## Mathematics is powerful and dangerous

**Mathematics
is powerful and dangerous**

John-Erik Persson

## john.erik.persson@gmail.com

It is very important that we always remember that mathematics is just a tool for doing physics. The fact that math really is very powerful, has a negative side in the high risk that we may forget to see this important distinction, and thereby be fooled by math. This fact is here demonstrated to be true in many areas of science.

# Euclidean geometry

In the geometry
regarding straight lines in a flat surface the concept parallelism between two
lines is defined by the statement, that parallel lines have no common point.
The fact that the point in question does not exist leaves the definition empty
and without substance. Euclid used a definition based on a concept that *did
not exist* and his definition is just a dream. A definition must be real and
not imaginary.

Vi must base our
definition on something that is essential for the defined concept. A
characteristic property of parallelism can be constant distance, or separation.
So, we can state that: *Two lines are parallel if, and only if, two arbitrary
points in one of the lines are on the same distance to the other line.*
Based on this definition we can see that one point and one line define a unique
line, that is parallel to the given line. This means that a line has only one
parallel in a given point.

An interesting effect of Euclid’s mistake is the invention of non-Euclidean geometry. A 2-dimensional surface in the model was bent and regarded as a property of 3-dimensional space. This was also regarded as a property of nature. Although the ether was abolished, and space regarded empty, gravity nevertheless was explained as the bending of nothing. This absurd idea was inspired by the idea that the number of parallels to a point and a line can be different from one.

# Planetary motions

Tycho Brahe devoted his whole life to studies of planetary motions from an island between Sweden and Denmark. He moved his observations from a tower to an underground observatory, and thereby reduced disturbances from wind and background light. He also made his instruments by himself, and improved precision several times, in relation to earlier observations for hundreds of years. Brahe was the most important astronomer and he produced a large database.

Johannes Kepler was an assistant to Brahe and Kepler made the mathematical analysis of Brahe’s data. Due to the high precision in the data Kepler could see that ellipses described observations better than circles, as earlier was assumed. He derived 3 laws describing planetary motions. He also tried, in vain, to explain the separations between planetary orbits, by the use of Platonic bodies.

# Apparent motion of fix stars

When the telescope was invented, the astronomical observations could be done with even higher precision and Bradley observed an apparent motion of fix stars. The maximum value of this aberration is a small angle of the same size as the relation between the orbital velocity of Earth and the velocity of light. One explanation to this phenomenon has stated that an ether motion, transverse to light direction, should alter the wave front orientation. However, this idea is in conflict with the wave model for light, stating that an ether wind inside the wave front has no relevance in coherent systems like telescopes, that are based on detection of phase – not of amplitude. Phase based detection means therefore that ether wind inside the wave fronts is irrelevant, and light in coherent systems should be described as wave velocity plus longitudinal component of ether wind only (the ray concept). The vector sum of ether wind and wave velocity is of interest only if light is focused into a beam and max amplitude is of interest (the beam concept). This distinction between beam and ray is important.

However, there
is a more realistic explanation to stellar aberration based on the fact that an
observer motion, transverse to moving light, changes the direction of the
relative motion between observer and light. This means that observer motion
creates an *illusion* of wave front tilting.

The reasoning above applies also to the behavior of light in the reference arm of the test (MMX) that Michelson did together with Morley. Coherent detection in a telescope (and light generated in a collimator) means constant wave front orientation in relation to the ether wind. So, no tilting (suggested in error by Potier 140 years ago) means no effect of ether wind in the reference arm of MMX – according to the wave model. No effect in the reference arm means no support for time dilation in MMX. In the measuring arm the predicted effect is real, but not observable due to a compensating effect due to length contraction. See below about the ether.

# Gravity

Newton found the
law of gravity by pure mathematics, based on the laws for planetary motions. The
law of gravity predicts a spherically symmetric field of gravity. But Newton did
not observe that this math demands spherical symmetry for involved bodies also.
This demand, for *perfect* spherical symmetry, is hidden by the fact that
gravity produces *approximate* spherical symmetry. Therefore, when
Newton’s law is used in physics, we must regard the law as an approximation. This
fact was observed in space stations navigated at very low altitude over the
Moon. It was observed that gravity over a mountain is a very small amount
larger than over a valley for very low altitudes. As an alternative Newton’s law
should be applied to small volume elements, to avoid the demand for spherical
symmetry, and then integrated in order to gain better relevance and provide
more explanation power.

Fatio sent a quantum theory for ether and gravity to Newton about 300 years ago. This model was based on small and fast ether particles moving in all directions. But Newton said that he did not need this explanation. Fatio’s model was abolished – in error – by the fact that the model did not predict aberration, like the aberration that is observed in light. The error here was that the ether particles were assumed to collide with matter. Instead, they are absorbed by matter, and this means that the force of gravity emerges inside matter due to effects from the ether. This explains no aberration in gravity. Therefore, Fatio’s model can be united with Newton’s model expressed by an integration. By disregarding Fatio’s idea Newton made a devastating mistake, and a good explanation to gravity was missed. We can see this by observing that attenuation (by absorption) in a body, A, reduces the number of particles leaving A and produces a net effect of an ether wind in radial direction towards A. This effect causes an asymmetry in the ether inside a nearby body, B. Gravity is two effects: A on ether and ether on B. Therefore, this asymmetry causes a force to emerge inside B in direction towards A due to an asymmetry in the absorption. So, the force of gravity can be explained by a radial (in relation to the gravitating body) ether wind. This ether wind can also explain the illusion of Big Bang.

In order to explain Big Bang, we can regard a celestial body, not moving in relation to an observer. The radial ether wind causes blue-shifted light to be generated in ether’s frame. But the ether is moving away from the observer and therefore light is red-shifted in relation to the observer. Together these two effects are causing a second order red-shift. Therefore, Big Bang is an illusion caused by ether motion – not body motion – a second order Doppler effect.

The Doppler
effect has been regarded as caused by the difference in speed between source
and observer. But when we introduce an ether, we get two effects. We get one
effect between source and ether and another effect between ether and observer.
With B_{n} equal to observer and source speeds divided by light speed
we get total effect on *f’/f *equal to (1+B_{1}-B_{2}-B_{1}·B_{2}). If B_{1}=B_{2} we get only second
order term or (1-B^{2}). So, the ether wind generates a second order
Doppler effect although source and observer are in the same state of motion. By
introducing an ether, we can explain cosmological red shift without Big Bang.

The very large red shifts of second order that we observe in celestial bodies indicates that these bodies have very large masses.

# Atomic clocks

The special
theory of relativity (SRT) is said to be supported by time dilation, whereby
clock frequency is changed from *f* to *f’, *due to a satellite speed
of *v _{O}* in the relation

*f’=f(1-v*. Here

_{O}^{2}/c^{2})^{1/2}*v*is around 0.3 km/sec on Earth (rotation) and 3.9 km/sec in the GPS satellite.

_{O}The general
theory of relativity (GRT) is said to be caused by gravity potential. However,
this potential is related to the escape velocity *v _{E}*, and this
is a more concrete concept than the abstract energy concept. So, we use this
concept instead. We therefore get

*f’=f(1-v*. Here

_{E}^{2}/c^{2})^{1/2}*v*is 11.2 km/sec on Earth and is 5.5 km/sec in the GPS satellite.

_{E}This relation can
be united with Fatio’s model, indicating a radial ether wind. Apparently, the
radial ether wind is equal to the escape velocity, *v _{E}*. This
assumption means that SRT and GRT are united, not only by their predictions,
but also theoretically, if we regard

*v*as well as

_{O,}*v*as ether winds. So, we get one model only. Instead of 2 kinds of

_{E}*time dilation*we get 1 kind of

*clock dilation*due to the ether wind.

# The ether

Most of our knowledge about the ether emanates from Faraday, who studied the electromagnetic properties of the ether in almost his whole life. His work was (together with works from others) converted to mathematical form by Maxwell. This resulted in an ether specification in 4 equations, to a large extent a work of Faraday, although named after the translator, Maxwell. These equations are printed on T-shirts, although scientists deny the existence of the defined concept.

The effect of
ether wind in 1-way light was demonstrated by Sagnac for a closed light path.
The same effect in an open light path is demonstrated by VLBI (very long base
interferometry) instruments in the pulsar aberration. This aberration (Sagnac
effect) disappears when calculations are transferred to the *velocity* of
the Sun – not the *position* of the Sun.

The Sagnac
effect in 2-way light failed in MMX, since the combined effect in 2
antiparallel light motions is compensated by the effect in 2 antiparallel motions
of forces controlling atomic separations. However, the 2-way Sagnac effect in
microwave signals is demonstrated in the Pioneer anomaly, where the effect not
is compensated. This depends on the radial ether wind (equal to the escape
velocity) implied by Fatio’s quantum gravity. Therefore, 2-way light speed is *increasing*
with range to the Sun, and this fact simulates Pioneer speed to be *decreasing*
with range. The illusion is caused by ether motion – not by body motion.

# Reality and model I

Brahe did a lifelong unique work in astronomy and Kepler did a normal mathematical analysis, but became the most famous. Fatio provided an explanation to gravity and Newton did mathematical modelling and became more famous. Faraday did a lifelong work on the electromagnetic ether and Maxwell translated it to mathematical form and became more famous. Therefore, it seems as we are valuing mathematical models more than physical explanations, and form more than content. We are fooled by math. It also seems unhappy that we preferred Newton’s mathematics instead of Fatio’s physics, since these two theories are not in conflict.

# Quantum physics

Quantum physics starts with the radiation from hydrogen with spectral lines indicating that a bound electron has stability over long time only for discrete values on the radius of the orbits. We can explain this by assuming that the period of orbiting must be a multiple of periods of an internal process in the electron – perhaps spin. Possible explanations may exist in energy considerations. However, this does not necessarily demand energy itself to be structured into quanta, although this is the common opinion. But this conclusion may be a devastating mistake caused by ignoring all disturbances from other electrons and other atoms. Instead, we can assume that this electron behavior just is an adaptation between electron and kernel. We do not need quanta of energy.

An assumed argument
for quanta of energy is also found in the fact that radiation from hydrogen
does not contain radiation from stable states themselves. Instead, the
radiation contains interferences from the *differences* in frequency
between these states. This phenomenon is said to demonstrate that electrons
radiate only when they are jumping between states, although the simple model
used not even allows for jumping. There exists no motivation at all for how an
electron, by itself, can switch radiation on and off. Therefore, this
explanation must be regarded as wrong and another explanation searched for. So,
this radiation most probably is continuous.

If the radiation
is continuous, we have to find an explanation to the fact that radiation at the
primary frequencies is not observable. We can easily see a possible explanation
in a well-known *wave* phenomenon called destructive superposition. This
follows from the fact that all electrons in the same state produce, and sense, radiation
at the same frequency. It is therefore very realistic to assume that these
interactions can result in almost zero radiation and we need contributions from
*many* electrons to be able to detect radiation. The production of
radiation at the frequencies of interference is distributed over the whole
volume and can therefore not be neutralized by the same mechanism.

Another false
motivation is found in the law for black-body radiation where the constant *h*
is said to indicate quanta to *exist* in light. However, light is not
visible, so instead of light we observe matter in the form of electrons
produced by the photo-electric effect, since this effect can cause quantization
in the form of charges in a its output. This means that Planck’s constant, *c*,
seems to be a property of the electron’s charge – not of energy and not of light.

The
photo-electric effect is an effect in opposite direction in relation to thermal
radiation, and is also used as an argument for quantization. Light particles
moving *towards* a crystal are said to cause electrons to move *away*
from the crystal. This is not logical and a wave, instead of a particle, for
light can explain the effect by the assumption of an absorption instead of a collision.
We see this by regarding an interference effect between periodic light motion and
periodic electron motion at the same frequency. So, a light **wave** changes
the *potential* energy of the electron (interference), according to Lenard.
This contrasts to the current idea that a light **particle** changes *kinetic*
energy in an electron (collision). So, we see again that the wave model is more
logical. We do not need quanta based on *h *in light either. Since the
electron’s kinetic energy is not changed, we can explain why this energy
depends on frequency of light and not of intensity of light.

We have seen how the wave model for light gives more logical explanations than the particle model. The tricky explanations based on light particles seem to be an effect of very bad understanding of the wave model, and also due to the fact that the ether concept was abolished; and without the ether we could not unite Fatio’s physics with Newton’s model. We could not explain gravity without aberration either. By the use of the wave model, we have seen that we do not need energy quanta and not light quanta at the Planck level. The only quantization we need is in Fatio’s quantum gravity/ether. The abolishing of the ether has also had the effect that the law of energy conservation has been applied in error.

# Light waves are all we need

According to the
wave model bound electrons can generate light waves continuously and absorption
of an electron can generate X-ray wave packets, and this process can also go in
opposite direction whereby an X-ray wave packet causes an electron to escape.
Therefore, we can explain the Compton effect, in accordance to the wave model
for light, by assuming a process in two steps. First an X-ray wave packet causes
an electron to escape, and in the second step capturing of the same electron in
another atom generates a secondary wave packet. Photo-luminance can also be
explained in almost the same way, and we have earlier seen explanations to
thermal radiation and photo-electric, effect based on the wave model. So, we
can therefore conclude that *waves are all we need for light.* We have not
understood the wave model for light and therefore we have got tricky
explanations based on particles and collisions instead waves and absorption.

# Reality and model II

Modern physics
predicts electrons to switch radiation on and off. Particles moving *towards*
a crystal are said to collide and cause an electron to move *away* from
the crystal in the explanation to the photo-electric effect. So, the particle
model for light is tricky. We can very easily avoid these conflicts by
abolishing the particle model for light, and describe light just as
electromagnetic waves. So, it is difficult see any reason why we have not given
up light particles long time ego. However, it is not difficult to see how the
problem started, since we have lots of experience about particles but not about
the abstract wave model. So, we chose the tool we *know* – not the tool we
*need*. We are also lazy and prefer Newton’s math instead of Fatio’s
physics, perhaps fooled by Occam’s razor, and we are often tempted to export
mathematical concepts (like discreteness and probability) into physics.

# Fooled by math

So, we have seen
that we are really fooled by math in most areas of physics. In the area of
particle physics this phenomenon has got an interesting analysis in a book by
Sabine Hossenfelder^{1}. Our bad understanding of the wave model is
described by this author^{2,3}.

# Summary

Newton was
fooled by mathematics when he stated that “hypotheses non fingo” and ignored
Fatio’s suggestion. He did not observe a mathematical demand on spherical
symmetry in bodies in his theory, that predicted spherical symmetry in the
field of gravity. So, application of his law in physics means that the law
should be used on small volume elements and integrated, in order to get rid of
the demand for spherical symmetry. If we use the law without doing so, we must
remember that we are using an approximation. The reason to Newton’s mistake is
that Nature is hiding this fact by producing *approximate* spherical form
in large bodies. So, the Devil is in the details.

In the physical
model presented by Fatio we also find an important error on detailed level,
caused by our preference for well-known particles (collisions) instead of
unknown waves (interferences) to cause the effect we observe in electrons. Therefore,
Fatio’s model was abolished in error, since it was not observed that *absorption*
of ether particles can explain the lack of aberration in gravity, since gravity
emerges inside matter. In the same way we regarded ether as a difficult concept,
and abolished it, which means that we apply the law of energy conservation in
error, by not regarding energy exchange with the ether. We also were unable to
explain the Big Bang and the Pioneer anomalies, since these phenomena are caused
by ether motions – not by motions of bodies.

Coherent systems like telescopes and collimators operates on phase, and not on amplitude. Therefore, wave front normal, and not total light motion, is conserved. So, no wave front tilting in stellar aberration and not in the reference arm in MMX either. Therefore, MMX does not support time dilation according to the wave model. MMX is useless also in the measuring arm, since the predicted effect – although real – is compensated due to length contraction.

In quantum
physics we have made an absurd assumption about electrons to be able to turn
electromagnetic emission on and off, instead of assuming a well-known *wave*
property of destructive superposition to explain a phenomenon in hydrogen
radiation. Instead, electrons can radiate continuously. Since we cannot see the
light, we observe matter in the form of *discrete* electrons from a photodetector.
So, the constant named after Planck may indicate an electron property – not a
light property. We find conflicts in quantum physics and the problem here seems
also to be related to a bad understanding of the wave mode. There appears to be
explanations to most phenomena based on the *wave* model. So, we seem to
be fooled by math to use the particle model for light by the simple fact that
we do not understand the wave model. We seem also to be fooled in another way
by assuming mathematical properties in the model to have physical reality, like
probability and not continuous functions.

# Conclusions

- No quantization of energy and of light at the Planck level.
- Quantization of ether into neutrino-like, small and fast particles is constituting an ether. This ether transmits gravity by an ether motion (in radial direction to a gravitating body) equal to the escape velocity. This ether also transmits light.
- Big Bang and Pioneer anomalies are caused by motions of the ether – not motions of bodies.
- The behavior of atomic clocks in the GPS system is caused by motions of the ether – not of dilation of time.
- We have not understood the wave model for light and missed the distinction between beam and ray.
- Scientists seem not to be very interested in looking backwards.

# References

^{1}Sabine
Hossenfelder, “Lost in Math: How Beauty Leads Physics Astray.” Basic Books
(June 2018).

^{2}John-Erik
Persson, “The wave-particle dilemma in light.” Phys. Essays **34**, 211
(2021).

^{3}John-Erik
Persson, “The wave theory of light gives better explanations for key phenomena
in physics.” Phys. Essays **35**, 1 (2022).