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---Curious

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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.

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---Curious

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Welcome to PF;

*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.

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

No it doesn't - but I'll get to that...CuriousQ said:So, I understand that The Theory of Relativity, very simply, states that time is relative to our velocity.

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}## ...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?

What SR is saying is that

But we could ask how much of a discrepancy has built up of 4.5billion years Earth time between us and the Sun.Is the Sun a lot older than we think it is?

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.

---------------------

[*] 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

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

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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.

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Simon Bridge said:[*] 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.

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

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

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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.

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