# Tag Info

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Analyzing one moving clock from the perspective of one stationary person will be inadequate to derive special relativity from. With just that set-up, you aren't actually using the key fact that the speed of light is the same for all observers – all you're actually using is just the fact that the speed of light is finite. With just taking into account that ...

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I assume you used the formulae $f_o = fs\sqrt{\frac{1+v/c}{1-v/c}}$ for the clocks ahead of you and $f_o = fs\sqrt{\frac{1-v/c}{1+v/c}}$ for the clocks behind you. Those formulae do imply a singularity for the clock that is closest to you. Which equation to use? The answer is neither. Those expressions assume the travel is along the line of sight to the ...

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It's not a mechanism so much as a misconception of the nature of space (and its relationship to time): at low velocities, everything looks linear and Euclidean so we assume it is, but in reality it is not (as can be determined by appropriate experiments). It's kind of like asking by what mechanism you can reach something to your west by traveling east: if ...

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To understand this paradox it's best to forget about everything you know (even from SR) because all of that just causes confusion and start with just a few simple concepts. First of them is that the space-time carries a metric that tells you how to measure distance and time. In the case of SR this metric is extremely simple and it's possible to introduce ...

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An observer with zero comoving velocity (i.e. zero peculiar velocity). Such an observer can be defined at every point in space. They will all see the same Universe, and the Universe will look the same in all directions ("isotropic"). Note that here I'm talking about an "idealized" Universe described by the FLRW metric: $$\mathrm{d}s^2 = ... 24 I am wondering whether is it taken as a postulate or a proven phenomenon that c is constant irrespective of observer's speed? Either one. Both. Einstein took it as a postulate in his 1905 paper on special relativity. From it, he proved various things about space and time. The frame-independence of c is also experimentally supported. This is what the ... 19 Calculating the effect of acceleration in special relativity is straightforward, but I suspect the algebra is a bit much at high school level. See John Baez's article on the Relativistic Rocket for a summary, or see Chapter 6 of Gravitation by Misner, Thorne and Wheeler for a more detailed analysis. When you're first introduced to SR you tend to be told ... 18 Are we talking quantum mechanics? Then I'd say that a "measurement" is any operation that entangles orthogonal states of the system under consideration with orthogonal states of the environment. "Measurement" is the important thing in most formulations of QM. Colloquially speaking, an observer is something that performs measurements. The only other place ... 17 There is a definine velocity and momentum, we just don't know it. Nope. There is no definite velocity--this was the older interpretation. The particle has all (possible) velocities at once;it is in a wavefunction, a superposition of all of these states. This can actually be verified by stuff like the double-slit experiment with one photon--we cannot ... 16 This is a simple and clear issue, with a unique answer. I see other replies mentioning weather conditions, dark adaptation and so on. That's just so much hand waving, given that the first thing you said was "I've always lived in somewhat large cities". The core problem here, by a very wide margin, is light pollution if you live in a large city. This is the ... 16 The alien doesn't really see our future. He's still seeing our past, but a more recent past than he did before. Assuming that the alien is 100 light years away when he starts cycling then he is seeing what happened to us 100 years ago. If he "cycled" fast enough (i.e. at an appreciable percentage of the speed of light) so that he was now only 50 light ... 16 Yes, the observed energy content differs between different observers: Energy is manifestly no Lorentz invariant quantity, as it is the zeroth component of the momentum four vector, and hence differs between different inertial frames. Thus, rather trivially, different frames will observe different energy contents for the same system. This does not mean that ... 15 The "paradox" in the twin paradox is that a naive view of the problem would suggest that the situation ought to be perfectly symmetric: each twin should believe that he or she is really at rest, while the other twin is the one who moves off at high speed then returns. This is incorrect, though, because one of the two necessarily accelerates, which provides a ... 15 You can't travel at the speed of light. So it's a meaningless question. The reason some people will say that time freezes at the speed of light is that it's possible to take two points on any path going through spacetime at less than the speed of light and calculate the amount of time that a particle would experience as it travels between those points along ... 15 It is true that, from an outside perspective, nothing can ever pass the event horizon. I will attempt to describe the situation as best I can, to the best of my knowledge. First, let's imagine a classical black hole. By "classical" I mean a black-hole solution to Einstein's equations, which we imagine not to emit Hawking radiation (for now). Such an ... 15 The right way to think about this is geometry--- but the geometry mixes up space and time. I wrote some answers about this here: Einstein's postulates <==> Minkowski space. (In layman's terms) and here: Help Me Gain an Intuitive Understanding of Lorentz Contraction and if you read these first, you can easily understand the effect. The Lorentz ... 14 Manishearth's answer is correct, and this is just a minor extension of it. Manishearth correctly points out that the problem is your statement: There is a definine velocity and momentum, we just don't know it. Your statement is the hidden variables idea, and courtesy of Bell's theorem we currently believe that hidden variables are impossible. Take the ... 13 This is just a footnote to Crazy Buddy's answer (which is correct! :-): Length contraction is a real phenomenon, and indeed the RHIC observes this every day because the nuclei are moving so fast that the collision is between two disks not two spheres. However to see something you need to have light emitted from the object reach your eye, and the light from ... 13 Indeed you made one mistake: the infalling observer does not see the outside universe "speed up". Look at what happens in a space-time diagram. At the spacetime point where your astronaut passes the horizon, he can only see what's in his past light cone, and that's the universe at early times only. It's the signals that he sends back (or tries to) that reach ... 13 This kind of question has a long and honorable history. As a young student, Einstein tried to imagine what an electromagnetic wave would look like from the point of view of a motorcyclist riding alongside it. But we now know, thanks to Einstein himself, that it really doesn't make sense to talk about such observers. The most straightforward argument is ... 12 If you are standing up, and your friend is inclined on a tilted incline of slope 45 degrees, and you are both the same height, you would say that your friend is shorter by a factor of .707. But from his tilted point of view, you are also shorter by the same factor. There is no contradiction, and there is no need to invoke an absolute notion of up. This is ... 12 "Relativity" is actually a misleading word that Einstein didn't like. It doesn't mean "every vantage point is equivalent and it's all relative". It really means only inertial, non-accelerating vantage points are equivalent. You could think of it as, prior to relativity, people believed that there was an absolute position/speed to the universe. Special ... 12 Intuition and perception (or the lack of there of) can be a big problem when you're trying to comprehend the implications of special/general relativity. You must understand that in everyday life which fuels our intuition is pretty slow. Most people don't move faster than 900 km/h or 250 m/s. And that's a luxury for most, to travel by a fast jet. The ... 11 The sphere is contracted in the horizontal axis and perceived as an ellipsoid. This is what we believe about length contraction and this happens only, when we take Einstein's simultaneity into account. But, the stationary observer would see the sphere appearing as the sphere always (i.e) the circular outline would still be there at any velocity relative to ... 11 Your question is a natural one to ask, but it has no answer. It is a bit like asking by what mechanism the angles of a triangle always wind up adding to 180 degrees (in Euclidean geometry). There is no mechanism for that - no one is going around checking all the triangles to make sure their angles add up right. It is just a logical consequence of the theory ... 11 An observer is a timelike worldline with 4-velocity u^{\mu} and an orthonormal basis e_{\hat{\alpha}} with e_{\hat{0}} = u such that e_{\hat{\alpha}} is transported along the worldline under some transport law e.g. Lie transport, Fermi transport, or parallel transport. Physically the Lorentz frame represents a local set of three orthogonal meter ... 10 To make progress we need to be clear what we mean by the laws of physics and observer. A law of physics is just some set of equations that we use to predict what happens. So if for example we're trying to describe how charges interact with light our set of equations, i.e. our law of physics, would be Maxwell's equations. But to write down Maxwell's ... 9 This is actually a rather subtle point never fully appreciated by students the first time they learn relativity. There is a difference between someone at A receiving the photons from event X, and event X actually occurring. In physics classes (as distinct from astronomy), we are almost always talking about the occurrence of the event, not its observation. ... 9 Indeed, nothing can get under the horizon. The stuff close to the event horizon does move outwards as the BH radius increases. Even more with any BH deformations such as waves on its surface, the tidal deformations or the change of the rotation speed, all the oblects close enough to the horizon remain "sticked" to it and follow all the changes of the BH ... 9 Yes, I agree with David. If somehow, you were able to travel at the speed of light, it would seem that 'your time' would not have progressed in comparison to your reference time once you returned to 'normal' speeds. This can be modeled by the Lorentz time dilation equation:$$T=\frac{T_0}{\sqrt{1 - (v^2 / c^2)}} When traveling at the speed of light ...

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