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49

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 ...


44

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 ...


44

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 ...


37

One result of special relativity is that the magnitude of all 4-velocity vectors $\vec{u}$ is the speed of light. Written with the (-,+,+,+) signature: $$\vec{u}\cdot\vec{u} = -c^2$$ One way to think of this is that everything is always moving the speed of light in some direction. When I stand still, I move the speed of light in the time direction. My ...


35

This is is known as the Wigner's friend thought experiment. According to the many World's interpretation, the superpositions are not a problem. The whole universe ends up in a superposition where all experimental outcomes are realized, but such a superposition is entangled with the environment, from a macroscopic point of view it takes the form of a ...


30

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 ...


29

In a bubble chamber experiment, film was the detecting medium, but film was taken automatically, by the thousands of frames. These bobbins of film went to the various laboratories involved in the experiment, and were scanned for interesting events which were measured and the cross sections for the interactions recorded. This is a clear example of an ...


28

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 = a^2(\tau)\left[\...


27

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 ...


26

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 ...


25

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 ...


24

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 ...


24

Imagine a slightly different scenario: two pilots, Alice, and Bob, are in their spaceships. They move towards a tunnel of length $L$ at a velocity $v$, and remain a distance $l'$ apart. Alice is closest to the tunnel and thus enters first, approaching a wall at the end of the length of the tunnel. Just as Bob enters he decelerates, coming quickly to a halt ...


22

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 ...


22

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 ...


21

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 ...


20

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 ...


20

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 ...


17

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 ...


17

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 ...


17

This is the fundamental postulate of special relativity: Light (in vacuum) moves at the same speed no matter what you measure it relative to. Pretty much everything in SR is just a mater of figuring out the deductive consequences of this basic fact. It is an experimental fact that it is so, and it was so even before Einstein -- in particular, light had ...


16

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 ...


16

The conceptual key here is that time dilation is not something that happens to the infalling matter. Gravitational time dilation, like special-relativistic time dilation, is not a physical process but a difference between observers. When we say that there is infinite time dilation at the event horizon we don't mean that something dramatic happens there. ...


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

"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 ...


14

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 ($v=c$...


14

In relativity there is no standard-clock that tells you which time is "right". That's the point about relativity. There is no need for a absolute reference to compare with. Everything is just the way you observe it (that is, relative to you). Things may slightly differ from observer to observer but the qualitative behaviour stays the same just as classical ...


13

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 form....



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