, thank you as well for your posting your questions! This has been very good material for discussion.
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what I was suggesting was the problem of infinity. It's like dividing by zero. You can't do it.
Yes, of course. I think of infinity as a concept, not a number. The simplest case is to imagine dividing something into smaller and smaller pieces. The smaller the pieces, the more of them you get, and "in the limit" that the size of the pieces goes to zero, the number of them trends to infinity. What infinity means here is that no matter how small you make your cuts, I can in principle choose a smaller cut and obtain a larger number of pieces. But dividing something into pieces of zero
size makes no physical sense. "Infinity pieces" is not a number of pieces.
With the Big Bang theory, I can happily say that none of our understanding of the universe is contingent upon dividing by zero. The Big Bang theory is about when the size of the universe was very small, but not zero. The temperature and density and so forth are very large, but finite. Presumably what really happens with the initial instant of expansion at t=0 is that these quantities are not truly infinite, and the size not truly zero, but just very, very close to them.
With black holes, the classic prediction is that everything that falls into them goes to a point of zero size at the center. We recognize this is absurd. Whatever the "singularity" in the black hole really is is probably not an infinitesimal point, but something "close" to that. However there is a very nice property of gravitational field
which says the gravity outside of any spherically symmetric clump of matter is exactly the same as if that clump were compressed to a point. In other words, it doesn't matter whether it's a true singularity or something small but of finite size inside the black hole. The rest of the black hole's properties are exactly the same in either case. So we can treat it as a true singularity and get all of the correct predictions for how black holes behave!
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I was told many years ago (and its possible this was false, or has since been disproven), by a reliable source (a professor), that tests had been conducted in a vacuum (or at least as close as it is possible to get) dropping a feather and a ball, and though the time difference was extremely small, the objects did not touch the ground at the same time, which contradicts our understanding of gravity and the laws of motion. Is this some sort of science myth?
That would be a test of the "equivalence principle"
, which says that all objects, independently of their mass, fall with the exact same acceleration in a gravitational field (after excluding any other forces, like drag with the air). It is an important principle for general relativity, and there are many ways to test it, such as with pendulums, dropping objects in vacuum, and observing satellites in orbit.
I don't doubt someone may have done a drop test and found a difference in their fall times, but I would strongly doubt that the difference was real and not caused by imperfections of their setup or failure to account for other effects. At the very least, dropping two objects in a vacuum chamber is not a very high precision test. Here is a history of some experimental tests of the equivalence principle, and their precision:
In other words, the equivalence principle has been tested and shown to be correct to within 1 part in a billion billion! So I believe you can be confident in using the equivalence principle in any situation you may encounter which might depend on it.
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A universe which always "was" and has no limits or boundary, simply does not compute. But then again one that began at t=0, does not either.
I don't think that either case would be nonsensical or forbidden by nature. Ask instead, "what is consistent or inconsistent with observations?"
Let's propose for the moment that the universe is infinite in size and age and uniformly filled with the same stuff. If this is true, then the night sky would be as bright as the surface of a star, because every line of sight would intersect a star. Obviously, this contradicts observations. So that set of propositions must be false.
What parts are false? Maybe space is no longer filled with stars after some distance. Can we test that? Actually, we can! If this was the case, then we would observe that edge as a sudden cutoff in the amount of light reaching us after a certain distance and redshift. It would also contradict the principle of homogeneity, where we observe the universe is uniformly filled with the same stuff at all distances.
Maybe instead the universe is finite in size? Again that can't be the case because if it was also infinitely old then we would see that edge.
The solution is that the age
is finite. The night sky is not as bright as a star because only light emitted from within a certain distance of us has had the time to reach us. We know that this is the case, because we can observe how the universe has changed over time. The farther back we look, the hotter and denser it was, ultimately going back to what was very nearly a singularity state of extraordinary high temperature and density. We observe the Cosmic Microwave Background radiation, emitted from when the universe was 1100 times denser, and so hot that atoms could not exist. Before that and even closer to that initial moment of expansion we call the Big Bang, conditions were so extreme that even protons and neutrons could not exist. The universe was a violent sea of exotic subatomic particles.What conditions were like "before the Big Bang", or if there is even a meaningful answer to it, is totally unknown. But we may as well call this initial hot and dense state "the birth" of the universe as we know it.