# Help me to kill my paradox

1. Aug 16, 2011

### fluidistic

I've thought about something that is a paradox to me. I think I know what would happen in reality but I can't explain why the other option is discarded.

Imagine you are an observer that can live "forever". You are over the Earth and looking toward the Sun. For the sake of simplicity, let's assume the Earth doesn't rotate on itself, but only moves in orbit around the Sun.
I've calculated (with special relativity only) that if the observer was to leave the Earth and wait for it to come back 1 year later, this observer would age 0.2 s more than someone that stayed on the Earth for 1 year. I assumed 1 year=365 days, the speed of the Earth with respect to the observer: 30 km/s. Since this outer space observer isn't moving with respect to the Sun, it also means (neglecting general relativity) that you will see the Sun aging 0.2 s less than you (you are still over the Earth), after 1 year.
After 1000 years this makes 200 s, etc.
So when you look at the Sun and it has been existing since say around 4.5 billions years ago (assume Earth too is this old); is the Sun older than 8 minutes, say several years old?
I say 8 minutes because it's approximately the time that photons leaving out Sun's surface take to reach the Earth.
I know that the answer is indeed around 8 minutes, but because of special relativity, I'm totally confused.
Equation: $\Delta t = \gamma \Delta t '$.

2. Aug 16, 2011

### Staff: Mentor

I'm not sure I understand your question. The fact that it takes light 8 minutes to reach the Earth from the Sun has nothing to do with how much older or younger the Sun might be than the Earth, due to their relative motion. By your calculation, taking only SR into account, the observer on the Sun would have aged by an additional 1 billion seconds or so (which is about 30 years) compared to an observer on the Earth, over the 4.5 billion years since the solar system was formed. The 8 minutes just means that, if the two observers were exchanging radio messages, say, updating each other on how much they have aged, each one, at any given time, would be receiving a message that was sent 8 minutes earlier by the other.

Does this help any?

3. Aug 16, 2011

### rede96

If the observer is not moving with respect to the sun then there will be no time dilation between them. (Ignoring gravitational time dilation.)

As for the rest of your question, I am not too sure what you are asking, sorry.

4. Aug 16, 2011

### ghwellsjr

The sun and the space observer will age at the same rate. The earth bound observer (and the earth) will age 0.2 seconds less per year than the sun. So that means that the earth and the earth bound observer, if he's been there since the beginning, will be about 29 years younger than the sun. However, when looking at the sun from earth, you will see it as it appeared 8 minutes earlier (according to the rest frame of the sun).

5. Aug 16, 2011

### fluidistic

Ah thank you all guys. Now I think I understand...
Basically the Sun would age more (I correct because in my OP I stated less) than an observer on the Earth as you said guys.
Yes this helps a lot (what you all told me).
Thanks a lot. I realize these are 2 totally different "effects".