Special Relativity: Time dilation

[ntknow]

Hello. This is not a concrete problem, rather conceptual question.

Homework Statement

2. Homework Equations
3. The Attempt at a Solution [/B]
Spaceship with speed v with respect to the Earth is traveling from the Earth to say some distant star, which is distant L apart from the Earth looking by observer who is in the Earth frame. Analysis from both observers point of view:
Earth observer:
observes that spaceship travels the distance in time T₁ = L/v. In addition to that, he observes that clock in the spaceship during the travel advances by T₀=T₁/ ɣ, i.e. less than his clock.

Spaceship observer:
by relativity he sees that the Earth observer's clock is ticking slower than his clock, however, by above argument total travel time in his frame is smaller than in the Earth frame. Additional facts are that he observes length, L, contracted and time reading difference between clock in the Earth and clock, for example, in the star.

Problem for me:
Could someone summarise / make me clear / point out flaws in the reasoning why total travel time is still smaller as observed by spaceship observer than by the Earth observer if spaceship observer during all the time then Earth gets farther from him sees the Earth observer's clock running slower?

 

[PeroK]

Hello. This is not a concrete problem, rather conceptual question.

Homework Statement

2. Homework Equations
3. The Attempt at a Solution [/B]
Spaceship with speed v with respect to the Earth is traveling from the Earth to say some distant star, which is distant L apart from the Earth looking by observer who is in the Earth frame. Analysis from both observers point of view:
Earth observer:
observes that spaceship travels the distance in time T₁ = L/v. In addition to that, he observes that clock in the spaceship during the travel advances by T₀=T₁/ ɣ, i.e. less than his clock.

Spaceship observer:
by relativity he sees that the Earth observer's clock is ticking slower than his clock, however, by above argument total travel time in his frame is smaller than in the Earth frame. Additional facts are that he observes length, L, contracted and time reading difference between clock in the Earth and clock, for example, in the star.

Problem for me:
Could someone summarise / make me clear / point out flaws in the reasoning why total travel time is still smaller as observed by spaceship observer than by the Earth observer if spaceship observer during all the time then Earth gets farther from him sees the Earth observer's clock running slower?

Have you covered the "relativity of simultaneity" or the "leading clocks lag" concept yet?

 

[ntknow]

Have you covered the "relativity of simultaneity" or the "leading clocks lag" concept yet?

Yes, I am familiar with these concepts.

 

[PeroK]

Yes, I am familiar with these concepts.

Can you analyse the journey from the ship's RF? Hint: you need three clocks. Two "rest" clocks: one on Earth and one at the distant star. And one clock moving with the ship.

 

[ntknow]

.

 

[J Hann]

Restating PeroK's comment: Proper time is measured by a single clock in a single place.
Only the clock on the spaceship (in the frame of) meets this requirement.