You get three different possible answers.
It's devoid of common sense.
Three Experiments Challenging SRT
- Thread starter Masterov
- Start date
It's devoid of common sense.
If you are thinking in terms of different frames, then you may get three different answers that are related by Lorentz transformations, describing relativitsic effects on the screen itself. They will not be incompatible with one another.
For simplicity, if different observers all flash light pulses onto the same point on a screen, then the order in which the flashes reach the screen is the same in all reference frames (as long as the screen itself is not moving faster than the speed of light).
In relativity, the order in which any two events occur is always the same (it is frame independent) as long as communication between the two events is possible at less than the speed of light. It is true that relativity has some implications for causality. But this has been studied, and the result we know is that there are no causality problems as long as faster than light communication is not possible.
You know, it's obvious that's been your only real argument against SRT since the beginning. On this you have simply been outvoted: most physicists do not think SRT is so obviously foolish.
Who the frig is Morly?
Morley as in Michelson and Morley. He uses a English Russian translation program and many things don't translate clearly...
In some cases there may not have been enough clarity to start with.
SRT destroys the human brain.
A smart man grow stupid and are lost talent to think logically.
___________________________
Let the left-observer projected onto the screen red picture-area.
Let the right-observer projected onto the screen blue picture-area with the same frequency.
Let the screen have a device, which will define a frequency of the picture-area: if the frequency of the reds are above - a red light flash.
If higher frequency the blues - a blue light flash.
The Left should see the red light flash.
The Right should see the blue light flash.
What light will actually and - why?
=========================================
СТО разрушает человеческий мозг.
Умный человек глупеет и теряет талант мыслить логически.
___________________________
Пусть Левый наблюдатель проецирует на экран красные кадры.
Пусть Правый наблюдатель проецирует на экран синие кадры с той же частотой.
Пусть экрана имеет устройство, которое будет определять частоту кадров: если частота красных выше – загорается красная лампочка.
Если более высокая частота голубых кадров - загорается голубая лампочка.
Левые должны увидеть, что загорелась красная лампочка.
Правый должны увидеть, что загорелась синяя лампочка.
Какой свет будет на самом деле и - почему?
A smart man grow stupid and are lost talent to think logically.
___________________________
Let the left-observer projected onto the screen red picture-area.
Let the right-observer projected onto the screen blue picture-area with the same frequency.
Let the screen have a device, which will define a frequency of the picture-area: if the frequency of the reds are above - a red light flash.
If higher frequency the blues - a blue light flash.
The Left should see the red light flash.
The Right should see the blue light flash.
What light will actually and - why?
=========================================
СТО разрушает человеческий мозг.
Умный человек глупеет и теряет талант мыслить логически.
___________________________
Пусть Левый наблюдатель проецирует на экран красные кадры.
Пусть Правый наблюдатель проецирует на экран синие кадры с той же частотой.
Пусть экрана имеет устройство, которое будет определять частоту кадров: если частота красных выше – загорается красная лампочка.
Если более высокая частота голубых кадров - загорается голубая лампочка.
Левые должны увидеть, что загорелась красная лампочка.
Правый должны увидеть, что загорелась синяя лампочка.
Какой свет будет на самом деле и - почему?
Last edited:
Masterov, your thought experiment sounds interesting but it is very difficullt to understand it clearly.
possibly if you are willing we can thrash it out so that in English it reads better and clearer?
Suggestion:
If you could post the Russian version of "full text" here I will work on a translation to English for you...
I have a friend who is native Russian speaker who may be able to assist in translation.
example your dialogue above in Russian:
Пусть левая наблюдателя проецируется на экран изображение красной области.
Пусть правом наблюдателя проецируется на экран синего картинка-зона с той же частотой.
Пусть экрана есть устройство, которое будет определять частоту картинка площадь: если частота красных выше - красные вспышки света.
Если более высокая частота блюз - голубая вспышка света.
Левые должны увидеть красные вспышки света.
Право должны увидеть синим светом.
Какой свет будет на самом деле и - почему?
=================
My offer:
Маsterov, ваш мысленный эксперимент звучит интересно, но это очень difficullt, чтобы понять это ясно.
возможно, если вы готовы, мы можем бить его так, что в английском языке он читает лучше и яснее?
Предложение:
Если бы вы могли разместить русской версии "полный текст" Здесь я буду работать над переводом на английский для вас ...
У меня есть друг, который является родным русским языком, которые могут быть в состоянии помочь в переводе.
Here's more:
Suppose that there are two identical planets that fly away from each other at a constant speed.
Let one traveler (of one of planets) migrated.
If there is a delay of time, then the time traveler will slow.
Let the traveler returns to the first planet.
Then his time slow again, because the problem back to the original problem.
Traveler will live on their own planet and will have double time dilation: all atoms of body of this to change spectra and other nonsense with it should be.
Do you believe it?
Are you willing to accept it?
_____________________________________
Вот ещё:
Пусть существуют две одинаковые планеты, которые улетают друг от друга с постоянной скоростью.
Пусть с одной из планет на другую перелетел путешественник.
Если существует замедление времени, тогда время путешественника замедлится.
Пусть путешественник возвращается на первую планету.
Тогда его время замедлится ещё раз, поскольку задача вернулась к исходной.
Путешественник будет жить на своей планете и его время будет дважды замедлено.
Атомы в его теле изменят свои спектры и прочая чушь с ним должна случиться.
Вы в это верите?
Вы готовы это принять?
Suppose that there are two identical planets that fly away from each other at a constant speed.
Let one traveler (of one of planets) migrated.
If there is a delay of time, then the time traveler will slow.
Let the traveler returns to the first planet.
Then his time slow again, because the problem back to the original problem.
Traveler will live on their own planet and will have double time dilation: all atoms of body of this to change spectra and other nonsense with it should be.
Do you believe it?
Are you willing to accept it?
_____________________________________
Вот ещё:
Пусть существуют две одинаковые планеты, которые улетают друг от друга с постоянной скоростью.
Пусть с одной из планет на другую перелетел путешественник.
Если существует замедление времени, тогда время путешественника замедлится.
Пусть путешественник возвращается на первую планету.
Тогда его время замедлится ещё раз, поскольку задача вернулась к исходной.
Путешественник будет жить на своей планете и его время будет дважды замедлено.
Атомы в его теле изменят свои спектры и прочая чушь с ним должна случиться.
Вы в это верите?
Вы готовы это принять?
Thank you for wanting to help me.
I will post and russian-text and my version of english.
(I have already added the Russian text above.)
In the future, I will be publish two versions of my texts.
And if you do it will be easy, correct my english-text.
So I quickly learned how to write the English language correctly.
====================================
Ñïàñèáî çà æåëàíèå ïîìî÷ü ìíå.
ß áóäó ðàçìåùàòü è ðóññêèé òåêñò è ìîé âàðèàíò àíãëèéñêîãî.
(ß óæå äîáàâèë ðóññêèé òåêñò âûøå.)
 äàëüíåéøåì ÿ áóäó äâà âàðèàíòà òåêñòà ïîñòèòü.
È åñëè âàì ýòî áóäåò íåòðóäíî, èñïðàâëÿéòå ìîé àíãëèéñêèé òåêñò.
Òàê ÿ áûñòðåå íàó÷óñü ïèñàòü íà àíãëèéñêîì ÿçûêå ãðàìîòíî.
And here's more:
Two of the planet and traveler again.
But the traveler does not return to the first planet, and started with the second planet in any direction.
How will be change time of his?
The rate of flow of time of the traveler will depend on the direction in which the traveler started (which violates the isotropy of space): If he will fly towards the home planet - its time will be speed-up, otherwise on the home planet time of his will be slow.
If the traveler starts in the opposite direction, then time of his will slow down, because its speed relative to the first planet will be increases.
How to change the speed of the flow of time travel in other directions?
I do not know the answer.
Thus, time dilation leads to the anisotropy of the space, and this anisotropy becomes ambiguous: for observers in different inertial frames of reference, this anisotropy will be different.
=============================
И вот еще:
Опять: две планеты и путешественник.
Но путешественник не возвращается на первую планету, а стартует со второй планеты в произвольном направлении.
Как изменится его время?
Скорость течения времени путешественника будет зависеть от направления, в котором стартовал путешественник со второй планеты (что нарушает изотропию пространства): если он полетит в сторону родной планеты – его время ускорится, иначе на родной планете его время будет замедленным.
Если путешественник стартует в противоположном направлении, тогда его время будет замедляться, т.к. его скорость по отношению к первой планете возрастёт.
А как изменится скорость течения времени путешественника по другим направлениям?
Я ответа не знаю.
Таким образом, замедление времени приводит к возникновению анизотропии пространства, причём эта анизотропия становится неоднозначной: для наблюдателей в разных инерциальных системах отсчёта эта анизотропия будет разной..
Two of the planet and traveler again.
But the traveler does not return to the first planet, and started with the second planet in any direction.
How will be change time of his?
The rate of flow of time of the traveler will depend on the direction in which the traveler started (which violates the isotropy of space): If he will fly towards the home planet - its time will be speed-up, otherwise on the home planet time of his will be slow.
If the traveler starts in the opposite direction, then time of his will slow down, because its speed relative to the first planet will be increases.
How to change the speed of the flow of time travel in other directions?
I do not know the answer.
Thus, time dilation leads to the anisotropy of the space, and this anisotropy becomes ambiguous: for observers in different inertial frames of reference, this anisotropy will be different.
=============================
И вот еще:
Опять: две планеты и путешественник.
Но путешественник не возвращается на первую планету, а стартует со второй планеты в произвольном направлении.
Как изменится его время?
Скорость течения времени путешественника будет зависеть от направления, в котором стартовал путешественник со второй планеты (что нарушает изотропию пространства): если он полетит в сторону родной планеты – его время ускорится, иначе на родной планете его время будет замедленным.
Если путешественник стартует в противоположном направлении, тогда его время будет замедляться, т.к. его скорость по отношению к первой планете возрастёт.
А как изменится скорость течения времени путешественника по другим направлениям?
Я ответа не знаю.
Таким образом, замедление времени приводит к возникновению анизотропии пространства, причём эта анизотропия становится неоднозначной: для наблюдателей в разных инерциальных системах отсчёта эта анизотропия будет разной..
I can create many different stories with the traveler who throws out the window the clock, and every time started from the clock in different directions. But each time his journey ends on the home planet.
If the time-dilation exist, then the astronaut returns to his planet with his own time, the time-dilation of which it is impossible to calculate.
================================
Ìîæíî ïðèäóìàòü åù¸ ìíîãî ðàçíûõ èñòîðèé ñ ïóòåøåñòâåííèêîì, êîòîðûé â èëëþìèíàòîð âûáðàñûâàåò ÷àñû, è êàæäûé ðàç óäàëÿÿñü îò ýòèõ ÷àñîâ â ðàçëè÷íûõ íàïðàâëåíèÿõ. Íî ïðè ýòîì êàæäûé ðàç åãî ïóòåøåñòâèå çàêàí÷èâàåòñÿ íà ðîäíîé ïëàíåòå.
Åñëè ñóùåñòâóåò çàìåäëåíèå âðåìåíè, òî êîñìîíàâò âåðí¸òñÿ íà ñâîþ ïëàíåòó ñî ñâîèì ñîáñòâåííûì âðåìåíåì, ñêîðîñòü òå÷åíèÿ êîòîðîãî ïîñ÷èòàòü íåâîçìîæíî.
If the time-dilation exist, then the astronaut returns to his planet with his own time, the time-dilation of which it is impossible to calculate.
================================
Ìîæíî ïðèäóìàòü åù¸ ìíîãî ðàçíûõ èñòîðèé ñ ïóòåøåñòâåííèêîì, êîòîðûé â èëëþìèíàòîð âûáðàñûâàåò ÷àñû, è êàæäûé ðàç óäàëÿÿñü îò ýòèõ ÷àñîâ â ðàçëè÷íûõ íàïðàâëåíèÿõ. Íî ïðè ýòîì êàæäûé ðàç åãî ïóòåøåñòâèå çàêàí÷èâàåòñÿ íà ðîäíîé ïëàíåòå.
Åñëè ñóùåñòâóåò çàìåäëåíèå âðåìåíè, òî êîñìîíàâò âåðí¸òñÿ íà ñâîþ ïëàíåòó ñî ñâîèì ñîáñòâåííûì âðåìåíåì, ñêîðîñòü òå÷åíèÿ êîòîðîãî ïîñ÷èòàòü íåâîçìîæíî.
As I was able to get rid of the time-dilation?
Answer: I reduced all space-time scale of SRT in all directions equally (on $$\sqrt{1-v^2/c^2}$$).
SRT:
$$\Delta x'=\Delta x\sqrt{1-v^2/c^2}$$
$$\Delta y'=\Delta y$$
$$\Delta z'=\Delta z$$
$$\Delta t'=\Delta t/\sqrt{1-v^2/c^2}$$
MT:
$$\Delta x'=\Delta x\sqrt{1-v^2/c^2}\ \times\ \sqrt{1-v^2/c^2}=\Delta x\(1-v^2/c^2)$$
$$\Delta y'=\Delta y\ \times\ \sqrt{1-v^2/c^2}=\Delta y\sqrt{1-v^2/c^2}$$
$$\Delta z'=\Delta z\ \times\ \sqrt{1-v^2/c^2}=\Delta z\sqrt{1-v^2/c^2}$$
$$\Delta t'=\Delta t/\sqrt{1-v^2/c^2}\ \times\ \sqrt{1-v^2/c^2}=\Delta t$$
=======================
Как я смог избавиться от замедления времени?
Ответ: я уменьшил все четыре релятивистских масштаба SRT во всех направлениях одинаково, пропорционально (на $$\sqrt{1-v^2/c^2}$$).
Answer: I reduced all space-time scale of SRT in all directions equally (on $$\sqrt{1-v^2/c^2}$$).
SRT:
$$\Delta x'=\Delta x\sqrt{1-v^2/c^2}$$
$$\Delta y'=\Delta y$$
$$\Delta z'=\Delta z$$
$$\Delta t'=\Delta t/\sqrt{1-v^2/c^2}$$
MT:
$$\Delta x'=\Delta x\sqrt{1-v^2/c^2}\ \times\ \sqrt{1-v^2/c^2}=\Delta x\(1-v^2/c^2)$$
$$\Delta y'=\Delta y\ \times\ \sqrt{1-v^2/c^2}=\Delta y\sqrt{1-v^2/c^2}$$
$$\Delta z'=\Delta z\ \times\ \sqrt{1-v^2/c^2}=\Delta z\sqrt{1-v^2/c^2}$$
$$\Delta t'=\Delta t/\sqrt{1-v^2/c^2}\ \times\ \sqrt{1-v^2/c^2}=\Delta t$$
=======================
Как я смог избавиться от замедления времени?
Ответ: я уменьшил все четыре релятивистских масштаба SRT во всех направлениях одинаково, пропорционально (на $$\sqrt{1-v^2/c^2}$$).
Last edited:
LT:
$$x'=\frac{x-vt}{\sqrt{1-v^2/c^2}}$$ - Why are increased the spatial-scale?
$$y'=y$$
$$z'=z$$
$$t'=\frac{t-vx/c^2}{\sqrt{1-v^2/c^2}}$$
MT (for visual ccordinates):
$$x'=(x-vt)(1-v^2/c^2)$$
$$y'=y\sqrt{1-v^2/c^2}$$
$$z'=z\sqrt{1-v^2/c^2}$$
$$t'=t-vx/c^2$$
I'm not assured.
$$x$$ - real coordinate
$$x'$$ - visual coordinate
$$V=\frac{dx}{dt}$$ - real speed
$$dx'=(dx-vdt)(1-v^2/c^2)$$
$$\frac{dx'}{dt}=(V-v)(1-v^2/c^2)$$
$$dt'=dt-vdx/c^2$$
$$\frac{dt'}{dt}=1-vV/c^2$$
$$V'=\frac{dx'}{dt'}=\frac{dx'}{dt}\frac{dt}{dt'}=(V-v)\frac{1-v^2/c^2}{1-vV/c^2}$$ - visual speed
$$x'=\frac{x-vt}{\sqrt{1-v^2/c^2}}$$ - Why are increased the spatial-scale?
$$y'=y$$
$$z'=z$$
$$t'=\frac{t-vx/c^2}{\sqrt{1-v^2/c^2}}$$
MT (for visual ccordinates):
$$x'=(x-vt)(1-v^2/c^2)$$
$$y'=y\sqrt{1-v^2/c^2}$$
$$z'=z\sqrt{1-v^2/c^2}$$
$$t'=t-vx/c^2$$
I'm not assured.
$$x$$ - real coordinate
$$x'$$ - visual coordinate
$$V=\frac{dx}{dt}$$ - real speed
$$dx'=(dx-vdt)(1-v^2/c^2)$$
$$\frac{dx'}{dt}=(V-v)(1-v^2/c^2)$$
$$dt'=dt-vdx/c^2$$
$$\frac{dt'}{dt}=1-vV/c^2$$
$$V'=\frac{dx'}{dt'}=\frac{dx'}{dt}\frac{dt}{dt'}=(V-v)\frac{1-v^2/c^2}{1-vV/c^2}$$ - visual speed
Last edited:
The offer only applied to the post it refers to... I am not going to translate every post you make.
The Russian text relating to the first post has to be more detailed and descriptive as it doesn't appear to be specific enough to make a valid assessment.
===========
Предложение распространяется только на POST это относится к ... Я не собираюсь переводить каждый пост вы делаете.
Русский текст для первого поста должно быть более подробными и информативными, он не появляется, чтобы быть достаточно конкретным, чтобы внести весомый оценки.
The Russian text relating to the first post has to be more detailed and descriptive as it doesn't appear to be specific enough to make a valid assessment.
===========
Предложение распространяется только на POST это относится к ... Я не собираюсь переводить каждый пост вы делаете.
Русский текст для первого поста должно быть более подробными и информативными, он не появляется, чтобы быть достаточно конкретным, чтобы внести весомый оценки.
This is silly. SRT essentially just takes the idea of rotational symmetry and generalises it to a rotation-like symmetry in spacetime. For anyone who understands that structure, it is trivial to understand that SRT is logically self-consistent.
Is there any significance to the screens being "red" and "blue"?
If not, this is not complicated. If the left and right observers emit the same frequency in their rest frames, and they are moving toward or away from the screens with the same velocity, then neither light will flash because the Doppler shifts are the same, so the frequencies reaching the screens will be the same.
If the velocities are different, then you need to account for the Doppler effect. Which light flashes will depend on which observer is moving toward or away from the screens the fastest. Either way, there will be only one answer. There is no paradox of any kind here.
This is another trivial one. The error is here:
This argument is invalid. Relativity predicts no such thing. As viewed from the original planet, the traveller's velocity reduces to zero and his time dilation rate becomes 1. It is really that simple.
This argument seems to be a manifestation of your confusion with reciprocity of time dilation. As I [POST=2975943]already explained[/POST], you are having this problem because you are ignoring the relativity of simultaneity effect. A consequence of this effect is that if observer B is time dilated by a factor $$\lambda$$ compared with A, and C is time dilated by a factor $$\mu$$ compared with B, you can not claim that C is dilated by a factor $$\lambda \mu$$ compared with A. In particular, you cannot conclude that an observer is time dilated by a factor $$1 / (1 \,-\, v^{2}/c^{2})$$ compared with himself.
This one also doesn't follow through. In the first planet's rest frame, there is no violation of isotropy because the situation is not isotropic to begin with: the traveller starts from the second planet, which is not stationary but moving in a particular direction. If the traveller leaves the second planet with some given velocity, then his time dilation rate in the first planet's rest frame depends on the speed of the second planet and the direction it is moving in.
Relativity is perfectly consistent with isotropy. In physics, isotropy - the idea that there is no "preferred" direction in space - is synonymous with rotational symmetry. SRT has rotational symmetry built into it: the rotation group completely contained within the Lorentz group. This is most obvious from Minkowski's equation
This equation is the defining property of Lorentz transformations. In the special case of zero velocity, $$t' \,=\, t$$, and the equation reduces to
This is the defining property of rotations. Every spatial rotation is a Lorentz transformation, and every Lorentz transformation with the time fixed ($$t' \,=\, t$$) is a rotation. Thus, the Lorentz group also contains the complete rotation group, and SRT fundamentally cannot violate isotropy.
Is there any significance to the screens being "red" and "blue"?
If not, this is not complicated. If the left and right observers emit the same frequency in their rest frames, and they are moving toward or away from the screens with the same velocity, then neither light will flash because the Doppler shifts are the same, so the frequencies reaching the screens will be the same.
If the velocities are different, then you need to account for the Doppler effect. Which light flashes will depend on which observer is moving toward or away from the screens the fastest. Either way, there will be only one answer. There is no paradox of any kind here.
This is another trivial one. The error is here:
This argument is invalid. Relativity predicts no such thing. As viewed from the original planet, the traveller's velocity reduces to zero and his time dilation rate becomes 1. It is really that simple.
This argument seems to be a manifestation of your confusion with reciprocity of time dilation. As I [POST=2975943]already explained[/POST], you are having this problem because you are ignoring the relativity of simultaneity effect. A consequence of this effect is that if observer B is time dilated by a factor $$\lambda$$ compared with A, and C is time dilated by a factor $$\mu$$ compared with B, you can not claim that C is dilated by a factor $$\lambda \mu$$ compared with A. In particular, you cannot conclude that an observer is time dilated by a factor $$1 / (1 \,-\, v^{2}/c^{2})$$ compared with himself.
This one also doesn't follow through. In the first planet's rest frame, there is no violation of isotropy because the situation is not isotropic to begin with: the traveller starts from the second planet, which is not stationary but moving in a particular direction. If the traveller leaves the second planet with some given velocity, then his time dilation rate in the first planet's rest frame depends on the speed of the second planet and the direction it is moving in.
Relativity is perfectly consistent with isotropy. In physics, isotropy - the idea that there is no "preferred" direction in space - is synonymous with rotational symmetry. SRT has rotational symmetry built into it: the rotation group completely contained within the Lorentz group. This is most obvious from Minkowski's equation
$$(ct')^{2} \,-\, x'^{2} \,-\, y'^{2} \,-\, z'^{2} \,=\, (ct)^{2} \,-\, x^{2} \,-\, y^{2} \,-\, z^{2} \,.$$
This equation is the defining property of Lorentz transformations. In the special case of zero velocity, $$t' \,=\, t$$, and the equation reduces to
$$x'^{2} \,+\, y'^{2} \,+\, z'^{2} \,=\, x^{2} \,+\, y^{2} \,+\, z^{2} \,.$$
This is the defining property of rotations. Every spatial rotation is a Lorentz transformation, and every Lorentz transformation with the time fixed ($$t' \,=\, t$$) is a rotation. Thus, the Lorentz group also contains the complete rotation group, and SRT fundamentally cannot violate isotropy.
It's normal. The distance between two points at rest in the $$(x'\, t')$$ system (e.g. the end points of a box) is longer than the distance between the two points in the $$(x,\, t)$$ system.
For example, set $$x'_{1} \,=\, L'$$ and $$x'_{2}$$. Then you find $$x_{1} \,=\, vt \,+\, L'/\gamma$$ and $$x_{2} \,=\, vt$$, so the distance $$L \,=\, x_{1} \,-\, x_{2} \,=\, L'/\gamma$$ is length contracted as expected.
If instead you set $$x_{1} \,=\, L$$ and $$x_{2} \,=\, 0$$, you get the opposite result: $$L' \,=\, L/\gamma$$.
Is SRT logically self-consistent?
SRT-time can accelerated and slow-down at the same time.
Self-consistent?
Doppler effect is absent: the distance between the screen and the observer are huge, and the observers are moving across to the beams projections.
Each observer sees time dilation of another observer.
What they see on the screen?
Simple?
Time accelerated and slow-down at the same time - How is it possible?
When the traveler returns, he has the time-slowing to the second planet and he has the time-accelerated to the first planet.
Time accelerated and slow-down at the same time - How is it possible?
?!?!?!?!...
Both planets are identical.
Between planets be absent any distinction.
But I have demonstrated to you that the isotropy of space get out of order when the traveler started from the second planet.
===============
I think, and when I think, I use common sense, and then apply the math.
Mathematics only helps us to think, but we should think ourselves.
You're trying to force the math to it think for you.
Last edited:
I'm going to focus on this, since I think it's the most important to address:
This is not an accurate statement. As I have already explained, the time dilation formula is a special case of the Lorentz transformation with limitations to how and where it can be used and what can be deduced from it.
The full relation between coordinates is always described by a Lorentz transformation in SRT. If you use the Lorentz transformation, there is no problem. rpenner has already explained this (though his post has apparently disappeared due to some error in the forum). If you apply a Lorentz transformation, and then apply another Lorentz transformation with the same speed in the opposite direction, they cancel each other out and you just get back what you started with.
Set:
Then perform another Lorentz transformation in the opposite direction (so replace $$v \,\rightarrow\,- v$$):
You will find that you will return to the same coordinates you started with:
So SRT does not predict that an observer can be time dilated compared with himself. SRT does not predict that an observer can have more than one time dilation rate in a single reference frame.
So think then. This is your opportunity to do that. I say that you will find $$t'' \,=\, t$$ and $$x'' \,=\, x$$. Don't believe me. Do the calculation yourself. Then think about what the result means, and/or we can discuss what it means and why it is important.
This is not an accurate statement. As I have already explained, the time dilation formula is a special case of the Lorentz transformation with limitations to how and where it can be used and what can be deduced from it.
The full relation between coordinates is always described by a Lorentz transformation in SRT. If you use the Lorentz transformation, there is no problem. rpenner has already explained this (though his post has apparently disappeared due to some error in the forum). If you apply a Lorentz transformation, and then apply another Lorentz transformation with the same speed in the opposite direction, they cancel each other out and you just get back what you started with.
Set:
$$
\begin{eqnarray}
t' &=& \gamma ( t \,-\, \frac{v}{c^{2}} x ) \\
x' &=& \gamma ( x \,-\, v t ) \,.
\end{eqnarray}
$$
\begin{eqnarray}
t' &=& \gamma ( t \,-\, \frac{v}{c^{2}} x ) \\
x' &=& \gamma ( x \,-\, v t ) \,.
\end{eqnarray}
$$
Then perform another Lorentz transformation in the opposite direction (so replace $$v \,\rightarrow\,- v$$):
$$
\begin{eqnarray}
t'' &=& \gamma ( t' \,+\, \frac{v}{c^{2}} x' ) \\
x'' &=& \gamma ( x' \,+\, v t' ) \,.
\end{eqnarray}
$$
\begin{eqnarray}
t'' &=& \gamma ( t' \,+\, \frac{v}{c^{2}} x' ) \\
x'' &=& \gamma ( x' \,+\, v t' ) \,.
\end{eqnarray}
$$
You will find that you will return to the same coordinates you started with:
$$
\begin{eqnarray}
t'' &=& t \\
x'' &=& x \,.
\end{eqnarray}
$$
\begin{eqnarray}
t'' &=& t \\
x'' &=& x \,.
\end{eqnarray}
$$
So SRT does not predict that an observer can be time dilated compared with himself. SRT does not predict that an observer can have more than one time dilation rate in a single reference frame.
So think then. This is your opportunity to do that. I say that you will find $$t'' \,=\, t$$ and $$x'' \,=\, x$$. Don't believe me. Do the calculation yourself. Then think about what the result means, and/or we can discuss what it means and why it is important.
Do not rush to write formulas, because we have a frank chicken-feeds: we have the logic-collision.
After moving to another planet, we have (we get) the time-dilation.
So assert the SRT.
Going back to his planet, we have (we get) the time-dilation once again.
So assert the SRT. (If we see to the traveler with the second planet.)
If we see to the traveler with the first planet: we have (we get) the time-acceleration.
So assert the SRT.
Answer the question: What are we going to have: the double time-dilation or the time-dilation+acceleration?
SRT assert that we have (we get) both (inter-exclusionary) variants at once.
------------------------
No need to write a formula.
Just logically explain for us: which of the two options is correct, and - why not?
If you state that the traveler will return the normal time, then explain us: why you replaced second time-dilation to time-acceleration?
If a descendant of the traveler go back to the planet of his ancestor, then his time get the time-dilation or the time-acceleration? What?
If the traveler returns to the planet with his descendant together?
=======================================
Íå ñïåøèòå ïèñàòü ôîðìóëû, ïîòîìó ÷òî ó íàñ îòêðîâåííûå ôèãíÿ ïîëó÷àåòñÿ: ëîãè÷åñêàÿ êîëëèçèÿ âîïèåò.
Ïîñëå ïåðååçäà íà äðóãóþ ïëàíåòó, ó íàñ åñòü (ìû ïîëó÷àåì) çàìåäëåíèå âðåìåíè.
Òàê óòâåðæäàåò ÑÒÎ.
Âîçâðàùàÿñü ê ñâîåé ïëàíåòå, ïóòåøåñòâåííèê ïîëó÷àåò çàìåäëåíèå âðåìåíè åùå ðàç.
Òàê óòâåðæäàåò ÑÒÎ. (Åñëè ìû âèäèì ïóòåøåñòâåííèêà ñî âòîðîé ïëàíåòû.)
Åñëè ìû âèäèì ïóòåøåñòâåííèêà ñ ïåðâîé ïëàíåòû, òî ìû (ïóòåøåñòâåííèê) èìååì óñêîðåíèå âðåìåíè.
Òàê óòâåðæäàåò ÑÒÎ.
Îòâåòüòå íà âîïðîñ: ×òî ìû (ïóòåøåñòâåííèê) áóäåì èìåòü: äâîéíîå çàìåäëåíèå âðåìåíè èëè çàìåäëåíèå+óñêîðåíèå?
ÑÒÎ óòâåðæäàåò, ÷òî ó íàñ åñòü (ìû ïîëó÷àåì) äâà (âçàèìî-èñêëþ÷àþùèõ) âàðèàíòà ñðàçó.
------------------------
Íå íóæíî ïèñàòü ôîðìóëû.
Ëîãè÷åñêè îáúÿñíèòå: êàêîé èç äâóõ âàðèàíòîâ ïðàâèëüíûé, è - ïî÷åìó?
Åñëè âû áóäåòå óòâåðæäàòü, ÷òî ïóòåøåñòâåííèê âåðíåòñÿ â îáû÷íîå âðåìÿ, òî îáúÿñíèòå: ïî÷åìó âòîðîå çàìåäëåíèå âðåìåíè âû çàìåíèëè íà óñêîðåíèå?
À åñëè ïîòîìîê ïóòåøåñòâåííèêà âåðíóòüñÿ íà ïëàíåòó ñâîåãî ïðåäêà (âìåñòî ñàìîãî ïóòåøåñòâåííèêà), òî åãî âðåìÿ çàìåäëèòñÿ èëè óñêîðèòñÿ?
À åñëè ïóòåøåñòâåííèê âîçâðàùàåòñÿ íà ïëàíåòó ñî ñâîèì ïîòîìêîì âìåñòå?
After moving to another planet, we have (we get) the time-dilation.
So assert the SRT.
Going back to his planet, we have (we get) the time-dilation once again.
So assert the SRT. (If we see to the traveler with the second planet.)
If we see to the traveler with the first planet: we have (we get) the time-acceleration.
So assert the SRT.
Answer the question: What are we going to have: the double time-dilation or the time-dilation+acceleration?
SRT assert that we have (we get) both (inter-exclusionary) variants at once.
------------------------
No need to write a formula.
Just logically explain for us: which of the two options is correct, and - why not?
If you state that the traveler will return the normal time, then explain us: why you replaced second time-dilation to time-acceleration?
If a descendant of the traveler go back to the planet of his ancestor, then his time get the time-dilation or the time-acceleration? What?
If the traveler returns to the planet with his descendant together?
=======================================
Íå ñïåøèòå ïèñàòü ôîðìóëû, ïîòîìó ÷òî ó íàñ îòêðîâåííûå ôèãíÿ ïîëó÷àåòñÿ: ëîãè÷åñêàÿ êîëëèçèÿ âîïèåò.
Ïîñëå ïåðååçäà íà äðóãóþ ïëàíåòó, ó íàñ åñòü (ìû ïîëó÷àåì) çàìåäëåíèå âðåìåíè.
Òàê óòâåðæäàåò ÑÒÎ.
Âîçâðàùàÿñü ê ñâîåé ïëàíåòå, ïóòåøåñòâåííèê ïîëó÷àåò çàìåäëåíèå âðåìåíè åùå ðàç.
Òàê óòâåðæäàåò ÑÒÎ. (Åñëè ìû âèäèì ïóòåøåñòâåííèêà ñî âòîðîé ïëàíåòû.)
Åñëè ìû âèäèì ïóòåøåñòâåííèêà ñ ïåðâîé ïëàíåòû, òî ìû (ïóòåøåñòâåííèê) èìååì óñêîðåíèå âðåìåíè.
Òàê óòâåðæäàåò ÑÒÎ.
Îòâåòüòå íà âîïðîñ: ×òî ìû (ïóòåøåñòâåííèê) áóäåì èìåòü: äâîéíîå çàìåäëåíèå âðåìåíè èëè çàìåäëåíèå+óñêîðåíèå?
ÑÒÎ óòâåðæäàåò, ÷òî ó íàñ åñòü (ìû ïîëó÷àåì) äâà (âçàèìî-èñêëþ÷àþùèõ) âàðèàíòà ñðàçó.
------------------------
Íå íóæíî ïèñàòü ôîðìóëû.
Ëîãè÷åñêè îáúÿñíèòå: êàêîé èç äâóõ âàðèàíòîâ ïðàâèëüíûé, è - ïî÷åìó?
Åñëè âû áóäåòå óòâåðæäàòü, ÷òî ïóòåøåñòâåííèê âåðíåòñÿ â îáû÷íîå âðåìÿ, òî îáúÿñíèòå: ïî÷åìó âòîðîå çàìåäëåíèå âðåìåíè âû çàìåíèëè íà óñêîðåíèå?
À åñëè ïîòîìîê ïóòåøåñòâåííèêà âåðíóòüñÿ íà ïëàíåòó ñâîåãî ïðåäêà (âìåñòî ñàìîãî ïóòåøåñòâåííèêà), òî åãî âðåìÿ çàìåäëèòñÿ èëè óñêîðèòñÿ?
À åñëè ïóòåøåñòâåííèê âîçâðàùàåòñÿ íà ïëàíåòó ñî ñâîèì ïîòîìêîì âìåñòå?
Last edited: