Looking at other questions in this topic I would want to contribute to those questions with my considerations in the order of the Theory of Reference Frames:

1.question raised by Nathalie Olivi-Tran

Friedmann’s cosmological models aren’ t direct object of my studies, but I would want to do a few notes: a) if pressure is defined p=F/r^3, then the integral on F/r^3 doesn’ have the dimensions of a pressure; b) the indefinite integral on F/r^3 is (- F/2r^2 + constant). The definite integral can take on any value, positive or negative, subject to bounds of integration; c) in the Theory of Reference Frames there aren’t two redshifts as in Einstein’s SR and GR (Doppler redshift and cosmological redshift) but only one redshift due to the new relativistic Doppler effect.

2.question raised by Ehsan Talebian

In Newton’s second law there is the acceleration of moving body, while in Maxwell’s equations there is the speed of light. Acceleration is invariant for inertial reference frames, speed isn’t invariant for inertial reference frames. Anyway in the Theory of Reference Frames different transformations of space-time are used and the invariance of Maxwell’s equations is demonstrated.

3. Question raised by Shu-Chang Zang

In order to complete your study on the invariance of Maxwell’s equations I would want propose also the reading of my paper:

Daniele, I know what are the dimensions of a pressure...

about the definite integral of f/r^3,instead take the derivative of f/r^2: d(f/r^2)/dr=-2f/r^3

Nathalie, following your line of thought my calculation results in that pressure is always positive for any distance from the singularity.

I think Friedmann’s cosmological models and the same theory of the big-bang have to be examined critically.

Dear Prof. Sasso can I ask is your work contains a remark that the time measured by microscopic particles is differ from the time measured by classical objects?

Dear Sadeem, in the Theory of Reference Frames the following equation between mass and time is demonstrated: dt/dt'=m/m' , where t' and m' are time and mass with respect to the moving physical system, t and m are time and mass of the same physical system with respect to the reference frame of supposed resting laboratory.

From this equation we deduce measured or calculated time depends on the mass variation with respect to the two reference frames (supposed resting frame and moving frame).

Classical objects have always the same time with respect to all reference frames because they don't undergo a mass real variation. Elementary particles have a different physical behavior because we know accelerated particles emit radiant energy at the expense of electrodynamic mass.

Therefore in TR answer to your question is positive.

Thank you for your answer

I have proved in TR Lorentz's transformations need a strong correction. In Physics and in Science nevertheless experiments have the last word and I think a few physical phenomena don't have been enough investigated and understood. I refer in particular to two physical situations: black holes in cosmology and accelerated particles in particle physics. I am sure the gravitational theory for black holes and the calculation of the speed for accelerated particles are inadequate.

Dear Dolce Donatello,

through your interesting paper "Cyclic spacetime dimensions" I have learned about the existence of a paper "A clock directly linking time to a particle mass" in ref[7]. This paper demonstrates the connection between time and mass through the Compton frequency. The relativistic connection between time and mass is also one of basic concepts of the Theory of Reference Frames, where I have formalized this relativistic connection.

Thanks for your casual notice.

Daniele Sasso

I would want to clarify an aspect of Special Relativity that produces often misunderstanding and doubts because of a mistaken conclusion of this theory. In SR in fact all mass M of the universe is considered similarly: every shape of mass m fulfils the law of transformation of mass to energy E=mc^2 and therefore also the whole mass M of the universe should fulfil this law E=Mc^2.

In the Theory of Reference Frames that law of transformation isn't valid similarly for all masses but only for the electrodynamic mass of accelerated charged elementary particles and for free unstable particles. Free charged unstable particles then have negative electrodynamic mass and because for complex structures of matter that law applied only to mass deficit it is inferable that the Boltzmann constant doesn't apply to mass M of the whole universe but only to a small part.

Einstein's Theory of Relativity (Special and General) has represented certainly an important progress in the scientific thought. It needs nevertheless to say sometimes it has caused also a few ambiguities and misunderstandings in basic concepts of physics as energy and mass, space and time. For instance space and time are measured by different units of measurement but the same tensor non-linear element in whether Minkowski's or Einstein's space-time at times is measured by metres and at times by seconds as it is represented at times by real numbers and at times by imaginary numbers. The Theory of Reference Frames, whose I will publish a new paper in September, has also the object of clarifying those concepts besides of presenting innovative physical concepts.

The new paper on the Theory of Reference Frames is ready and you can know it reading the attachment.

Not nature but observers need reference frames.

Daniele

I believe you are correct when you say "Einstein's Theory of Relativity (Special and General) has represented certainly an important progress in the scientific thought. It needs nevertheless to say sometimes it has caused also a few ambiguities and misunderstandings in basic concepts of physics as energy and mass, space and time because space and time are measured by different units of measurement but the same tensor non-linear element in whether Minkowski's or Einstein's space-time at times is measured by metres and at times by seconds as it is represented at times by real numbers and at times by imaginary numbers.

Do you think it would it be possible to resolve this issue by redefining Einstein's space time universe in terms of four *spatial* dimensions as we have attempted in our article Reference frames http://www.theimagineershome.com/blog/?p=45

Jeff

Dear Jeff, congratulations for your beatiful website.

You give much importance to imagination that is certainly one of the most important qualities of humans in all ranges of knowledge and life. Also in physics the imagination can be very important but physics has to consider the reality. Having said that, now I would want to answer your question.

I wouldn't disappoint you, but I don't see the necessity for a fourth spatial dimension. For me the initial space is an empty geometric space that is three-dimensional. In my article https://www.researchgate.net/publication/256391945_Physico-Mathematical_Fundamentals_of_the_Theory_of_Reference_Frames?ev=prf_pub

I have also defined that the space is infinite, infinitesimal and discrete. Besides I distinguish the empty geometric space from the empty physical space, which is characterized by 3 main physical properties: permittivity, permeability and mechanical resistance.

I don't believe Theories of Everything or Unification Coercive Theories which want to unify all, also what isn' possible to unify. I strive to understand nature in simple way because I think nature is simple, also if I know necessary mathematics often isn' simple.

My best regards.

Daniele

Article Physico-Mathematical Fundamentals of the Theory of Reference Frames

Agreed one must always attempt to explain nature in terms of the reality of observations and I can agree with you regarding the relativistic properties of three dimensional space. However have you been able to define a mechanism based on the reality of what we can see all around us for those properties as we have attempted in our article.>

Dear Jeff, it seems to me you agree with Special and General Relativity and you aim at the maximum to improve those theories. Instead I think those theories are now obsolete and new paradigms are necessary. You introduce the fourth spatial dimension for rationalizing the curvature of spacetime (General Relativity). I don't believe the curvature of spacetime and therefore I don't need the fourth spatial dimensioin. I think there is no intrinsic kinematic relation between space and time (Lorentz's Transformations in Special Relativity).

I think and I have demonstrated in the Theory of Reference Frames (TR) there is a mathematical relation between time and mass but it doesn't have kinematic meaning and it is connected only with the considered physical phenomenon. It means that also if there is a relativistic effect of time (for instance for elementary particles) this regards only that phenomenon while the kinematic time goes on always in synchrounous way. Similarly I think there isn't a linear(SR) or non-linear (GR) element defined in an unique space-time. For me space and time are two independent kinematic quantities of the physical reality and the only relation between space and time is defined through the velocity which is a dependent quantity.

You write in your site "Therefore, the energy/mass of an object would be dependent on its relative motion because one must add the energy/mass associated with its motion to its rest energy/mass." I agree with this statement but in TR I have demonstrated this concept must be differentiated.

For mechanical systems the "dynamic mass" increases with the speed and this concept of dynamic mass is a virtual concept.

For electrodynamic systems (elementary charged particles) the "electrodynamic mass" decreases with the speed and this concept is real.

Modern theories aim to unify, I aim to differentiate in order to understand nature and physical reality.

If the only part of the observable reality of our universe was the dynamic properties of mass I would agree with you. However part of that reality involves not only how and why we observed the dynamic properties of mass to be what they are but also how and why mass dynamically interacts gravitationally. Correct me if I am wrong but I do not think that your "Theory of Reference Frames" addresses its gravitational properties.

I have difficulty understanding how one can explain or theorize about one property of mass and not address the others. In other words if you want to have your ideas accepted by the scientific community with regards to the dynamic properties of mass you must try to include all of its properties because mass because I believe you have defined it is unique entity. Therefore to be taken seriously one would expect a theory that involves mass to be able to explain then all in one logical and consistent theoretical model.

There are many evidences that Quantum Mechanics, Special Relativity, General Relativity and Standard Model are obsolete theories on a pair with Classic Physics. An obsolete theory isn't necessarily a wrong theory but certainly it isn't more able to fulfil all requirements that are demanded to a scientific theory. Many scientists and students of science claim they not will leave those theories because they are elegant theories.

I think instead Science isn't a fashion show and elegance isn't a primary quality that is demanded to a scientific theory. Primary qualities that are necessary for a scientific theory, from my viewpoint, are: utility, simplicity, efficacy, consistency, agreement with reality.

Стандартный подход к системам связан с преобразованием координат нелинейным образом содержащим время (Фок). Существует определение равноускоренной НСО, связанное с преобразованием Меллера. Система Меллера является жесткой по Борну, но разные частицы среды движутся с разными ускорениями. Поэтому система Меллера-Риндлера не является глобально равноускоренной и имеет горизонт. Система из заряженной пыли, движущейся в однородном электростатическом постоянном поле без начальной скорости является глобально равноускоренной. Но эта система не является жесткой по Борну Требование, чтобы заряженная пыль удовлетворяла критериям релятивистской жесткости и была равноускоренной несовместны в пространстве Минковского. Это доказанная мною теорема. Из полученных мной уравнений структуры вытекает, что оба эти условия будут выполнены в пространстве Римана. Однако тензор Римана-Кристоффеля не связан с ОТО. Если на каждую частицу посадить наблюдателя с акселерометром (лагранжева сопутствующая НСО), то все акселерометры покажут одинаковые, ускорения а 3-расстояния между мировыми линиями частиц в такой НСО будут неизменными. Это решает парадокс Белла, который в пространстве Минковского решения не имеет. Вместо частиц в электрическом поле, рассматривается множество одинаковых ракет. (Извините, что пишу по русски, но английским владею недостаточно)     

Caro Podosenov,  apprezzo la tua decisione di dare un contributo a questo forum ma purtroppo non conosco la tua lingua. Io conosco l' Italiano e un pò l'Inglese. Perciò se vogliamo colloquiare e scambiare punti di vista, dobbiamo trovare un modo per conseguire quell' obiettivo.

Dear Podosenov, I appreciate your decision to give a contribution to this forum but unfortunately I don't know your language. I know Italian language and a little English. Therefore if we wish to converse and to exchange views, we would have to find a way for reaching that objective.

There are other questions where that problem is considered and I gave my viewpoint there.

Под новым временем я понимаю временной параметр,  сохраняющийся на гиперповерхности ортогональной мировым линиям. Эта гиперповерхность определяется интегрированием уравнения Пфаффа. В согласии с Сингом эти гиперповерхности существуют при отсутствии вращений среды.Все эти вопросы подробно изложены в моих книгах, указанных в списке литературы в статьях. Препятствием является мое плохое знание английского и отсутствие хорошего переводчика. По этой причине я не понимаю здесь многих сообщений, которые при переводе на русский выглядят абсурдными. Когда решу проблему доброкачественного перевода, тогда вопросы и ответы будут более осмысленны.

Dear Thierry de Mees, classical physics (from Copernico to Maxwell) has for me a great scientific value because it is based almost entirely on the Galilean experimental scientific method. The only concepts of classical physics that don't have experimental foundation are the Newtonian concepts of absolute space and of absolute time that Newton introduced for a metaphysical exigence rather than for a scientific exigence and those concepts led to the concept of absolute reference frame coinciding with the Aristotelian ether, that nevertheless the Michelson-Morley experiment proved wrong. Modern physics leaved often that method giving more importance to thought aspects and on this account  I don't subscribe many concepts of modern physics.

I see you support a theory based on an equivalence between electromagnetic field and gravitational field. In the abstract of paper that you propose I read:

"causal dependencies in electromagnetic phenomena are found to be described by solutions of Maxwell's equations in the form of retarded electric and magnetic field integrals. A consequence of this discovery is that, contrary to the generally accepted view, time-variable electric and magnetic fields cannot cause each other and that both fields are simultaneously created by their true causative sources -- time-dependent electric charges and currents".

I think instead causal dependences in em phenomena are perfectly described by the same four equations:

1. In the Gauss-Poisson law the charge density is the cause and the electric field is the effect

2. In the Ampere-Maxwell law the current density and the time variation of electric field are causes and the magnetic induction is the effect

3. In the Faraday-Newmann-Lenz  law the time variation of the magnetic induction is the cause and the electric field is the effect

4. With regard to the fourth equation, it is represented in standard equations by divB=0, but in my research I replaced it with the Lorentz equation for reasons that I explained in my papers. In the Lorentz equation the magnetic induction and the particle's speed are concauses and the Lorentz force is the effect.

Therefore it seems to me causal dependencies in electromagnetic phenomena are well described by the equations and solutions have to tell us how the electric field and the magnetic field vary in space and in time.

With regard to the equivalence that you propose between gravitational field and electromagnetic field it could exist only considering a time-dependent gravitational field while ordinary gravitational fields that we consider are static and time-independent. To that end nevertheless the hypothesis about the existence of five forces between two bodies appears the resut of an inappropriate mathematical model. The existence then of time-dependent  gravitational fields requires masses that are time-dependent  themselves and about this much research is necessary.

Dear Daniele

I read now your article « Physico-Mathematical Fundamentals of the Theory of Reference Frames», and I see that I don’t understand something.

“"physical speed" of light and EM-waves and the "relativistic speed".”

Two speeds of light in one reference frame are very bad for the theory.

"discreteness"

Previously the definition of the term "discreteness" was another: "the Distance "d" can not be made less predetermined value d0". An unusual interpretation of the properties of discreteness made in this article will confuse readers.

“fact in SR the simultaneity of two … is defined through paths that different rays of light follow”

No, formally in SR the definition of "the simultaneity of the two phenomena" is not related to the paths of movement of the light: "In the reference frame the events are simultaneous then and only then, when synchronized clocks in places of events show the same time." In SR for simultaneity there is no need in the observer O and the observer O' in Fig. 1. And in SR the procedure of synchronizing the fixed hours in the IFR does not depend on the pathway of light, and the distance between events is the same due to the symmetry of function of the distance |AB|=|BA|, therefore in SR there are no violations of those conditions of symmetry.

Having considered the case of the influence of the conditions of placement and movement of the observer on the simultaneous receipt of signals, the Author makes a completely wrong conclusion about the dependence of simultaneity of events at these conditions. While it is clear that the simultaneity of events in space, and the simultaneous production of signals by the observer can be completely unrelated.

The space, event space, their simultaneity or non-simultaneity do not depend on the observer as author himself considers in his examples. The events take place in different places, so the observer cannot even assess their simultaneity, as he is not in more than one place. The observer can assess the simultaneity only for events occurring at place of his clock. Events in space can be synchronous, regardless of the conditions in which the observer exists. Thus, the Author generalized his statement about the dependence of simultaneity of events from the conditions of the observer but he did it is logically incorrect.

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Уважаемый Daniele

Я читаю Вашу статью « Physico-Mathematical Fundamentals of the Theory of Reference Frames», и вижу, что не все понимаю.

  «"физическую скорость" света и ЭМ-волн от "относительной скорости".»

Две скорости света в одной системе отсчета – это очень плохо для теории.

«дискретность»

Раньше определение термина «дискретность»  было другим: «Расстояние "d" не может быть сделано меньшим заданной величины d0». Примененная в этой статье необычная трактовка свойства дискретности, будет запутывать читателей.

« в SR одновременность двух явлений, …, определена через пути, по которым различные лучи света следуют»

Нет, формально в SR определение термина «одновременность двух явлений» не связано с путями движения света: «В системе отсчета события одновременны тогда и только когда, когда синхронизированные часы в местах совершения событий показывают одинаковое время». В SR нет необходимости ни в наблюдателе O, ни в наблюдателе O' с Рис. 1. И в SR процедура синхронизации неподвижных часов в ИСО не зависит от путей движения света, а расстояния между событиями одинаковы в силу симметричности функции расстояния |AB|=|BA|, поэтому в SR нет нарушения какого-то условия симметрии

Рассмотрев случай влияния условия размещения и движения наблюдателя на одновременность получения им сигналов, Автор делает совершенно неверный вывод о зависимости одновременности событий от этих условий. Хотя очевидно, что одновременность событий в пространстве, и одновременность получения сигналов наблюдателем могут быть никак не связаны между собой.

 Автор сам рассматривает в своих примерах не зависящими от наблюдателя: пространство, события в пространстве, их  одновременность или неодновременность. События происходят в разных местах, поэтому наблюдатель не может даже дать оценку их одновременности, так как сам находится не более чем в одном месте. Наблюдатель может давать оценку одновременности только для событий, происходящих в точке расположения его часов. Таким образом, Автор неправомочно обобщил заявление о зависимости  одновременности событий от условий, в которых находится наблюдатель. События в пространстве могут быть одновременными не зависимо от условий, в которых находится наблюдатель, но он сделал это логически неверно.

Dear Alexander,

thank you for having read my paper and for your criticism.  Nevertheless I have to correct a few misinterpretations of  "Physico-Mathematical Fundamentals of the Theory of References Frames (TR)".

1.  Speed. 

The physical speed of light and the relativistic speed are not related to the same but to different references frames. The physical speed is always and only the speed with respect to the privileged, non-absolute, reference frame where light is generated and propagates. The relativistic speed instead is related to any other reference frame that is in relative motion with respect to the privileged reference frame.

2.  Discreteness.

I make use of this word in the mathematical meaning for which a discrete quantity is a finite, different from zero, quantity. I don't see confusions. If I consider a finite or discrete quantity do,  and if I double or halve it with continuity I will obtain always still a discrete or finite quantity.

3.  Simultaneity.  You say:  " In SR for simultaneity there is no need in the observer O and the observer O' in Fig. 1. And in SR the procedure of synchronizing the fixed hours in the IFR does not depend on the pathway of light, and the distance between events is the same due to the symmetry of function of the distance |AB|=|BA|, therefore in SR there are no violations of those conditions of symmetry."

But here I am defining the simultaneity in TR, not in SR, and I prove the relative motion produces with respect to the same observer a breaking of symmetry that exists at rest.  

4. You say still: "The space, event space, their simultaneity or non-simultaneity do not depend on the observer as author himself considers in his examples. The events take place in different places, so the observer cannot even assess their simultaneity, as he is not in more than one place. The observer can assess the simultaneity only for events occurring at place of his clock. Events in space can be synchronous, regardless of the conditions in which the observer exists. Thus, the Author generalized his statement about the dependence of simultaneity of events from the conditions of the observer but he did it is logically incorrect."  

If the observer is at rest in the middle point between two resting points he is able to assess the simultaneity of two events (for example the simultaneity of two rays of light that leave the two points). I agree, all in nature happens independently of the observer, but the observer is integral part of the natural process seeing as he wants to understand the nature. The important thing is that the observer's presence doesn't change the physics of event. This condition is essential for every experimental verification.

Dear Daniele

Thanks for the clarification.

1. Speed:

Then you should change the phrase "The physical speed of light is constant with respect to all reference frames", as the word "all" means that two speeds of a body– physical and relative - will be considered in each RF..

3. Simultaneity in SR:

I made here this comment to your interpretation of simultaneity in SR in phrase: "In fact SR in the simultaneity of two events..." but not to your definition of simultaneity in TR.

4. Simultaneity in TR^

“If the observer is at rest in the middle point between two resting points he is able to assess the simultaneity of two events (for example the simultaneity of two rays of light that leave the two points).”

By your definition of time in RF of the observer - he must have synchronized clock at each point of his RF, and that will be enough to determine the simultaneity of events, wherever they occurred. Time of arrival of signals to the observer is additional, optional information, which does not effect on assessment of simultaneity of events by the observer, moreover the observer should assess the simultaneity of events at different distances from him.

Building the privileged RF can't change the simultaneity of events and assessment of them by observer.  Therefore, the observer does not need in definitions of privileged reference frames! Introduction of them to the theory adds nothing except complexity and possible errors.

Dear Alexander, I agree that sometimes my English isn't clear like in the case that you consider  with regard to the physical speed. In other points of my papers I was clearer about that concept. Anyway the meaning is clearest if one considers the Principle of Reference that is at the foundation of TR. I have specified in every physical situation there is only one non-absolute privileged reference frame and changing the considered physical event also the non-absolute privileged reference frame changes.

Dear Daniele

 “changing the considered physical event also the non-absolute privileged reference frame changes.”

But if you must have different privileged reference frames for the different events, then you cannot describe any whole process in one reference frame, that is, for a one observer! For what do we need such a privileged RF and  such a Principle of Reference?

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Уважаемый Даниэль!

Но если вы должны иметь разные привилегированные системы отсчета для разных событий, то Вы не можете описать весь процесс в одной системе отсчета, то есть, для одного наблюдателя! Для чего нам нужен такой принцип и такая привилегированная система отсчета?

Уважаемые коллеги! Я доказал теорему. Переход из инерциальной системы отсчета в неинерциальную связан с изменением геометрии пространства- времени. Это справедливо при условиях: 1. Заданы из физических предположений тензоры скоростей деформаций. 2. Тензоры вихря. 3. Векторное поле 4-ускорения. Полученные уравнения структуры ограничивают область применимости GR Эйнштейна. Уравнения Максвелла требуют применения геометрии Римана в неинерциальных системах отсчета. Теория непосредственно не связана с GR Эйнштейна. Спасибо Александру Чепик за помощь в переводе.

Dear Alexander,  classical and neoclassical physics considers the privileged reference frame is pre-existent with respect to any physical event and on this account it becomes absolute.  In modern and postmodern physics there aren't privileged reference frames or in other words all reference frames are privileged similarly. In TR the reference frame is a necessity of observer in order to describe a physical event that pre-exists to the reference frame as opposed to classical and neoclassical physics. Because observer desires to describe a physical event he has to choose the suitable reference frame that allows him to understand and to describe the real physics of the event. This non-pre-existent reference frame, but chosen by the observer, is the privileged reference frame and it isn't unique in the universe but it depends on the considered physical event.

I think this example can contribute to clarify my thought: the fall of a body. If body falls on the earth, it is convenient that the earth's observer chooses a reference frame S[O,x,y,z,t] with the origin O placed in one point of the earth. If body falls on the moon (or other celestial system), it would be convenient  that observer and origin of the reference frame would be in one point of the moon. In the first case the privileged reference frame is the earth's reference frame, in the second case the privileged reference frame is the moon's reference frame. In the absence of moon's observer  the earth's observer isn't and cannot  be considered a privileged observer in order to observe and describe the fall of a body on the moon.

It is also interesting to observe because the fall of a body on the moon isn't observable QM denies the existence of that physical event.

Уважаемый Даниэле Сассо! Пожалуйста, добавьте вложение. Правда, мне пока трудно вести дискуссию. Языковый барьер.

S. A. Podosenov wrote on page  3.10

“Dear colleagues!

I proved the theorem. The transition from the inertial reference system in noninertial one is associated with changes in the geometry of space - time. This is true under the following conditions. It must be next data (from  of physical assumptions):

 1. tensors of rate of  strain.

 2. Tensors of the vortex.

 3. Vector field 4-acceleration.:

The derived equations of structure limits the range of applicability of Einstein's GR. Maxwell's equations require the use of Riemann geometry in non-inertial reference systems. The theory is not directly related to Einstein's General relativity. 

Thanks to Alexander Chepick for assistance in translation.“

 Dear Stanislav,

Since Your theory is not related to GR then there is no need in principle of relativity, i.e., in the same forms of laws, including for Maxwell's equations. Did you take it into account? Therefore, the appearance of Riemann geometry remains questionable.

Can we see a sample of the transformation in the simplest case, for example, for the Absolute Theory where transformation from allocated reference frame into IRF is:

AT: t'=t/γ; x'=x-Vt; y'=y; z'=z;  γ is the Lorentz factor.

The usual method easy obtains the coordinate transformation into a uniformly rotating reference frame (Ω around the axis OZ) with a fixed center.

 Denote  r2=x2+y2, and  cos φ=x/r; then the coordinate transformation should be:

t'=t/γ; φ'=φ - rΩt; r'=r; z'=z.

where γ =(1-r2Ω2/с2)-1/2.

Can you say what your method will do? (There are no spatial deformations; therefore the rate of deformation is absent.)

---

Поскольку Ваша теория не связана с GR, то нет необходимости в принципе относительности, то есть, в одинаковых формах законов, в том числе и для уравнений Максвелла. Вы это учитывали? Поэтому появление геометрии Римана остается «под вопросом».

Можно ли посмотреть пример вывода преобразований в простейшем случае, например, для абсолютных преобразований из выделенной СО в ИСО:

AT: t'=t/γ; x'=x-Vt; y'=y; z'=z;  γ- коэф. Лоренца.

Обычным методом можно просто получить преобразование координат в равномерно вращающуюся (с Ω вокруг оси OZ) систему отсчета с неподвижным центром.

Обозначим r2=x2+y2, cos φ=x/r; тогда преобразование должно быть таким:

t'=t/γ; φ'=φ - rΩt; r'=r; z'=z. где γ =(1-r2Ω2/с2)-1/2

Можно узнать, что получится вашим методом? (Здесь нет пространственных деформаций, поэтому  скорость деформации отсутствует.)

Dear Daniel

Thanks for the clarification.

S. A. Podosenov asks you to add an attachment.

"The absence of fact the moon landing" of Lunohod allowed him to descend to the moon. Then it sent the pictures of the lunar surface that also "was not exist". :)

 Likewise with Mars and Venus. 

--

Уважаемый Даниэль

Спасибо за разъяснения.

S.A. Podosenov просит вас добавить вложение.

«Отсутствие факта прилунения» лунохода позволило ему опуститься на Луну, и после этого передавать снимки «не существующей» лунной поверхности.   :)

Аналогично с Марсом и Венерой.

Dear Daniel

Principle of Reference : «Moreover the privileged observer has to be placed symmetrically inside this preferred reference frame."

To build a privileged reference system it is necessary to find a place relatively symmetric for multiple events occurring simultaneously, and therefore, the movement of such a reference system in the physical space will greatly depend on the position of the events. For example, consider the rotation of two bodies around of the third body with different angular velocities. In every moment these bodies will be in some points of space, therefore, these events are simultaneous.

A symmetrical position of a privileged observer "O" will be at the point of intersection of the perpendiculars constructed in the midpoints of the segments connecting bodies. So every time when all three bodies will be on the same straight line then the point "O" must escape to infinity, and in the reference frame of observer O this system of three bodies must escape to infinity in a finite time, i.e., with infinite speed and infinite acceleration! It is physically impossible, but else these three bodies must go to infinity in one direction, and at the same moment they must arise from the opposite direction. And this is despite the fact that in physical space these bodies move quietly on a circle with the ultimate speed without infinite accelerations!

Moreover, in general, for four or more simultaneous events it is impossible to construct a symmetric point, i.e., for 4 or more events a privileged reference frame does not exist. Therefore, more than three events cannot be considered in the privileged reference frame.

 Thus, I think that the Principle of Reference is completely wrong!

---

Для построения привилегированной системы отсчета необходимо найти симметричное место относительно нескольких событий, происходящих одновременно, следовательно, движение такой системы отсчета в физическом пространстве будет существенно зависеть от положения рассматриваемых событий. Например, рассмотрим вращение двух точечных тел вокруг третьего тела с разными угловыми скоростями.  В каждый момент эти тела будут находиться в каких-то точках пространства, следовательно, в этих положениях события будут одновременными.

А симметричное положение привилегированного наблюдателя «O» будет находиться в месте пересечения перпендикуляров, построенных в серединах отрезков, соединяющих тела. Тогда каждый раз, когда все три тела будут находиться на одной прямой, точка O должна убегать в бесконечность, а в системе отсчета наблюдателя O эта система из трех тел должна убегать в бесконечность за конечное время, то есть, с бесконечной скоростью и с бесконечным ускорением!  Мало того, что это физически невозможно, но эта тройка тел должна уйти в бесконечность в одном направлении, и в тот же миг она должна возникнуть с противоположного направлении. И это при том, что в физическом пространстве эти тела спокойно движутся по кругу с конечными скоростями и без бесконечных ускорений!

К тому же, в общем случае для четырех и более одновременных событий нельзя построить симметричную точку, то есть, для 4 и более событий не существует привилегированной системы отсчета. Следовательно, в привилегированных системах отсчета нельзя рассматривать более трех событий.

 Таким образом, Принцип Ссылки полностью неверен!

Dear Alexander, thank you for your criticism. In your interesting description I think you confuse the goemetrical concept of symmetry with the concept of barycentre. In the example with three bodies, the point of symmetry coincides with the centre of concentric circumferences that represent trajectories of other two rotating bodies and not with barycentre. For four or n bodies the same reasoning is valid if (n-1) bodies rotate round the first body.

I agree with Stanislav about the concept of surface of celestial bodies that "not would exist" in QM. With regard to attachment I think Stanislav asks the paper about the "Teoria dei Sistemi di Riferimento"

 Dear Daniel

Then you should clarify the Principle of reference – which symmetry should be used. From Fig.1.and explanations in the article, it follows that the symmetrical position of the observer must be in the center of the line segment connecting the position of a pair of simultaneous events or on the perpendiculars constructed in this midpointsts. If there are three or more events, position of the observer must be on the line of intersection of planes perpendicular to the midpoints of the segments. So for four events most often you can find such a point, and for five events and more almost never (I was mistaken when I said about the three events).

 Well, when the body revolve in a circle, then the center of the circle can be considered as some symmetry  . But if the motion is not circular. Even the ellipsoids have no symmetry; and if the process is more complex, or even chaotic, for example, many reflections of  two beams from the rotating mirrors, etc. In these cases, there is no symmetry .

I wasn't talking about the barycenter (center of mass of the system), but about the symmetric position of observer for position pairs of simultaneous events. And if these events are shifted due to the motion of the sources, then the privileged position of the observer must shift.

--

Уважаемый Даниэль.

Тогда вам следует уточнить Принцип ссылки – какая симметрия должна использоваться. Из Рис.1.и пояснений в статье следует, что положение симметричное положение наблюдателя должно находиться в центре отрезка, соединяющего положения пары одновременных событий. Если событий три или более, то положение наблюдателя должно быть на линии пересечения плоскостей перпендикулярным серединам отрезков. Поэтому для четырех событий чаще всего можно найти такую точку, а для пяти событий и более почти никогда (я ошибся, когда сказал о трех событиях).  Ну ладно, когда  тела вращаются по кругу,  то  можно симметрией считать центр круга. А если движение не круговое. Даже по эллипсам уже нет симметрии. А если процесс более сложный или вообще хаотичный, например, много отражений двух лучей от вращающихся зеркал, и т.п. В этих случаях вообще нет никакой  симметрии .

Я говорил не о барицентре (центре масс системы), а о симметричном положении наблюдателя для положения пары одновременных событий. И если эти события смещаются из-за движения источников, то и положение привилегированного наблюдателя должно смещаться. 

Dear colleagues! There is an opinion that for weak field GR corresponds to the gravitation of Newton. This view is mistaken. If the body rests on the surface of the Earth, according to Newton the sum of the forces equal to zero and the absolute acceleration is zero. Einstein body corresponds to the global line with non-zero acceleration. This acceleration is directed along the reaction forces of the support and opposite in sign to the free fall acceleration. And Vice versa. A freely falling body has according to Newton, the acceleration g. Einstein the body corresponds to a geodesic line with zero acceleration. What principle of conformity can be said?

Dear Andrè,

I deduce accelerated electrons emit electromagnetic energy just from Maxwell's equations. This effect is already present in literature. An electric current is composed of a flow of electrons. A constant electric current is characterized by electrons at constant speed and it doesn't generates an e.m. field and it doesn't emit e.m. energy. A variable electric current is characterized by electrons at variable speed and it emits e.m. energy generating an e.m. field as per the Maxwell's equations. A moving single electron is a small current (or nanocurrent) and at constant speed it doesn't emit e.m. energy. A single accelerated electron emits a small quantum of energy generating an e.m. nanofield (or e.m. nanowave) always as per M.E. for nanowaves. The only difference is that the variable current emits e.m. energy in continuous statistical shape while the single electron at variable speed emits e.m. energy in quantum shape. Just like electrons that emit an energy quantum when they transit from a level at greater energy to a level at smaller energy (as you say). However there are experimental evidences of that emission by accelerated charged particles, also in accelerators. This emission of e.m. energy by accelerated particles is an important point in the TR in order to define electrodynamic mass of particle

Dear Daniele,

The TR is based on new relativistic transformations of space-time.. is a very promising approach to an alternative to the theory of an expanding universe.

What is the relation of the "Theory of Reference Frames" to normalized complex Minkowski-coordinates u?

u=(t,i(x,y,z)) with the imaginary unit i leads to a finite, homogneous and isotropic geometry. We see that any displacement du in that geometry

given by u'=u+du can be written as u'=ln(exp(u)*exp(du)). The following five definitions contain more detaled explanations:

The exp and ln functions transform to and from quaternionic coordinate representations.

The finiteness is a consequence of the trigonometric meaning of the imaginary exponentiation and the resulting quaternion multiplication.

The metric du² is given by du²=dt²-dX².

dt is the time needed for the displacement.

t' in u' is given by t`=d+dt and represents the time after the displacement.

Is there any relation beween TR and complex Minkowski-coordinates?

Does TR also lead to a finite, homogeneous and isotropic geometry?

In a finite non expanding Universe a near equilibrium state of the cosmic microwave background and the temperature of all non radiating matter is statistically much more likely as in an non equilibrium state of an expanding universe.

Dear Wolfang,

you raise a very interesting question regarding the relation between the Theory of Reference Frames and Minkowski's spacetime metric. This metric is based on the definition of linear element du given by du2=dX2-c2dt2 in which dX2=dx12+dx22+dx32 and x1, x2, x3 are space coordinates. Minkowski reached the conclusion that space and time don't exist separately but the physical reality is represented by an inseparable unification of space and time. This concept was considered after by Einstein with some slight change.

In the Theory of Reference Frames (TR) instead space and time continue to be two independent realities: in fact we continue to measure space in metres and time in seconds while we know no method for measuring the inseparable spacetime. In TR the only connection between space and time is represented firstly by the concept of velocity and secondly by the concept of acceleration. In TR besides the empty space is 3D and it has properties of homogeneity and isotropy. In TR imaginary coordinates have no physical meaning while in Minkowski's metric the time coordinate is imaginary. We know in the dynamic analysis of physical systems imaginary solutions are possible but they are always in pair of imaginary and conjugate solutions that as per Eulero's relations give anyway a real solution. In Minkowski's metric instead complex numbers don't represent solutions in pair of conjugate complex numbers of a dynamic Mathematical model but they represent the point of start of the metric.

With regard to the structure of the universe, the TR formulates a hypothesis on the origin of the universe in which the universe wasn't generated by one bigbang but by the succession of subsequent stages starting from the zero stage.

Dear Daniele,

you mentioned "du²=dX²-c²dt²" and "..while in Minkowski's metric the time coordinate is imaginary.."

This definition leads to an imaginary spacetime distance for v

Dear Wolfang,

it is right, the relation du2=dX2-c2dt2 represents Minkowski's metric while the relation du2=dt2-dX2 represents Einstein's metric. We can do the following considerations on the two metrics:

1. In Minkowski's metric du, dX and cdt have the same physical dimensions (metres). Einstein's metric instead is sketchy on this question: in fact X has dimensions of a length while t has dimensions of a time. It follows that in some situations the same quantity u has dimensions of length and in others has dimensions of time. From my viewpoint this assumption isn't acceptable and indeed this assumption has opened the way for all scandalous processes of Mathematical normalization that are very frequent in the present physics.

2. Both metrics accept the basic element du can be real or imaginary (unreal) according to situations. In Minkowski's metric du is imaginary when dX2

Dear Daniele,

a very touchy point is the question if Einsteins metric leads to a space property, which only has an influence on displacements. It is the imagination of a constantly curved space, which has in any point and in all directions slightly divergent geodesics.The divergency is only noticeable for moving masses or moving energy and acts like a gravitational impact.

This would finally show, that Einstein was right with his cosmological constant.

Dear Wolfang,

the cosmological constant was introduced by Einstein in order to explain a static space. Afterwards the cosmological constant has assumed different meanings in the order of the theory of expansion of the universe. I think the model of the big bang and the subsequent theory of the uniform expansion of the universe doesn't represent efficiently the physical reality. I have described my viewpoint on the origin and on the evolution of the universe in my last papers. Anyway the main question regards always fundations of physics. In GR Einstein assumed the hypothesis that mass acts on the spacetime producing a curvature of the same. Geodetics in GR therefore are forced lines of spacetime in the presence of gravitational field. In TR instead mass doesn't act on the spacetime but it generates directly a gravitational field in every point of space and that field is constant if mass is constant. Only when a second mass, for instance a test mass, is placed inside the gravitational field produced by the first mass, there is an interaction, different from the Newtonian force at distance, between the primary gravitational field and the test mass that produces, if the test mass is free, a mouvement of the test mass that can be described by an equation with respect to space and to time. Geodetics in TR consequently aren't a property of the curved spacetime but they are lines that allow the object to move along a line of minimum energy. Therefore in TR geodetics aren't a static property of the spacetime, but they are a dynamical property of motion as per questions of energy.

Dear Daniele,

the conclusion of our discussion are indications for a spacetime with the property that the motion of mass and energy follows curved geodetics.

The remaining point is how to prove that the motion of energy can lead to red shift.

I think we cannot exclude the existence of the rectilinear motion. In that case geodetics aren't curved geodetics.

Yes rectilinear motion surely exists, the question is only if it is force free in a space with direction dependent curvature.

It is known the free fall happens along a rectilinear trajectory that is perpendicular to the Surface of the celestial body where the free happens. I see in this case no curvature.

The motion I had been talking about is over cosmic distances without influence of any masses.

Dear Wolfang,

I accept the theory of fields in which forces are always tangent to force lines of field. I didn't understand your last specification. If you are referring to curvature of spacetime predicted in General Relativity, then it happens only in the presence of masses. But perhaps I didn't understand your thought. Please do you can specify?? Thanks.

Dear Wolfang,

with regard to your question "The remaining point is how to prove that the motion of energy can lead to red shift", I think the motion of energy happens when energy is in wave shape. In that case the Doppler effect is able to explain well whether redshift or blueshift. Anyway I woud want to specify my considerations are always inside the Theory of Reference Frames that is critical towards mainstream theories (SR, GR, QM, SM). Regards.

Dear Daniele,

the base of my thought is that the spacetime displacement is given by:

u'=u+du=ln(exp(u)*exp(du)); exp(u) = quaternion

exp(u)= (exp(t)*(cos(|X|)/|X|, sin(|X|)/|X|*(ix,jy,kz))), [X=(x,y,z)),u=(t,iX)],

which leads for the displacements to a finite geometry of constant curvature.

The impact of the curvature is only visible for moving objects with mass or energy and is direction dependent in the sense that it is exactly the same for a movement from A to B and from B to A for any position A and B.

Would that be compatible with the Theory of Reference Frames?

Dear Wolfgang,

in the Theory of Reference Frames (TR) there isn't an entangled spacetime for which, as Minkowski wrote, "space and time are only shades and only a sort of union between the two concepts is real".

In TR instead space and time are two independent realities that we measure independently. In this view the Mathematical model of quaternion, that is an extension of complex numbers, is inappropriate in TR.

In TR the elementary linear displacement of the three-dimensional space is given by du2=dx2+dy2+dz2 and dt represents the elementary linear displacement of the one-dimensional time. These displacements are appropriate also for non-linear elementary displacements.

For non-elementary linear displacements we have

Delta(u)2= (x2-x1)2+(y2-y1)2+(z2-z1)2 and Delta(t)=t2-t1.

For non-linear and non-elementary displacements,the space displacement Delta(u') happens along the force line of the field that produces curvature of geodetics. In that case Delta(u')>Delta(u).

Do you can propose a calculation of Delta(u') in the order of the TR without considering quaternions? It would be very ineresting also for TR.

Dear Daniele,

after reading your paper about electromagnetism, my impression is, that there are no new relativistic transformations of space-time involved in your theory of reference frames. The validity of your theory only involves local space-time properties.

You wrote in your paper ".. Those equations nevertheless disregard the Lorentz force.." This is something I do not understand.

The only force in electromagnetism is the impact of an electric field on a electric charge. The Lorentz force is simply caused by an induced electric field, described by the law of induction, one of the Maxwell equations.

Why do you think, that the Lorentz force is disregarded?

Dear Wolfgang,

I prefer to distinguish the question of electromagnetism from the question of relativity.

With regard to the question of relativiti you claim in the Theory of Reference Frames there aren't new transformations of space and time. Probably you didn't read a few papers of mine in which I have demonstrated new transformations of space and time. For instance you can read

Article Relativistic Physics of Force Fields in the Space-Time-Mass Domain

or

Article Physico-Mathematical Fundamentals of the Theory of Reference Frames

With regard to the question of electromagnetism, it is known that the classical Group of four Maxwell's equations, due also to Heaveside, don't contain the equation of Lorentz's force F=qvxB, that gives the force acting on an elementary charged particle when with velocity v it goes into a field of magnetic induction B. I think this equation is very important but it isn't included into the classical Group of electromagnetism equations. And in fact in the paper that you read, I have replaced the equation divB=0 that effectively isn't a true equation but it is an always satisfied identity, with the equation of Lorentz's equation.

Dear Daniele,

indeed as mentioned up to now I only had read one of your papers.

Upon considering equation one in your first article I think there is an inconsistency in equation one. Your relation dt=m0/mdt should also be applied to the definition of v.

Concerning the Lorentz force

I had learned that the Lorentz force is redundant within the set of Maxwellian equations.

In the Wikipedia article about the Heaviside version of the Maxwell equations "A Dynamical Theory of the Electromagnetic Field" is an according comment to the fourth equation D) concerning the Lorentz force:

This Maxwellian electromotive force represents the effect of electric fields created by convection, induction,[5] and by electric charges.

Dear Wolfgang,

you are right, in fact the relation dt'=m'dt/m, in which m is the resting mass and m' is the moving mass, effectively is connected with the velocity v, only nevertheless for mass elementary particles, by the following relation m'=m(1-v2/2c2). It follows that the relation becomes dt'=(1-v2/2c2). For ordinary bodies instead m'=m and dt'=dt. For details abot this procedure you can see the second article

Article Physico-Mathematical Fundamentals of the Theory of Reference Frames

With regard to the Lorentz force, the question is controversial. In fact it is possible effectively to demonstrate the Lorentz force is connected with Faraday law, but it happens only in a particular case when the variation of the magnetic induction B is due to cut flux. In the general csse nevertheless this connection there isn't and consequently it is suitable to assume the Lorentz force is independent of the Maxwell classic equations.

Dear Daniele,

if you take into account V=dX/dt your equation 1 is simply:

P(x,y,z,t)=P'(x',y',z',t')+Integral(0,t) over dX

This defines a path integral and does not provide any arguments related to m0 and m'.

With regard to the Lorentz force you say, that the connection to Faradays law is only given in the case of cut flux. I assume you mean the case, when there is a movement perpendicular to the field lines of a static magnetic field.

But the Lorentz force (in Heaviside notation) is f=u(vxH)-dA/dt-grad P, which also includes the dynamic case with a non static magnetic field. And Faradays law also includes both cases, the induction caused by movement relative to magnetic field lines and induction caused by time varying magnetic fields.

This means the Lorentz force only reflects f=E with E as a sum of the gradient of the electric potential and the induced electric field.

Therefore taking into account the Lorentz force in addition to the Maxwell equations cannot lead to something new.

Dear Wolfgang,

with regard to transformations of space and time, that are valid in TR, the two equations (1) must be considered together and consequently the question that you raise is solved considering both equations and not only the first.

With regard to the Lorentz force, you are right. In that case nevertheless in Maxwell's equations it needs to replace the Faraday equation with the Lorentz force (in Heaviside notation). In my Group of electromagnetism equations, I have preferred instead to introduce the classical Lorentz equation and to mainain the classical Faraday equation. It a question of choices.

Let me take advantage of this comment for sending you Best Wishes for a Happy New Year.

Daniele