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Physcists say that the universe is approx. 13 billion years old. However, the amount of time that has elapsed since the big bang differs per object, dwpending on the trajectory that that object has travelled through spacetime (so far as I understand).

So what does the number 13 billion refer to?

Is it the time that has elapsed for a reference frame that has followed the earth (i.e. the particles that make up the earth)?

Qmechanic
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user56834
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It is the time elapsed for so-called comoving observers; that is, those at rest with respect to the expansion. This is also the rest-frame of the cosmic microwave background. The Earth is moving several hundred km/s relative to the CMB, and so the age of the universe according to Earth clocks is only very slightly different (well-within the 68% confidence limit of the accepted age measurement).

bapowell
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  • how do you define/find the rest frame of CMB? I think: if you are in its rest frame, CMB frequency/ies are isotropic, in another rest frame they will be red or blue shifted, depending on the direction you are measuring. Is this correct? – magma Mar 20 '18 at 20:02
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    That's right. Earth's motion relative to the CMB is betrayed by the so-called "dipole" anisotropy: the CMB is a few mK warmer in one hemisphere than the other. – bapowell Mar 20 '18 at 20:06