Question

Say there is a spaceship really far away from Earth moving at 80% the speed of light (away from Earth-edited), at some point a radio signal is sent by observers on Earth. I need to be able to calculate how long it would take for the signal to reach the spaceship. Would calculating the time required for the signal to reach the spaceship in Earth's frame, which is pretty straight forward and then applying time dilation directly be valid? If not please explain what the issue behind the approach is. The other approach would be to apply Lorentz transformations, but honestly I don't get what exactly makes one approach right and other one wrong in certain scenarios.

Options:

A) Calculating the time required for the signal to reach the spaceship in Earth's frame and applying time dilation directly is a valid approach.
B) Applying Lorentz transformations is the correct method to determine the time taken for the signal to reach the spaceship.
C) Both approaches are equally valid and yield the same result in this scenario.
D) Neither approach is suitable for accurately calculating the time it takes for the signal to reach the spaceship.

Answer 1

The correct method to calculate the time it would take for a radio signal to reach a spaceship moving at 80% the speed of light from Earth is to apply the Lorentz transformations, as simply applying time dilation does not take the relative motion into account.

Step-by-step explanation:

If a spaceship is really far away from Earth, moving at 80% the speed of light, and a radio signal is sent from Earth, the approach to calculate how long it will take for the signal to reach the spaceship can involve either using the Lorentz transformations or calculating the time in Earth's frame and then applying time dilation. However, only one of these methods is correct in this scenario due to the nature of special relativity.

The correct method is to apply the Lorentz transformations, which account for the relative velocities between observers in different inertial frames. Calculating the time in the Earth's frame and simply applying time dilation directly would not be accurate because time dilation alone does not account for the relative motion between the Earth and the spaceship for signals traveling between them.

Answer option B) is correct: Applying Lorentz transformations is the correct method to determine the time taken for the signal to reach the spaceship. Lorentz transformations comprehensively deal with the effects of relative motion on time and space measurements between different inertial frames. Simply applying time dilation would not be mathematically correct as it ignores the fact that the spaceship itself is moving, and thus the distance the signal needs to travel is changing over time.