geometric quantity X represents.

5. Horizon Distance from Both Endpoints

For an observer height h above a spherical Earth of radius R, the approximate geometric horizon distance is:

d ≈ √(2Rh)

The maximum separation for mutual direct line of sight between two elevated endpoints is approximately:

dmax ≈ √(2Rh1) + √(2Rh2)

ignoring refraction and intervening terrain.

This relation provides a quick sanity check for laser experiments. If both laser and detector are only a few feet above water and the separation is many miles beyond their combined geometric horizons, a direct straight path at those heights is not expected.

If light is nevertheless detected, at least one of the following must be investigated:

The final possibility is logically allowed. The mistake is jumping to it before measuring the much more ordinary optical and metrological variables.

6. A Laser Beam Is Not an Infinitely Thin Line

Textbook diagrams draw a laser as a line because a line is convenient. Real lasers produce beams with finite diameter and angular divergence.

Even a well-collimated laser spreads because of diffraction. Real commercial pointers and inexpensive alignment lasers usually diverge more than an ideal diffraction-limited Gaussian beam because of diode geometry, optics, manufacturing tolerances, and beam quality.

NIST treats laser beam diameter, beam profile, and divergence as measurable quantities requiring metrology and uncertainty analysis.[4][5]

A long-range curvature test must therefore know:

Without those measurements, “the laser hit the target” may mean only that some low-intensity portion of a broad beam footprint reached it.

7. Beam Divergence Becomes Enormous over Miles

For small angular divergence θ, a beam diameter increases approximately linearly with range:

ΔD ≈ θL

where L is propagation distance. If θ is the full-angle divergence, it approximately gives the added full beam diameter; if θ is quoted as half-angle divergence, the convention must be handled accordingly.

Suppose a pointer has a full-angle divergence of 1 milliradian. One milliradian is only about 0.057 degrees—visually tiny.

At 1 kilometer, that contributes about 1 meter of beam spread. At 10 kilometers, about 10 meters. At 10 miles, roughly 16 meters, or more than 50 feet.

A 0.5 mrad beam can still spread by roughly 26 feet over 10 miles. A 2 mrad beam can spread by more than 100 feet.

This alone can overwhelm the curvature signal in many informal tests.

If a target panel 6 feet above water glows faintly at 10 miles, but the laser footprint is tens of feet tall, the observation does not establish that the central beam axis remained 6 feet above the water. The core could be far higher or lower while the wing of the intensity profile reaches the detector.

This is why beam divergence must be measured before the experiment rather than guessed from the fact that the beam looks narrow nearby.

8. Gaussian Beams Do Not Have Hard Edges

Many lasers approximately produce Gaussian-like transverse intensity profiles. In a Gaussian beam, intensity decreases smoothly away from the center rather than terminating at a sharp edge.

A common beam radius convention defines w where intensity has fallen to 1/e² of its central value. But detectable light exists outside that nominal radius. A sensitive camera in darkness may record portions of the beam far beyond what looks like the “spot” on a daylight target.

This matters enormously in online demonstrations. One side films a bright central spot at short range and assumes that the beam remains that diameter. At the far station, a high-ISO camera records a weak green glow several feet across. The experimenter treats the glow as proof that “the beam is here.”

But the relevant geometric quantity is the beam axis or another defined central statistic—not the faintest detectable photon.

Professional beam metrology therefore uses defined intensity thresholds, calibrated sensors, and profile measurements. NIST’s laser-beam-diameter calibration work exists because beam size is not a trivial visual quantity.[5]

If the target can detect light at one percent or one-thousandth of peak intensity, the effective visible footprint may be much larger than the quoted nominal diameter.

9. Tiny Pointing Errors Become Large Height Errors

Long-range alignment is brutally sensitive to angle.

For a small pointing error α, the vertical displacement at range L is approximately:

Δy ≈ Lα

A pointing error of only 0.1 milliradian is about 0.0057 degrees.

At 10 miles, 0.1 mrad produces a vertical shift of roughly 1.6 meters—more than 5 feet.

At the same range, 1 mrad produces about 16 meters—more than 50 feet.

This means that a laser mount can look perfectly level to the eye while being vertically wrong by many feet at the receiver.

A consumer bubble level is usually not an adequate angular calibration for a multi-mile curvature experiment. The laser diode may also be misaligned relative to the housing. Mount flex, thermal expansion, tripod settlement, vibration, and the operator touching the device can shift the aim.

To use the laser direction as evidence, the experiment must establish the optical axis relative to local gravity with angular precision substantially better than the effect being tested.

10. “The Laser Was Level” Must Be Demonstrated, Not Asserted

The word level has a technical meaning in surveying. A properly leveled optical instrument establishes a line perpendicular to the local plumb direction. The local plumb direction follows gravity.

NOAA’s geodetic leveling manual treats this relationship carefully because leveling is ultimately tied to equipotential surfaces of Earth’s gravity field.[6]

Putting a cheap spirit level on top of a laser housing does not necessarily establish the laser beam as a geodetic horizontal. There are several potential offsets:

A serious experiment should reverse the instrument or otherwise calibrate collimation error. Surveying instruments are built around such error-control procedures precisely because “it looked level” is not enough.

11. Tripod Height Is Not Enough

Laser experiments often report a number such as “the laser was 3 feet above the water.” How was that measured?

The relevant height is the optical axis above the reference water surface at the instant of measurement.

Measuring from a dock deck to the laser base is not sufficient. The dock may be above the water by an uncertain amount and may move. Measuring from a beach to waterline can be distorted by slope and waves. A target attached to a piling may have a known mark height but the local water level may differ because of tides, setup, wind, or seiche.

For high-quality work, endpoint heights should be tied to surveyed benchmarks or simultaneously measured water levels. On tidal water, both stations need a consistent vertical datum. On a large lake, wind setup and seiches can produce real water-level differences.

GPS height from a phone is not a substitute for centimeter-level vertical control. Consumer GNSS vertical error can be many times worse than horizontal error, and ellipsoidal height is not identical to orthometric height above the geoid.

If the predicted curvature effect is 10 feet but endpoint height uncertainty is ±5 feet at each end, the experiment cannot support a precise conclusion.

12. Seeing Laser Light Is Not the Same as Measuring the Beam Axis

This is perhaps the most common observational error after refraction.

A distant target may show a green patch, flash, or glow. The experimenter marks the center by eye and declares the beam height. But the visible patch can be shaped by:

A rigorous setup would use a large calibrated detector array or target with known coordinates and capture the full two-dimensional intensity distribution. The centroid or fitted beam center could then be measured with uncertainty.

A human observer saying “I can see green at six feet” is not equivalent to measuring the optical axis at six feet.

13. Camera Bloom and Exposure Can Manufacture Giant Laser Spots

Digital cameras can make laser light look much larger than the physical high-intensity core.

When pixels saturate, charge can spread or adjacent pixels can clip at maximum brightness. Internal lens reflections, sensor blooming, demosaicing, sharpening, compression, and overexposure can turn a small bright point into a large glowing blob.

Nighttime footage is especially vulnerable because cameras raise gain and exposure. Green light can appear very bright to both cameras and human vision. A target that seems covered by a foot-wide or meter-wide patch may have a much narrower central irradiance distribution.

Therefore screenshots are poor metrology. Raw sensor data, fixed manual exposure, calibrated targets, neutral-density filtering where appropriate, and multiple exposures are better.

The same problem affects claims that a distant receiver “saw the laser exactly at the waterline.” If the camera is overexposed, apparent spot boundaries can shift dramatically with exposure settings while the beam itself has not moved.

14. Scattered Light Can Be Detected When the Core Misses the Target

Light does not need to strike a detector directly for the detector to register something.

Atmospheric molecules and aerosols scatter light. Water droplets, fog, spray, dust, insects, target edges, boat surfaces, shoreline structures, and waves can scatter laser light into a camera.

This is why a laser beam is sometimes visible from the side at night: you are not looking directly down the beam axis; you are seeing light scattered into your eyes.

Over miles of atmosphere, even weak scattering integrated over a long path can create visible streaks or glows. A receiver may therefore detect evidence that the beam passed somewhere nearby without establishing that the beam center intersected the claimed coordinate.

A properly baffled photodetector with angular filtering is better than an exposed camera pointed toward a bright laser source. Better still, measure the intensity map across a known target plane rather than treating any detection as an axis crossing.

15. Water Is Level—but “Level” Is Not an Infinite Straight Plane

Flat-Earth laser experiments frequently begin with the true statement that water seeks its level.

In geodesy, a level surface is an equipotential surface of Earth’s gravity field. The local vertical is the direction of gravity, and the local horizontal is perpendicular to it. Because the gravity direction changes over Earth’s surface, a large level surface is curved rather than an infinite Euclidean plane.

NOAA’s National Geodetic Survey explains that geodetic leveling follows equipotential surfaces and that a horizontal sight line departs from those curved level surfaces with distance.[6]

At small scales the curvature is tiny, so a lake looks flat and builders can use straight levels. This is no contradiction. A large-radius curve is locally indistinguishable from a straight line over sufficiently short distances.

Thus “the water is level” does not decide the experiment. The experiment is intended to determine whether the level surface is globally planar or curved.

16. The Water Surface Is Not a Perfect Geometric Reference

Even if the mean water surface follows a gravitational equipotential, the instantaneous surface is dynamic.

Waves create local height variations. Wind setup can push water toward one end of a lake. Seiches oscillate lake levels. Tides alter coastal water height. Atmospheric pressure changes can depress or raise sea level slightly. Currents and temperature produce dynamic topography. A boat wake can change the reference by more than the effect some experiments claim to measure.

At the shoreline, measuring “height above water” becomes especially ambiguous because waves run up and down a sloped bank. A dock or pier may flex or float.

Averaging water level over time can help. Tide gauges or surveyed marks tied to a common datum are much better. The experiment should distinguish instantaneous surface roughness from the underlying mean level surface.

Otherwise the laser may be aligned relative to one crest while the receiver height is measured relative to a trough miles away.

17. Near-Water Refraction Is the Central Experimental Problem

If one fact should be remembered about laser-over-water experiments, it is this: a ray skimming close to water is traveling through the atmospheric boundary layer, where refractive-index gradients can be unusually strong and unstable.

Air refractive index depends on density and therefore on temperature, pressure, and humidity. If those variables change with height, light bends.

NOAA’s geodetic leveling manual requires atmospheric measurements specifically because refraction changes the line of sight. It calls for air-temperature, solar-radiation, and wind observations and discusses special procedures when atmospheric conditions become extreme.[7]

This is not an obscure correction relevant only to astronomers. It is built into terrestrial surveying.

Near water, strong temperature differences can form because water changes temperature more slowly than air. Cold water beneath warm air can produce an inversion. Warm water beneath colder air can produce a different gradient. Sunrise and sunset can rapidly change the boundary layer. Wind can mix layers and weaken gradients.

The resulting ray curvature can shift a beam vertically by feet over multi-mile distances.

18. Temperature Gradients Bend Optical Rays

Light bends toward regions of higher refractive index. In the lower atmosphere, refractive index generally increases with air density.

If denser, colder air lies beneath warmer air, a nearly horizontal optical ray may bend downward. Under other profiles, it may bend upward.

This is the physical basis of familiar mirages. The “shimmering road” effect on hot pavement occurs because strong near-surface temperature gradients curve rays. Over cold water, the sign can reverse and produce superior mirages or looming.

A laser mounted only a few feet above water is therefore not guaranteed to follow a straight chord. The path can curve in the same vertical plane in which the experiment is trying to detect Earth curvature.

That is a devastating confounder because the signal and nuisance effect can have the same form: a vertically displaced beam at the distant target.

A good experiment must either measure the refractive-index profile well enough to model the ray or design the geometry so refraction largely cancels.

19. Looming and Superior Mirages Are Directly Relevant

NOAA maritime guidance describes looming as an atmospheric-optics effect that can make objects appear higher than their true elevation and can bring objects normally below the horizon into view.[8]

This matters because many laser tests are performed in exactly the same environment where looming occurs: long, low paths over water.

If a distant target can be optically raised by refracted light, a laser ray can also be bent. The physics is reciprocal: light propagation through a refractive-index field does not care whether the source is a building, lighthouse, or laser diode.

A strong inversion can therefore let a beam reach a receiver that would be geometrically hidden from a straight ray.

The appropriate conclusion is not “refraction can explain anything.” It is “refraction must be measured before the observation is attributed to geometry.”

20. Strong Refraction Can Rival or Exceed Geometric Curvature

Under ordinary conditions, terrestrial refraction often bends a ray downward modestly, effectively increasing the optical horizon. Surveying sometimes models this as an effective Earth radius slightly larger than the geometric radius.

Under stronger gradients, ray curvature can increase substantially. In radio propagation, NOAA describes superrefraction and ducting where rays remain unusually close to the surface or bend back toward it.[9]

Optical wavelengths do not behave identically to microwave radar in every detail, but visible-light looming and superior mirages demonstrate that strong refractive bending occurs optically as well.

If the refractive ray radius approaches Earth’s radius, a near-horizontal beam can maintain approximately constant height above a curved surface for a surprising distance. If the ray bends even more strongly, it can intersect the water.

This is precisely why an apparent “same-height” hit over water cannot be interpreted without atmospheric information.

21. Refraction Changes with Time

A powerful diagnostic is to leave the geometry fixed and watch what happens over time.

If the beam spot drifts vertically by several feet over minutes or hours, Earth’s radius has not changed. The optical path has.

Sunrise can produce rapid transitions as land and air warm differently from water. Sunset can generate stable inversions. Passing clouds alter surface heating. Wind can break up a layered atmosphere. Fog and humidity change the refractive environment.

Online laser demonstrations often celebrate the moment when the beam suddenly appears on a distant target after hours of adjustment. That moment may actually be evidence of changing refraction or pointing, not of a geometric surface.

A scientific experiment should record the beam position continuously and correlate it with meteorological measurements. A single successful frame selected from a long night is weak evidence.

22. Turbulence Causes Beam Wander and Scintillation

Even when the mean refractive gradient is understood, small-scale turbulent fluctuations distort laser propagation.

Pockets of air with slightly different temperature and density act like weak, moving lenses. The beam can wander, broaden, break into speckled intensity structures, and fluctuate in brightness. Astronomers see the same atmospheric turbulence as stellar twinkling and image blur.

Over a long horizontal path near the ground or water, turbulence can be strong because the beam remains inside the lowest atmospheric layers for its entire journey.

The receiver may therefore see the spot jump up and down or flicker. If the experiment marks the highest or lowest observed position instead of the time-averaged centroid, the result is biased.

Professional free-space optical communication and laser-ranging systems explicitly account for atmospheric propagation effects because they influence received power and pointing stability.

23. Wavelength and Atmospheric Transmission Matter

Not all lasers propagate identically through the atmosphere.

Refractive index varies slightly with wavelength. Molecular and aerosol scattering also vary with wavelength. Green laser pointers appear particularly bright to human vision, which makes them popular for demonstrations, but perceived brightness is not a measure of geometric accuracy.

Some inexpensive green lasers may also produce unwanted infrared emissions if poorly filtered, while cheap diode lasers can have irregular beam shapes.

For a measurement experiment, the beam should be characterized instrumentally rather than by eye. Wavelength, output power, beam divergence, beam shape, and stability should be documented.

More power is not automatically better. Increasing power can saturate detectors, enlarge apparent spot size through bloom, and create serious eye and aviation hazards. The FDA notes that Class 3B and Class 4 lasers can cause immediate injury and should be used only with proper controls.[1]

24. What Professional Geodetic Leveling Does Differently

Surveyors have spent centuries solving almost exactly this class of problem: how do you measure elevation differences across a curved Earth while optical lines of sight are refracted by the atmosphere?

NOAA’s National Geodetic Survey describes differential leveling as the most accurate traditional technique for establishing vertical control.[10]

The solution is not “shoot one long beam and assume it is straight.” It is nearly the opposite.

Precise leveling uses short, balanced sight lengths. The instrument sits between calibrated staffs. A backsight and foresight are taken at approximately equal distances. Because curvature and many refractive effects are similar over equal sight lengths, they largely cancel in the elevation difference.

Then the instrument advances and the process repeats through many setups.

NOAA’s manual explicitly states that curvature error grows with the square of sighting distance and that balancing backsight and foresight distances greatly reduces it.[6]

This is telling. Professional metrology avoids very long near-surface optical rays because those rays amplify exactly the errors that viral laser experiments ignore.

25. Why Balanced Sights Cancel Curvature and Refraction Errors

Suppose a level instrument is exactly midway between two staffs. The horizontal sight line is tangent to the local level surface at the instrument.

Because both staffs are nearly the same distance away, the Earth-curvature departure is almost the same on each side. Subtracting the two staff readings cancels that common curvature term.

Atmospheric refraction also tends to be similar for the two equal-length paths when conditions are comparable. It therefore cancels to first order as well.

This does not mean surveyors “ignore curvature.” It means they deliberately design the measurement so curvature and refraction do not contaminate each incremental height difference.

Over a long route, many such local height differences establish elevations following Earth’s equipotential surface.

Compare that with a flat-Earth laser test: one grazing beam travels for 5, 10, or 20 miles through unstable air, while the experiment assumes zero refraction. The professional method exists partly because that assumption is unreliable.

26. Long Water Crossings Are Recognized as Special Problems

Surveying manuals devote special attention to river and valley crossings because long sights over inaccessible terrain or water defeat the ordinary short-balanced-sight procedure.

NOAA’s geodetic leveling manual includes dedicated procedures for water and valley crossings.[6] This is important context: the professionals who actually measure elevation do not regard a long laser skim across water as the easy version of the problem.

Long crossings require specialized techniques to control collimation, curvature, refraction, target identification, and timing. Reciprocal or simultaneous observations may be used so atmospheric effects can be reduced.

This does not imply that long-range optical tests are impossible. It means the uncertainty budget becomes more demanding as the path grows.

The popular intuition “longer distance means more curvature, so the test gets easier” is only half true. The curvature signal grows with distance, but beam spread, pointing sensitivity, atmospheric path length, and refractive uncertainty grow too.

27. Precision Laser Ranging Corrects Atmospheric Propagation

Lasers are used in some of the most precise geodetic measurements on Earth—but not by assuming laser light propagates through atmosphere without correction.

NASA’s International Laser Ranging Service supports satellite and lunar laser ranging for geodesy, Earth orientation, orbit determination, and reference-frame maintenance.[11]

NASA notes that laser-ranging data products include corrections associated with atmospheric effects.[12]

The contrast is instructive. Professional laser geodesy sends carefully characterized pulses to known spacecraft retroreflectors, measures round-trip time with extraordinary precision, models station coordinates and orbital dynamics, and corrects propagation through the atmosphere.

A laser is an excellent measurement tool. What makes the measurement precise is not the word laser; it is calibration, geometry, timing, atmospheric modeling, and uncertainty analysis.

The idea that “laser light is straight, therefore my beam proves flatness” strips away the very disciplines that make laser metrology trustworthy.

28. Testing the Classic Same-Height Laser Setup

Consider the canonical experiment:

The flat-Earth interpretation is immediate: equal height at both ends means the water is flat.

But before accepting that conclusion, a proper analysis asks:

  1. Were both optical-axis heights actually surveyed to the same vertical datum?
  2. Were water levels measured simultaneously?
  3. Was the emitter optical axis independently calibrated to local horizontal?
  4. Was the beam aimed after setup until the receiver saw it?
  5. What was the measured vertical divergence?
  6. What was the far-field beam diameter?
  7. Was the beam centroid measured or merely some visible light?
  8. What was the temperature profile from the water surface upward?
  9. Did the spot move during the observation?
  10. Were there mirage distortions visible in background objects?
  11. Was the detector or camera saturated?
  12. How accurately was the 10-mile range known?

If these questions cannot be answered, the experiment has not isolated curvature.

29. Worked Example: 10 Miles at 6 Feet

Take two points each 6 feet above an ideal spherical sea surface, separated by 10 miles.

The geometric horizon from a 6-foot eye is about 3 miles. Two 6-foot endpoints therefore have a combined unrefracted mutual horizon of roughly 6 miles. At 10 miles, a straight line joining the two equal-height endpoints would intersect the spherical surface.

Thus under a no-refraction globe model, the endpoints are geometrically hidden from one another at those heights.

Suppose, however, the laser has a 1 mrad vertical divergence. Over 10 miles the beam can be more than 50 feet tall in its far-field footprint depending on the divergence convention and near-field diameter.

Suppose the emitter is pointed only 0.2 mrad above the intended direction. That alone shifts the beam axis more than 10 feet vertically at 10 miles.

Now add a temperature inversion capable of bending the ray downward. The beam may reach a low receiver even though the straight geometric ray would not.

Therefore the observation “green light was seen at 6 feet” is insufficient. The competing effects are already comparable to or larger than the geometric signal.

30. Worked Example: 20 Miles at 10 Feet

Now place emitter and receiver axes 10 feet above water and separate them by 20 miles.

The geometric horizon from 10 feet is roughly 3.9 miles, so the combined direct-visibility distance is only around 7.8 miles without refraction. Twenty miles is far beyond that.

This seems like it should make the globe test decisive—and geometrically, it does. But the optical challenges also become much larger.

A 0.5 mrad beam spreads by roughly 53 feet over 20 miles. A 1 mrad beam spreads by more than 100 feet. A pointing error of only 0.1 mrad shifts the axis by roughly 10.6 feet. A 0.5 mrad aiming change shifts it more than 50 feet.

The beam is now traveling through more than 30 kilometers of low-altitude atmosphere. Strong near-water refraction can dominate the vertical path.

If a camera at the receiver detects a faint glow at 10 feet, that still does not identify the beam axis. The test needs much better instrumentation as distance increases.

This is a crucial experimental tradeoff: increasing distance strengthens the curvature signal but also magnifies beam and atmosphere systematics.

31. Why Beam Size Can Swallow the Predicted Signal

Suppose a spherical model predicts that the beam axis should arrive 20 feet above a chosen reference, while the flat model predicts 0 feet.

If the laser spot at the receiver is 60 feet tall, both predicted heights may lie inside the illuminated footprint.

Seeing light therefore does not discriminate between the models.

To distinguish them, the uncertainty in the beam centroid must be much smaller than the 20-foot separation between predictions. If the centroid can be located to ±2 feet, the test may be informative. If it is known only to ±30 feet, it is not.

The same reasoning applies to detector sensitivity. A bright beam core may pass high above the receiver while a faint low-intensity tail reaches the board. A camera set to extreme exposure sees the tail and produces a dramatic green patch, but the physical axis remains elsewhere.

A proper paper would report beam diameter and centroid uncertainty numerically. Most viral tests do neither.

32. Why Alignment Error Can Swallow the Predicted Signal

Angular error is often even more serious than beam divergence.

Imagine the flat and globe predictions differ by 15 feet at a receiver 10 miles away.

The angular separation corresponding to 15 feet over 10 miles is only about:

15 ft / 52,800 ft ≈ 0.000284 rad ≈ 0.284 mrad ≈ 0.016°

That is a tiny angle.

If the laser’s “level” calibration is uncertain by more than about sixteen-thousandths of a degree, the pointing uncertainty alone exceeds the entire signal.

A handheld bubble level, visual alignment, or inexpensive construction laser may not establish the optical axis to that accuracy over miles.

This is why survey instruments specify angular accuracy in arcseconds and are calibrated for collimation. One arcsecond is about 0.00485 mrad. Precision angular metrology exists because small angular errors become large positional errors at long range.

33. Why Atmospheric Error Can Swallow the Predicted Signal

Refraction is harder than pointing because it cannot be calibrated once in the laboratory and assumed constant.

The atmosphere changes along the path.

NOAA’s geodetic leveling manual says atmospheric refraction depends strongly on temperature gradients and requires measurements of temperature, solar radiation, and wind for correction.[7] The manual treats extreme atmospheric conditions as situations requiring special precautions.

A 10-mile beam a few feet above water passes through exactly the regime where vertical temperature gradients may be strongest.

If the refractive path uncertainty corresponds to even a few tens of microradians integrated over the path, the far-end vertical displacement can become feet. Strong inversion conditions can do much more.

Therefore an experiment claiming a few-foot curvature discrepancy without atmospheric profiling is not resolving Earth geometry at the claimed precision.

34. Bedford Level and the Danger of Low Sight Lines

The nineteenth-century Bedford Level experiments are relevant because they used a long, straight waterway and low optical lines—the same basic idea as modern laser tests.

Samuel Rowbotham reported that distant targets remained visible along the Old Bedford River and interpreted this as evidence that water was flat.

Alfred Russel Wallace later designed a different experiment using multiple markers elevated above the water. The central marker appeared displaced in the manner expected from curvature. A contemporary report in Nature described the result.[13]

The historical dispute is instructive because terrestrial refraction near water can strongly affect low sight lines. A target merely remaining visible does not uniquely determine the surface geometry.

Modern lasers improve brightness and targeting, but they do not repeal atmospheric optics. A green diode is still a light source propagating through refractive air.

35. Why Modern Viral Laser Tests Still Repeat the Old Mistake

Modern experiments often appear more technical because they use lasers, digital cameras, phone GPS, rangefinders, and curvature calculators. But sophisticated-looking equipment does not automatically improve experimental design.

The recurring pattern is:

  1. choose a long water path;
  2. measure approximate heights with tape measures;
  3. level a laser with a bubble or construction mount;
  4. adjust the beam until someone at the far end sees it;
  5. record a camera image of green light;
  6. compare it with an “8 inches per mile squared” calculation;
  7. declare missing curvature.

Almost every step can compromise the conclusion.

Adjusting the beam to acquire the target destroys independent knowledge of launch angle. Approximate endpoint heights undermine vertical geometry. Long near-water propagation maximizes refractive uncertainty. Camera detection does not locate the beam axis. Beam divergence creates a large footprint. Tangent-drop calculations may not match the actual endpoint geometry.

What looks like a direct experiment is therefore often an underdetermined inverse problem: many combinations of beam tilt, divergence, refraction, and height error can produce the same observed spot.

36. Common Objections Tested One by One

“Lasers travel perfectly straight.”

In a homogeneous medium, geometrical-optics rays travel straight. Earth’s lower atmosphere is not perfectly homogeneous. Refractive-index gradients bend rays. This is measured in surveying, astronomy, radar propagation, and atmospheric optics.

“A laser is more accurate than eyesight.”

A laser can be a highly accurate tool when its beam geometry, pointing, calibration, and atmosphere are controlled. Merely replacing an eye with a laser does not remove systematic errors.

“The laser was level because I used a spirit level.”

The spirit level establishes the orientation of its own vial relative to gravity within its accuracy. It does not automatically establish the laser’s optical axis unless the instrument has been calibrated for that relationship. A tiny angular offset becomes large over miles.

“The beam hit the target at the same height it left.”

Was the beam centroid measured, or merely visible light? Was the target height tied to the same datum? Was the beam aimed after setup? Was refraction measured? Without those controls, equal apparent heights do not uniquely determine geometry.

“Beam divergence is horizontal, not vertical.”

Many diode beams are elliptical and can have different divergence in orthogonal axes. Vertical divergence must be measured for the actual laser and optical orientation.

“The dot was only a few inches wide when we tested it nearby.”

Near-field spot size does not determine far-field size. Divergence accumulates with range. A beam that is millimeters wide nearby can be meters wide kilometers away.

“We could see the laser with the naked eye, so the core must have hit us.”

No. Human eyes and cameras can detect scattered or low-intensity light. The beam core can pass elsewhere while scattered light remains visible.

“Refraction only bends light upward.”

The direction depends on the refractive-index gradient. Different temperature profiles can bend rays upward or downward.

“Refraction is too small to matter.”

Under normal surveying conditions it may be a modest correction. Near water during strong inversions it can be much larger. NOAA explicitly treats extreme refractive conditions as important to geodetic measurements.

“Invoking refraction makes the globe unfalsifiable.”

No. Refraction can be measured and modeled. A better experiment records temperature profiles, uses reciprocal observations, raises the line of sight, and repeats under different conditions. If the same geometric discrepancy persists after refractive uncertainty is constrained, it becomes significant.

“Water is flat, so the beam should stay the same height.”

Water is locally level. In geodesy a level surface follows gravitational equipotential geometry. Whether that large-scale surface is planar or curved is the very question under test; it cannot be assumed in the premise.

“If curvature existed, the laser should shoot into the sky.”

A locally horizontal tangent ray does increase in height above a curved surface with distance. But low emitters also have finite horizons, and the real beam may be refracted. Exact endpoint geometry must be calculated rather than described verbally.

“We set the laser and target to exactly the same height.”

Same local height above water does not mean the two points share a single global horizontal plane. Their local vertical directions differ on a curved Earth.

“We measured the water with a tape, so GPS error is irrelevant.”

Tape measurements can establish local height above instantaneous water, but the water level itself may differ between endpoints or over time. On tidal water or large lakes, a common datum is needed for precise work.

“There were no visible mirages.”

Refraction does not have to create dramatic inverted images. Smooth ray bending can occur with little obvious visual distortion.

“It worked on multiple nights.”

Repeatability is valuable, but similar weather can reproduce similar refractive conditions. Strong evidence would report the beam position across a wide range of measured atmospheric profiles and show agreement with one geometry after correction.

“A stronger laser makes the experiment better.”

Not necessarily. Higher power does not improve angular calibration or reduce refraction. It can worsen detector saturation and safety hazards. Measurement quality comes from metrology, not brightness.

“The receiver was beyond the geometric horizon, so the globe is disproved.”

A receiver beyond the straight-ray geometric horizon can still receive refracted light. The question is whether the measured refractive conditions are sufficient. Simply detecting light does not discriminate.

“Surveyors use lasers, so our test uses the same principle.”

Surveyors use calibrated instruments, controlled sight lengths, redundant measurements, reversals, benchmarks, closure tests, and atmospheric error controls. The mere use of a laser does not make two experiments methodologically equivalent.

37. How to Design a Much Better Curvature Experiment

A good experiment should make the flat and curved predictions numerically distinct while keeping systematic uncertainty substantially smaller than the difference.

Use surveyed fixed stations

Establish emitter and receiver coordinates and orthometric elevations from reliable benchmarks or survey-grade GNSS tied to a geodetic datum. Do not use approximate shoreline heights.

Raise the optical path

Avoid skimming inches above water. Raising the beam several meters reduces the influence of the strongest surface-layer temperature gradients and minimizes obstruction by waves.

Characterize the laser before deployment

Measure vertical and horizontal divergence, near-field beam profile, optical-axis alignment relative to the mount, power stability, and wavelength. NIST beam-metrology practice demonstrates that these are genuine measurable parameters.[4]

Use a calibrated gimbal or surveying instrument

Mount the source on equipment capable of measuring launch angle independently. Record the angle; do not manually aim until the receiver sees the beam and then call that direction “level.”

Use a detector array

At the receiver, record the two-dimensional intensity profile across a tall target so the beam centroid can be measured. Avoid relying on a camera’s visual glow.

Use multiple receiver heights

A vertical array of photodiodes or calibrated cameras can show how intensity is distributed and whether the beam is drifting.

Record the atmosphere

Measure air temperature at several heights above the water at both ends, plus water temperature, pressure, humidity, wind, and solar conditions. Intermediate measurements are even better.

Repeat through time

Record continuously for hours. If the beam moves while hardware remains fixed, quantify that movement as atmospheric or instrumental uncertainty rather than cherry-picking one frame.

Make reciprocal measurements

Send beams in both directions simultaneously using independent calibrated systems. Reciprocal geometry can help separate curvature from asymmetric refraction and alignment errors.

Add a midpoint station

A surveyed midpoint target provides a powerful geometric constraint. The experiment no longer depends on only one endpoint intersection.

Pre-register the predictions

Before collecting data, calculate the expected target-centroid heights for a flat plane, a spherical/ellipsoidal Earth with no refraction, and a range of measured refractive profiles. State the acceptance criterion.

Publish uncertainties

Report endpoint height error, angular error, divergence, centroid error, range uncertainty, atmospheric model uncertainty, and water-level uncertainty. If the model difference is smaller than the combined uncertainty, the result is inconclusive.

Design for safety first

Use the lowest practical optical power and engineering controls appropriate to the detector. Avoid open beams near public travel corridors. Do not aim toward aircraft or navigable airspace. The FAA provides formal guidance for outdoor laser operations that may affect aviation.[14]

38. Better Still: Use Surveying Methods That Do Not Depend on One Grazing Beam

If the actual scientific goal is “measure curvature,” a single low beam across water is not the best available experiment.

Several designs are much stronger:

Three-height marker test

Place three surveyed targets at equal orthometric height above a level datum, with one near each end and one near the midpoint. Observe the relative vertical positions with calibrated instruments from both directions. Curvature produces a predictable midpoint displacement.

Reciprocal zenith-angle survey

Use survey-grade total stations at two benchmarks to measure vertical angles simultaneously in both directions. This constrains refraction much better than a one-way laser.

Geodetic leveling around the route

Connect the endpoint elevations through differential leveling or a validated geodetic network, then compare line-of-sight geometry. NOAA requires forward and backward leveling runs as a quality check and classifies work by closure error.[10]

High-elevation sight lines

Use towers, hills, or structures to keep the ray well above the water boundary layer. The higher path still experiences refraction, but it is generally less dominated by the immediate water-air interface.

Multiple wavelengths and atmospheric sensing

In an advanced experiment, multi-wavelength optical data plus meteorological profiles can constrain atmospheric refractivity.

Satellite laser ranging

At the professional extreme, laser ranging to satellites and lunar retroreflectors measures Earth-scale geometry and dynamics with high precision. NASA’s laser-ranging network contributes directly to the terrestrial reference frame.[11]

The lesson is not “do not experiment.” It is to design the experiment so the desired signal is not entangled with a larger uncontrolled nuisance effect.

39. What Result Would Actually Challenge the Globe Model?

A scientifically meaningful falsification criterion can be stated in advance.

Suppose a long-water experiment used surveyed endpoint and midpoint elevations, calibrated optical axes, measured beam profiles, controlled detectors, reciprocal simultaneous rays, and atmospheric profiling. Suppose the spherical/ellipsoidal Earth model predicted a vertical displacement of 20 feet after refraction correction, with a total uncertainty of ±1 foot.

If repeated observations instead produced 0 ±1 foot under multiple atmospheric conditions, that would be a serious anomaly.

The correct response would not be to say “refraction” indefinitely. Investigators would test calibration, instruments, atmosphere, local gravity, datum realization, and geometry. If the discrepancy survived independent replication, the underlying model would require revision.

That is falsifiability.

By contrast, a beam of unknown divergence manually aimed across a lake through unmeasured inversion layers and seen as a bright patch on a board has an uncertainty too large to perform that test. The experiment is not “suppressed evidence.” It simply lacks the controls needed to discriminate the hypotheses.

Conclusion

Laser-over-water experiments are not inherently bad curvature tests. Poorly controlled laser-over-water experiments are.

The central attraction is legitimate: a long optical path above a level surface should encode Earth geometry. But extracting that geometry requires more than shining a visible laser across a lake.

The first problem is geometry. Equal local heights at two endpoints are not points on one infinite global horizontal plane if Earth is curved. Tangent drop, hidden height, mutual horizon distance, and endpoint line of sight are different quantities. A test must calculate the correct one.

The second problem is the laser itself. Real beams have finite diameter and divergence. At multi-mile ranges, even a milliradian-scale divergence can create a footprint tens of feet tall. Gaussian-like beams have no hard edge, so cameras can detect low-intensity light well away from the core. Seeing a green spot therefore does not automatically locate the beam axis.

The third problem is pointing. A few hundredths of a degree of vertical misalignment can move the beam by tens of feet at long range. A spirit level on a consumer laser does not necessarily establish the optical axis to survey-grade accuracy.

The fourth problem—and usually the most severe—is atmospheric refraction. Near-water temperature gradients bend optical rays. NOAA’s geodetic manuals explicitly require refraction controls because atmospheric density gradients alter lines of sight. Maritime guidance documents looming and superior mirages that can raise normally hidden objects into view. The water boundary layer is not a neutral optical laboratory.

Turbulence adds beam wander and scintillation. Waves, tides, seiches, wind setup, and uncertain endpoint heights degrade the geometric reference. Camera saturation and scattering can further enlarge or displace the apparent beam.

This is why professional geodetic leveling uses short balanced sight lengths, repeated runs, calibrated rods, closure tests, and atmospheric precautions instead of relying on one long grazing ray. It is also why professional laser ranging to satellites corrects for atmospheric propagation rather than assuming a laser is a perfect Euclidean ruler.

The popular demonstration—“laser leaves at 6 feet, is seen at 6 feet ten miles away, therefore no curvature”—does not isolate Earth shape unless it also proves the launch angle, receiver height, beam centroid, beam divergence, refractive path, and datum geometry to precision better than the predicted difference.

A better experiment is entirely possible. Survey the stations. Raise the optical path. Calibrate the beam. Use detector arrays. Measure the atmosphere. Observe simultaneously in both directions. Add a midpoint target. Repeat under different thermal conditions. Publish an uncertainty budget and pre-register the flat and globe predictions.

If such an experiment consistently contradicted ellipsoidal-Earth predictions by many times its uncertainty, it would deserve serious scientific attention.

What the existing class of casual laser-over-water demonstrations generally shows, however, is something less revolutionary and more useful: long horizontal optical propagation through the near-surface atmosphere is difficult metrology. Surveyors already know this. Atmospheric physicists already know this. Laser engineers already know this. Once the same standards are applied, the claimed contradiction with Earth curvature disappears.

For the broader visibility geometry behind these tests, see Testing “You Can See Too Far for Earth Curvature”. For the wider model in which laser tests are commonly presented, see Testing Flat Earth. The related atmospheric arguments are addressed in Testing “Atmospheric Pressure Requires a Container”.

Sources and Further Reading

  1. U.S. Food and Drug Administration — Frequently Asked Questions About Lasers. Describes laser hazard classes, eye hazards, pointer safety, and the dangers of higher-powered Class 3B and Class 4 devices.
  2. Federal Aviation Administration — Laser Laws & Enforcement. Explains U.S. federal law prohibiting aiming laser pointers at aircraft.
  3. NOAA National Geodetic Survey — Geopotential Surfaces. Explains physical level surfaces and the relationship between gravity, the geoid, and vertical datums.
  4. NIST — Laser Beam Metrology for AM-Bench 2022. Discusses beam power-density distribution, beam characterization, measurement variability, and uncertainty.
  5. NIST Special Publication 250-87 — Calibration Service for Instruments that Measure Laser Beam Diameter. Describes standardized laser-beam diameter and profile measurement.
  6. NOAA Manual NOS NGS 3 — Geodetic Leveling. Explains curvature error, equipotential level surfaces, balanced sights, water/valley crossings, and professional vertical-survey procedures.
  7. NOAA National Geodetic Survey — Geodetic Leveling, Atmospheric Conditions. Requires measurements of temperature, solar radiation, and wind for refraction correction and discusses temperature-gradient effects.
  8. NOAA U.S. Coast Pilot — Refraction, Looming, Towering, and Mirages. Documents atmospheric optical effects capable of changing apparent elevation and bringing normally hidden objects into view.
  9. NOAA JetStream — Radar Beams and Atmospheric Refraction. Explains normal refraction, superrefraction, subrefraction, ducting, and Earth-curvature effects on electromagnetic propagation.
  10. NOAA National Geodetic Survey — Geodetic Leveling. Describes vertical-control practice, forward and backward runs, closure, and quality classification.
  11. NASA Goddard — International Laser Ranging Service. Describes satellite and lunar laser ranging as core techniques in modern space geodesy and terrestrial-reference-frame maintenance.
  12. NASA Space Geodesy Project — Data and Products. Notes that laser-ranging data include range/time observations together with atmospheric corrections.
  13. Nature — “The Rotundity of the Earth” (1870). Contemporary report of Alfred Russel Wallace’s Bedford Level experiment using multiple elevated markers.
  14. FAA Advisory Circular 70-1B — Outdoor Laser Operations. Provides safety and notification guidance for outdoor laser operations that may affect aircraft in U.S. navigable airspace.
  15. NOAA Technical Memorandum NOS NGS 34 — Corrections Applied by the National Geodetic Survey to Precise Leveling Observations. Describes refraction, collimation, orthometric, tidal, scale, and temperature corrections applied to precision leveling.
  16. NIST — Calibration Experiments of a Laser Scanner. Discusses accuracy, precision, distance, incidence angle, and beam divergence in laser-scanning metrology.
  17. Federal Aviation Administration — Laser Safety. Current aviation-safety guidance concerning outdoor laser illumination and aircraft hazards.