Hot answers tagged spacetime
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If the universe is infinite there is obviously an infinite number of ways of arranging the matter within it, so there is no requirement for the universe to repeat at large scales. What the article is suggesting is more subtle than this.
Suppose we take a finite volume. This could be as small as you, or as large as the observable universe, but in both cases ...
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Why don't you want to assume gravity? Gravity it is an experimental fact, a starting point for doing physics. General Relativy is a geometrical theory of gravity, built on the basis of Special Relativity and always having in mind that it should recover the non-relativistic Newtonian theory of the gravitational field.
The "pull down" is a deviation of the ...
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but they assume a "pull down" force themselves.
The images of flat sheets "pulled down" where the planets are do not reflect the fact that the curvature of spacetime is an intrinsic curvature that is measured by geodesic deviation.
What has been done, in order to help visualize the spatial curvature, is to take a two dimensional spatial slice and ...
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The gravitational field can indeed be assigned an energy. Unfortunately though whereas for, say, the EM field you can define an energy density at a point ($\bf{E}^2+\bf{B}^2$), for the gravitational field you can't do this. - Whichever way you define the energy in terms of the Christoffel symbols, you run into the problem that you can make them, and hence ...
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After the question was originally asked, the OP changed it to exclude the Big Bang. I don't understand the motivation for imagining that there would be a boundary anywhere else. The following answer addresses the question as originally asked.
First, we should recognize that any answer to this question is going to be model-dependent. The Big Bang is the only ...
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Spacetime (probably) does indeed have at least one boundary. Crazy Buddy mentioned three related questions in his comment, and reading these will help you understand why spacetime has a boundary in the past i.e. the Big Bang. This is a singularity and it is a boundary because you cannot follow geodesics back through it to earlier times.
If the universe were ...
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In your diagram where the black hole is just behind the observer on the line between the observer and the object being observed the answer is "yes", the apparent size of the object will shrink. The color of the object will be blue-shifted and the whole universe will appear to contract.
There is a great demo of the effect at Journey into a Schwarzschild ...
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Block time is not a physical theory. It's a philosophical interpretation. It can't be tested empirically. For these reasons it doesn't really make sense to ask for its status or whether it's accepted. You can poll physicists on whether they like it (there have been polls like this, for example, on the Copenhagen interpretation versus many-worlds), but the ...
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Since a worldline along the time axis on Minkowski diagram is at rest, it is more intuitive to measure angles from that axis instead, as then 'slope' is (space)/(time), i.e., a velocity. Then we have the trigonometric relationship:
$$\frac{v}{c} = \tanh\alpha$$
where Minkowski spacetime follows hyperbolic trigonometry because of the sign difference in the ...
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Why do you stop your largest angle with ten 9s after the decimal point? If you added more of them, then you'd get a smaller bound for the velocity. And you keep adding 9s ad infinitum and you'll "eventually" reach $89.\bar{9}=90$. So eventually, you'll see that the velocity could be arbitrarily small. This just means that the worldline can be vertical... and ...
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Early in the universe the expansion rate was much greater than it is today, which is a way of saying that spacetime was strongly curved. You really need general relativity to properly work out what happens, but a good way to think about it is that by the time a light ray gets from A to where B was, the expansion of the universe has carried B even further ...
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Massive objects distort spacetime, as described by the Einstein Field Equations. In turn, this causes particles to accelerate: the GR equivalent of $\mathbf{F}=m\mathbf{a}$ are the geodesic equations:
$$
\frac{\text{d}^2x^\alpha}{\text{d}\lambda^2} + \Gamma^{\alpha}_{\mu\nu}\frac{\text{d}x^\mu}{\text{d}\lambda}\frac{\text{d}x^\nu}{\text{d}\lambda} = 0,\qquad ...
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Angular momentum is a bivector, $J = x\wedge p$, and since the exterior/wedge product is antisymmetric, you do indeed get $n(n-1)/2$ independent components for any bivector. In general the Hodge dual provides an isomorphism between $k$-vectors and $(n-k)$-vectors. In three dimensions, $\star(x\wedge p)$ is an axial vector which and we call this ...
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Nielsen identifies a quantity, a ratio of "Casimirs", which he thinks is maximized by the particular gauge symmetry groups and space-time symmetry groups that we see.
He has previously had the idea that some of the observed properties of physics are "random" or "accidental" - e.g. that there is some complicated deeper theory and the simple observed ...
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Does the expansion of the universe soon after the Big Bang affect the
amount of time that light takes to reach us?
The time light has had to travel is simply by the age of the universe (or slightly less, because the very early universe was opaque). The age of the universe is 14 billion years, so that's how long the most ancient light has had to ...
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All points in the observable universe are "connected" in the sense that they can be acted upon by forces that have an infinite range (gravity and electromagnetism).
However, points that are outside of our cosmological horizon (due to the expansion of the universe) are no longer causally connected with points in our local vicinity, since they are receding ...
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The FLRW metric can be static, this is the solution that Einstein concocted before Hubble observed the expansion of the universe. The only way that Einstein could make his equations static was by introducing the infamous cosmological constant $\Lambda$. The general FLRW metric has the form
$$
\text{d}s^2 = -c^2\text{d}t^2 + a(t)\left[\frac{\text{d}r^2}{1 - ...
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All of our known physical laws including GR (which have so far assumed spacetime to be smooth and quite flat) breakdown at singularities due to the infinite curvature of spacetime. Hence, we say, "One second after the big bang..., An hour after the big bang..., etc." Because, we simply don't know what happened at the instant of big bang. If there were events ...
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It is General Relativity that changed our concept of space and time. Even special relativity assumes that time and space exist as coordinates even though it changes the metric with respect to the Galilean (Newtonian) relativity.
As physics started to be rigorously mathematically formulated in the eighteenth century , space and time were considered as ...
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