Rozman napisal/-a:Zbe - predlagam, da se osredotočimo na bolj preproste sisteme od kroženja.
Ja, osredotočimo se zgolj na učinke PTR. Zaenkrat naj nas ne zanimajo učinki STR. Enostavnejši primer kroženja dvojčkov je, če enega dvojčka damo na GPS satelit, drugi pa je na Zemlji.
Pa saj nihce ne omenja STR. Ali morda kdo omenja gravitacijske ucinke? Se drugic: ce privzamemo raven prostorcas, potem lahko pospesujes/krozis oz. delas kar hoces in vse to gibanje opises s PTR. Pa povej mi, kako je lahko enostavnejsi primer od krozenja.... krozenje?
Zbe - Ne locis tudi med: "vidis" in "izracunas".
Vedno računam, kaj bom videl in svoje videnje skušam opisati v matematičnem modelu.
Ja ne vem, zakaj svojih izracunov potem ne prilimas zraven v prispevek, da lahko ostali preverimo?
Predvidevam, da razumes anglesko, zato ti bom prilimal lep opis tega, kar imam v mislih:
George Jones (physicsforums.com) napisal/-a:In reality, the phrase "a moving clock runs slow" does not necessarily mean "a moving clock is seen visually to run slow." A clock moving directly away from an observer appears visually to run slow, but a clock moving directly towards an observer appears visually to run fast. In both cases, what is seen visually is given by the Doppler expression, which is always different than the time dilation expression. In both cases, the time dilation expression, used appropriately, does apply.
Consider the following example.
Assume that Alice is moving with constant speed directly towards Ted. When Ted uses his telescope to watch Alice's wristwatch, he sees her watch running at a faster rate than his watch. Ted sees Alice's moving watch running fast, not slow! Ted sees this because of the Doppler shift. Because Alice moves towards Ted, the light that Ted sees from her watch is Doppler-shifted to a higher frequency. But the rate at which a clock or watch runs is like frequency, i.e., a second-hand revolves at a certain frequency, and all frequencies are Doppler-Shifted., so ted see Alice's wristwatch running fast.
To explain what "A moving clock runs slow." means, I first have to explain how Ted (with help from Bob) establishes his frame of reference.
Starting from Ted, a series of metre sticks, all at rest with respect to Ted, are laid end-to-end by Bob along the straight line joining Alice and Ted. At each joint between two consecutive metre sticks, Bob places a small clock. The metre sticks and clocks all are at rest with respect to Ted. Initially, none of the clocks are running; before turning them on, the clocks have to be synchronized. To do this, Ted directs a laser pointer along the line joining Ted and Alice, and then sends a flash of light. Each clock is turned on when the flash of light reaches it. The speed of light is not infinite, so the time taken for the light to travel from Ted to each clock has to be taken into account. To do this, the clocks' hands are set initially as follows. The clock one metre away from Ted is set to the time taken for light to travel one metre; the clock two metres away from the tower is set to the time taken for light to travel two metres; ... .
This whole setup of metre sticks and clocks establishes Ted's reference frame.
Now, As Alice moves toward Ted, Ted uses his telescope to watch Alice's wristwatch, and to watch his clocks. First, he watches one of the distant clocks in his reference frame. The time he sees on the clock is the time at which the light he sees set out from the clock, so Ted sees an earlier time on the distant clock than he sees on his wristwatch. Because the clock is stationary in his frame, Ted does, however, see the distant clock running at the same rate as his watch. Similarly, Ted's sees all the clocks in his frame running at the same rate as his watch.
As Alice approaches Ted, she whizzes by clock after clock of Ted's reference frame. Using his telescope, Ted sees that Alice is beside a particular clock, and he notes the time on her watch and the time on the clock adjacent to her. Some time later, Ted sees Alice beside a different clock, and he again notes the time on her watch and the time on the clock adjacent to her.
Ted checks his notes, and he finds that the time that elapsed on Alice's watch as she moved between these two clocks of his frame is less than the difference of the readings of the two clocks. This what is meant by "A moving clock runs slow."
Unfortunately, "time dilation" in general relativity and "time dilation" in special relativity often have different operational meanings. Suppose observer A hovers at a large distance from a Schwarzschild black hole, and that observer B hovers near the event horizon. If observer A uses a telescope to observe B's watch, A will see B's watch running more slowly than his own watch. In this context, gravitational time dilation is something that is seen visually.
Pa prosim, ce si zgornji quote preberes VSAJ dvakrat!
Motore - Seveda v primeru trkalnika ni razlike v starosti dvojčkov Če bi dvojček v raketi nadaljeval potovanje z enakomerno hitrostjo ter se nikoli ne bi vrnil nazaj, razlike v starosti ne bi bilo.
Zamisliva si torej enega dvojčka v GPS raketi in drugega na Zemlji. Motore, če te prav razumem, vsakemu ura v svojem sistemu opazovanja teče normalno. Ura na GPS naj bo taka, da dvojček na Zemlji lahko vidi uro na GPS, ko satelit leti preko njega. Tu pa dvojček za Zemlji, če te prav razumem, uro na GPS vidi teči počasneje. Njun poskus traja toliko časa, da dvojček na zemlji vidi, da ura dvojčka na GPS zaostaja že na primer dve uri. Ker imata radijsko zvezo, se pogovarjata tudi o tem koliko je ura. Dvojček na Zemlji trdi, da ura na GPS v tem trenutku kaže na primer 10.00, dvojček na GPS pa pravi, da pravkar gleda to isto uro in kaže 12.00. Morore, ali te prav razumem?
Se tretjic: krozenje je NEinercialen sistem! Drzi se preprostejsih primerov.
Zanima me tudi, zakaj vsakih 5 postov spremenis svoj primer? Kako se bos sploh kdaj kaj naucil, ce zamenjas temo se preden jo zastopis?