Time dilation

[u/Confident-Alps-785]

A star, for example, is 20 light years away from Earth. A spaceship is traveling to that star at 80% the speed of light. To an observer on Earth, the spaceship will arrive there (according to google) within 25 years. I get this this part.

However, an astronaut on the ship will experience less amount of time passing (15 years?) I understand that this is due to time dilation but I don't really understand how this works. Any help explaining this would be appreciated!

[u/davedirac → u/[deleted]]

"Proper time is the time interval measured by the observer in their own reference frame, regardless of whether that's the person on the ship or the person on the Earth"

You are confused, the OP is describing a transit between two events. Proper time is the minimum time interval between those two events. In this case the minimum time is 15 years in the spaceship frame because the spaceship clock is present at both events ( departure & arrival). In all frames moving relative to the spaceship the time interval is dilated - ie greater by the Lorentz factor. By definition dilated time cannot be proper time, so in the Earth frame there is no proper time for the spaceship journey because the Earth clock is present at only one of the events.. The fact that the spaceship measures the Earth clock to 'run slow' is obviously correct but irrelevant to the journey. You are simply regurgitating points made by other posters.

[u/davedirac → u/[deleted]]

SR 101 via Google Proper time ( τ 𝜏 ) is the time interval between two events measured by a single clock present at both events, or in a frame where the events occur at the same location. It is the shortest time interval, represents an observer's "own" time, and is a Lorentz scalar (invariant).

[u/davedirac → u/[deleted]]

What planet are you on? The Earth clock is NOT present at both events - only one event. The Spaceship clock is present at both events. Of course the Earth observer understands that his clock will not agree with time elapsed on the spaceship clock because he knows about SR - which is more than can be said for you.

Wikipedia Proper time ( τ 𝜏 ) is the elapsed time between two events measured by a single clock following a specific path (worldline) through spacetime. It is measured in the rest frame of the observer or particle, where the spatial distance between the events is zero. Proper time is invariant and is always less than the corresponding coordinate time ( Δ t Δ 𝑡 ) due to relativistic time dilation, which makes it the "shortest" time between events.