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How do we know that space expanded faster than a speed of light in inflation? Let us start from the beginning, on the reason that the Big Bang theory was proposed as a model for the universe. The reason was the observations that all clusters of galaxies were receding from each other. This is what happens from an explosion at the center, in three ...


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Inflation does not violate any local speed of light physics and there is no global prohibition in general relativity against spacetime points that are moving away from each other faster than the speed of light. Such spacetime points are simply not causally connected, i.e. there is no physical way to communicate between them (since light signals from one can ...


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time delation is very simple phenomenon.Time delation occurs because the speed of light is same for all observer in same media.so the rate of time experienced by the observer changes with respect to object moving near to speed of light because two events in space time having different time origin with respect to each other never coincide with each other.


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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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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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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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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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This effect was originally predicted in special relativity, time slows for an object undergoing acceleration compared to the observer, but Einstein's big leap to general relativity was realising that gravity is an acceleration - standing on the surface of the Earth or sitting in a rocket accelerating at 9.8m/s/s are (as far as the time dilation go) the same ...


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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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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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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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I read that an object at rest has such a stupendous amount of energy, $E=mc^2$ because it's effectively in motion through space-time at the speed of light and it's traveling through the time dimension of space-time at 1 second per second as time goes forward. This is wrong. What troubles me here, is the fact that it is traveling through space-time ...


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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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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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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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I know that on the smallest scales, general relativity predicts that space-time is flat It's part of the Einstein Equivalence Principle that on a small scale spacetime is approximately described by the Minkowski metric, but you need to be clear that this is an assumption used to construct general relativity and it is not a prediction of general ...


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I know that on the smallest scales, general relativity predicts that space-time is flat. This is not the case. First of all, General Relativity assumes that the spacetime on the smallest scales is flat. This is a pre-condition for GR mathematical apparatus to start to work. So, this cannot be the prediction of the theory. Second, if we try to predict ...


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"Quantum foam" is a physical phantasy, for which no evidence exists, so far. Having said that, contradictions between actual theories are normal and nothing to be upset about. Every theory has a range of applications, which is partly defined inside the theory and partly by its experimental limits. It is well understood, that Newtonian mechanics has nothing ...


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I would guess that Kaku is referring to the brane world scenario, though he has had to simplify it for popular consumption to the point where it is barely recognisable. String theory is most naturally formulated in ten spacetime dimensions, one time dimension and nine space dimensions, so the question is why don't we see all these dimensions. The brane ...


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Of course there are forward and backward. Now reduce the number of dimensions to just one, leaving just a magnitude Note that it is a magnitude, not an absolute magnitude. a direction paramaterized by two discrete symbols +,- has been added. No. There is only one value there which is a member of $\mathbb{R}$. The sign is part of the value. ...


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You're confusing the definition of a vector. A vector always has magnitude and orientation regardless of the dimensionality and they are not independent. In typical physics applications, the magnitude is the Euclidean norm of the vector. So in 3D, you have 3 components defined by scalars multiplied by the unit, or basis, vectors. In 2D, you have 2 ...


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I think that many different dimensions and metric signatures have their specific “privileges”. More general, different geometries in a broader sense, and, even more general, different underlying mathematical structures (such as fields other than ℝ) also could be models for space-time of some alternative physics. But is was just (necessary for me) ...


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My apologies that I can't follow your question enough to answer everything, in particular I can't see how you project your images. If you extended them in what look like straight lines to you, you'll get radial lines expanding from your position, but it seemed like you wanted a Cartesian grid. However I do want to answer the part about strain and its ...


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There is a known example where it looks like a black hole on the outside but is flat spacetime on the inside. Imagine the funnel shaped exterior of a black hole and take the entire part outside of the event horizon, which is a spherical shell of surface area $4\pi r^2$. Then take a spherical ball of Minkowski space of radius $r$ and sew the two together ...


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The radius of the event horizon of a black hole of mass $m$ is given by: $$ r_s = \frac{2GM}{c^2} \tag{1} $$ Let's consider your idea of taking $n$ black holes of mass $M$ and arranging them into a sphere. The total mass is $nM$, and the radius of the event horizon corresponding to this mass is: $$ R_s = n\frac{2GM}{c^2} \tag{2} $$ Now let's see how ...


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It is in principle possible, at least for some time, to have a collection of black holes gravitating along the surface of a sphere such that one can still escape from the inside of that sphere. In other words, the inside of the sphere need not be hidden behind a gravitational horizon. However, as soon as the density of black holes exceeds a critical value, ...


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General Relativity allows black holes of any size (though making a small one might be hard or worse than hard). So as a thought experiment that means that you can consider a small black hole that curves spacetime exactly as much as the sun does. This black hole would be much smaller than the sun, but to us out here spacetime would look the same (except we ...



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