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**Physics, Astronomy & Cosmology / Re: How Can We Know The Cosmos Age If We can Only See The Observable ?**

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**Today**at 15:12:44 »

A quick question, Halc: taking your example of a time dilation factor of 4, suppose our galaxy was receding slightly faster, say 1.03c, what becomes of the Lorentz factor? It will now be a complex number. Does this feed through to a complex age?The recession rate of 0.97c was relative to the 'inertialish' frame of the distant place. Under such a frame, recession rates cannot exceed c. The recession rates you see published are rates of increase of proper distance over time, not speeds. They're relative to an expanding frame, and in such frames, recession rates are rapidities, not speeds. (see bottom of post for example) Rapidity adds the regular way and has no upper bound. If, relative to this expanding frame, galaxy X is receding from us at .8c and Y (at twice the distance) is receding from X at 0.8c, then Y would be receding from us at 1.6c. The speeds don't add the relativistic way that they do in inertial frames.

Few of the typical rules of physics apply in such a non-inertial frame. Neither energy nor momentum is conserved. Moving objects tend to come to rest. The wavelength of a light pulse grows over time, the energy going down with it. Light does not travel at c except locally.

Relativity of simultaneity still applies, hence if one is considering the 'current age' of the entire universe of points in space well outside our visible universe, given the right choice of frame, one can make, at that distant location, any point in time be simultaneous with us at Earth, hence the distant parts of the universe having no defined age. So they define a preferred frame, which is the frame in which all events on comoving worldlines at similar gravitational potential as us, are simultaneous with each other. This is known as the frame of constant cosmological time (or just cosmological frame), and it is not an inertial one.

Apologies if that got a little complex. I did several edits trying to make it simpler/more clear.

An example of rapidity. There is a highway to the next galaxy with little signs every light year like mile posts. In my fast ship, I can measure my rapidity by the rate at which they go by. One sign per year is a rapidity of c. If I accelerate more, I can see one go by every day, and hence I can cross to the next galaxy before I die with a fast enough ship. The ship is moving at a speed of under c, but a rapidity of 365c in this case (not yet fast enough to get to the next galaxy in a lifetime)

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