# Time relativity

Lets say that I am on a spaceship moving with the speed of 0,90c and I am looking on my friend who stayed back on earth. My friend is looking on me.

From my perspective, my friend is moving 7 times slower then "normal" and from his perspective I am moving 7 times slower then "normal".

Lets say that seven years passes on earth which means that I am one year older and my friend is seven years older.

But if I was moving for one year and I was seeing him moving 7 times slower shouldn't he be 1/7 year older not 7?

Can someone explain that to me?

• Neither of you will appear only 1/7 year older: each of you will measure 7 years on your own clock and see 1 apparent year pas for the other. 1/7 of a year would be 49 times slower, not seven as you originally stated. – Asher Aug 26 '15 at 16:32

## 1 Answer

If you are abit more careful about making the statements, then "both perspectives" are actually correct. Let me be more concrete and explain.

Let $E$ be the one who stays on Earth and $S$ be the one who is on the spaceship. The first issue you have is you said "let's say seven years passes on Earth" - this is an ambiguous statement: from whose perspective?

Let's say seven years passes on Earth from $E$'s perspective. $E$ will indeed see $S$ to age only a year. Note that during this interval, $S$ will only see 1/7 years to have passed on Earth.

But wait a second, did I just say that $E$ sees $S$ to age slower and $S$ sees $E$ to age slower? Yes! And both are correct from their own perspective.

Hmm, but maybe you are still not very convinced. You might ask: how can $E$ be both 7 years older and 1/7 years older at the same time? The answer: $E$ is 7 years older from $E$'s frame, but 1/7 years older from $S$'s frame. These are two different frames, and one cannot just compare like this.

More concretely, from the viewpoint of $S$, all the clocks in $E$'s frame are at all moving slower BUT they start at different times (clocks at the 'rear' have a headstart). See bottom left of diagram. The $E$-clock that is staring right in front of the face of $S$ reads to $S$: 7 years elapsed. But the $E$-clock that is located on Earth reads to $S$: 1/7 years elapsed.

(You might have to download and zoom in to see the clock timings, especially the negative signs) Extension (to comment): What happens if $S$ turns back to Earth; when both $S$ and $E$ are on Earth, how can $E$ and $S$ both see each other to have aged less? This is known as the twin paradox. The correct "answer" is $E$ has aged 14 years and $S$ has aged 2 years. This was $E$'s perspective all along, so why is $S$'s perspective now "wrong"? The caveat is that when $S$ turns around to return to Earth, $S$ has changed inertia frame/has experienced acceleration. If you know how to deal with accelerating frames, you can compute that $S$ will perceive $E$ to suddenly age $13 \frac{5}{7}$ years during the short interval when $S$ turns around. So $S$'s perspective, when rightfully accounted for, will see $E$ to also age $1/7 + 13 \frac{5}{7} + 1/7 = 14$ years as well.

• The last paragraph is a bit hard to understand. But I have another question. If S will travel on his ship for two years and then come back on Earth he should see E 14 years older, right? How is that posiible if time on Earth will be 7 times slower then S time? – Krzysztof Majewski Aug 26 '15 at 9:09
• Aha! I was going to talk about that. And I was going to draw a diagram to explain the last paragraph. I'll update in about an hour. – suncup224 Aug 26 '15 at 9:15
• @KrzysztofMajewski hopefully this helps – suncup224 Aug 26 '15 at 9:41