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So we all heard about the twins paradox to explain einstein's time space relativity.

Wikipedia Quote :" In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as traveling, and so, according to a naive application of time dilation, each should paradoxically find the other to have aged more slowly. "

So what if the universe has been travelling at varying speeds (increasing or descreasing), wouldn't this effect our measurements on age of the universe?

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With respect to what would the Universe (all there is) have a relative motion? –  Alfred Centauri Jun 22 '13 at 1:18
    
relative motion to its past? for example if im moving at 10kmh today and at light speed tomorrow, then how much i age will change per day. So if you are measuring my total age by how I aged today + how many years have to pass so I can become what I look like. It would result wrong –  Ahmet Yıldırım Jun 22 '13 at 9:30

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If the universe were non-homogenous, you'd have a point. But the key point of Robertson-Walker cosmology is that you fit the data very well by having a universe that is very nearly spatially homogenous. This means that, if each observer clicks of $T$ amount of time since the big bang, then they will all agree that there is no special point in the universe (like a center or an edge), and will all agree on the general geometry and shape of the whole universe.

Since you have this global time parameter, you don't get the effects you imply in your question. Everyone can agree on what $7 billion years after the big bang, at this point) means.

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As with the twin paradox, you need something to break the symmetry between two observers, or else there's no way you can get any effect. The standard way of defining the passage of time in cosmology is in terms of a clock that is at rest relative to the average motion of matter (CMB, Hubble flow). The universe is very nearly homogeneous, so there is nothing to break the symmetry between two such clocks that are located at different places.

As a side issue, you can't apply the usual special-relativistic equation for kinematic time dilation to cosmology. This is because general relativity doesn't have any unambiguous way of defining the velocity of one object relative to another object separated from it by a cosmological distance. I can say that galaxy A is moving away from galaxy B, or I can say that they're both at rest and space is simply expanding between them, causing their distance from each other to increase.

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I was thinking breaking symmetry not between 2 present observers but with past & present of the universe. What im saying is; what if universe was not expanding at a constant speed. So if we are calculating the age of the universe by (Current Expansion) / (Expansion per day) We would end up with a wrong answer. Because Expansion rate might change over time. Which can also cause difference in length of yesterday and today, for example. –  Ahmet Yıldırım Jun 22 '13 at 9:55
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@AhmetYıldırım: current observation actually says taht the expansion rate IS changing with time--the term 'Hubble constant' is a bit of a misnomer. That doesn't change the fact that the age of the universe is a calculable number. –  Jerry Schirmer Jun 22 '13 at 23:36

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