Is the Sun Really Older Due to Relativity?

[CuriousQ]

Hey everyone. Let me preface this by saying, I love physics and astronomy, but am by no stretch an expert in either subject. I had a question that I thought someone on this site might be able to answer, I have been looking around the internet, but couldn't find one. So, I understand that The Theory of Relativity, very simply, states that time is relative to our velocity. I also understand that the Earth orbits the sun at roughly 67,000 miles/hour. Now, my understanding is that the sun is essentially motionless in the center of our solar system, and all the planets orbit it. So, my question is, wouldn't the Earth and all of its inhabitants be "aging" much slower than the Sun? Is the Sun a lot older than we think it is? I mean, if time slows the faster you move, and the Earth has always been moving faster than the Sun, then I feel like after a few billion years, the difference in our "time" and the Sun's "time" would have to pretty huge by now. This might be a stupid question, but I would like a legitimate answer.

---Curious

 

[Simon Bridge]

Welcome to PF;

So, I understand that The Theory of Relativity, very simply, states that time is relative to our velocity.

No it doesn't - but I'll get to that...

I also understand that the Earth orbits the sun at roughly 67,000 miles/hour. Now, my understanding is that the sun is essentially motionless in the center of our solar system, and all the planets orbit it. So, my question is, wouldn't the Earth and all of its inhabitants be "aging" much slower than the Sun?

It is a little complicated because the Earth is accelerating[*] ... but what SR is predicting is that clocks on the Earth are ticking slower than the sun by a factor of $\gamma = 1/\sqrt{1-v^2/c^2}$ ... from the POV of the Sun. For our POV, the Sun's clock is the one ticking slower.

What SR is saying is that there is no absolute reference frame ... another observer, moving at a different speed again, will disagree with us about the age of the Sun. There is no physical reason to prefer one reference frame to another.

Is the Sun a lot older than we think it is?

But we could ask how much of a discrepancy has built up of 4.5billion years Earth time between us and the Sun.

67000mph may sound fast, but it is how this compares to the speed of light[**] that counts ... and in terms of the speed of light the Earth is only doing 0.0001c. In SR this is very slow.

so $$\gamma = \frac{1}{\sqrt{1-0.0000001}}=\frac{1}{\sqrt{0.9999999}}$$ ... which is about 1.00000005 ... which means that a clock on the Earth and a clock on the Sun will differ by about 8-9years over the 4.5billion years the Sun has been around.

So... do you think this is "a lot"?
Well - the age of the solar system (and thus, the Sun) is about 4.5 to 4.55 billion years ... so 8-9years is very small compared to the overall uncertainty of 25000000years.

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[*] Also General Relativity adds an extra complication - the Sun's gravity also affects time. I've done this entirely in terms of Special Relativity.
[**] speed of light is about 670000000mph

 

[Chronos]

Time on Earth is not affected due to orbital velocity around the sun. Do the math.

 

[russ_watters]

Even if the difference were significant, it wouldn't make our measured age "wrong", it would just make it relative to our frame of reference.

 

[Simon Bridge]

Even if the difference were significant, it wouldn't make our measured age "wrong", it would just make it relative to our frame of reference.

My twin and I check each others wall clocks and it seems we are a decade apart after all this time - he says I'm younger and I say he is ... we'd meet up to check in person but we cannot agree on which of us should make the trip.

 

[DrStupid]

[*] Also General Relativity adds an extra complication - the Sun's gravity also affects time. I've done this entirely in terms of Special Relativity.

Due to the GR effect the clocks on Earth run by the factor 1.000002 faster compared to clocks on the surface of the sun. Thus the above mentioned SR effect is negligible.

 

[CuriousQ]

Thanks for the answers, you all are great. The internet is a beautiful thing.

 

[russ_watters]

My twin and I check each others wall clocks and it seems we are a decade apart after all this time - he says I'm younger and I say he is ... we'd meet up to check in person but we cannot agree on which of us should make the trip.

Do you and your twin understand relativity? If yes, then you're both right. If no, you're both wrong.

 

[twofish-quant]

The important thing is how accurate you want to be. If you want to figure out the age of the earth/sun to within a year or even ten years, then relativistic effects are going to be important. As it is, our knowledge of the age of the solar system is +/- ten million years so that's not enough to take into account relativity.

Note there that in dealing with spacecraft and planets we can time things down to less than a second and within one meter, so these effects become extremely important.