# Tag Info

21

The answer is no. The simplest proof is just the principle of relativity: the laws of physics are the same in all reference frames. So you can look at that 1-kg mass in a reference frame that's moving along with it. In that frame, it's just the same 1-kg mass it always was; it's not a black hole.

20

Special Relativity is based on the invariance of a quantity called the proper time, $\tau$, which is the time measured by a freely moving (i.e. not accelerated) observer. The proper time is defined by: $$c^2d\tau^2 = c^2dt^2 - dx^2 - dy^2 - dz^2$$ This is similar to Pythagoras' theorem as learned by generations of schoolchildren, except that it includes ...

19

@Florin is absolutely right, but sometimes a picture is worth a thousand words. This website has multiple pictures and explanations about how the future light cone starts to point only to the inside of the black hole once you pass the event horizon. Here is one of the images: Time is vertical, the cylinder represents the event horizon and the cones are ...

16

Nothing. From Nature's perspective speed of light is entirely artificial number. Imagine that you've discovered an alien culture that measured horizontal length $\ell$ and height $h$ in different units. They live on a planet with very strong gravitational force, and for them it is very difficult to rotate stuff in vertical plane. Such kind of rotations are ...

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 ...

15

Edit regarding 3+1 spacetimes and causality I'll keep adding to the answer as I get more information, and hopefully everything will just evolve along. At the very least, I'll have a set of notes to work from in the future :) This is also the first, broadest, cut at an actual answer regarding causality. Alcubierre sets out to find his warp drive metric ...

15

1) No, because it's actually going slower from your perspective. In special relativity, "the fastest wristwatch is always your own". 2) Yes, but remember that it's farther away from us now, so it will take some time to get to us (if it was travelling at 0.5c it will take 50% longer to get to us). 3) Mostly in that as an observer the redshift effect would ...

14

Photons always travel at $c$ (not completely true, but a good simplification for this question's purposes). Common sense tells us that if person A running at velocity $v$ is chasing person B with velocity $u$, the velocity of person B with respect to person A ($w$) is: $$w=u-v$$ But our common sense is misleading, and this equation is only an approximation ...

13

In physics, it is often true that theories or theoretical paradigms with vastly, "qualitatively" different assumptions and "pictures to imagine what is going on" yield virtually indistinguishable predictions, and Newton's vs Einstein's physics is the simplest example of that. According to Newton, for example, time was absolute. According to Einstein, time ...

13

I wish those who popularize science would stop talking about the speed of light. It just confuses people. Forget about speed. Think in terms of energy. You'd need an infinite amount of energy to get out of it. Infinite. Meaning, it's like dealing with the Mafia: no matter how much you're spending, it's still not enough. Think in terms of topology. From the ...

13

Yes--- this is directly analogous to the following statement from geometry: The plane curve with everywhere constant curvature is the circle. You could prove this by integrating the condition of constant curvature (which is just as messy as in relativity), or by doing an arclength parametrization (which is clean, see below). But easiest of all is to note ...

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 ...

11

Since the Lorentz transformations are a consequence of the postulate of constancy of the speed of light, together with some homogeneity and parallel postulates, it is a little difficult to make precise the request for a Lorentz-transformation free demonstration. But I will interpret the question as asking for a synthetic proof of the addition of velocities. ...

10

It's just funny. Note that your equation doesn't actually use any single general quaternion. You only use the $i,j,k$ imaginary units in an ad hoc way to get three minus signs whenever you need them. If you were using an actual quaternion $$q = t + xi + yj + zk,$$ then the only semi-natural real bilinear invariant you may construct out of it is $$q\bar q ... 10 The object you're talking about is called, in mathematics, a Clifford algebra. The case when the algebra is over the complex field in general has a significantly different structure from the case when the algebra is over the real field, which is important in Physics. In Physics, in the specific case of 4 dimensions, using the Minkowski metric as you have in ... 10 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 ... 10 It appears to me the issue is understanding momentum conservation. An even cruder example would be to shine a bright torch out the back of your vehicle. Even though the photons have no mass, wouldn't the vehicle move forward? You also refer to mass in this manner in the paraphrasing of Newton's third law "proportional opposite mass/acceleration ratio ... 10 The conclusion derives from looking at how tachyon signals would behave as seen in slower-than-light inertial frames, not from trying to consider a tachyon's own "time" (if you can call it that, since a tachyon's worldline would have to be space-like, not time-like)--basically, it's a consequence of the relativity of simultaneity. It can be shown that any ... 9 I'm going to dare to give a very brief answer that's likely not what most folks would expect, but is deeply rooted in experiment: The speed of time is just the speed of a clock -- that is, of how fast some kind of a repeated cycle can be done. Clocks thus only have meaning relative to each other. You can set one as a standard, then measure other by it, but ... 9 One way to think of a "moving shadow" is by following the last photon that was allowed through. In that case, the speed of a shadow is exactly the speed of light. On the other hand, you could also define the speed of a shadow as the speed of the boundary between dark and light. In that case there is no thing that's actually moving, so there's no bound on ... 9 It cannot. This is because energy and momentum are not both conserved if a free charged particle (say, an electron) emits a photon. It needs interaction with at least a second charged particle in order to do so (as in Bremsstrahlung). The mathematic involved is that of the energy of a photon E=\hbar \omega, energy of a particle E^2 = m^2 c^4 + p^2 c^2, ... 9 It is mathematically possible to create some instances in which an object goes back in time relative to some observer. For example, simply going faster than light causes such an effect, but of course, speed of light is the limit for any massive object. While it is mathematically possible, there are many paradoxes caused by time travel to past, unless you ... 9 I endorse Ron's answer – it's the systematic way to proceed. The velocity v/c may be written as \tanh \eta where \eta, the rapidity or whatever, is the hyperbolic (Minkowski) counterpart of the (Euclidean) angle. The addition of velocities then boils down to an addition formula for \tanh(\eta_1+\eta_2) because the rapidities just add additively. Let ... 9 There are solutions to Einstein's field equations, which have closed timelike curves. For example Godel's solution. Would that constitute time travel, if you can reach the same point on your world line in finite time? One objection may be that such solution do not describe the universe, but examples as the Tipler's cylinder suggest that at least in theory we ... 8 One thing to be aware of is that the principle of relativity would not apply to this computer--rotating reference frames are not inertial, and therefore, will not be related to 'stationary' reference frames by simple Lorentz transformations. Also note that if there are any capacitors or anything along those lines in the computer, then they would be ... 8 All basic laws of physics are frame-independent. They either exhibit Galilean (non-relativistic) or Lorentzian (relativistic) invariance. Examples are Newton's laws (Galilean), Maxwell's equations (Lorentzian), Navier-Stokes equations (Galilean), etc. A notable exception is formed by Schrödinger's equation which, upon closer inspection, can be fixed into ... 8 There is a classic treatise on "Relativity, Thermodynamics and Cosmology" from R. Tolmann from the 1930s - it is still referenced in papers today. This generalises Thermodynamics to Special Relativity and then General Relativity. As a simple example the transformation law for Temperature is stated as: T=\sqrt(1-v^2/c^2)T_0 when changing to a Lorentz moving ... 8 Dear rubenb, yes, what your professor says is surely based on solid maths. The reason is that the 4-component Dirac spinor is actually composed of two separate 2-component pieces. The elementary "spinors" for 3+1 dimensions have two complex components. That results from the isomorphism between groups$$SL(2,C) \sim Spin (3,1). Note that both groups have 6 ...

8

There is indeed a scalar field model of gravity, in fact Einstein originally tried that before settling on a spin 2 description. Scalar gravity is called Einstein-Nordstrom gravity, here is a link to wikipedia: http://en.wikipedia.org/wiki/Nordstr%C3%B6m%27s_theory_of_gravitation. At the nonlinear level it amounts to using $R$ in Einsteins equations instead ...

8

In addition to the Hypnosifl's answer: in lots of modern theories tachyons do not violate causality. For example, in QFT you can choose the mass-squared term in the action to have a negative sign, that would make your field's quanta tachyons. You can check it by looking at the propagator, which oscillates at space-like region and decreases exponentially ...

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