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Observation from Single reference frame and STR 
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#1
Dec1511, 07:08 AM

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Last thread that I initiated was titled `Simultaneity is directional while Time Dilation is not', which presented a scenario for the Nondirectional property of Time Dilation in STR. Which I think, needs to be reconsidered. And I believe this is the reason why `STR can only be worked out when we consider one reference frame at a time only'.
Being Nondirectional implies: Time dilation would occur to each and everyone, NO matter which direction they tend to move. Let us try to realize the above statement by considering a simple thought experiment : Let us suppose that, there exist two very distant stars, of which sun lies at the middle of the line joining these two stars. Naming them star A and star B, two twin astronauts Adam and Bob in their identical and respective rockets blast off from the Earth at the same time. Destination of Adam is star A whereas for Bob it is star B. They return to earth let's say after 10 years completing their identical trip in reference frame of Earth. Now, the question is `Will the brothers still be of the same age, i.e age of Adam = age of Bob?' since, according to Adam, Bob is getting younger due to relative motion, whereas, according to Bob, Adam is getting younger due to relative motion. Moreover, if your answer is `yes', then undoubtedly, Earth is a preferential reference frame for your calculations, which violates the `Principle of relativity'. Note: gravitational effects should be neglected. 


#2
Dec1511, 09:58 AM

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They will be the same age when they return, however, they will both have aged less than the earth did during their trip.
The title of your thread says it all, "Observation from Single reference frame", assuming that you mean an inertial reference frame. It won't matter which reference frame you use, except that the calculations are trivial in the earth's rest frame and much more complicated in other frames, but they will arrive at the same result as far as the amount of aging for the twins and the earth during the trip. So first let's consider a frame in which Adam is at rest during his outbound portion of the trip. Bob is traveling at an even faster rate than he is in the earth's rest frame and is experiencing more time dilation than he is in the earth's frame during his outbound portion of the trip. However, during his inbound portion of the trip, he will be at rest in this frame and during Adam's inbound portion of his trip, he will be traveling at the same high speed that Bob was traveling during his outbound trip. So the two twins will both experience an interval of rest and an interval of high speed and the total amount of aging will be the same. If you understand what happens in that frame of reference, I think it will be easy to see that a frame in which Bob is at rest during his outbound portion of his trip will have the same result. Just remember, in Special Relativity, you can pick any one inertial frame to describe, demonstrate and analyze what is happening to all observers/object/clocks, they don't each get there own individual frame. Then you can use the Lorentz Transform to see what the same scenario looks like in any other inertial frame. 


#3
Dec1511, 11:44 AM

P: 303

My question why can't we calculate the Time Dilation of one astronaut from the reference frame of the other. That is, observing the whole situation from the eyes of one of the astronauts. That is, Even in the reference frame of the Earth the two astronauts are moving relative to each other during the whole trip, and STR says relative motion induces Time Dilation. 


#4
Dec1511, 12:44 PM

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Observation from Single reference frame and STR
You can calculate the Time Dilation of both astronauts and earth from any inertial reference frame but since the astronauts do not remain inertial, you cannot say that you will use the reference frame of the other astronaut.
STR says motion relative to an inertial frame induces Time Dilation. 


#5
Dec1511, 01:16 PM

P: 303

I think that STR can easily be extended, as far as linear change in speed or linear acceleration is concerned. Only those reference frames requires curvature or nonlinear acceleration, need to be considered through GR.
That is, we can always calculate the results of STR Time Dilation as long as there is no curvature. Look at it like this: Time dilation of Muons(\mumesons) will occur just like the extended theory, as long as the Muons are moving relative to the Earth based laboratories. And it does not matter if they are accelerating or decelerating, you can always put the average velocity to calculate the Time Dilation. 


#6
Dec1511, 09:38 PM

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As long as gravitational effects are neglected, as you stated in your first post, then you don't need to use the extended theory of GR. SRT can handle accelerating things with no problem, you just don't want a frame to be accelerating unless you are a real expert. It's never necessary.
But there is never a preferred frame, even for the case of muons. Even if they are changing speed, you can calculate the exact time dilation, as long as you know how the speed varies. I doubt that you could even calculate an average speed except maybe in the simplest case. 


#7
Dec1511, 09:54 PM

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#8
Dec1611, 01:39 AM

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