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6

Update: According to this paper, "On the Interpretation of the Redshift in a Static Gravitational Field", the answer I give below is a common but misleading interpretation. The classical phenomenon of the redshift of light in a static gravitational potential, usually called the gravitational redshift, is described in the literature essentially in ...


5

The thing is, we don't completely base our understanding of the expansion of space on galaxies 7 to 14 billion light-years away. For evidence that the universe is expanding, look at Edwin Hubble's original paper in which he confirmed what we now call Hubble's law. The galaxies he studied are on the order of millions of parsecs away. Multiply that by 3.26 to ...


4

This is yet another instance of taking the ubiquitous balloon analogy too far. See, while it's a wonderful way to express the expansion of the universe, there are some misconceptions that arise from it: We live in a universe of finite size (we don't know, but we think not) and non-zero curvature (according to WMAP, we don't, or at least we think we don't) ...


4

This is a commonly considered idea, of which one variant is the "Hubble bubble". Anything that happens outside of the visible universe, is, after all, in principle unknowable to us.


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I'll answer your question with an analogy. Imagine a really small balloon, so small that it occupies a point. Now, imagine that the balloon is expanding uniformly outward from that point. Note that that central point is not part of the balloon. It's the same idea as to what happened with the BB. In this analogy, the universe is the surface of the balloon. ...


3

The problem is analogous to the physics of gases. Do we need to describe the chaotic motion of every molecule before we can determine overall properties? No.


3

The width of a SN light curve is changed due to a time dilation between the source and the observer. If the source emits light with wavelength $\lambda_\text{em}$, it will be observed with wavelength $\lambda_\text{ob}$, so that its redshift is $$ 1 + z = \frac{\lambda_\text{ob}}{\lambda_\text{em}}. $$ We can also write everything in terms of frequencies ...


2

First of all, it appears that you assume the centre of mass of the two-body system lies in the middle of the path between these bodies. This, however, isn't true. The centre of mass will lie closer to the star because that is where the majority of the mass is situated. If we define $r_M$ as the distance between the star and the c.o.m., and $r_m$ for the ...


2

The definition of conformal time is actually $$ a\,d\eta = dt\Leftrightarrow d\eta=\frac{dt}{a} $$ which gives you the correct result.


2

I'm not sure if that touches your question, but the universe is thought to be non-chaotic in the long term behaviour because of some anisotropy in the initial conditions (at least this is the general opinion). I watched a cool vid about that a couple of days ago. The point for which I agree with you, is that if looking at a certain situation, in general one ...


2

You seem to be misunderstanding the depth of the prediction we've made of the past in saying that the Big Bang happened. You do make a very valid point that chaotic systems even with as few elements as the solar system are practically impossible to past-predict (I'm going to start using the word "postdict"1 because it makes me feel better). I'm more than ...


2

The problem with this question is in the premise that where dynamical chaos is applicable nothing is predictable or can be extrapolated to the past. This is a wrong premise. Take this demonstration of a chaotic system. Note that it is computer simulation and of course it fits real data. Computer simulations are time symmetric, so the individual points can ...


2

Galaxies are not moving away from us, it is the space between us and the galaxies (and everything, in general) that is continually expanding. This is allowed to happen faster than the speed of light, because no object actually crosses the light speed barrier in the process. So consequentially, the universe has no size constraint like the one you've stated.


2

As Ben Goldacre says, "I'm afraid it's a bit more complicated than that." Phil Plait (Bad Astronomy) has occasionally written about this. Astronomers don't have a firm definition for the 'border' of a galaxy, tho' certainly objects classified as belonging should show some sort of contained orbit. But it gets worse, as they also have rough categories of ...


2

The latest data is from the Planck satellite, and you can find the results in this 15MB PDF. The matter and dark energy densities are; $$\begin{align} \Omega_M &= 0.315 \pm 0.017 \\ \Omega\Lambda &= 0.686 \pm 0.020 \end{align}$$ So we get a total density of $\Omega = 1.001 \pm 0.026$. So within the 2.6% experimental error spacetime is flat.


2

No. It is perfectly possible to have a flat universe that expands forever and is accelerating. Dark energy is what makes this possible. Whilst the curvature of the universe is defined by the sum of all the energy densities in it, the effects of matter (baryonic or dark) and dark energy are quite different on its dynamics. It is in fact quite possible to ...


2

No, the argument is not correct. The spatial "conformal" coordinate $R$ in which, together with the conformal time $\tau$, the angle of the light rays is 45 degrees is not $\rho$ but nothing else than $r$: $$ ds^2 = -dt^2 + a(t)^2 dr^2 = a(t)^2 (-d\tau^2 + dr^2) $$ If you want a diagram with $\tau$ on the vertical axis where the light rays are drawn at 45 ...


1

it must have started from a single point This is a common misconception popularized buy the media. Imagine this grid: Imagine each square getting larger. If you think about it, you will see that each point on the grid is expanding. The grid is the universe. Each point on the universe is its own "singularity".


1

Well, yes. "Expansion" of time as you call it is the cosmological age. The "direction" of progression of the time defines cosmological arrow of time.


1

As somebody said in the comments, physics has no "proofs". It has measurements/data and mathematical models that attempt to fit the data with specific assumptions. At most models are validated, not proven, if all known observations are consistent with the mathematical model. In the case of dark matter the first indications of its necessity in a ...


1

The balloon analogy imagines the universe as a 2D surface expanding around a central point as it moves through a 3rd dimension of time. This may be the origin of confusion as in reality there is no 2D surface of expansion, like a wave front, but rather an expansion of 3D spacetime, wherein every point in space quite literally is its own central point from ...


1

There are two ways I can answer this question. I'm pretty sure one of the ways is, while technically correct, mostly worthless to you because it ignore the question you're trying to ask and focuses on the question you did ask. So let's start with that one. The redshift used by Hubble comes from expansion only and from gravity only. In general relativity, ...


1

Let us suppose the holographic principle is indeed correct and that there is a (3+1)-dimensional quantum gravity theory that explains our universe, which has an equivalent description as a (2+1)-dimensional system. This simply means that the two descriptions cannot be distiguished so there is no physical experiment that could determine if we "actually" live ...


1

On the scale of the Solar System the cosmological constant makes a negligable difference, and the Schwarzschild metric remains an excellent description of the geometry. If you want to include the effect of the cosmological constant this can be done by using the Schwarzschild-de Sitter metric instead.


1

As pointed out in the answer above, the observations that lead to the dark energy theory were not all distant (7-14 billion light years), but less so. Dark Energy expansion is observed throughout much of the observable universe - not just the very distant. Also, consider the basic hubble discovery - galaxies 4 billion light years away were moving way from ...


1

It seems that you are mixing up the distance between the planet and the star and the distance between the star and the centre of mass (both are called $r$ in your derivation). Try to use $r = r_M + r_m$, where $r$ is the total distance between planet and star, $r_M$ is the distance between the star and the combined centre of mass,and $r_m$ is the distance ...


1

It is not the laws of Physics that evolve, it is our understanding of them which does. Well, I cannot prove that there exist constant a priori laws that the Universe obeys, but I sure have elevated this practically to an axiomatic state within my worldview. But what we call 'constants' obviously need not be fundamental constants - the only reason they were ...


1

Some redshifts are an example of the Doppler effect, familiar in the change in the apparent pitches of sirens and frequency of the sound waves emitted by speeding vehicles. A redshift occurs whenever a light source moves away from an observer. The energy balance is with the source of the photons. If the source is moving away the photons have less energy ...



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