This derivation assumes, that the velocity is constant throughout the existance of the universe. But the essential message of Hubble is that the velocity increases with distance. The cleaner derivation assumes a sphere where the radius increases with constant velocity and then ask for the time when the radius was zero. In more detail the distance on a sphere is D = R×delta angle. The receding velocity is dD/dt. The delta angle keeps constant. So v = dR/dt delta angle. When this is brought into the Form v = H×D, replacing delta angle with D and R and assuming the radial velocity vr = vconst×t, the same result is obtained.
How can we calculate the age of the Universe by reversing expansion when we only know the size of the observable universe, couldn’t the actual size of the universe be 10 or 100 times bigger? In other words How can we calculate the age of the Universe by reversing expansion when for d=distance you are using the farthest “observable” star or galaxy, couldn’t there be galaxies 10 or 100 times farther away whose light has not reached us yet or never can reach us?
You don't need to know the size of the universe in order to know its age. You find another galaxy, let's say 50 million light years away and you determine how fast it is moving away from us. Then you use the equation: d = v t or t = d/v to find the age of the universe.
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Wow, you did a great job simplifying a very complicated concept. Thank you!
Thank you. Glad it was helpful!
This derivation assumes, that the velocity is constant throughout the existance of the universe. But the essential message of Hubble is that the velocity increases with distance. The cleaner derivation assumes a sphere where the radius increases with constant velocity and then ask for the time when the radius was zero.
In more detail the distance on a sphere is D = R×delta angle. The receding velocity is dD/dt. The delta angle keeps constant. So v = dR/dt delta angle. When this is brought into the Form v = H×D, replacing delta angle with D and R and assuming the radial velocity vr = vconst×t, the same result is obtained.
The unpleasant insight we get from this is that we live on the 3D surface of a 4D sphere.
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How can we calculate the age of the Universe by reversing expansion when we only know the size of the observable universe, couldn’t the actual size of the universe be 10 or 100 times bigger?
In other words
How can we calculate the age of the Universe by reversing expansion when for d=distance you are using the farthest “observable” star or galaxy, couldn’t there be galaxies 10 or 100 times farther away whose light has not reached us yet or never can reach us?
You don't need to know the size of the universe in order to know its age. You find another galaxy, let's say 50 million light years away and you determine how fast it is moving away from us. Then you use the equation: d = v t or t = d/v to find the age of the universe.