# When Will We Arrive? Calculating Time Differences in Special Relativity

• Robin64
In summary, two former classmates on a spaceship traveling to Alpha Centauri come up with a plan to celebrate their arrival at the exact moment that their ship is observed by scientists on a space station. To do this, the astronauts must calculate the time according to the clock on their spaceship and the clock at the space station. By considering the time dilation equation t'=γt, where γ is the Lorentz factor, and the length contraction equation L'=L/γ, the time elapsed in the space station frame can be calculated as (d/v)/γ, where d is the distance to Alpha Centauri and v is the constant velocity of the spaceship. However, the signal of the astronauts' arrival must also travel a distance of
Robin64

## Homework Statement

:
You are the first astronaut aboard a ship to travel to Alpha Centauri. Coincidentally, a scientist working on an outer space station post is one of your former classmate. Your ship, with your former classmate onboard, leaves the space station traveling at constant velocity v on its way to Alpha Centauri, a distance d away from the space station. You and your former classmate devise a clever plan to celebrate your arrival at Alpha Centauri exactly when scientists at the space station observe, through their telescope, your ship arriving at Alpha Centauri. To do this, you have to calculate the time according to the clock on the spaceship and the time at according to the clock at the space station.
[/B]

## Homework Equations

t'=γt, L'=L/γ[/B]

## The Attempt at a Solution

: as seen by the astronauts on Alpha Centari, the time elapsed in the space station frame from when they started their trip to when they saw the scientists on the space observe their arrival is: (d/v)/γ +2d/c where 2d/c is the time it takes the signal of the astronauts arrival to reach the space station plus the time it take the signal of the space station observing that arrival to reach the astronauts at Alpha Centari. From here, I'm stumped.[/B]

Robin64 said:
plus the time it take the signal of the space station observing that arrival to reach the astronauts at Alpha Centari.
I don't think you are supposed to add that. You celebrate when the space station crew sees the event, not when you see the crew seeing it.

The astronauts change their reference frame in between. It is easier to calculate everything as seen by the space station.

That still means that d/c has to be added as that's the time it takes for the space station crew to receive the signal of the astronaut's arrival, right?

Sure.

## 1. What is the concept behind Special Relativity?

Special Relativity is a theory developed by Albert Einstein in 1905 that explains how objects move and interact in the universe. It is based on two principles: the laws of physics are the same for all observers in uniform motion, and the speed of light in a vacuum is constant and independent of the observer's motion.

## 2. How does Special Relativity differ from Newton's laws of motion?

Special Relativity differs from Newton's laws of motion in that it takes into account the effects of objects moving at high speeds, close to the speed of light. Unlike Newton's laws, which assume that time and space are absolute, Special Relativity shows that they are relative to the observer's frame of reference.

## 3. What is time dilation in Special Relativity?

Time dilation is a phenomenon predicted by Special Relativity where time moves slower for objects that are moving at high speeds. This means that a clock on a spaceship moving close to the speed of light will appear to tick slower compared to a clock on Earth. This effect has been confirmed through experiments with atomic clocks.

## 4. How does Special Relativity explain the concept of length contraction?

Length contraction is the idea that an object's length appears to decrease when it is moving at high speeds. This is a consequence of Special Relativity, where the faster an object moves, the shorter it appears to be in the direction of its motion. This phenomenon has been observed in experiments with subatomic particles.

## 5. Can Special Relativity be applied to all objects in the universe?

Special Relativity is a fundamental theory that applies to all objects in the universe, regardless of their size or speed. However, it is most noticeable for objects moving at speeds close to the speed of light. The effects of Special Relativity are negligible at everyday speeds, but they become more significant as an object's speed approaches the speed of light.

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