# Tag Info

29

This is a rather lengthy answer as I tried to go a bit in depth; there is a short summary at the end. Will we see more or fewer stars with time? The short answer to this is: We see less stars with time, due to the fact that cosmic expansion is accelerating. Although what we really see at the relevant distances are galaxies; single stars are far too far away ...

18

Light from recombination is not "constantly shining" and that's why you see it. At a given time in the universe's history (actually a slightly extended period but I'll keep things simple), and only at that time, photons decoupled from the ambient plasma and started travelling freely from all points in the universe. The photon background you see at any time ...

17

Individual photons certainly don't have a rest frame. However, there is a rest frame in which the CMB is almost perfectly isotropic (the deviations from a perfect blackbody spectrum are of the order of 1 part in 100,000), and for convenience we call that the rest frame of the CMB. That frame is essentially the rest frame of the plasma which emitted the CMB, ...

17

The problem lies in the boundary conditions. Ignoring factors of $G$ and $\pi$, gauss's law of gravitation relates the gravitational potential $\Phi$ to the mass density $\rho$ by $$\rho=-\nabla^2 \Phi.$$ In order to have a unique, well-defined solution, we need to specify boundary conditions for $\Phi$. Usually, we assume that $\rho$ dies off sufficiently ...

16

It is not possible to calculate the coordinates of the point where the Big Bang happened, because there is no such point. All of space is expanding away from the rest of space, in a manner that looks the same throughout space (the technical term is that the universe is homogeneous). The Big Bang happened everywhere in space.

14

I'm going to respond to (v1) of the question, which asks why the night sky is dark (black and unlit) compared to the day sky even though there are many light sources at night. The updated question references Olber's paradox, which has been answered many times before. Like most things we see in everyday life, there are a number of reasons contributing to this....

13

Let's start with some general notions. The Cosmological Principle postulates that at each location in the universe one can define a hypothetical observer to whom the universe appears isotropic and homogeneous. Such observers are called comoving observers, and we can define a comoving coordinate system, in which these observers remain at rest; this means that ...

11

Explanatory Framework: Foliated Spacetime In General Relativity, which is used to describe the universe on cosmological length scales, spatial and temporal distances are no longer absolute quantities. Furthermore, in astronomy, there are several methods to determine a distance, which could disagree on cosmological length scales. Therefore, it is ...

9

As it happens this issue has just been mentioned in the Science Fiction Stack Exchange. The simple answer is that we cannot know that there is anything outside the observable universe. The best we can say is that it seems likely. We approximate the universe using the a spacetime geometry called the FLRW metric. This is based on the assumption that the ...

8

Who is interested can find detailed information at wiki, or here The problem is known (as you added in your edit) as Olbers' paradox, and was posed already in the mid 1500's, by Johannes Kepler in 1610 and even later by Edmond Halley in the eighteen century, and curiously, even the novelist an poet Edgar Allen Poe anticipated possible explanations as to why ...

8

The CMB origin at about 380,000 years after the Big Bang is indeed the furthest we can see, IN THE ELECTROMAGNETIC spectral domain. And you are right that this is not about the full universe vs the observable universe, you are talking about a portion of the observable universe which is simply occluded from us not in principle, but because photons could not ...

7

You are thinking that the big bang happened in a particular point in space and then expanded outwards from that point. This is not true. The big bang happened at all points in space. This is because space itself expanded in the actual bang. Therefore each point in space has its own "horizon" of 13.7 billion light years across. This edge is due to light ...

6

If the Universe were "just expanding", there would be no limit to amount of CMB photons received. This is the gist of the Ant on a rubber rope puzzle: No matter how fast you expand a rubber rope / a Universe, it is always possible to travel an arbitrarily large distance in a finite time. And since CMB photons were emitted from everywhere in the Universe ...

6

Firstly, the light year measures distance, and not age. But I see your question here: "Can the radius of the universe(in ly) be more than its age (in y)?" The answer is (surprisingly) yes. In fact, this is indeed the case. Firstly, a little side story: This is something that confounded Einstein himself, way before we even knew about the Big Bang. When he ...

6

The bit about the spacelike hypersurface is simply a complex way of saying those observers can define their own notion of simultaneity. They pick a slice of space and say "the time value is the same everywhere here. I HAVE SPOKEN!". Of course, they have to define it in a way that preserves homogeneity and isotropy, but they can always do this if they are ...

6

The universe is not believed to have a boundary. But the global topology of space does not have to be a 3-sphere $S^3$ (for constant positive curvature), infinite flat space $R^3$ (for zero curvature) or a 3D hyperbolic pseudosphere $H^3$ (for negative curvature). General relativity only describes the local structure and curvature, not the global topology. ...

6

Updated 07.11 We can chose the model to discuss the problem and so let us chose: Model: Newtonian mechanics/Newtonian gravity, with the Universe filled with uniformly dense matter, interacting only gravitationally (in cosmology this called “dust matter”), and at the initial time of our spaceship journey all this matter is at rest. Hence my spaceship ...

5

If you knew the maximum entropy $S_{\text{max}}$ possible for a system then you know how many possible states there are because $$S_{\text{max}}=\sup_{p_n}\left\{-\sum_nkp_n\log p_n\right\}=k\log N,$$ where $k$ is Bolzmann's constant, and $N$ is the number of states. There is a limit to the amount of entropy a volume of space can hold, and such a maximally ...

5

What we do know is that the universe is expanding at an accelerating rate. (you've been incorrect in formulating that the observable universe gets larger with time, the observable universe actually gets smaller, with more and more galaxies and stars getting red-shifted to the point of invisibility.) So to claim that there is nothing more than the observable ...

5

You're right that the surface of last scattering (SoLS) is the farthest we can see in practice. This light is seen as the cosmic microwave background (CMB), observed e.g. with the Planck spacecraft. The term "observable Universe" refers to the farthest we can see in theory, and is defined as the distance a photon is able to travel in the time from the Big ...

5

One of my favourite dark matter theories is mirror dark matter: the entire dark sector has exactly the same physics as ours: there are dark electrons, dark photons, dark protons etc interacting with each other. This is exactly as complex as our physics. However, the theory then needs to find a creative way of explaining the relative smoothness of dark matter ...

5

First of all, how is it possible to think CMB, a bath of blackbody (BB) photons in space, as a reference frame? Doesn't quite match my Newtonian notion of reference frames. But it does. The references frame of $X$ is one where $X$ has zero momentum, and a photon bath has a measurable momentum and by choosing the right frame that can be made to be zero. ...

5

by choosing the location of × I can make it accelerate in any direction. This freedom of choice is the key to the puzzle. I'll assume Newtonian gravity in a static universe filled with a homogeneous dust. Let the ship be at the origin. The ship feels a force proportional to $x$ towards the centre of the sphere of radius $x$ centered at $\pmb{x}$, but it ...

4

I don't think so because the atoms would have had to travel faster than the speed of light to get to you (to form you) before the light they reflected got to you, and from what I understand, nothing travels faster than light.

4

The following passage is extracted from Stephen Hawking's book "A Brief History of Time": In fact, various contemporaries of Newton had raised the problem, and the Olbers' article was not even the first to contain plausible arguments against it. It was, however, the first to be widely noted. The difficulty is that in an infinite static universe ...

4

This is a very hard question to answer in detail as it requires several pages of mathematics to derive the required formulas (there is no easy fit like $F=-kx$ as you suggested) I will not derive the formula (it can be found in e.g. Dodelson) but after some work you obtain: \Delta(m-M) = 5\log\left\{ \left( \frac{c}{H_0}\sqrt{\frac{k}{\Omega_{total}-1}}(...

4

For the record: the question is based on a misapprehension of the FLRW model. The model assumes the universe is isotropic and homogeneous, and homogeneity requires the density of matter to be the same everywhere. If the universe is infinite, which is not ruled out by observation, then it contains an infinite amount of matter all at the same (average) ...

4

Why do we keep dark matter models simple? It's partly because science progresses best if, when we realise current theory is missing something we try the simplest way to address that first; if even that turns out to be empirically wrong we can add further complexity, but if we add complexity prematurely it can harm falsifiability (e.g. due to having more ...

4

If the universe has a FLRW metric, then there is a cosmological time $t$ that all observers at rest relative to CMB or the matter in the universe will experience at the same rate. This is true regardless of the curvature and whether the universe is infinite or merely unbounded. The radius of the observable universe (in co-moving coordinates) is calculated ...

4

The original definition of the problem is the best: if space is infinite and there are an infinite number of stars, eventually every ray hits a star. This has the implicit assumption that stars are finite, so I think your thought experiment fails on that note - if there are an infinite number of finite spans on [0,1], as opposed to points, then everything is ...

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