# Tag Info

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Firstly, it should be made clear that being isotropic is a very special and rare property. (A spacetime can never be truly isotropic because no isometry can map spacelike vectors to timelike vectors, for example, so I'll talk about "space" being isotropic). There are very few spaces isotropic around every point, only very few spaces will even be isotropic ...

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Let me present a slightly different perspective to Alfred's answer, although I'm basically saying the same thing. I suspect you've got hung up on the idea that velocity causes the relativistic effects like time dilation, but the underlying cause is something different. All the weird effects in SR are caused by a fundamental symmetry of spacetime, which is ...

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We need to untangle this a bit but first: the cause of time dilation is the geometry of spacetime which is such that there is an invariant speed c. Now, remember that velocity or speed is not a property of an object; there is no absolute rest. Further, consider the case of three objects in uniform relative motion with respect to each other. If I choose ...

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If you define "now" to be all those points in space and time that have hypothetical, pre-synchronized, stationary clocks that read the same time as your clock, then there "currently" exists a hypothetical observer somewhere, who is moving relative to us, for whom "now" includes Earth, circa 1900. But these notions of "now" are different for the two ...

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The first statement is very much true. Light moves a finite, if very fast, speed. Even ignoring any movement/ relativistic effects this simply means that observers closer to earth will see it in it's most recent state. It may sound strange for light, but we see exactly the same phenomenon in sound, an observer noticeably closer to the source of a sound will ...

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No. Not that we know of unless we change the current laws of physics to allow faster than light travel or imaginary mass

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There seems a lot of conjecture in any event. Venus could have been a meteor, with an innate spin, that swung by the Sun and have been captured into our Solar systems anticlockwise orbital arrangement. Retaining her original spin momentum, clockwise relative to the others.

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I'd like to point out that there is a big difference between the physical reality and the mathematical model describing it. Science has developed various mathematical models to describe the physical reality: the universe of Newton is $T\times E_3$ where $T$ is the time-axis (geometrically speaking, a copy of the real line) and $E_3$ is the euclidean ...

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Take units $c=1$. You have $U_0^2-\vec U^2=1$, that is $\gamma^2(1-\beta^2)=1$. With some basic transformations, you will get : $\frac{\gamma - 1}{\beta^2}= \frac{\gamma^2}{\gamma + 1}$ Now, from your Wikipedia matrix, you have obvious term, $U_0 =\gamma , U_i =\gamma \beta_i$ You have $(\gamma -1) \frac{\beta_i\beta_j}{\beta^2} = \frac{\gamma^2}{\gamma ... 2 We could easily prove that more than four dimensions exist simply by observing a fifth dimension, but proving that only four dimensions exist is much harder and probably impossible. This is an example of the general case that proving something doesn't exist is usually impossible outside the halls of Mathematics. I wouldn't stake my life on no proof being ... 4 You are right, in this case, scalar means Lorentz invariant field. But it is not invariant under the transformations of SU(2)xU(1) of the electroweak model. And it is a scalar under the SU(3) of QCD. So the four real components of the Higgs are indeed invariant under space-time transformations. Physicists are usually not very clear in these distinctions, ... 3 There is no such thing as anti-time in physics. (Neither is there anti-space or anti-gravity.) Antimatter is a very specific term, namely for particles that have the same properties but opposite quantum numbers (charges) as the "regular" particles. Sometimes, antimatter refers only to molecules build from anti-particles. If you just slap "anti-" on a random ... 0 To add to Stan Liou's point: No, it's not possible because we don't measure$\pi$at all; rather, we define it in reference to Euclidean geometry, which is flat. However, Euclidean geometry probably has intuitive simplicity for humans because it closely matches the geometry of space in our environment. Here's one way of understanding explicitly what ... 8 I read about Goodwin's "proof" that π = 3.20... Its BS and I know that. What I am wondering is whether his technique may have stumbled on something ( a warped space) years before Einstein. In short, no. Slightly longer, noooo.... Notably, even if Goodwin made some coherent sense (and he did not), doing this before Einstein is not a significant ... 0 these papers are predicting the possibility of measuring a particle or electromagnetic waves to move faster than light without violation of Lorentz transformation or causality. According to the papers It could solve many paradoxes related to special relativity, Twin paradox, Ehrenfest paradox, Ladder paradox and Bell's spaceship paradox. in the papers it is ... 0 the astronaut [...] relative to us, is motionless in space, observing us I think what you mean is that the astronaut is in the same frame-of-reference as the centre of the 'super cluster'. If the astronaut was motionless relative to us then she/he would experience/measure the same flow of time as us. You should note that the commonality between Galilean ... 5 Whenever an amount of mass (or mass equivalent in energy) finds itself inside a volume smaller than the event-horizon for a Schwarzschild black hole of that mass ($R = \frac{Gm}{c^2}$), then you have the necessary and sufficient condition for a black hole. In fact, the black hole may form before the matter reaches this point, provided that it will reach it ... 2 Basically what your asking is if information can be transmitted faster than the speed of light. According to quantum mechanics, it is impossible to use quantum entanglement for transmitting data faster than light. This is know as Eberhard's theorem, more details about can be found here (i'll try to provide a link with full access to the article). ... -1 If a star Is 13.82 billion light years away It takes 13.82 billion years for us to see the Image so 13.82 billion + 13.82 billion = 27.64 billion years old because while that Image was flying through space, time was still moving forward also If I set up a camcorder telescope 1 light year away and look at earth then I can see the past on earth the closest ... 9 There's a very common misconception that the Big Bang happened at a point like a bomb going off. It doesn't help that almost ever TV documentary on the subject represents the Big Bang in this way. Explaining what actually happened is hard without going into the Maths, but here's an explanation I gave taken from (of all places) the Science Fiction Stack ... 5 The question you are asking yourself is ill defined. The universe has no center, thus you cannot ask what is there. The important thing to realize is that a singularity (presented in the Big Bang Theory) is not a physical thing, you can't say "oh look at that singularity over there"(from that point the universe started). In fact a singularity is merely a ... 3 As suggested in the comments, "lowering an index" is just coordinate notation for the isomorphism$\flat:TM\to T^*M$between defined by $$X^\flat (Y) = \langle X,Y\rangle\text{,}$$ where$X$and$Y$are arbitrary vectors. I've tried using the definition of the metric${g_{\alpha\beta}=\hat{\mathbf{e}}_\alpha\cdot\hat{\mathbf{e}}_\beta}$where ... 3 Also I've searched for it in books like Carroll's or Lawden's, but it's given pretty much as if it would be a definition. Because it is. No need for differential geometry, linear algebra is sufficient here: At a given point of space-time, the tangent space is just a vector space, the cotangent space its dual (ie the space of real-valued linear ... 1 String theory considers a 2-dimensional quantum field theory (in flat space) that contains, among other things, a set of 10 fields$\phi^\mu$, just like we consider an electric field as a group of 3 fields$E_x$,$E_y$,$E_z\$. Inside this 2-dimensional quantum field theory, there are a number of consistency conditions that must be satisfied in order for the ...

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David H is correct. If someone answered "Well, space is XYZZY" then you might, understandably, scratch your head and follow-up with "But... what is XYZZY". Ultimately, as has been mentioned here numerous times, we get to the level of fundamental constituents of the world such as, for example, electric charge. When we say that electric charge is a ...

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How do we prove that any directions are orthogonal? [...] we can use the pythagorean theorem. This involves of course a definition of (how to measure or compare) "angle(s)" in the first place; such that one may comprehend statements about (distinct) angles being "equal" (or else: "not equal") for instance in Euclid's 4th axiom (on "right angles") or in ...

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It depends on how you define orthogonality, or, as OSE puts it in his comment, "Orthogonality is usually tested using some defined inner product." I'll expand on this a bit. In order to mathematically answer the question Is direction A orthogonal to direction B? we need a definition of the terms "direction" and "orthogonal." The standard ...

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