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There are two parts to your question. First, why can we see things "46 billion light years away" if the Universe is only about 13.8 billion years old? Because the Universe is expanding. How far does a photon travel in 13.8 billion years in an expanding Universe? It depends on the rate of expansion. I'll give a simplified example to illustrate the point: ...


5

Is time an illusion? No. I think it's best to think of it as something like heat. You know what heat is, especially if you put your hand on a stove: szzz aaargh! Heat is definitely not some illusion. However it is an "emergent property". Think about the kinetic theory of gases. The temperature of a hot gas is something like a measure of the average kinetic ...


5

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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OK, I'll give this a shot, cause . . . why not. The article you quoted covers a lot of ground - perhaps too much ground. And I'm not sure the quote of Matt Strassler is fair because he's answering a very specific question and while the source is given, it's not mentioned that it's a specific question that he's answering. but, lets jump to this part: ...


3

This would contradict general relativity. Because there are no static solutions of the einstein equation with localized curvature not being caused by some mass distribution.


3

Not quite likely, simply because of these experimental facts: a.) Distant Gravitational lensed: We observed the following picture, and it can't be by luck for galaxies to arrange themselves like that. One strong suggestion is there is something big (therefore it can't be black hole) and massive between. b.) Gravitational rotational curve: Classical ...


3

The problem with your question is that velocity is relative so there is no absolute way to say whether something is travelling through space or not. Any observer can set up some time and space coordinate system $(t, x, y, z)$ to measure positions of spacetime points. The observer can then use these coordinates to measure changes in position with time i.e. ...


3

A black hole is a 4D object, but that's because all objects are 4D as they live in a four dimensional spacetime - three spatial dimensions and one time dimension. However what I suspect you're asking is whether there has to be an extra spatial dimension for space to bend in, making five dimensions in all. If so, then the answer is that no there is no extra ...


3

To expand a bit on the others' answers, a couple of ways to visualize/understand the difference between intrinsic and extrinsic curvature: Intrinsic curvature, as the name suggests, only deals with stuff that lies inside a surface/space/manifold etc. (I will use the term manifold) If your lines, triangles, etc. don't work the same way as they do in ...


2

Because near matter spacetime isn't expanding, and if it isn't expanding it can't be stretching the matter. The expansion of spacetime is a prediction of general relativity for the special case of a matter distribution that is homogenous and isotropic. If we feed in this condition we find that the geometry of spacetime is described by an equation called the ...


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No, because of the large scale. Doing things like this only seems instantaneous. The speed of a push on this object is actually the speed of sound in the object.


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There is quite a nice description of this area in the Wikipedia article on the shape of the universe. As well as the torus possible shapes include the Poincaré dodecahedral space and the Picard horn. Googling will find you lots of stuff about the duodecahedral shape, and despite its potential for causing sniggers there is quite a bit on Picard's horn as ...


2

The reason it's thought of as expansion of space rather than just things moving farther apart through space is that the math of general relativity describes it that way, and GR has been well-supported by experiments so far. GR is all about curvature of spacetime, and curvature of anything can be determined by how we measure distances. A lot of the math in ...


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

Let embrace your attitude here. If the atom is 'empty', all that we have is charge and mass. By Newton's third law we have that this 'empty' with charge and mass need to absorb energy and momentum too. Now we have an empty space with charge and mass that absorb momentum and energy. Furthermore, this empty are allowed to move through space, because is ...


2

Suppose Andromeda is at rest relative to earth. You are on earth, holding your ruler, which just touches Andromeda. Now you instantly start traveling toward Andromeda at a high speed. Your ruler, of course, travels with you, still pointing toward Andromeda. Your journey just began an instant ago, so neither you nor your ruler has yet moved appreciably. ...


2

Yes, you're quite correct that in the example you describe Andromeda can be moving faster than the speed of light. But that's perfectly in accord with special relativity. It's just that the rule that nothing can move faster than the speed of light is true only for unaccelerated motion. Although beginners are (usually) taught special relativity using ...


1

Just to complement John Rennie's answer, one can always perform a Lorentz transformation to a coordinate system such as the particle is at rest for a given time. It's called instantaneous rest frame (IRF). This frame changes point to point, unless the particle's velocity is constant. In such a frame, we have $ ds^2 = -c^2d\tau^2, $ where $\tau$ is the ...


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The high speed of travel causes both time dilation and space contraction, so the numbers add up from both frames of reference. For the astronaut traveling at near lightspeed, the space between him and Andromeda is contracted; at a very high speed, Andromeda would appear to be only 25ly from the Milky Way, but since the astronaut is traveling slower than ...


1

I feel like it is correct to call gravity a force. As you know, there are several models for how the universe works. The Newtonian model. The relativistic model. The quantum-mechanical model. Within certain different boundaries of scale, these each work very well at predicting things that will happen. However the language or terminology of each ...


1

Is it possible to travel ONLY through Time and not Space? Well, in a sense, we can't help but travel through time, but in the way that I think you mean, one way to do it is to hover just above the event horizon of a black hole - preferably a super-massive one so the tidal effects wouldn't be a problem. Park a spaceship at 1/10th of 1% greater ...


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Over the real numbers, any non-degenerate quadratic form is determined (up to a change of basis) by its signature, which consists entirely of $1$s and $-1$s.


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OK, let's take you questions one by one. Theoretically, the answer is yes. If you manage to observe the people on the planet from an area not in the vicinity of any significant mass, you would see the people moving much slower, clocks running slower, etc. Although the speed of light is a constant in a vacuum, the frequency of the light will be different ...


1

Our model for spacetime is that of a manifold, which is the mathematical term for something that looks like $\mathbb{R}^n$ in any zoomed-in patch, and where all these patches are stitched together in a sensible way. On our manifold we have $n$ coordinates -- real numbers that describe each point and vary smoothly from point to point. We also add to our ...


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Everything about special relativity is contained in the Minkowski metric. That single equation contains everything you need to know about SR. There are no end of questions in this site demonstrating how various things can be calculated from the metric. Re your comments above: note that it is an assumption that $ds^2$ is an invariant, and that the metric ...


1

You are absolutely correct that three-dimensional sections of space-time do not satisfy Euclidean geometry -- they are not flat. However, they are almost flat. On room-sized scales the curvature is very small indeed. I don't know the exact context where you read that "tridimensional space sections of space time continuum (whatever its number of dimensions) ...



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