PRINCIPLE OF RELATIVITY – CRITICAL ANALYSIS (ПРИНЦИП НА ОТНОСИТЕЛНОСТ – КРИТИЧЕН АНАЛИЗ)

           Abstract  (МТ)  

          The definition of the Principle of relativity allows misleading inaccuracies, mixing analytical thinking with not so flawless sense ideas. In fact, this principle needs the unmasking. To the purpose I will show that the movement of two systems against each other (+v,-v) is tantamount to their movement in one direction (+v,+v), (-v,-v), is equivalent to rest between them (the state of the systems is not dependent on the inverting of (-v) in (+v) and vice versa). The given definition appears a hidden form of relative peace between systems.

GENERAL AND PRIVATE TASKS FOR TRANSFORMING OF COORDINATES AND TIME ( ОБЩА И ЧАСТНА ЗАДАЧИ ПРИ ТРАНСФОРМИРАНЕ НА КООРДИНАТИ И ВРЕМЕ)

Abstract: As is known, in the fixed system K and the inertial system K', which is moving towards it, the Lorentz transformations look like this (only for the abscissa and the time): x'=(x-v.t)/b ; t'=(t-v.x/c²)/b, where b=(1-v²/c²)^1/2. We will show here that these expressions are inaccurate as a result of inadmissible mixing of two separate tasks: 1) General task: To find the formulas for the transformation of random event (x, t) in event (x', t'). 2) Special task: To find the formulas for the transformation of the "light signal" event (x, t) in the "light signal" event (x', t'). The solving of problems 1 and 2 can not be uniting because the random events occur without connection between the coordinates and the time while the coordinates and the time of the signal obey the dependence: x_s=c.t_s ; x'_s=c.t'_s , where "s" is the signal index. Videlicet, in the case of a light signal the Lorentz transformations should be indexed: x'_s=(x_s -v.t_s)/b ; t'_s=(t_s -v.x_s/c²)/b. In this situation, since x_s=c.t_s ; x'_s=c.t'_s , they can now be solved to the final form: x'_s=a.x_s/b ; t'_s=a.t_s/b, where a=(1-v/c). Only now the index "s" should be removed, to obtain a solution of the general problem: x'=a.x/b ; t'=a.t/b. It is in these extreme formulas, each pair of x, t from system K would correspond to a pair of x', t' of system K'.

With this study will make a partial analysis (only of § 3) of article of A. Einstein dated 1905, from which to appear clearly where and how inconsistencies are admitted in deducing the Lorentz transformations (only for the abscissa and the time): x'=(x-v.t)/b ; t'=(t-v.x/c²)/b, where b=(1-v²/c²)^1/2. To be most accurate, will follow verbatim author’s text¹, and afford only to change the system (k) of K' and the speed of light V of c (dots indicate omitted text).

Let’s begin with direct citation of § 3: 

            "§ 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former

Let us.....take two systems of co-ordinates.....Let the axes of X of the two systems coincide, and their axes of Y and Z respectively be parallel.....Now to the origin of one of the two systems К' let a constant velocity v be imparted in the direction of the increasing x of the other stationary system K.....To any system of values x, y, z, t, which completely defines the place and time of an event in the stationary system, there belongs a system of values x', y', z', t', determining that event relatively to the system К', and our task is now to find the system of equations connecting these quantities."¹

            This part of the text condition is the general, basic task: To find the formulas for the transformation of random event (x, t) of a stationary system K, in event (x', t') by moving toward it inertial system K'. We will explicitly note that random events occur with no relation between the coordinates and time.

            Continuation follows, where points are confused:

"From the origin of system К' let a ray be emitted at the time t' along the X-axis.....For a ray of light.....x'=с.t'.....At the time t=t'=0, when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system K. If (x, y, z) be a point just attained by this wave, then x²+y²+z²=с².t². Transforming this equation with the aid of our equations of transformation we obtain.....x'²+y'²+z'²=с².t'²."¹

            This part of text condition presents the special task: To convert the coordinates and time of a light signal. Here we have to emphasize that these coordinates and time of signal are subject to the known dependence: x_s=с.t_s ; x'_s=с.t'_s.

            Theory is ignorant for these two separate problems. It does not realize that the particular case should be different marked by the general case, since the condition with the independent (freely elective) parameters of random events and the condition with interdependent parameters of the event "light signal" simply cannot be merged into a single condition. That aggregation, if performed, will represent arranging of circumstances created by the mind leading points outside of the limits of reality.

Theory, however, using the same markings, starts just on this route of self-delusion and arrange "general" dependencies: x'=с.t' ; x'²+y'²+z'²=с²t'² and x=с.t ; x²+y²+z²=с²t². While the undeniable truth is that these links will be true and will apply only under indexation "s" of the light signal, i.e. Lorentz transformations known to us are nothing more than private relationships and they has to be written like this: x'_s=(x_s-v.t_s)/b ; t'_s=(t_s-v.x_s/c²)/b . However, these equations transforming only the parameters of the light signal are not solved to the end. Since there are links x_s=с.t_s ; x'_s=с.t'_s, they apparently must be rationalized to the final form: x'_s=a.x_s/b ; t'_s=a.t_s/b, where a=(1-v/c). Only now the index "s" should be removed, to obtain a solution of the general problem: x'=a.x/b ; t'=a.t/b. It is in these extreme formulas, each pair of x, t from system K would correspond to a pair of x', t' of system K'.

It remains to clarify one more important detail. For this purpose let set aside the indexation and to write transformations as given by the theory: x'=(x-v.t)/b ; t'=(t-v.x/c²)/b. Now let’s think on the meaning of the terms in parentheses. As we know, the presence of factor v.t in the conclusion for x' and factor v.x/c² in the conclusion of t' is interpreted by physics as some inseparable intertwining of spatial and time dimensions, so math stop here. In fact, within specified combinations there’s nothing unusual. Just up to moment t, beginning O' of system K' is shifting from the beginning O of system K at a distance v.t , which the signal travels for time v.x/c² or (v/c).(x/c) or. (v/c).t ..

From the equivalent format: x'=(x-Δx)/b ; t'=(t-Δt)/b, where Δx=v.t, Δt=v.x/c² and Δx/Δt=c, it becomes obvious the fact that the very transformations eliminate displacement of systems through the corrections: x_cor=x-Δx ; t_cor=t-Δt and x'=x_cor/b ; t'=t_cor/b, i.e. there is performed a comparison of the parameters of the systems in matched beginning, but keeping all the changes caused by the movement.

Ultimately, we can summarize those transformations given by the theory as a result of confusion rise incorrect, speculative suggestions and ideas about reality.

  

             Reference

1. A. Einstein – ON THE ELECTRODYNAMICS OF MOVING BODIES

http://www.fourmilab.ch/etexts/einstein/specrel/www/

ОБЩА И ЧАСТНА ЗАДАЧИ ПРИ ТРАНСФОРМИРАНЕ НА

КООРДИНАТИ И ВРЕМЕ

Резюме: Както е известно, при неподвижна система K и движеща се спрямо нея инерциална система К', Лоренцовите трансформации изглеждат така (само за абцисата и времето): x'=(x-v.t)/b ; t'=(t-v.x/c²)/b, където b=(1-v²/c²)^1/2. Тук ще покажем, че тези изрази са неточни като резултат от недопустимо смесване на две отделни задачи: 1) Обща задача: Да се намерят формулите за преобразуване на произволно събитие (x, t), в събитие (x', t'). 2) Частна задача: Да се намерят формулите за преобразуване на събитието „светлинен сигнал“ (x, t), в събитие „светлинен сигнал“ (x', t'). Решаването на задачаи 1 и 2 не може да се обедини, понеже произволните събития се случват без обвързаност между координатите и времето, докато координатите и времето на сигнала се подчиняват на зависимостта: x_с=c.t_с ; x'_с=c.t'_с , където „с“ е индексът за сигнала. Сиреч, в случая със светлинен сигнал Лоренцовите трансформации трябва да се индексират: x'_с=(x_с-v.t_с)/b ; t'_с=(t_с-v.x_с/c²)/b. При това положение, понеже x_с=c.t_с ; x'_с=c.t'_с, те вече могат да се решат до крайната форма: x'_с=a.x_с/b ; t'_с=a.t_с/b, където a=(1-v/c). Едва сега индексът „s“ следва да отпадне, за да се получи решението на общата задача: x'=a.x/b ; t'=a.t/b. Именно по тези крайни формули, на всяка двойка x,t от система К ще съответства двойка x',t' от система К'. 

Ще се спра отново на днешната проблемна трансформация на координати и време, с цитиране (без да превеждам) на оригиналната статия "A. Einstein – ON THE ELECTRODYNAMICS OF MOVING BODIES, 1905г" (http://www.fourmilab.ch/etexts/einstein/specrel/www/). Ще си позволя само да променя система (k) на К' с параметри x', y', z', t' и скоростта на светлината от V на с (многоточията означават пропуснат текст).

"§ 3. Theory of the Transformation of Co-ordinates and Times from a Stationary System to another System in Uniform Motion of Translation Relatively to the Former

Let us.....take two systems of co-ordinates.....Let the axes of X of the two systems coincide, and their axes of Y and Z respectively be parallel.....Now to the origin of one of the two systems К' let a constant velocity v be imparted in the direction of the increasing x of the other stationary system K.....To any system of values x, y, z, t, which completely defines the place and time of an event in the stationary system, there belongs a system of values x', y', z', t', determining that event relatively to the system К', and our task is now to find the system of equations connecting these quantities."

Същият текст на руски (http://path-2.narod.ru/02/03/kedt.pdf).

"§ 3. Теория преобразования координат и времени от покоящейся системы к системе, равномерно и прямолинейно движущейся относительно первой

Пусть.....даны две координатные системы.....Пусть оси X обеих систем совпадают.....Пусть теперь началу координат одной из этих систем К' сообщается.....скорость v в направлении возрастающих значений x другой, покоящейся системы K.....Каждому набору значений x, y, z, t, которые.....определяют место и время событий в покоящейся системе, соответствует набор значений x', y', z', t', устанавливающий это событие в системе К', и теперь необходимо найти систему уравнении, связывающих эти величины."

Тази част на текстовото условие представя общата и главна задача на Теорията: да се намерят формулите за преобразуване на произволно събитие (x, y, z, t) от система K в събитие (x', y', z', t') от система К'. Нека напомня, че произволните събития се случват без обвързаност между координати и време.

Следва продължението (където постановката тотално се обърква):

"From the origin of system К' let a ray be emitted at the time t' along the X-axis.....For a ray of light.....x'=с.t'.....At the time t=t'=0, when the origin of the co-ordinates is common to the two systems, let a spherical wave be emitted therefrom, and be propagated with the velocity c in system K. If (x, y, z) be a point just attained by this wave, then x²+y²+z²=с²t². Transforming this equation with the aid of our equations of transformation we obtain.....x'²+y'²+z'²=с².t'²".

Същият текст на руски (http://path-2.narod.ru/02/03/kedt.pdf).
"Пусть из начала координат системы К' в момент времени t' посылается луч света вдоль оси X.....Для луча света.....имеем x'=с.t'.....пусть в момент времени t=t'=0 из общего.....для обеих систем начала координат посылается сферическая волна, которая распространяется в системе  K со скоростью с. Если (x, y, z) есть точка, в которую приходит эта волна, то.....имеем: x²+y²+z²=с²t². Преобразуем.....с формул преобразования; тогда получим: x'²+y'²+z'²=с²t'²."

Тази част от текстовото условие представя частната помощна задача на Теорията: преобразуване на координатите и времето на светлинен сигнал (частното решение служи за преход към общото). Тук се налага да изтъкна, че събитието "светлинен сигнал" се подчинява на строга зависимост между координати и време.

Видно е, че Теорията не схваща посочените две отделни задачи и, прекрачвайки отвъд реалноста, вкарва тяхното решаване под един знаменател – този на зависимостите: x'=с.t' ; x²+y²+z²=с²t² и т.н. (самозаблуда, внушаваща умозрението за единно пространство-време). Докато неоспоримата истина е, че тези връзки са в сила единствено за светлинния сигнал, че ще са верни само под негова индексация, да речем (x_с, y_с, z_с, t_с): x_с'=с.t_с' ; x_с²+y_с²+z_с²=с²t_с² и т.н. Фактически Лоренцовите трансформации са: x_с'=(x_с-v.t_с)/b ; t_с'=(t_с-v.x_c/c²)/b – уравнения, преобразувщи само параметрите на светлинния сигнал. При това, нерешени докрай, подлежащи на още операции до окончателния си вид: x_с'=a.x_с/b ; t_с'=a.t_с/b , където a=(1-v/c) ; b=(1-v²/c²)^1/2 (същото се вижда и от трансформацията t'=[t-(v/c²).x]/b, която всъщност е t'=[t-(v/c).(x/c)]/b или t'=(1-v/c).t/b). Т.е. изкривените и половинчати трактовки на Теорията не стават за преобразуване на произволни събития. Другото е диктат на обременена, настояваща за вярване рутинност, видимо задъхваща се в похода за повече Наука

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Александър Николов © 2010-2016 Всички права запазени (COPYRIGHT © 2010-2016).

RELATIVE MISUNDERSTANDINGS (РЕЛАТИВНИ НЕДОРАЗУМЕНИЯ)

Трябва дебело да подчертаем, че Релативната теория решава само частната задача за координатите и времето на светлинен сигнал, изхождайки от неговите гранично точни връзки: радиусвектор R_с=с.t_с ; R'_с=с.t'_с  и (с.t_с)²=x_с²+y_с²+z_с² ; (с.t'_с)²=x'_с²+y'_с²+z'_с² като единно за системи К и K' геометрично място на челата на сигналите от общото начало O'=O. Физиката обаче се нуждае от решение за общия случай на произволните събития с параметри x, y, z, t. Тук уподобяването R=V.t (където V е съизмерима с v) е безпредметно...субординацията (V.t)²=x²+y²+z², като геометрично място на тяхното случване, не съществува. Но дори и да е възможна, приложеното от Теорията механично заместване на обобщената величина (V.t) с частната (с.t_с) във вида (с.t_с)²=x²+y²+z² е изцяло некоректно. Тази компилация ще е вярна пак и пак само за светлинен сигнал. Т.е. (с.t_с)²=x²+y²+z² в действителност е (с.t_с)²=x_с²+y_с²+z_с², което означава, че Релативната теория все още няма трансформации за общия случай на преобразуване на произволни събития.

ABOUT THE CORRECT FORM OF LORENTZ TRANSFORMATIONS (ЗА КОРЕКТНАТА ФОРМА НА ЛОРЕНЦОВИТЕ ТРАНСФОРМАЦИИ

Abstract  (MT)

(ABOUT THE CORRECT FORM OF LORENTZ TRANSFORMATIONS) We are facing the task to transform arbitrary coordinate x and time t of the stationary system K in moving system K' and vice versa. Its direct solution is impossible as x, t of K we measure with scales K and x', t' of K' – with scales K', with no connection between the two measurements. For the realization of such a link, we are introducing a light signal whose unchanging speed is a scale, united for both systems. But x, t and x', t' are independent in the general case, while, at the signal, they are bound in the form: x_с=c.t_с and x'_с=c.t'_с. We therefore have necessarily a distinguishable between controls and fields. However, the relative theory only works with ones indications on what passes for a regime of arbitrary x, t ; x', t' in a regime of interdependence x=c.t  x'=c.t' and comes back as it sees fit. From here, result essential misunderstandings.

ANATOMY OF LORENTZ TRANSFORMATIONS (АНАТОМИЯ НА ЛОРЕНЦОВИТЕ ТРАНСФОРМАЦИИ)

           Abstract     (МТ)    

      To working out of the Lorentz transformations, we must deal with two tasks in strict technological sequence: First we need to solve the auxiliary private task: Converting of the coordinates and time of the particular event "light signal" from system K in system K' (and vice versa). Then we need to solve the main common task: Converting of the coordinates and time of arbitrarily event from system K in system K' (and vice versa). The second decision constitutes generalizing of the reached private conclusions. Of exceptional importance is these two steps meticulously to distinguish since, in the stage of the private solving, the quantities x, t and x', t' are parameters of the light signal, thus they are directly bound to the dependences x=c.t, x'=c.t . While, in generalizing of the private solutions, the quantities x, t already are arbitrarily parameters of arbitrarily event. And because there has been a private task the mathematical rules require its solving to bring to an end. Only then becomes possible the wanted generalization of the conclusions.

           After the made clarifications, already we can objectively to estimate that the Relative theory is not quite clearly with these hard marks. In particular, the Theory expectedly starts in the way of solving of the private task (no alternative approach). Applying the dependencies x=c.t, x'=c.t', it reaches to the following equations (replace b=(1-v2/c2)1/2): <<x'=(x-vt)/b ; t'=(t-vx/c2)/b - viewpoint K' (1)>>. Here, contrary to all rules and without justifications the Theory terminates the further rationalization wantonly declaring that equations (1) are wanted most general transformations to transfer of an arbitrarily coordinates and time from one system to another. And, in fact, the operating procedure is still in the regime of solving of the private task since mathematical operations are clearly not exhausted. I.e. at expressions (1) continues to be in force the private connection x=c.t. With its application the same expressions take on the type (replace a=1-v/c): <<x'=(a.x)/b ; t'=(a.t)/b - viewpoint K' (2)>>. Formulas (2) are the final decision of the private task. Only now we have the right to move on to the second step - to generalizing conclusions (2) already as a solution of the common task. With this the purpose of the assignment can be considered definitively achieved.