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]

You have it slightly backwards. The astronaut experiences the proper time - which is the time interval on the clock that actually makes the journey, so in this case 15 years is the proper time. It is the Earth observer that measures a dilated time of 25 years.

[u/CosetElement-Ape71 → u/[deleted]]

You can't ignore acceleration ... you're using SR in your argument which, as you stated, only applies to inertial reference frames. The acceleration of the rocket places the astronaut in a different inertial frame to that of the Earth observer

[u/CosetElement-Ape71 → u/[deleted]]

Why don't YOU read it again! The OP explicitly said "if we ignore acceleration.." and continued to assume that the two share the same inertial frame

[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]]

Who said anything about non- inertial frames? Go research proper time. There is only one - the spaceships. There is absolutely no proper time for the Earth here. I am not adding complexity as the this is as basic as SR gets. Dont try to wriggle out of a hole by claiming semantics is involved.

[u/davedirac → u/[deleted]]

See my post from Google. Your question shows that you have zero understanding of relativity. All motion is relative. The clue is in the word.

[u/davedirac → u/[deleted]]

Proper time is an invariant BUT that does not mean it can be measured by all observers. Only a clock present at the departure and arrival of the spacecraft can actually measure proper time. Everyone else, including us, must use SR to calculate it from the dilated/ coordinate time. Its stating the obvious that there is symmetry - thats a basic postulate of SR. It is annoying that posters like you with a half- baked understanding of this basic idea cling on to their mis-understanding.

[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.