|MadSci Network: Physics|
This is not a "stupid question" but rather gets at one of the misconceptions about the Big Bang. The Big Bang was NOT the expansion of the universe from a very tiny object to a very large object. A variety of evidence, most notably the size scale of variations in the cosmic microwave background as imaged by the Wilkinson Microwave Anisotropy Probe (WMAP), make it clear the universe is _infinite_ in size. The parts of the universe we can see are not infinite because the universe is of a finite age so light from regions more than 13.7 billion light years away has not had time to reach us yet.
A proper view of the Big Bang comes from considering that the observational evidence of galaxy redshifts suggests the universe is expanding. Run that expansion backwards and you find that the early universe, even if infinite in size, was much DENSER than it is today. Furthermore, like any gas, if you condense it, it will get hotter, so the early universe was HOTTER and DENSER than the universe today.
Now, to consider the velocity problem you brought up... you correctly note that velocity is typically defined
v = d/twhere "d" is change in position (a.k.a. displacement) and "t" is the change in time (or time elapsed). Notice I said "change in time"... The universe has a finite age, so the "t" is not infinite, but finite. So there is no problem with "dividing by infinity" which would lead to zero velocities and not infinite ones. If you try to argue at times approaching the Big Bang, the time elapsed approaches zero (since dividing by zero time gives you infinite velocity), you are ignoring the fact that the distances covered by objects during these tiny time intervals is also very tiny. A small number (distance) divided by a small number (time) need not be infinite.
In fact, if you rewrite the above equation:
t = d/vyou can see that the time elapsed equals the distance covered divided by the velocity (i.e. - How long does it take to go 30 miles at 60 miles per hour? 30 mi/(60 mi/hr) = 0.5hr). A neat little experiment you can pull off is to measure the apparent velocities of galaxies (v) using redshifts, then estimate their distances (d) from us. If you then try to figure out how much time it would have taken the galaxies (or the gas that initial formed it) to cover the distance between us and the current location of the galaxy, it turns out the times for all the galaxies to cover these widely varying distances are about the same, indicating all the galaxies were once near us at around the same time, roughly the time of the Big Bang. In fact, Hubble's law, which describes the velocity of galaxies as a function of distance from us, reflects just this fact.
By the way, one subtle issue that actually gets closer to the issue of velocities greater than the speed of light... Galaxies can be receding from us at velocities greater than the speed of light (and are therefore not visible to us). This occurs because it is NOT the galaxy that is moving, the space between us and the galaxy is expanding. The 'speed of light' limit applies to the motion of matter, not to the expansion of the space between the objects.
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