# Tag Info

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What you see depends on what light does before it gets to you. You can not discuss the reality inside a falling reference frame and "ignore lack of actual vision". Information can only travel with the speed of light. In General Relativity there is no instantaneous measurement. You also have to keep in mind that you are describing a dynamical black hole; its ...

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The is no absolute rest frame as far as we know (and we know quite a bit about it). So there is no such thing as completely still in spacetime. However, that's boring and I'm in the mood for a debate, so I'm going to phrase this answer in the form of a debate where I will be arguing on your behalf. Me: The is no absolute rest frame, so this question makes ...

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Is there any other scientific theory that proves that big bang is the origin of time ? Here is a gross misunderstanding of what a scientific theory is. A scientific theory can never be proven. It is successful if it fits data and observations, then one says it is validated, and if its predictions are always validated. An invalid prediction requires drastic ...

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Studying big bang itself gives a lot of evidences to believe in it.however redshift ,given by Edwin Hubble , is one of the major theory that supports it by giving evidence of expanding universe.cosmic wave background is also a big point to support it.

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The change in the geometry is not entirely certain. One can appeal to exact solutions. With the Schwarzschild solution for a non-rotating black hole the conformal diagram illustrates region I that is the exterior universe and region III for the black hole interior. The line separating them is the event horizon. There is another region II that is another ...

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So the answer is no. An electric field has energy and energy generates a gravitational field, just like any mass. See the charged black hole solution is the Wikipedia article https://en.m.wikipedia.org/wiki/Charged_black_hole The charge of a black hole, if nonzero, changes the metric and solution to account for the charge and electric field. That ...

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The brief answer is 'yes’. Here is a thought experiment which I think makes it easy to see that the answer must be yes. Consider the standard twin 'paradox': twin a hangs around in free-fall; twin b zooms off on their spaceship at some enormous speed with respect to twin a, turns around (in some smooth way, undergoing acceleration), and returns. Well, ...

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Toward position y. Gravity couples to itself (Einstein's equations are nonlinear), so yes, gravity can cause itself to curve. Another way to see it is that photons and gravitons are both massless and so they both travel along identical null geodesics, so wherever you see light coming from, you'll feel the gravity from the light source pulling you in the ...

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The fancy word for a Universe that expands equally in every direction is an isotropic Universe, and one that expands at different rates in different directions is anisotropic. The usual assumption is that the expansion rate is the same in all directions (i.e., the Universe is isotropic); this is the standard Freidman-Robertson-Walker metric for an ...

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We believe that the universe expand in every direction evenly. Even-if there's any unevenness, it's hard to see, and will only be clear at very very large scales. Some people have combed the CMB (cosmic microwave background) and argue that there's maybe some evidence that things aren't perfectly even, but it's not really clear. Right now it really looks like ...

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Short answer: Yes Explanation: The answer to this question is something well documented in astrophysics. The "Size" of a universe is modeled by metaphorical expanding fluids known as the Freidman Equations. These equations say that from a singular point, the universe will expand at rates according to the travel of its components: energy and matter, for ...

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It is an assumption that the universe expands evenly in all directions, and the experimental evidence so far confirms the assumption. Our mathematical description of the expanding universe is based on the assumption that on a very large scale the universe is homogeneous and isotropic, which basically means it's the same everywhere and in all directions. ...

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You are over complicating what appears to be your interest. You are asking in essence if there is an energy change in a particle as it moves in a gravitational field, i.e., a given spacetime metric. The answer is simple: except for singularities (i.e., what happens there, which is unknown, that's where any particle path ends in general relativity), a ...

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Various "black holes"[1] are simply solutions to the Einstein Field Equations, and, if the EFE are an accurate picture of reality, then "bent time" (nontrivial spacetime curvature tensor) is exactly what the Einstein Field Equations tell us. In particular, the EFE predict a situation where, if there is enough energy in a region of space, then the geometry of ...

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Your thinking about general relativity. Gravity actually changes time and the reason why we know this (other than our equations that tell us it is so) is because we have measured it. Time flows slower on earth than on our satellites. People who design satellites need to change their clocks so that they match up with earth. Even spending your life on a plane ...

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Our universe looks not only isotropic (the same in all directions) but also homogeneous (the same at each x, y, z at any one time). The fact that our position is not unique is not a principle, it is determined to be so from astrophysical and cosmological observations. Of course, the meaning is that these are so for cosmological distances, i.e., in the large, ...

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Because when we look around, we see that things are, on large scales, the same in all directions. This would be true in such a model only if we were at the centre of this system. That seems ludicrously unlikely: what are the chances that we are lucky enough to be at the one place in the universe where everything looks the same in all directions? So ...

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One talks about the size of the universe in the context of a model where spacetime is foliated by three-dimensional spacelike leaves. The "size of the universe" means the size of one of those leaves, not of all spacetime. For example: If you imagine spacetime to be filled with galaxies, the worldlines of those galaxies give a preferred global time ...

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It is special relativity that tells us space and time are different aspects of the same thing--spacetime. And indeed quantum mechanics does not respect the covariance principle of special relativity. That's exactly one of the reasons of why we need to invent quantum field theory(QFT) when we already have QM at hand. To make the space and time on the same ...

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In book "from eternity to here" by sean carroll he described distortion of spacetime near a black hole. also you can change the visualization to realize milder distortions. Before you go forward you should know about light cones in GR. it is explained in book but I assume you know it. He says: [But a real black hole, ..... It is a true region of no return—...

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Distance measurements in $n$ dimensional flat space follows the same pattern for $n$ equal 1,2,3, or higher values. I'm going to assume a straight line, change in position to simplify the math (that is we're measuring what a introductory book would call the "displacement" $s$ rather than distance. But then distance is just an accumulation of many magnitudes ...

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ANSWER WITHDRAWN I am withdrawing my answer because I am persuaded by Henning and others that I am mistaken about the impossibility of catching up with someone who has crossed the Event Horizon. I have also withdrawn my Vote-to-Close. Original Answer What do you mean that your friend has "fallen into a black hole"? If you mean that he has crossed the ...

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Assuming that the black hole is large enough that one can cross the event horizon without being spaghettified by tidal forces, and the that when the accident happened, the both of you were hovering in place above the black hole with your jetpacks, rather than orbiting it: You can still see your friend (no matter how long you dally, the part of his worldline ...

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One meter is a unit defined in the "real world" around us – places we can actually visit. Or it is used for the lengths and dimensions of objects we can touch. It only makes sense to use the same "meter" for other worlds if we can actually get to those worlds. If two worlds are completely separated from each other, it makes no sense to apply the units of ...

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Whatever unit you're using for distance in 1D is still good in any number of dimensions. Kilometers in manifold of dimension n is fine (assuming non-compactified dimensions).

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The answer by @peterh is accurate on the factual information about the Einstein Field Equations and that it describes how the matter distribution affects spacetime. There is more that may be added that hopefully will help understand more of it. First, just to be totally clear, gravity as described by GR (general relativity, through Einsteins Field ...

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No, it depends on the metric of the Universe described by the Friedmann model. It is a general relativistic theory. In GR, gravity is not a force. Instead, there is actually two equations: The Einstein Field Equations, describing how the distribution of matter affects the geometry of the spacetime, There is also equations showing how matter moves in the ...

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These notes put some numbers on @ACuriousMind 's answer: one needs to be looking at length scales of 100 Mpc and greater for the FLRW metric to be a realistic description of reality. That's a staggering distance, and equivalent to timescales amounting to the whole Mesozoic era, comprising the rise and fall of the Dinosaurs! So one cannot expect the ...

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The quantity $T^{\mu\nu} T_{\mu\nu}$ appears in the TOSEC (trace of square energy condition). The quantity can become negative, for instance in the stress energy tensor of the Unruh vacuum in the Schwarzschild metric, hence I would not recommend taking its square root.

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Komar mass is only well defined, i.e. Invariant, in a stationary spacetime, i.e., one admitting a timelike Killing vector. Your derivation seems to be good only for a static spacetime, i.e., no rotations, so a Kerr metric for instance would not be admitted. Not only that, you seemed to assume a diagonalized metric also in the space coordinates, not sure if ...

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While I'm sure it's a translation issue, your claim that the Moon (an astronomical object) is more than a light-year away is false. As a matter of fact most of our visible Solar System is only light-minutes or light-hours distant. By the way, while is may be a cultural issue, it is never correct to claim "we all know X". The wide variety of human experience ...

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No, this is not a thing that can be directly observed -- for several reasons. First, in order to observe a difference, some concrete event would have to happen out at Alpha Centauri, which can be observed here with sufficient accuracy that the two observers can even form concrete impressions about when it happened. That's not a commonplace occurrence over ...

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Let me take parts 2. and 3. of the question first: The 10 dimensions of string theory are, a priori, not "coiled up" or anything else. They are derived for a string theory where the classical version of the string propagates in d-1 spatial dimensions and 1 temporal dimension, i.e. Minkowski space $\mathbb{R}^{1,d-1}$. "Dimension" here is dimension of a ...

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I guess you are talking about the Planck lebgth, not the planck-constant. But this is no minimum distance either. Its just the minimum space in which action can be defined. Its the distance, which is traveled trough by light in one planck second. But that does not mean it is the smallest distance to exist.

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To carry forwards with John Rennie's response let us divide the metric by $dt^2$ $$\left(\frac{ds}{dt}\right)^2~=~1~-~a(t)\left(\frac{dr}{dt}\right)^2$$ and with the generalized Lorentz gamma factor $\Gamma~=~\left(\frac{dt}{ds}\right)^2$ means we have $$\Gamma~=~\frac{1}{\sqrt{1~-~a(t)\left(\frac{dr}{dt}\right)^2}}$$ This factor explodes at $t~=~0$ and ...

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This is essentially the same as the narrowing of the light cones that happens as you approach the event horizon of a Schwarzschild black hole, and it occurs for the same reason i.e. the coordinate velocity of light tends to zero as you approach the horizon. There is nothing physically interesting in this. It is a result of the coordinates we are using. If ...

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What we intuitively think of as "solid objects" are actually electromagnetic force-fields repelling each other. So you are correct; atoms are 'empty' in that they contain no solid objects or things. On the other hand, they are 'full' of basic force field which, in the aggregate, on a macro-scale, creates the illusion of 'solidity' that is what we perceive to ...

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A few million to about 30 million years from now. I.e., we'd be able to measure a change in the previously observed redshifts for galaxies a few to about 10 Mega parsecs away. A parsec is a little more than 3 light years. The reason is that closer in galaxies are in our local group or cluster, and we are to a great extent gravitationally bounded to them. ...

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Because of the Pauli exclusion principle, it's extremely difficult to compress atomic matter beyond a certain density. It's not impossible, because there are always higher-energy electron states available, but there's a very strong force opposing it (called electron degeneracy pressure). This is what it means for space to be full. If you define "empty space"...

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As it is said in the article referred to in my post we can take any theory and reformulate it so that it is covariant under any group of transformations we pick; the problem is not physical, it is merely a challenge to our mathematical ingenuity. As @Lewis Miller pointed out the Lagrangian formulation of Newtonian mechanics is general-covariant, ...

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A charged particle like electron maybe is point-like (of radius zero), but it is "long-handed" as it is "felt" far away. In this sense it is not so "point-like".

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Although it's commonly said that fundamental particles are point particles you need to be clear what this means. To measure the size of the particle to within some experimental error $d$ requires the use of a probe with a wavelength of $\lambda=d$ or less i.e. with an energy of greater than around $hc/\lambda$. When we say particles are pointlike we mean ...

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Yes, elementary particles such as electrons and quarks (inside protons) are point-like or at least, their internal structure is incomparably smaller than the size of the atom. So the atom is mostly empty space. However, that doesn't mean that atoms may penetrate each other. Matter is impenetrable because of a combination of the uncertainty principle that ...

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Spacetime in string theory is a kind of strings field. Some said that this field is infinite - or in infinite expansion - other that spacetime strings appear in the same as the universe grow; others that the strings stretch. If you consider the spacetime a string field it is easy to understand how and like and how occured the born of a strings of matter and ...

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He says: The length of the red line is the same in both figure 1 and figure 2. I guess his meaning of red line is the space-time distance travelled by the same particle between points (space-time states) A and B. It makes sense. Actually, it doesn't. Because there is no motion in spacetime. See relativist Ben Crowell saying so here: "Objects don't move ...

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Yes, I also never liked the visualization with the 2D-plane and the ball. It is not even partially true. I think there is no possible way to visualize the mathematical and physical effects, because its mathematical formulation is so complicated that you wont ever have a 100% true visualization. But maybe this picture of a parralel transport of a vector on ...

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You sound confused but it cannot be otherwise - you are trying to make sense of the absurd consequences of Einstein's 1905 false constant-speed-of-light postulate. I am not going to continue (gatekeepers will delete my answer anyway) - just to note that Motl's "Newton's theory of motion was ruled out by the Morley-Michelson experiment" is both silly and ...

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We are only allowed to add quantities with the same units. Time and distance can't be added just like apples and oranges shouldn't be mixed. To add them, one must first convert them to quantities of the same unit, and a speed is needed. The speed of light in the vacuum $c$ is the right speed that produces geometry of space and time as seen in the ...

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The similarity of time and space is limited to Lorentz symmetry. Beyond Lorentz symmetry, the time dimension cannot be assimilated to space dimensions. Within spacetime, time is not intrinsically curved: Any observed time corresponds to the proper time of a clock, and the clock is always counting straightforward, even if according to our coordinates we may ...

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Two or more timelike dimensions is a situation that is difficult if not impossible to reconcile with the notion of causality. Suppose you want to think of a five dimensional universe with three spatial and two time dimensions. What you mean then is the metric has a $(2,\,3)$ signature, which means that at each point Riemann normal co-ordinates centered at ...

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