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The idea behind Boltzmann brains are that if you are willing to wait a long enough time, then very unlikely statistical fluctuations will be observed. One such fluctuation would be for a brain to momentarily fluctuate into existence complete with a set of memories corresponding to, say, your total life experiences to date. The brain would then promptly ...

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These are not easy questions and there is no definite answer for them. There are plenty of cosmological models which we believe to be at least partialy true, and they do adress some of these questions. However, it is difficult to be entirely confident in their validity. I think most of cosmologists believe that there is infinite amount of matter in the ...

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Invariants are useful, in general, because they represent something that all observers can agree upon. Relativity showed us that the concept of time-intervals, spatial-distances, and even sequences of events can be drastically different from different observers. So how can one observer 'relate' to another? I.e. how could I, standing still, figure out what ...

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The spacetime interval invariance property allows us to, for example, compare the rate of time passing for two observers moving at relative velocities to each other. Although no observer in the universe is at complete rest, the interval is a benchmark for comparison of the physical effects of differences in velocity, or indeed location. Say one observer is ...

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It's flat as in "the sum of the angles in a triangle is 180 degrees". In curved spaces this well known result from Euclidean geometry does not hold. On the surface of Earth, for instance, the sum of all angles is always greater than 180 degrees, we just don't notice it when we are looking at a small piece of the surface, but take a globe or a beach ball ...

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I will use most of @Ted answer to describe 'hot' but I will ask a more basic question: I think the best way to think about it is that the sentence "the photons have cooled" is simply describing a fact, not explaining that fact. At early times, the photons at any given location had a thermal (blackbody) distribution corresponding to a high ...

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First of all, the Universe isn't expanding according to "current theories". It is an observational fact. Second, there is no center of the Universe. Space was created, and started expanding. This expansion pulls everything away from each other. Galaxies lie approximately still in space, but space is expanding. This means that no matter where you are located ...

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First of all, there is NO centre in the universe. I know it's not a good analogy, but think of the universe as the surface of a balloon. Forget the interior, we're only looking at 2 dimensions, whereas the real universe has 3 of them. Put some ink dots on the balloon, which represent galaxies (note: NOT planets). Now inflate that balloon. You'll see that ...

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EDIT: My first answer seemed to imply that radiation is at rest in the Cosmic Rest Frame. Radiation is not in rest in any frame. See below. The sentence shouldn't be read as "[velocity of energy] forms", but "velocity of [energy forms]"$^\dagger$. The sentence refers to "energy forms", i.e. the different forms in which energy can manifest itself. These ...

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An infinite "universe full of water" is actually very close to how the real universe is typically modeled, except that instead of water it's the right mix of ordinary matter, dark matter, radiation, curvature and cosmological constant. On large scales it's reasonable to assume that the density of each component is everywhere equal at a given time. And ...

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