# Tag Info

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The definition of entropy is $$S = -k \log(\Omega),$$ where Omega is roughly the number of microstates (ways of ordering your particles) compatible with the macrostate (what you observe macroscopically). Intuitively, you can say that, if you have particles inside a box, and you increase the size of the box, you can arrange them in more ways; therefore, the ...

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We model spacetime as a manifold and a metric. Broadly, the manifold gives us the dimensionality and connectivity while the metric provides a method of specifying distances. The equations of General Relativity allow us to calculate the metric from the stress-energy tensor (or vice versa if you're Miguel Alcubierre). The point that jinawee is making in his ...

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I don't think we know for sure. For example see this article (the paper is on the Arxiv here) suggesting that the acceleration could be anisotropic. However if there is an anisotropy then it's small, and to a first approximation yes the acceleration is isotropic.

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The (nearby) "separation between objects" you are referring to is the space-time metric. A metric in cosmology describes the expansion of space on large angular scales (low $\ell$ on the angular power spectrum of the universe). Without going into the mathematics, the expansion of space is driven by cosmic inflation, and is affected by things the amount and ...

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There is a three dimensional shell of galaxies (none currently observed) that have a gravitational redshift relative to us that is consistent with a relative motion at the speed of light. If you moved to any other galaxy in the universe, there is a very high probability that they would observe a different such bubble. If you look sufficiently far into ...

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This going to be a rather approximate answer because it involves lots of estimated quantities like the current density of matter and the value of the cosmological constant. The second Friedmann equation tells us: $$\frac{\ddot{a}}{a} = \frac{-4\pi G}{3}\left( \rho + \frac{3p}{c^2} \right) + \frac{\Lambda c^2}{3}$$ It's conventional to take $a = 1$ at ...

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If you are sincerely asking about the fate of spaceship departing the solar system, then you are asking a question about the standard model of cosmology. Instead of worrying about relativistic effects we'll concern ourselves with a photon that leaves our galaxy in a direction so that it hits nothing, and just keeps traveling. Faster than any spacecraft that ...

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Fundamentally, the misconception here is that something that is expanding must be finite. This is simply not true. When we say the universe is expanding, we mean the distance between two stationary observers, sitting still as best they can, grows over time. But it is entirely possible for an infinite thing to have this property. Imagine the real number ...

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To start with, space was not created, space had always been there (yes even before the big bang). What was yet to be created was the incredible and ever expanding universe(Big bang ?). Space is infinite on it`s vastness and time because literally, space is the absence of stuff (sorry, couldnt think of a better word). Back to the answer: As you have heard ...

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The molecules do not expand, because they are kept together by the electromagnetic interaction. The same applies to hadrons (strong force). These interactions have their own coupling constants, independent of gravity. So space expanding in an atom is like trying to pull the atom apart very slowly by a force which does not hold the atom together. The ...

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You can see the expansion with the Doppler Effect. Nothing else is expanding in the Universe except from the Universe. The Planck length is the same because it's a constant length. The stars and the Galaxies are getting pushed away from each other due to the red shifts. Here's a video on redshifts: http://www.youtube.com/watch?v=TLwiOToY79I The objects in ...

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Your question is hypothetical since the universe is almost certainly not closed and will not recollapse (pace Andrei Linde). However if we assume an FLRW metric and a closed universe then all comoving observers will agree on the time between the Big Bang and the Big Crunch so the twins will have aged the same amount. If you have in mind a different scenario ...

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