SR Inertial Frame Scenario Confusion

[werewolf]

I'm new to the study of SR and GR. I have a question that I have not been able to find any discussion about.

In the case of two frames of reference where we are comparing events from the point of view between a 'stationary frame' (inertial) to an excelerating frame like the twin paradox is the scenario I'm using as a thought excerise.

Say the excelerating frame is approaching the speed of light, like 90%. Then the traveller shines a flashlight toward a mass in the distance that is in the same frame as the inertial frame. If the distance to the object is for example 100 light years away, then it will take the light 100 years to reach that object.

Now, since the traveller is going .9/speed light, it stands to reason that the traveller will reach the object in 90 light years from the travellers frame of reference.

My question is, what would the observer in the stationary frame see relative to the traveller? i.e. the observer would measure the speed of light as 186,000 mi sec and the traveller at 167,400 mi sec, but would the observer see the traveller arrive after 9 years? That would not seem to be the case based on time dilation and length contraction so I'm a little confused here.

Any help with the math to calculate this and explanations would be greatly appreciated.

Please help me correct any inaccurate terminology if you would. Thanks.

 

[Mentz114]

Welcome, Werewolf.

By 'excelerating' frame do you mean an inertial frame traveling at 0.9c wrt to some other oberver whom we call stationary ? The rules of SR would be tricky to apply if the traveling observer was accelerating all the time.

the observer would measure the speed of light as 186,000 mi sec and the traveller at 167,400 mi sec

The speed of light won't change for different observers. How do they measure the speed of light ?

 

[JesseM]

In the case of two inertial frames of reference where we are comparing events from the point of view between a 'stationary frame' to an excelerating frame like the twin paradox is the scenario I'm using as a thought excerise.

Actually the definition of "inertial" frame is that it's not accelerating...from the perspective of an inertial frame, any other inertial frame will be moving at constant speed in a straight line, whereas accelerations always involve either changes in speed or direction (which result in G-forces experienced by the accelerating observer, like the 'centrifugal force' you feel when moving in a circle).

Say the excelerating frame is approaching the speed of light, like 90%.

Let's just say that the second frame is moving at a constant velocity of 0.9c relative to the first, all right? And one thing to point out is that there's no such thing as absolute velocity in relativity, only relative velocity--the second frame isn't moving at 0.9c in any absolute sense, it's just moving at 0.9c from the perspective of an observer at rest in the first frame, while that observer will be moving at 0.9c from the perspective of an observer at rest in the second frame.

Then the traveller shines a flashlight toward a mass in the distance that is in the same inertial frame as the stationary frame. If the distance to the object is for example 100 light years away, then it will take the light 100 years to reach that object.

Different inertial frames measure distances and times differently. If the object is 100 light years away from the Earth in the first frame which you are labeling the "stationary" one (although as I said 'stationary' has no absolute meaning, the traveller is stationary in his own rest frame), and the traveller shines the light at the moment he passes the Earth, then then according to clocks at rest in this first frame, it will take light 100 years to get from the traveller to the distant object. However, in the second frame where the traveller is at rest, the distance from the Earth to the destination is shorter due to length contraction, so the time is shorter too.

Now, since the traveller is going .9/speed light, it stands to reason that the traveller will reach the object in 90 light years from the travellers frame of reference.

90% the speed of light is 0.9 * c, not 0.9/c. And since speed = distance/time, that means the time to cross a certain distance is distance/speed, not distance*speed as you seem to have assumed, so in the first frame of reference the time for the traveler to reach the destination is (100 light years)/(0.9 light years/year) = 111.11... years, not 90 years. However, in this frame it also appears that the traveler's clock is slowed down by a factor of \sqrt{1 - 0.9^2} = 0.43589, so in the 111.11... years it takes for the traveler to reach the destination in this frame, the traveller's clock only ticks forward by 111.11... * 0.43589 = 48.43 years. And this makes sense in the traveller's frame too...as I said, the distance from Earth to the destination is shrunk in this frame due to length contraction, by the same factor of 0.43589, so the distance from Earth to the destination is only 100 * 0.43589 = 43.589 light-years in the traveller's rest frame. And in this second frame the traveller is at rest while the destination approaches at 0.9c, so the destination will take 43.589/0.9 = 48.43 years to reach the traveller, the same number I got above looking at things from the perspective of the first frame.

 

[werewolf]

Thanks for the responses. I'm going to digest this information and may have some more questions for you guys.

I'm really surprised at how much I'm liking physics; esp. SR and GR. I'm actually a little obsessed! But it is a good obsession. Like a drug actually.

Thansk again.