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Flat earth debunking gone wrong - How german public service TV failed at flat earth debunking
Flat earth debunking gone wrong
The ZDF is a german public service television broadcaster. Under the Terra-X brand, they have been broadcasting a variety of documentaries from various fields of science. It is a mixture of entertainment and educational television. In October 2020, the episode "Ein Fall für Lesch & Steffens" - Die Wahrheit über die Lüge (english: "A case for Lesch & Steffens" - The truth about the lie) was released. It dealt with debunking various conspiracy theories among them the flat earth theory and somehow they managed to botch that segment completely.
External content: Link to ZDF; Video "Ein Fall für Lesch & Steffens - Streiten für die Wahrheit" from the Terra-X channel.
This article is not about defending the flat earth theory. It is about exposing bad science presentation. We know that the Earth is spherical in shape. That argument has been settled for centuries. Today the "modern" theory of the flat earth is only seriously advocated by a few individuals. It is a colorful mix of religious fundamentalists, conspiracy theorists, and trolls.
Congresses are held, books and T-shirts are sold, and podcasts and videos generate advertising revenue and attract new followers. Some of the protagonists of this movement are media-savvy and know exactly how to misrepresent the laws of physics and how to use oversimplified models to overwhelm laymen with their arguments. They are scientifically literate conman.
It is a subject matter that would be interesting for a popular science show, but the attempt of Terra-X to address this topic was marred by factual errors and inaccuracies. It was a case of packaging triumphing over content, with natural science simplified to the point of unrecognizability.
Confusing Earth's curvature with lens distortion
The first mistake happens right at the beginning. Video footage of "Project Red Bull Stratos", Felix Baumgartner's stratospheric jump is shown. In the background of the footage, supposedly a clear curvature of the earth can be seen at the height of 38 km. The Terra-X team is here falling into an all too common trap. They tried to demonstrate a curvature of the horizon in photos taken with a fisheye lens, without having carried out the necessary lens correction beforehand. It is an astonishingly stupid mistake. Flat earthers must be having a field day already. The narrator states:
"The cameras show, in passing, the obvious: the spherical shape of the earth."
That is precisely what the cameras do not show! They largely show lens distortion and only to a small extent the actual curvature of the earth. The impact of a fisheye lens on an image is demonstrated exemplarily in the two photos below. For licensing reasons, I cannot use original footage of Baumgartner's jump here. But I spared neither expense nor effort to recreate the photos.
"Obvious spherical shape" or just lens distortion?
(Link to the corresponding section in the Terra-X documentary)
The corrected version no longer shows "earth curvature".
There are two types of wide-angle lenses: rectilinear and fisheye lenses. Rectilinear lenses depict straight lines in the image as straight, while fisheye lenses do not. For this reason, photographers prefer rectilinear lenses. However, because they have a complex structure with several lens groups, they are more expensive, complicated, and larger. Fisheye lenses can be built more cheaply and especially smaller, which is why they are often used in small action cameras. The design is compact and it is easily possible to correct image distortion later on the computer, if it is even bothersome.
During his jump, Felix Baumgartner wore 5 cameras of the brand "GoPro Hero HD" on his body [1]. These are action cameras with fisheye lenses. Without subsequent correction, no statement can be made about the curvature of the earth from pictures taken with that camera. In fact, the Terra-X team should have noticed that the "horizon curvature" in this part of the video constantly changes. This is a typical effect of fisheye lenses, which is particularly noticeable in moving footage of straight lines when the camera orientation relative to the horizon is changed.
At what height is the curvature of the horizon visible?
The curvature of the horizon is only visible from a height of about 15 kilometers or above. The cruising altitude of an intercontinental flight is not high enough for this. At the starting height of Felix Baumgartner's jump at 38 kilometers, however, the curved horizon is visible, but much weaker than claimed in the broadcast.
The image in the bottom right provides an impression of how high one would have to be to see the curvature of the Earth, as suggested by Terra-X. An astronaut in space who sees such a pronounced curvature has to be thousands of kilometers high and also have an overview of a considerable part of the Earth's sphere.
Only at increasing heights does the curvature of the Earth become clearly visible. As a rule of thumb, it becomes recognizable from a height of about 15 km. This is higher than intercontinental flights fly but much lower than Baumgartner's stratospheric jump. He was able to see the curvature of the Earth, but much more subtly than claimed by Terra-X.
"Astronaut" with an Earth curvature, comparable to the one from the Terra-X broadcast, taken with a rectilinear lens. Would anyone come up with the idea that this Earth curvature can be seen at a height of 38 km? The astronaut is looking at Cuba and the North Atlantic here. You would have to be thousands of kilometers high for that!
For more detailed information on this topic, I can recommend Walter Bislin's papers on the subject of lens distortion and curvature of the horizon.
Debunking "Universal Acceleration"
Link to the explanation of universal acceleration in the Terra-X broadcast. (External content: Link to ZDF; Video "A case for Lesch & Steffens - Arguing for the truth" from the Terra-X channel.)
A little later, an attempt is made to refute the frequently used argument of flat earthers that gravity does not exist at all. Here, too, an opportunity is missed. One gets the impression that only the alleged stupidity of the statement is being mocked. The narrator presents the flat earthers' argument for why a ball falls back to Earth (see link left):
For gravity, flat earth people have an alternative idea. The ball doesn't come back to Earth, the Earth comes to the ball. It moves constantly upwards. The "universal acceleration" is at work.
Both the animation and the explanation given are misleading. Flat earthers do not claim that the Earth is constantly moving upwards. If that were the case, nothing would happen in the absence of gravity. A ball thrown upwards would fly further away and everyone on the flat earth would be weightless. What they claim is that the flat earth is constantly accelerating upwards. Their argument can be summarized as follows:
Gravity does not exist. On a flat earth, there is no need for gravity, because its effect is indistinguishable from the effect of an Earth's disk accelerated at 9.81 m/s² upwards.
They call it the "Universal Acceleration". It is an interesting argument because it is true that, on a flat earth, the function of gravity could essentially be replaced by an upwards acceleration. With this trick, the Earth is mentally removed from its resting inertial system. Thus, the Newtonian equations of motion change in such a way that it becomes possible to replace the Earth's gravity acceleration with an upwards acceleration of the inertial system.
The "Potsdam Schwerekartoffel" is a representation of measurable differences in the strength of the
gravitational field on Earth. These differences would not be explainable if the force of gravity were replaced by a "Universal Acceleration"! (© German Research Centre for Geosciences, Potsdam; Image Source)
At the surface of the Earth, the equation of motion for a free fall under the influence of gravity is as follows:
\begin{equation}
m \cdot \vec{a} = \vec{F_G} \label{eq:eqn_of_motion1}
\end{equation}
If a body moves upwards in a resting inertial system, a force must act on it. In the case of free fall in a gravitational field, this is the gravitational force:
\begin{equation}
\vec{F_G} = m \cdot \vec{g} \label{eq:eqn_of_motion1a}
\end{equation}
However, one could also argue that the Earth is a linearly upward accelerating inertial system. Then the equation of motion for free fall in the gravity field is a bit more complicated:
\begin{equation}
m \cdot \vec{a} = \vec{F_G} - m \cdot \vec{u} \label{eq:eqn_of_motion2}
\end{equation}
\begin{equation}
m \cdot \vec{a} = m \cdot (\vec{g} - \vec{u}) \label{eq:eqn_of_motion2b}
\end{equation}
Where \(\vec{u}\) is the acceleration of the inertial system and \(\vec{g}\) is the acceleration due to gravity. (Note: u and g have different signs). The right-hand side of the equation now consists of the addition of two forces. However, they cannot be separated and measured individually. Hence, one could also argue that Earth's gravity acceleration is zero and the entire measurable acceleration is caused solely by the acceleration of the inertial system upwards.
Of course, this is a logical fallacy, but a quite creative one. Therefore, it should have been addressed in the show, because the "Universal Acceleration" is easy to refute: The gravitational acceleration of the earth is not the same at every point on the surface of the earth! If the acceleration were to come from an acceleration of the inertial system, then parts of the flat earth would have to be accelerated at different speeds. But that would tear the "flat earth" apart, because larger and larger differences in altitude would emerge between the parts that were accelerated more slowly and faster. Consequently, an acceleration of the inertial system as the supposed cause of the gravitational acceleration must be ruled out. Gravity is real!
"Universal Acceleration" and Relativity Theory
Although the idea of Universal Acceleration is false, its creativity demonstrates that it is superficially compatible with the theory of Relativity. A frequently heard, but false counter-argument is that with a permanent, constant acceleration of 9.81 m/s² the speed of light would be reached very quickly. However, the Theory of Relativity allows for a constant acceleration without ever reaching the speed of light. The speed would asymptotically approach the speed of light, but would never reach it. [7]
The energy required to accelerate the "flat earth" would, however, quickly become infinite. But a flat earther could argue that in modern physics there is also a concept of "dark energy" in which the ever faster expansion of the cosmos does not seem to be an energy problem. So why can't he solve his energy problem with a "dark acceleration"? Such an argument is futile when dealing with scientifically educated trolls.
The Experiment at the Lake
The location of the experiment was Ratzeburg Lake.
(C) OpenStreetMap Contributors.
The segment about the flat earth ended with an experiment that could best be described as misleading. It involves shooting a laser beam across a lake with the aim of proving that the earth is not a disc. A rather unabmitious scope for an experiment and one that will be badly executed.
What is the problem? The experiment as shown would come to very similar results if it were carried out on a flat earth. In the described form, it only works because knowledge of the spherical shape of the earth and its radius was already taken into account in the experimental setup.
It begins with the words:
"We only need a boat, a lake and a laser"
The ZDF did a good job in choosing the lake. It took place on the Ratzeburg lake, south of Lübeck [2]. If one had to create a lake to measure the curvature of the earth, it would look similar to this one. The lake stretches north-south over 8 kilometers and offers an approximately 8400-meter-long view of the surface of the water when viewed from the south. The earth's curvature is over 4 meters at this distance! These would have actually been ideal conditions for a scientifically solid experiment.
The possible variants of the laser experiment
We begin with the first explanation of the program: If one wants to prove that the earth is flat, one must use a laser to shine horizontally across the surface of a lake and measure the height of the light point at different points on the lake with a boat. If the earth is flat, the height should not change.
"The laser is incorruptible, Dirk. Everyone knows that a laser beam goes completely horizontal. If you want to prove that the earth is a disk, all you have to do is show that the earth is as horizontal as the beam."
This statement is at best imprecise. A science program should not confuse the error "completely horizontal" with "completely straight". The laser runs horizontally only when it has been adjusted to the horizontal and that will become a problem in this experiment. Adjusting a laser to the horizontal is actually simple: measure the height of the laser on one side of the lake and then drive to the other side to adjust the laser so that it has the same height there.
Variant 1a: The proof of a hypothetical flat earth with a laser would actually be simple. For the laser adjustment,
the beam would need to be adjusted so that it has the same height on both sides of the lake.
This also works on a spherical earth but there Earth would curve under the laser beam. To prove that earth is not flat one only has to measure the height of the beam across the lake and show that it is not a straight line. Only at the center of the lake would the laser beam be horizontal.
Variant 1b: The experiment on the spherical earth is carried out in the same way. Only the result is different.
As can be easily seen, the height of the laser beam on a spherical earth decreases towards the center of the lake. On the shores, however, it is at its maximum. This was apparently too complicated for the Terra-X team which is why an alternative experiment was designed, in which the laser must be aligned exactly horizontally on one side of the lake.
Variant 2a: Experimental setup according to Terra-X. The basic requirement is a laser precisely aligned horizontally at the lake shore.
The laser alignment problem
In theory the experiment still works, but now we have a problem with the laser alignment. How do we know when the laser is exactly horizontal? There are no reliable reference points left to align it and the horizon cannot be determined with sufficient accuracy using a spirit level or precision tilt sensors. The curvature of the earth at 3000 m is about 0.67 m. The expected errors when aligning with a tilt sensor are significantly larger.
| Tilt measuring instrument | Accuracy | Alignment error at 3000 m |
|---|---|---|
| Spirit level | 0.057° | ≈4 m |
| Precision tilt sensor | 0.01° | ≈1.5 m |
Perhaps Terra-X thought this was the better setup because the effect they wanted to measure would have been much stronger if the laser had been pointed in that particular way. They did not think about the alignment problem because in their world a laser beam always goes horizontally.
"Everyone knows that a laser beam goes perfectly horizontally ..."
The approximate direction and length of the laser pass in the experiment. (C) OpenStreetMap contributors.
However, a laser beam does not just go "perfectly horizontally" on its own, and a tilt sensor cannot be used for the alignment. A fact that did not elude Harald Lesch one of the hosts, who explained:
"What we're doing now is sending the laser over there and aligning it there."
But how do you align the laser on the other side of the lake so that it runs exactly horizontally? In experimental variant 1 this is achieved automatically by the design of the experiment. Not so in the experiment conducted by Terra-X! The height that the laser must have on the other side of the lake is greater if the earth is a sphere. Exactly by how much depends on the earth's curvature, which is actually unknown within the scope of the experiment. Demonstrating the curvature is the goal of the experiment!
The only way to perform this "adjustment" is to measure the length of the lake and simply calculate the height difference with the beforehand knowledge of the radius of Earth. Then you adjust the laser so that it arrives at the other shore exactly this amount higher. Although the Ratzeburger lake is over 8.4 km long, the way Terra-X aligned the laser, the distance to the opposite shore is only about 3 km. The earth curves about 67 centimeters over 3 kilometers.
So the "alignment" consists of adjusting the laser so that it arrives 67 centimeters higher at the other shore. That is astonishingly stupid for an experiment whose sole purpose is to show that the light point from the laser will change its height when measured across the lake. We already know it will because we tilted the laser slightly upwards! Why even bother crossing the lake? We already know the result from the other lake side: It's 67 cm!
Let's assume for a moment that the Flat Earthers were right. What would the Terra-X experiment look like if on a flat earth the laser was aligned for this experiment in the "incorrect" assumption that the earth is round? Even on a flat earth with this aligment you would observe a change in the height of the light point across the lake. The desired result is already built into the experimental setup!
Variant 2b: This is what the Terra-X experiment would look like if flat earthers were correct. The same laser "alignment" was used.
You would also measure a consistent change in the laser point height across the lake!
What has Terra-X proven?
Let's move on to the results of the measurements. 4 points were measured for the show, the difference in height from point 1 to point 4 is about 60 centimetres. This would correspond to a boat distance of just under 3 kilometres. Interestingly, all the points move upwards by about the same amount. However, the Earth bends more sharply downwards as the distance increases. The points should move upwards more quickly if the boat travelled roughly the same distance between measurements.
Left: The spherical earth curves faster under the beam. Right: In the results of Terra-X, the light point
rises almost uniformly. This result would actually fit better to a flat earth!
The result is explained as follows:
There is only one explanation why the beam hit the boat higher and higher. The laser beam is no longer horizontal to the surface of the lake. The surface of the lake is curved.
The presented result is more similar to what would be measured under the same conditions on a flat earth. We remember: The laser's adjustment consists of aligning it with the horizontal. To do this, it must be set to a position that is slightly above the actual horizon. On a spherical earth, it would then be exactly horizontal, but on a flat earth, it would be slightly upwardly inclined.
In Terra-X's defence, it could be argued that they did not specify exactly where on the lake the laser points were recorded. They could have been measured at distances that would also support a spherical Earth. But the distances are not given in the programme. In order to use this data to prove a spherical shape, they would have to have been taken roughly at the positions given in the table below.
| Measurement point | Laser point height | Distance from boat to laser |
|---|---|---|
| Point 1 | 0 cm | 0 m |
| Point 2 | 20 cm | 1640 m |
| Point 3 | 40 cm | 2320 m |
| Point 4 | 60 cm | 2840 m |
There would only be a proper measurement point in the lake after 1640 meters. The problem here is that a laser beam widens as it moves away (so-called divergence). This can be counteracted with a so-called laser beam expander and indeed Terra-X had one on site (picture below left). However, even an expander cannot completely prevent divergence (see picture below right). The measurement points are at distances where the widening would already be a significant disturbance. The wider the beam diameter, the more difficult it becomes to find its center. In essence they want you to believe that most measurements were taken at a distance where the beam quality is already significantly degraded due to dispersion. (see right picture).
At the beginning, the laser beam has a diameter of about one centimeter.
Shown here is the laser beam expander. This widens the laser beam,
but makes it more parallel and thus also more easily measurable over longer distances.
(© ZDF / Terra-X "A Case for Lesch & Steffens - Fighting for the Truth"; https://www.youtube.com/watch?v=f7UvligKPCE&t=520s)
The image shows the laser beam widening during the experiment.
At some distance from the shore, the laser beam already has a diameter of over 10 cm.
(© ZDF / Terra-X "A Case for Lesch & Steffens - Fighting for the Truth"; https://www.youtube.com/watch?v=f7UvligKPCE&t=571s)
In this type of experimental setup, it would have been necessary to demonstrate the non-linearity of the light spot height curve in order to prove the curvature of the earth. This would only be measurable on a spherical earth. Because this did not happen, the presented results do not allow us to decide whether the earth is spherical or flat. It has only been proven that the light spot height changes. However, something like this would also happen with a laser that is tilted on a flat earth.
What probably happened?
The equipment they brought to the lake could be suitable for carrying out such an experiment successfully. The laser used is a class 4 laser device with laser beam expander and rifle scope for adjustment. It appears to be a modified version of a laser from the "RTI PIKO series".
As it is expensive to send someone to the other side of the lake to adjust the height of the laser beam at the same level, a more questionable method of adjustment was chosen. This was probably done directly with the rifle scope. (Quote: "What we're going to do is we're going to send the laser over there and we're going to adjust it there."). The laser beam was "adjusted" through a telescope on a shore 3 kilometres away. If it was adjusted at all. At that distance, the beam was probably 30-50 centimetres in diameter. If the adjustment had been taken seriously, it would have had to be set to the height of the table the laser was on, plus the height of the beam above the table, plus 67 centimetres. The 67 centimetres would have to be calculated from the distance to the other shore and the known diameter of the Earth.
Why all the effort? They had already decided on a method of execution that required them to know the radius of the earth beforehand. Scientifically completely worthless! So the laser was possibly simply tilted slightly upwards. The only criterion was presumably that it had to hit the boat over a relatively long distance. They only needed the images for television and only had to ensure that the laser changed its height on the boat. Therefore, the most plausible explanation for what actually happened might be this one:
The presented results can also be interpreted as simply adjusting the laser slightly upwards and then driving only a relatively short distance with the boat. On this short distance, the curvature of the earth did not fully come into effect and what was measured was essentially a laser that was tilted upwards.
This segment of the program concludes with the following dialogue:
Dirk Steffens:
"That's all well and good with the laser, but let's be honest Harald, we're only convincing people that already knew it."
Harald Lesch:
"Those who don't believe, they think it's a fake even though they could try it out themselves"
Dirk Steffens:
"Why do people believe in such nonsense that can easily be proven wrong?"
Harald Lesch:
"It's not so much about what they believe, but rather, what they don't believe. They don't believe the source of the information"
Despite the financial support from the public broadcasting corporation and the involvement of an astrophysicist, Terra-X was unable to debunk the nonsense flat earthers claim on a scientifically solid basis. They attempted an unnecessarily complicated and from the beginning nonsensical form of experimentation. The presented results are best explained as a result of "creative" laser adjustment. Nobody who seriously wants to prove the curvature of the Earth would choose this type of experimental method.
Others did it better
Netflix documentary "Behind the Curve"
Netflix did a better job covering the same topic in the documentary "Behind the Curve". The stylistic difference is noticeable. Where Terra-X ridicules, the Netflix documentary lets flat earthers talk, with all their contradictions. The scientists who speak are critical but not condescending. But they are also self-critical. Because behind every person who ends up in the camp of the flat earthers is always a failure to educate, to explain and to convince.
The Netflix documentary ends with an experiment in which flat earthers successfully prove the curvature of the Earth, exactly what Terra-X failed to do here. They receive the result with amazement and disbelief and reject it. There is an irony in that: Terra-X wanted to carry out the experiment but could not, the flat earthers were able to carry out a similar experiment, but did not want to believe its result.
National Geographic "Flat Earth vs. Round Earth"
A "National Geographic" documentary chose the simplest possible version of the experiment. They sailed towards the horizon on a boat in broad daylight and had markings with differently colored horizontal stripes attached to the boat. Using telescopes, it was then possible to observe from the shore that the lowest of the stripes were no longer visible at a certain distance. With knowledge of the width of the stripes, a rough estimate of the radius of the Earth could also have been made. This is a version that Terra-X could have done on Lake Ratzeburg. It would have worked, but would have been less spectacular. Instead, science theater with a laser show was chosen for the sake of visuals.
Amateur hour in laser safety
It seems that the whole measurement process shows how careless people were with their safety. At least, that's what it looks like, because I can't see anyone wearing laser safety glasses. Dirk Steffens holds his head, standing on a swaying boat, directly in front of a stationary laser beam with considerable power.
Practiced laser safety at ZDF. Dirk Steffens, without any identifiable protective glasses, standing on a swaying boat,
directly in front of a laser beam that he will cross seconds later.
After each measurement, he immediately took down the screen.
(© ZDF / Terra-X "Ein Fall für Lesch & Steffens - Streiten für die Wahrheit"; https://www.youtube.com/watch?v=f7UvligKPCE&t=555s)
Apparently, a RTI PIKO laser was used for the experiment. The models currently listed by the manufacturer have minimum power outputs of 27 watts. This is a Class 4 laser product. For products in this safety class, [5] applies:
- Dangerous for eyes and skin
- Technical, organizational and personal protective measures are necessary
- Scattered radiation is also dangerous
- Fire hazard for flammable materials
DLRG helpers apparently did not wear protective glasses either. Was the instruction here: "Just don't turn around"? Laser beams can behave unpredictably. Even if you're not looking in the direction of the beam, it can happen that it strikes a chrome strip on the boat and falls directly into the eye of one of the persons aboard with significant residual energy. Eye damage does not require long exposure times, as the eye's lens focuses the laser beam on the retina. Pilots in landing approach are repeatedly blinded by lasers [3] and have to seek medical treatment afterwards.
It should have been pointed out how dangerous strong lasers can be with improper handling. Instead, it was implied that anyone could recreate this experiment. The Netflix documentary show's what this looks like. In it, a flat earther obtains a 3 watt hand laser and tests it out right in front of his house, holding it towards a heavily trafficked street. All of this a few meters away from passing cars. Such handling of Class 4 lasers is grossly negligent and dangerous!
References
- ZDF / Terra-X: "A Case for Lesch & Steffens The Truth About Lies"; online; Broadcast of the Terra-X series of the Second German Television; October 2020
- Andy Stout: "Baumgartner: The video tech behind the jump"; online; Redshark News; 2012-11-06
- sueddeutsche.de: "Shooting for the ZDF series "Terra X" starts on Friday in Ratzeburg"; online; DPA report on sueddeutsche.de; 2022-08-03
- sueddeutsche.de: "Blinded with Laser - Helicopter pilot of the German Bundeswehr injured" online; DPA report on sueddeutsche.de; 2019-08-01
- raytechnologies.com: "RTI PIKO Series" via archive.org; product information from the manufacturer about the RTI PIKO series.
- laserworld.com: "Laser Safety FAQ - Laser Classes" online; explanations about different laser classes.
- Claude Semay: "Observer with a constant proper acceleration"; online; Groupe de Physique Nucléaire Théorique, Université de Mons-Hainaut, Académie universitaire Wallonie-Bruxelles; 2008-02-02
The Thing with the Red Bull Image License - Why No Pictures of Felix Baumgartner's Jump?
The picture definitely doesn't show Felix Baumgartner in his stratosphere jump. (Author: Volkmar Wentzel; U.S. Air Force; Public Domain)
The scenes of Felix Baumgartner's stratospheric jump used in the Terra-X video were made as part of the "Red Bull Stratos" project. Therefore, the copyright belongs to Red Bull. The ZDF probably had to purchase them as well.
Maybe I could have used screenshots with pictures from the video sequence of Baumgartner's jump, referring to the citation right (a german legal contruct). In this case, I found it too risky, so I asked Red Bull if it was ok to use the screenshots. In a friendly email, they told me that these images are premium content and offered me, if I remember correctly, 6000 euros for worldwide use. This was for screenshots in low resolution of a YouTube video, for a website with educational content! A video sequence that has been uploaded countless times by third parties on YouTube and apparently been there for more than 9 years without being objected to. In that case, I prefer to create my own images.
The "right to quote" in german law also does not allow any modification of the images. However, I wanted to correct the distortion to show how monumentally stupid the Terra-X explanation was at this point in the show. For this reason, I had to do without the images, and that is why we need "fair use" licenses in Europe as well.
