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Papers by koshun suto

Journal of Applied Mathematics and Physics, Dec 31, 2022

Journal of Applied Mathematics and Physics, 2020

The energy levels of a hydrogen atom, derived by Bohr, are known to be approximations. This is be... more The energy levels of a hydrogen atom, derived by Bohr, are known to be approximations. This is because the classical quantum theory of Bohr does not take the theory of relativity into account. In this paper, the kinetic energy and momentum of an electron in a hydrogen atom are treated relativistically. A clearer argument is developed while also referring to papers published in the past. The energy levels of a hydrogen atom predicted by this paper almost match the theoretical values of Bohr. It is difficult to experimentally distinguish the two. However, this paper predicts the existence of an n = 0 energy level that cannot be predicted even with Dirac's relativistic quantum mechanics. The only quantum number treated in this paper is n. This point falls far short of a finished quantum mechanics. However, even in discussion at the level of this paper, it can be concluded that quantum mechanics is an incomplete theory.

Physics Essays, Dec 1, 2012

This paper shows that the quantum condition that Bohr applied to the hydrogen atom is an approxim... more This paper shows that the quantum condition that Bohr applied to the hydrogen atom is an approximation. Also, as a result of calculations using a quantum condition newly assumed in this paper, it was possible to obtain, in addition to the orbital radius derived by Bohr, a physical quantity r e /4, which is thought to be the radius of the proton. The electron is thought to be an elementary particle that has no size, but if it is assumed that the electron has a size, then this paper presents a value that is a strong candidate. If it is assumed that because the mass of the electron is involved in the size of the proton, the mass of the proton is involved in the size of the electron, then it becomes possible to predict the radius of the electron. If it is assumed that the radii of the proton and electron have existed in a fixed state since before the measurement of their size by experiment, then it becomes necessary to review quantum mechanics.

Global Journal of Science Frontier Research, Sep 23, 2022

Einstein's energy-momentum relationship, which holds in an isolated system in free space, can... more Einstein's energy-momentum relationship, which holds in an isolated system in free space, cannot be applied to an electron in a hydrogen atom where potential energy is present. The author has previously derived an energy-momentum relationship which holds inside a hydrogen atom. Using an argument of Dirac, a solution is obtained for the positive and negative energy levels based on this relationship too. Even if the energy is described on an absolute scale, the electrons at negative energy levels have negative mass. The author has adopted the name "dark hydrogen atom (DHA)" for this type of unknown material composed of an electron with negative mass and a proton (atomic nucleus) with positive mass. The mass of a DHA is almost the same the mass of an ordinary hydrogen atom. However, a DHA is extremely small compared to an ordinary hydrogen atom, and thus can achieve states of ultra-high density. The author has pointed out that these DHAs, and the hydrogen molecules and other materials formed from them, are the true nature of the unknown material known as "dark matter" whose true nature is currently regarded as unknown. Recently, the author has derived a previously unknown formula for the energy levels of the hydrogen atom. According to this formula, physical quantities of DHA are involved in the energy levels of a hydrogen atom. This paper derives this formula for the energy levels of a hydrogen atom using another method. The author believes this formula to be strong evidence of the existence of DHAs.

Journal of Physical Mathematics, 2017

This paper discusses a thought experiment whose result contradict the predictions of the special ... more This paper discusses a thought experiment whose result contradict the predictions of the special theory of relativity. The reason why this contradiction appears is a velocity vector attached to an inertial frame. Since this sort of inertial frame exists in the natural world, the "principle of relativity" that regards all inertial frames as equivalent, cannot be regarded as a true principle. This paper concludes that the special theory of relativity, which assumes the "principle of relativity" in its development, is a theory with a built-in contradiction.

Applied physics research, Jul 19, 2017

It is thought that quantum mechanics is the physical science describing the behavior of the elect... more It is thought that quantum mechanics is the physical science describing the behavior of the electron in the micro world, e.g., inside a hydrogen atom. However, the author has previously derived the energy-momentum relationship which holds inside a hydrogen atom. This paper uses that relationship to investigate the relationships between physical quantities which hold in a hydrogen atom. In this paper, formulas are derived which hold in the micro world and make more accurate predictions than the classical quantum theory. This paper concludes that quantum mechanics is not the only theory enabling investigation of the micro world.

Physics Essays, Jun 24, 2014

The only velocity addition law currently regarded as correct is that for the special theory of re... more The only velocity addition law currently regarded as correct is that for the special theory of relativity. However, this paper concludes that there is a justification for the existence of velocity addition laws derived from the standpoint of Lorentz, who had doubts about the special theory of relativity. The velocity addition laws presented in this paper are not new, and are equations which are easy to understand in terms of common sense. Aside from the velocity addition law in the special theory of relativity, there are also velocity addition laws which match experimental results.

Applied physics research, Nov 27, 2016

In the thought experiment in this paper, we considered inertial frames M and A moving at a consta... more In the thought experiment in this paper, we considered inertial frames M and A moving at a constant velocity relative to each other. A light signal emitted from inertial frame A, when time of a clock in inertial frame A was 1(s), arrived at inertial frame M when time of a clock in inertial frame M was 2(s). In this paper, the time in inertial frame A when the time in inertial frame M was 2(s) was predicted by observers in inertial frames M and A by applying the special theory of relativity (STR). Predictions of the two observers did not match. Einstein regarded all inertial frames as equivalent, but there are cases where a velocity vector is attached to some inertial frame. Einstein overlooked this fact, and thus a discrepancy appeared in the values predicted by the two observers. It is not the case that all inertial frames are equivalent. This paper concludes that the STR is a theory incorporating a contradiction which must be corrected.

Journal of Applied Mathematics and Physics, 2021

Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous ... more Bohr assumed a quantum condition when deriving the energy levels of a hydrogen atom. This famous quantum condition was not derived logically, but it beautifully explained the energy levels of the hydrogen atom. Therefore, Bohr's quantum condition was accepted by physicists. However, the energy levels predicted by the eventually completed quantum mechanics do not match perfectly with the predictions of Bohr. For this reason, it cannot be said that Bohr's quantum condition is a perfectly correct assumption. Since the mass of an electron which moves inside a hydrogen atom varies, Bohr's quantum condition must be revised. However, the newly derived relativistic quantum condition is too complex to be assumed at the beginning. The velocity of an electron in a hydrogen atom is known as the Bohr velocity. This velocity can be derived from the formula for energy levels derived by Bohr. The velocity v of an electron including the principal quantum number n is given by αc/n. This paper elucidates the fact that this formula is built into Bohr's quantum condition. It is also concluded in this paper that it is precisely this velocity formula that is the quantum condition that should have been assumed in the first place by Bohr. From Bohr's quantum condition, it is impossible to derive the relativistic energy levels of a hydrogen atom, but they can be derived from the new quantum condition. This paper proposes raising the status of the previously-known Bohr velocity formula.

Physics Essays, Sep 1, 2010

This paper provides for the categories of "primary stationary system" and "conditional stationary... more This paper provides for the categories of "primary stationary system" and "conditional stationary system" for inertial frames of reference, which Einstein believed were all equivalent. The "primary stationary system" is a coordinate system in which all clocks are in sync, in absolute terms, even if clocks were not synchronized as proposed by Einstein. The "conditional coordinate system," on the other hand, is a coordinate system in which an observer in this coordinate system, in order to be able to state that light propagates isotropically from a light source in his coordinate system, must use the clock synchronization method proposed by Einstein to synchronize with the time of the clock in his coordinate system. This paper considered the coordinate system of rod 2, moving at constant velocity relative to a "conditional stationary system" (Einstein's inertial frame of reference), as considered in this paper as equivalent to inertial frame of reference of the special theory of relativity. Then, it was shown that, the actual time adjustment made by an observer in this coordinate system to synchronize two clocks at each end of a rod by using Einstein's method is not the same as the value predicted by the special theory of relativity. The reason for the discrepancy between experimental values and theoretical values is due to the unknown velocity v which is related to "conditional stationary systems," the 1 existence of which Einstein denied. This paper therefore concludes that Einstein was incorrect in considering all inertial frames of reference to be equal when developing the special theory of relativity.

Journal of Applied Mathematics and Physics, 2023

Einstein's energy-momentum relationship, which holds in an isolated system in free space, contain... more Einstein's energy-momentum relationship, which holds in an isolated system in free space, contains two formulas for relativistic kinetic energy. Einstein's relationship is not applicable in a hydrogen atom, where potential energy is present. However, a relationship similar to that can be derived. That derived relationship also contains two formulas, for the relativistic kinetic energy of an electron in a hydrogen atom. Furthermore, it is possible to derive a third formula for the relativistic kinetic energy of an electron from that relationship. Next, the paper looks at the fact that the electron has a wave nature. Five more formulas can be derived based on considerations relating to the phase velocity and group velocity of the electron. This paper presents eight formulas for the relativistic kinetic energy of an electron in a hydrogen atom.

Global Journal of Science Frontier Research, Feb 28, 2023

The classical quantum theory of Bohr does not take the theory of relativity into account. The ene... more The classical quantum theory of Bohr does not take the theory of relativity into account. The energy levels of a hydrogen atom, derived by Bohr, are known to be approximations. In this paper, the kinetic energy and momentum of an electron in a hydrogen atom are treated relativistically. This paper predicts the existence of an n=0 energy level present in a hydrogen atom. However, the state where n=0 is not an energy level of the electron comprising the hydrogen atom. It is thought that an electron in the n=0 state forms a pair with a positron, and constitutes the vacuum inside the hydrogen atom.

Physics Essays, Sep 1, 2009

It is theoretically possible for a hydrogen atom to have an energy level that is even lower than ... more It is theoretically possible for a hydrogen atom to have an energy level that is even lower than the ground state. Assuming that hydrogen atoms with this energy do exist, it would be also necessary to adjust the Rydberg formula, which predicts the wavelength of photons emitted during an electron transition. When solving for the photon wavelength using the formula newly derived in this paper, there is a slight discrepancy between the theoretical value and the experimental value thought to completely match this wavelength. This paper asserts the possibility of the existence of a hydrogen atom energy level even lower than the ground state, and concludes that an investigation of this is necessary.

Applied physics research, Mar 20, 2017

This paper discusses the "triplet thought experiment" in which accelerated motion is eliminated f... more This paper discusses the "triplet thought experiment" in which accelerated motion is eliminated from the famous twin paradox thought experiment of the special theory of relativity (STR). The author considers the coordinate systems of an inertial frame M and rocket A moving at constant speed relative to each other. First, an observer in inertial frame M performs the triplet thought experiment, and it is confirmed that the delay in time which elapses in the moving system agrees with the predictions of the STR. However, the delay in time predicted by the STR is observed even in the case when an observer A in rocket A carries out the triplet thought experiment. Before starting movement at constant velocity, rocket A experiences accelerated motion. The coordinate system of rocket A cannot be regarded physically as a stationary system. Even so, observer A observes the delay predicted by the STR. If the previous, traditional interpretation is assumed to be correct, observer A will never observe a delay in time agreeing with the predictions of the STR. To avoid paradox, the previously proposed traditional interpretation must be revised.

Applied physics research, Jan 29, 2019

Bohr's quantum condition is an indispensable assumption for classical quantum theory. However, st... more Bohr's quantum condition is an indispensable assumption for classical quantum theory. However, strictly speaking, Bohr's quantum condition does not hold when deriving the energy of an electron forming a hydrogen atom from the perspective of the theory of relativity. In this paper, it is thought that the relationship enfolded in Bohr's quantum condition, i.e., / / n v c α n = is suitable as a new quantum condition to replace Bohr's quantum condition. Also, in quantum mechanics, the energy of an electron is derived based on the theory of relativity, as exemplified in the theory of Sommerfeld. However, this paper points out that the previous energy formula based on the theory of relativity is mistaken. It also proposes a previously unknown formula for the kinetic energy of an electron.

Physics Essays, Dec 1, 2011

When determining the coefficients a i and b of the Dirac equation (which is a relativistic wave e... more When determining the coefficients a i and b of the Dirac equation (which is a relativistic wave equation), Dirac assumed that the equation satisfies the Klein-Gordon equation. The Klein-Gordon equation is an equation that quantizes Einstein's relationship E 2 ¼ c 2 p 2 þ E 2 0. Therefore, this paper derives an equation similar to the Klein-Gordon equation by quantizing the relationship E 2 re;n þ c 2 p 2 n ¼ E 2 0 between energy and momentum of the electron in a hydrogen atom derived by the author. By looking into the Dirac equation, it is predicted that there is a relativistic wave equation, which satisfies that equation, and its coefficients are determined. With the Dirac equation, it was necessary to insert a term for potential energy into the equation when describing the state of the electron in a hydrogen atom. However, in this paper, a potential energy term was not introduced into the relativistic wave equation. Instead, potential energy was incorporated into the equation by changing the coefficient a i of the Dirac equation. It may be natural to regard the equation derived in this paper and the Dirac equation as physically equivalent. However, if one of the two equations is superior, this paper predicts it will be the relativistic wave equation derived by the author. V

Applied physics research, Jul 26, 2018

In a previously published paper, the author made some mistakes in calculating the potential energ... more In a previously published paper, the author made some mistakes in calculating the potential energy of the electron in a hydrogen atom. Those mistakes occurred due to applying a potential energy formula with a certain range of application in a region where it is not applicable. Therefore, this paper corrects that error by deriving a formula for potential energy with no range of application. The paper also proposes a model in which a virtual particle pair present in the vacuum region inside a hydrogen atom simultaneously has a photon with positive energy and a photon with negative energy (In this paper, these photons are called dark photons). In the state where the relativistic energy re E is zero, the sum of the positive energy and negative energy of the virtual particle pair becomes zero. According to this model, this makes it possible for the particles to release photons, and capture negative energy.

Applied physics research, Sep 20, 2014

In this paper an equation with higher precision than the equation of quantum mechanics is derived... more In this paper an equation with higher precision than the equation of quantum mechanics is derived as an equation describing the energy levels of the hydrogen atom using only the principal quantum number n. That equation predicts the existence of an n=0 energy level. However, the state where n=0 is not an energy level of the electron comprising the hydrogen atom. The electron in this state forms a pair with a positron, which is the electron's antiparticle. The relativistic energy of the individual particles forming the pair is zero, but their momentum is not zero. The momentums of these particles are equal in magnitude but opposite in direction. By forming a pair, the sum of the momentums of two types of particles becomes zero. It is very significant that even the energy level of the electron pairs which comprise the vacuum have been incorporated into the formula for the energy of the hydrogen atom.

Physics Essays, Jun 1, 2009

In considering the potential energy of a hydrogen atom, we offered the hypothesis that this physi... more In considering the potential energy of a hydrogen atom, we offered the hypothesis that this physical quantity corresponds to the decrease in the electron's rest mass energy. It is not possible to establish the ground state energy of a hydrogen atom without quantum mechanics. However, for the atom's stability only, this can be explained even without using quantum mechanics. Our discussion reveals that there exists an off-limit boundary r c within the electron inside a hydrogen atom.

Applied physics research, Jan 20, 2022

The energy-momentum relationship in the special theory of relativity (STR) holds in an isolated s... more The energy-momentum relationship in the special theory of relativity (STR) holds in an isolated system in free space. However, this relationship is not applicable to an electron in a hydrogen atom where there is potential energy. Using three types of methods, the author has already derived an energy-momentum relationship applicable to an electron in a hydrogen atom. In the past, Dirac asserted that Einstein's relationship has negative solutions. This paper too obtains negative solutions (energy) from the derived relationship using Dirac's reasoning. However, the discontinuity peculiar to the micro world is not incorporated into that solution. Thus discontinuity is incorporated into the solution by using a new quantum condition already derived by the author. Next, the orbital radius of an electron with negative energy in an absolute sense is found, and that radius is compared with the orbital radius of an electron in an ordinary hydrogen atom. A search is conducted for experiments supporting the DM model advocated by this paper. A hydrogen atom at this ultra-low energy level is formed from an atomic nucleus (proton) with positive mass, and a single electron with negative mass existing near that. In this paper, this unknown type of matter will be called a dark hydrogen atom (DHA). This paper also points out that DHA accounts for part of the true nature of dark matter (DM), the mysterious material whose true nature is currently unknown. Although this differs from the conventional interpretation, this paper holds that the experiment which demonstrates the existence of DHA is triplet production. The paper points out that one of the two electrons produced in a triplet production experiment is the electron which forms a DHA. If the DM model advocated by this paper is correct, then DM has already been discovered.