# Special Relativity: Time dilation

• ntknow
In summary: This is because the spaceship is the only object in the frame that is moving. In summary, the clock on the spaceship "leads" the other two clocks by running slower than they do.
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?

Last edited:
ntknow said:
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?

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

Yes, I am familiar with these concepts.

ntknow said:
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.

.

Last edited:
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.

## 1. What is the concept of time dilation in special relativity?

Time dilation is a phenomenon in special relativity where time runs slower for a moving object as compared to a stationary observer. This means that time is relative and can be perceived differently depending on the relative motion of the observer and the object.

## 2. How does velocity affect time dilation in special relativity?

The faster an object moves, the slower time passes for that object. This is because as an object approaches the speed of light, its mass increases and the fabric of space-time becomes more distorted, causing time to slow down.

## 3. Can time dilation be observed and measured in everyday life?

Yes, time dilation can be observed and measured in everyday life, although the effects are very small at everyday speeds. For example, GPS satellites have to take into account time dilation due to their high speeds in orbit when calculating precise locations on Earth.

## 4. How is time dilation related to the concept of spacetime in special relativity?

Time dilation is a consequence of the concept of spacetime, which combines the dimensions of space and time into a single entity. In special relativity, the fabric of spacetime is affected by the motion and mass of objects, resulting in the phenomenon of time dilation.

## 5. Is time dilation only a theoretical concept, or has it been proven through experiments?

Time dilation has been proven through numerous experiments and observations, such as the famous "twin paradox" where one twin who travels at high speeds ages slower than the other twin who remains on Earth. It is a well-established principle in physics and has been confirmed by various experiments and observations.

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