Einstein defined time as the length of the light path divided by the speed of light. According to this definition, time can only change if either the length of the light path or the speed of light changes. Einstein replaced this objective mathematical truth with his idea that not only is the speed of light constant but also the length of the light path, so Einstein was able to define a constant proper time t(0) in all frames of reference. However, treating distances as constant contradicts the physical definition of motion. Therefore, Einstein's relativity not only violates mathematical and physical rules but also violates logical rules when it claims that the reason why clocks measure different times is that all clocks measure the same time t(0). Einstein's physical half-truth, which makes a false statement about the lengths of light paths, which cannot be constant, leads to contradictions with reality, which Einstein compensated for by mathematical corrections. This inevitably led to a mathematical pseudoreality that is described by theoretical physics according to Einstein's idea. However, Einstein's principle of relativity cannot be mathematically manipulated. If we compare at least three reference frames, we obtain contradictory results for the kinematic and gravitational time dilation. In this case, e.g., the paradox arises that an atomic clock must be able to count forward and backward at the same time. Comparing only two frames of reference, the proper time t(0) can be arbitrarily assigned to each of the two frames of reference without contradictions occurring. However, if an experimental setup is always chosen in such a way that at most two frames of reference are compared, and so Einstein's relativity cannot be falsified, a systematic error is applied, and the experiment is scientifically worthless as far as the confirmation of Einstein's relativistic SR and GR is concerned. (c) 2024 Physics Essays Publication.

Special relativity (SR) needs different speeds of light in the horizontal arm of the Michelson‐Morley interferometer to “explain” a constant speed of light in all inertial frames. To obtain equal speeds from the two different speeds of light (c−v) = [(1 ‐ v/c) × c] and (c + v) = [(1 + v/c) × c], Einstein mathematically accelerates the speed of the photons in the direction of Earth’s motion around the Sun from [(1 ‐ v/c) × c] to [(1 − v2/c2) × c], and in the opposite direction, Einstein decelerates the speed of the photons from [(1 + v/c) × c] to [(1 − v2/c2) × c]. Besides the fact that light cannot be accelerated or decelerated, a change of the speed of the photons in the inertial frame of the Sun would also change the speed c of photons on Earth, because in both inertial frames, the photons always move in horizontal light path of the Michelson‐Morley interferometer in the same direction. SR contradicts its own postulates: 1. SR contradicts the constant speed c of light on Earth; 2. SR contradicts the constant speed c of light in all inertial frames, respectively, in all frames of reference; 3. SR contradicts the principle of relativity. Einstein transformed photons into particles that are allowed to violate logical and physical laws but are not allowed to interact with gravity, so that they have to follow curved world lines. However, giving up logical and physical laws because of precise predictions of a physical theory means arguing pseudo-scientifically. Instead, a simple quantum physical explanation of gravity is presented.

Considering that an Einstein clock can travel at a speed no greater than c , from the principle of relativity, a kinematic time dilation factor can be derived whose value cannot be greater than 2 . In fact, however, the kinematic time dilation factor γ can approach an infinite value. This discrepancy demonstrates that the derivation of the kinematic time dilation factor γ in Einstein's special relativity (SR) cannot be physically justified by the principle of relativity, and that it is not physically possible that the speed of light is constant in any frame of reference. The mathematical method of Einstein's SR, which I refer to as the “mathematical method of relativity,” allows the calculation of constant physical values from different quantities of any physical unit and is thus scientifically worthless. Accordingly, it is not surprising that it is possible to predict so-called general relativistic phenomena, e.g., the phenomena observed at the binary pulsar PSR B1913 + 16, just by applying Kepler's second law and simple quantum physical considerations [R. G. Ziefle, Phys. Essays 33 , 99 (2020)]. A careful interpretation of interferometer experiments on Earth clearly shows that there is in fact no need for artificial time acceleration by length contraction. However, today's physicists seem to be lost in mathematics. The aim of this paper is to contribute to a physical theory of relativity that does not require mathematical tricks, such as time acceleration (length contraction), space-time curvature, and other mathematical tricks that follow from Einstein's mathematical methods and uphold the illusion that the belief in a constant speed of light c in any frame of reference is physically justified.

The physical mystery behind the constancy of the velocity of light is solved after the bias blind spot of Einstein's relativistic physics was illuminated precisely. We have given the physical law f = c/lambda. The relative frequency shifts of the longitudinal Doppler effect are calculated from the frequency ratio of the frequency f(r) at the receiver and the frequency f(e) at the emitter. The very small frequency shift of the so-called relativistic time dilation factor can be neglected for low velocities. Comparing electromagnetic radiation, when receiver and emitter are at rest, the wavelengths must be the same and are canceling, so that we obtain: f(r)/f(e) = (c/lambda(r))/c/lambda(e)) = c/c = 1/1. If the relative velocity c of light were constant in any inertial frame, independent of the motion of the receiver and emitter, no shift of wavelength and frequency would be possible. Einstein's special relativity excludes the possibility of the longitudinal Doppler effect. The longitudinal Doppler effect is explained according to relativity in dependence of gravity (RG), by which Einstein's illogical relativity is replaced. Why do we always measure the constant velocity c on Earth is now physically understandable. (c) 2022 Physics Essays Publication.

Einstein was led astray by a physically incorrect calculation by Michelson and Morley in the context of the Michelson‐Morley experiment. For the light beam in the horizontal light path, their calculation yields the claim that [(1 − v/c) × c] + [(1 + v/c) × c] = 2[(1 − v2/c2) × c]. This is incorrect and mathematically increases the horizontal light path 2d 0 by the factor [(1 + v2/c2)], which Einstein’s theory of special relativity corrects by introducing the time dilation factor γ and the length contraction factor 1/γ. When we calculate correctly, the mathematical increase in the length of horizontal light path no longer happens and Einstein’s mathematical corrections of the horizontal light path imply an inconstancy of the speed of light. This means that Einstein’s special relativity is just a mathematical correction of a physical calculation error, not a true physical theory, and it was thus pure chance that Einstein found the physically real kinematic time dilation factor γ. The null result of the Michelson‐Morley experiment, along with the kinematic and gravitational time dilation, must instead be explained by a constant value for the speed c of light with respect to the gravitational potentials of predominant gravitational fields, resulting from the principles of minimum energy and energy conservation. On this basis, it becomes possible to predict so-called general relativistic phenomena, e.g., the precession of Mercury’s perihelion or the phenomena observed in the binary pulsar PSR B1913 + 16, just by applying Kepler’s second law and simple quantum physical considerations. [R. G. Ziefle, Phys. Essays 33, 99 (2020)].

Einstein’s general relativity postulates that, at each positon within a gravitational field, we must measure the same frequency f 0 , but seen from a distance, the frequency at the position of another gravitational potential is different from f 0 . As gravity decreases with the increase in the distance from Earth, in the Pound‐Rebka experiment at the top of the tower, the frequency of electromagnetic radiation must be higher than at the bottom. If electromagnetic radiation was able to have the same frequency f 0 at the top of the tower as at the bottom of the tower, an observer at the top of the tower would have to be able to increase gravity to the same level that gravity has at the bottom. But the decrease in gravity with an increase in the altitude cannot be reversed. It is demonstrated that the relativistic interpretation of the Pound‐Rekba experiment showing a doubling of the gravitational frequency shift for “two-way” observations violates the principle of energy conservation, whereas the classical interpretation of the experiment identifies the doubling of the gravitational frequency shift as a pure mathematical effect that has no physical reality, which always occurs when we subtract relative differences with opposite algebraic signs from each other. It is shown that Einstein’s general relativity only seemingly corresponds with reality; thus, gravitational frequency (time) shifts must be interpreted according to classical considerations.

Einstein’s special and general relativity are relics from before quantum physics. If forces are transmitted by quanta, this must also apply to gravity. As light consist of quanta, it is only logical that gravitational quanta interact with light. In my article “Cognitive bias in physics with respect to Einstein’s relativity, demonstrated by the famous experiment of Pound and Rebka (1960), which in reality refutes Einstein’s general relativity” [R. G. Ziefle, Phys. Essays 35 , 91 (2022)], I could demonstrate that Einstein’s “proper time” t 0 does not refer to reference frames but to gravitational potentials. That is why “Newtonian quantum gravity” [R. G. Ziefle, Phys. Essays 33 , 99 (2020)] can predict the correct curvature of a light beam at the surface of the Sun. Also, the phenomena observed at the binary pulsar PSR B1913 + 16 can precisely be predicted by merely applying Kepler’s second law. If gravitational quanta move away from masses with the constant speed c of light, this coincides with Einstein’s postulate of a constant speed c of light with respect to reference frames, as a mass, such as a star or a planet, can also be defined as a reference frame. Therefore, Einstein’s found by chance an artificial and complicated method to calculate changes in space-time caused by motion, which are in reality additional gravitational effects caused by the relative velocity between gravitational quanta emitted by masses and other masses or photons.

The two equations E = h × f and E = (h × c)/λ for the quantum of energy of electromagnetic radiation provide the same result but describe electromagnetic radiation very differently. E = (h × c)/λ describes the quantum of energy of electromagnetic radiation to be located already in one wavelength and therefore like a particle. E = h × f describes the quantum of energy distributed over 299 792 458 m and therefore like a wave. To obtain h × f for the quantum of energy, we have to refer the quantum of energy to 299 792 458 m. Only then we obtain from E = (h × c)/(299 792 458 m), as the distance of 299 792 458 m of the velocity c is cancelling out now, E = h × 1/s = h × Hz, which is the precondition to obtain the correct value for the quantum of energy by multiplying Planck’s constant h by the frequency f. This already indicates the necessity of today's physics to have to speak of a particle-wave duality. It turns out that electromagnetic radiation consists of the first wavelength that carries the quantum of energy and behaves like a particle, which today is called “photon,” and a few following wavelengths that do not carry a further quantum of energy and behave like a wave, which today is called “electromagnetic wave.” By this knowledge, the particle-wave duality vanishes, and we obtain one single physical phenomenon, which I call “photon-wave.” The strange behavior of quantum objects at a single slit, at double-slits, and at beam splitters can now be understood in a causal way. “God does not play dice!” Einstein was right.

On Earth, we always measure the constant velocity c of electromagnetic radiation. Einstein assumed the velocity c of light to be constant in all inertial frames and developed his theory of special relativity by considering a light beam that moves back and forth, whereby he derived transformations between the coordinates of two reference frames: A moving reference frame represented by the coordinate system k and the coordinate system k that is at rest with respect to k . However, by applying Einstein’s theory of relativity, with its postulates of relativistic time dilation and length contraction, to electromagnetic radiation that moves only in one direction, either in the direction of or in the opposite direction to a moving inertial frame, it is demonstrated that the constancy of the velocity c of light is not compatible with Einstein’s theory of special relativity. It becomes obvious that Einstein’s relativistic physics must be an unrealistic theory, and consequently, we need an alternative, nonrelativistic, explanation of the constancy of the velocity c of electromagnetic radiation measured on Earth, and for the special and general “relativistic” phenomena.

Newtonian Quantum Gravity (NQG) unifies quantum physics with Newton's theory of gravity and calculates the so-called “general relativistic” phenomena more precisely and in a much simpler way than General Relativity, whose complicated theoretical construct is no longer needed. Newton's theory of gravity is less accurate than Albert Einstein's theory of general relativity. Famous examples are the precise predictions of General Relativity at binary pulsars. This is the reason why relativistic physicists claim that there can be no doubt that Einstein's theory of relativity correctly describes our physical reality. With the example of the famous “Hulse-Taylor binary” (also known as PSR 1913 + 16 or PSR B1913 + 16), the author proves that the so-called “general relativistic phenomena” observed at this binary solar system can be calculated without having any knowledge on relativistic physics. According to philosophical and epistemological criteria, this should not be possible, if Einstein's theory of relativity indeed described our physical reality. Einstein obviously merely developed an alternative method to calculate these phenomena without quantum physics. The reason was that in those days quantum physics was not yet generally taken into account. It is not the first time that a lack of knowledge of the underlying physical phenomena has to be compensated by complicated mathematics. Einstein's theory of general relativity indirectly already includes additional quantum physical effects of gravitation. This is the reason why it cannot be possible to unite Einstein's theory of general relativity with quantum physics, unless one uses “mathematical tricks” that make the additional quantum physical effects disappear again in the end.

An airplane flying in the sky cannot have a higher inertial mass just because a person on the ground is watching the airplane, as well as it cannot have different inertial masses, if observed from car drivers moving on the ground with different velocities. Einstein’s relativistic physics that postulates that one can influence the inertial mass of matter or the speed of physical processes (“time”) by observing another inertial frame is actually not understandable. Because the relativistic mathematical approach enables us to get usefully and numerally precise results of nature observable phenomena, relativistic physics is nevertheless generally accepted today. This can only be explained in such a way that most physicists subordinate their logical reasoning to their mathematical formalism. The author explains the constancy of the speed of light, as well as the slowing down of physical processes (time) and the increase in the inertial mass, which are caused by motion, cogently by the principle of energy conservation. Nonrelativistic explanations of the equivalence of inertial and gravitational mass and for the mass-energy equivalence are presented. It is demonstrated that the explanation of the inertial mass increase by Einstein’s relativity violates the principle of energy conservation. As relativity has therefore been refuted by nature, a paradigm shift is imperative.

The theory of gravity “Newtonian quantum gravity” (NQG) is an ingeniously simple theory, because it precisely predicts so-called “general relativistic phenomena,” as, for example, that observed at the binary pulsar PSR B1913 + 16, by just applying Kepler’s second law on quantized gravitational fields. It is an irony of fate that the unsuspecting relativistic physicists still have to effort with the tensor calculations of an imaginary four-dimensional space-time. Everybody can understand that a mass that moves through space must meet more “gravitational quanta” emitted by a certain mass, if it moves faster than if it moves slower or rests against a certain mass, which must cause additional gravitational effects that must be added to the results of Newton's theory of gravity. However, today's physicists cannot recognize this because they are caught in Einstein's relativistic thinking and as general relativity can coincidentally also predict these quantum effects by a mathematically defined four-dimensional curvature of space-time. Advanced NQG is also able to derive the gravitational constant G and explains why G must fluctuate. The “string theory” tries to unify quantum physics with general relativity, but as the so-called “general relativistic” phenomena are quantum physical effects, it cannot be a realistic theory. The “energy wave theory” is lead to absurdity by the author.

The theory of special and general relativity causes a “schizophrenic” dilemma in physics. It undeniably provides mathematically correct values, but it is undeniably epistemologically wrong in many respects. Including the relativistic explanation of the gravitational “time dilation” and the curvature of light beams at the surfaces of large masses, the author demonstrates the illogical character of relativistic physics. When one thinks the relativistic explanations of gravitational time dilatation and of the curvature of light rays by masses through to the end, they lead to absurd and contradictory logical conclusions.

In the experiments concerning time-dilation effects, physicists compare always only two atomic clocks, one that is stationary and one that moves or is within another position with respect to the gravitational potential. Using only two clocks, respectively, two physical states, the contradictions of relativistic physics are hidden. If more than two clocks are examined in an experiment, there result a lot of contradictions, as explained in the article. The presented empirical experiment proves that Einstein's theory of relativity is wrong. According to epistemological criteria, the theory of relativity has therefore to be considered obsolete and has to be replaced by another theory that has not yet been falsified. To accept this is not easy because the theory of relativity provides quantitatively very correct values. These quantitative values entered into computers, allow a very good applicability in physics and astrophysics. But on the one hand computers do not ask whether the quantitative values used were conclusively derived and on the other hand most physicists do not question relativistic physics anymore because of its great successes. (C) 2019 Physics Essays Publication.

The epistemological analysis presented in this article shows that the foundations of Albert Einstein's theory of relativity, which he developed in the context of his special theory of relativity, are inconsistent with several experiments. This is not the case with the general theory of relativity, whose predictions coincide with the experiments without contradiction and whose experimental confirmations were celebrated as great scientific achievements. The latter made the physicists obviously blind to the contradictions of the foundations of the theory of relativity and led to an immunization against critical statements on the theory of relativity. As now criticism of relativistic physics is reflexively rejected as unjustified and ignorant by the majority of physicists, a critical discussion of relativistic physics is practically not possible any more. But if this article is not ignored, a paradigm shift in physics will be unstoppable, just as the paradigm shift from the Ptolemaic cosmology to the Copernican cosmology of the 16th century. (C) 2018 Physics Essays Publication.

For the first time in the history of quantum physics, at least three unrecognized (or ignored) experimental falsifications of fundamental postulates of quantum mechanics are presented. Quantum mechanics postulates that quantum objects are already influenced by the pure intention of researchers to examine a certain quantum phenomenon, that quantum phenomenon have no defined status, until they are measured, that quantum objects being observed by researchers can change afterward what has already happened to another quantum object before, and that particles can have opposite spins at the same time. Although these imaginations are mathematically well founded, they seem to be quite mystical, while the assumptions of the author in contrast are apparent to our reason and cognition. (C) 2017 Physics Essays Publication.

The binary quantum model introduced here makes it possible to place the four basic fundamental forces on a common basis and to understand why the phenomena "dark energy" and "dark matter" must be indirect effects of gravity. It is also shown how the so-called fine-structure constant a and the Planck constant can be derived from experimental results. (C) 2016 Physics Essays Publication.

Present day gravitational physics experiences a huge success in obtaining better and better experimental results. In some cases, the observations do not fit with the present knowledge of established physics. Phenomena, like the increase of the Astronomical Unit by 7 m per century or the so-called anomalous secular increase of the eccentricity of the lunar orbit by about 9 x 10(-12) per year, which can neither be explained by Einstein's Theory of General Relativity, nor by the Newtonian Theory of Gravitation, can be explained by the New Theory of Gravitation [R. G. Ziefle, Phys. Essays 24, 213 (2011)]. (C) 2013 Physics Essays Publication. [http://dx.doi.org/10.4006/0836-1398-26.1.82]

From the example of the motion of Mercury around the Sun it is shown how Newton's theory of gravitation can be modified by taking into consideration the finite velocity of gravitational expansion and the concept of transmission of forces by virtual particles to be able to calculate so-called general relativistic phenomena as the additional motion of Mercury's perihelion, the curvature of a light beam at the surface of the sun, and the phenomena observed at the binary pulsar PSR (Pulsating Source of Radio Emission) 1913+16, maintaining classical conceptions of a Euclidean space and the Galilean principle of relativity. Present day gravitational physics experiences a huge success in obtaining better and better experimental results. In some cases the observations do not fit with the present knowledge of established physics. These phenomena, which can neither be explained by the general relativistic theory of Albert Einstein nor by the Newtonian theory of gravitation, can be explained by the new theory of gravitation of the author, in parts published in former articles of the author in Physics Essays [R. G. Ziefle, Phys. Essays 3, 468 (2003); Phys. Essays 18, 477 (2005)]. (C) 2011 Physics Essays Publication. [DOI: 10.4006/1.3567412]