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## Main Question or Discussion Point

I understand that the ~14.6 billion year age of the universe is in the cosmological frame, i.e., representing the coordinate time elapsed in a comoving reference frame. Of course this means (as has been discussed plenty of times here) observers in different frames would measure a different age due to Lorentz and gravitational time dilation effects. What I haven't been able to find is a conversion of this age to "earth time".

Now, I realize there are a number of issues with such a conversion; not least among the difficulties is that the earth itself is only about 4.5 billion years old. So, perhaps we can consider a more reasonable goal. Our measurements of the age of the earth are invariably made with earth-based clocks: that is, according to the radioactive decay of isotopes that, to very good approximation, have been at rest in the earth's reference frame for their whole existence. Gravitational effects will also have been quite small since the earth's geometry and make up hasn't changed much (as far as GR is concerned) since its formation. Thus, we can comfortably interpret the 4.5 billion year age of the earth as being

Would it be possible for us to determine how much comoving time elapsed for the universe during these 4.5 billion earth years? Or, equivalently, if a comoving observer were created with the universe at the instant of the Big Bang, how much proper time would they measure before they observed the formation of the earth (assuming their worldline brought them nearby in space at just the right time)? We know our current velocity with respect to the CMB due to measurement anisotropies, but do our cosmological models allow us to calculate its past values, as we (presumably) would need to know for such a conversion?

Now, I realize there are a number of issues with such a conversion; not least among the difficulties is that the earth itself is only about 4.5 billion years old. So, perhaps we can consider a more reasonable goal. Our measurements of the age of the earth are invariably made with earth-based clocks: that is, according to the radioactive decay of isotopes that, to very good approximation, have been at rest in the earth's reference frame for their whole existence. Gravitational effects will also have been quite small since the earth's geometry and make up hasn't changed much (as far as GR is concerned) since its formation. Thus, we can comfortably interpret the 4.5 billion year age of the earth as being

*our*time, according to*our*clocks.Would it be possible for us to determine how much comoving time elapsed for the universe during these 4.5 billion earth years? Or, equivalently, if a comoving observer were created with the universe at the instant of the Big Bang, how much proper time would they measure before they observed the formation of the earth (assuming their worldline brought them nearby in space at just the right time)? We know our current velocity with respect to the CMB due to measurement anisotropies, but do our cosmological models allow us to calculate its past values, as we (presumably) would need to know for such a conversion?

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