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Space is expanding. However, nearby atoms (e.g. those in a metre stick) are not moving away from each other because the inter-atomic forces restore them to their original positions. Similarly, as the space between the earth and the sun increases (at an insignificant rate), the gravitational force restores the earth and sun back to their equilibrium ...


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Have a read through Did the Big Bang happen at a point? and the answers to it. The singularity at the Big Bang is the zero time limit of the equation (the FLRW metric) that describes the expansion of the universe. Most physicists believe that this is a mathematical artefact and does not describe what actually happened. It seems likely that some quantum ...


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If the curve is a geodesic then in the coordinate system of an observer moving along the geodesic coordinate time and proper time are the same. That's because in the freely falling observer's coordinates $dx = dy = dz = 0$ and therefore $ds^2 = -c^2dt^2 = -c^2d\tau^2$. This makes proper time a natural way of parameterising the curve because it's just the ...


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You ask: Is it that space is not expanding within the smaller structures or is space expanding through these structures? where I've highlighted what I think is the key issue. The phrase space is expanding is a convenient metaphor to describe the expansion of the universe, but it is only a metaphor and taking it too literally can lead to confusion. It ...


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It seems to me that as the universe expands, it would lose density and therefore clocks would run faster as the universe expands. Is this correct? No. At a conceptual level, you can't define "faster" if you don't have something else to compare with. In technical terms, gravitational time dilation is only defined in a static spacetime, and cosmological ...


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In flat space the surface area of a sphere is $4\pi r^2$. In positively curved space the surface area of a sphere is less than $4\pi r^2$ and in negatively curved space the surface area of a sphere is greater than $4\pi r^2$. By $r$ I mean that if you start at the centre of the sphere with your trusty (infinitesimal) ruler and measure the distance to the ...


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It's a fundamental principle of both special and general relativity that the line element, $ds$, given by the metric: $$ ds^2 = g_{\mu\nu} x^\mu x^\nu \tag{1} $$ is an invariant. That is, all observers in any coordinate systems will calculate the same value for $ds$. It's this fundamental symmetry that is responsible for time dilation, along with all the ...


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There is a simple thought experiment that you can use to show this. Consider a rocket accelerating in space, and consider a clock at the top of the rocket, and a clock at the bottom of the rocket. If we do this, we'll note that, if the rocket is going away from us, then the clock at the front of the rocket will have sent light to us at a time when the ...


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No. Gravity, in GR terms, is the tendency of particles to follow, in the absence of other forces, the geodesics on the spacetime manifold as determined by the metric on it, which is in turn determined by the distribution of matter through the Einstein field equations. The four-velocity of a particle is the tangent vector to its worldline (which is, with ...


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The answers above are all correct as far as they go, but the next step is even more stunning. If I am A, the object at rest, then I am moving through spacetime at the speed of light. My friend B gets on a spaceship and rockets away at a high constant velocity and to me his time appears to slow down because of his velocity through space. But if my fried B ...


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This is a very late response, but there is no accepted answer as of yet, and none of the answer quite hit the mark. Regarding the magical collision hypothesis, that smacks of being rather non-scientific. Scientists as well as Missourians are wont to say, "Show me!" Other than the fact that Venus's rotation is anomalous, what, exactly, is the evidence for ...



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