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To answer your question think of how we get light from the far away galaxies. It is the same problem as you posed, though inversing the path of the light. Each photon that we get from a galaxy, travelled for billions of years (depending how far is the galaxy). However, take in consideration that the further we look into the sky, we have knowledge about the ...


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There is research on going on this The accelerators at the Helmholtz-Zentrum Dresden-Rossendorf (HZDR) provide ions – that are electrically charged particles – of most of the chemical elements available for experiments in materials research over a wide energy range. What is quite unique in the world is the fact that even very heavy metallic ions – beside ...


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Several misconceptions in your question. Let's focus on one statement: "For the twins paradox to be plausible, one of the twins must reach "99.995% the speed of light" (Lorentz factor of γ = 100 ) without being atomized." No. That's not true, for several reasons. Firstly, it is a RELATIVE speed, and relative to the frame of reference of a cosmic ray ...


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In theory, a massive particle can be accelerated asymptotically close to the speed of light. But one can never actually reach the speed of light because the kinetic energy of such a (massive) particle would be infinite. This is because the mass of the particle itself become heavier at higher speeds due to relativistic effects. Specifically: $$\text{Kinetic ...


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Well, by massive, I assume you mean objects that have non-zero rest mass. In that case, it would take infinite energy for that object to reach the speed of light. However, their speed would get closer and closer to the speed of light as more energy is put in, until their speed was practically (but not exactly) the speed of light. Additionally, the smaller ...


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First, I highly suggest reading up on the concept of Locality. The issue is where you're measuring the speed from... Remember that it isn't so much that light can't escape due to the escape velocity, as it is that space itself is being dragged into the black hole (and anything residing in it), which happens to be falling in at the speed of light where you ...


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Has this kind of phenomena ever been used to measure SR properties ? Yes. A similar apparatus, called a Fizeau apparatus, has been around for a long time... It uses a rotating cog rather than a falling box (for obvious reasons). http://en.wikipedia.org/wiki/Fizeau%E2%80%93Foucault_apparatus EDIT (re comment): Yes, lasers can also be used to measure ...


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Light will no longer be light as it gets absorbed in black hole . So there is nothing left to talk about its speed.


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Yes, you have very likely done what the teacher wanted you to do. But you should maybe mention to teacher that he has asked a poor question (actually... maybe you shouldn't mention it... or at least be diplomatic about it...) The reason the question is dumb is because, as pointed out in the comments, you could (reasonably) use the relativistic expression ...


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When you have a transformation from one frame to another, this tells you how measurements with meter sticks and stopwatches in one frame relate to measurements with meter sticks and stopwatches in another frame. If you had one transformation based on lightspeed, you'd get a relationship between measurements with meter sticks and stopwatches in one frame ...


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The Fermi velocity, the Fermi momentum and the Fermi temperature are all really just ways of rewriting the Fermi energy, $E_F$. The Fermi energy is the energy f or a gas of fermions such that at 0 temperature all states with energy below $E_F$ are filled and all states with energy above $E_F$ are empty. Leaving aside the details of relativistic QM, a Fermi ...


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You have to distinguish between spacetime and proper time: The vacuum would still continue to be part of the Minkowski spacetime continuum of the observers, in particular with respect to simultaneity (e.g. of events happening at this place before or after your experiment). If your experiment is lasting one hour, during this hour the clocks of the observers ...


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You are asking about time dilation. Using $$\Delta t' = \gamma \Delta t$$ where $$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$ We can rearrange for $v$ to get: $$v = \sqrt{c^2 - \frac{\Delta t^2}{\Delta t'^2} c^2 }$$ or maybe better $$\frac{v}{c} = \sqrt{1-\frac{\Delta t^2}{\Delta t'^2}}$$ to get the speed as a fraction of the speed of light. Plugging in ...


2

This question is quite broad, but I'll try my best. When making the jump from special relativity, we have two good rules of thumb: Wherever there is a Minkowski metric in SR, put a general metric in GR. Wherever there is a partial derivative in SR, put a covariant derivative in GR. Take, for instance, mass-energy equivalence. In SR, we have ...


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Since no one else has mentioned it ... If you want to have a better conceptual understanding of the apparent slowing of light (and other electromagnetic waves) in materials, I strongly suggest reading Richard Feynman's lectures, especially Chapter 31 of volume I. That will give you much more explanation than is possible in this forum. All the Feynman ...


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Speed of light is constant in vacuum but different electromagnetic waves travel at different speeds in different media due to different refractive index.


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At hyperrelativistic speeds, a massive object has the bulk of its energy in kenetic form so the invariant mass is small residue. It acts like a very low mass particle at meerly relativistic speeds, or a almost massless neutrino at any speed. A 7Tev proton is travelling at $0.999999991c$ and its mass is only contributing on the order of one one hundredth of ...


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Your question is so confused that it's hard to give a meaningful answer... if matter were to travel the speed of light, would it become energy? Anything that has a rest mass $m_0$ has an energy associated with that mass of $E=m_0 c^2$. If this mass is also moving with some momentum $p$, it has a kinetic energy associated with the motion. The total ...


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It is not correct saying that no force is applied. A photon carries momentum see PE here so on reflection there is momentum transfer. This is the idea behind laser propulsion discussed here. Concerning the speed it is even more complicated. The fact that light gets reflected usually requires an abrupt change in the index of refraction. To get reflected, ...


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You may feel the acceleration, but if you're not accelerating you won't notice anything. Other people may see you moving and observe you contracting, however, from your reference frame, you are not moving at all, and hence you won't notice any length contraction of yourself.


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Basically, no, you wouldn't experience length contraction or time dilation or increased mass or any effects like that. You'd feel acceleration, like you feel when a plane takes off, but acceleration and effects from close to light speed velocity aren't related. At .86 of the speed of light - time dilation would be 50%, So, lets say, You're traveling to ...


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Relative speed can be greater than "c". This does not mean that in an inertial frame fixed on one ship the other ship looks like it is going faster than "c". In an inertial frame fixed on one ship the other ship looks like it is going slower than "c", so light from one could in principle reach the other. In an inertial frame fixed on one ship the other ship ...


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Any time you read a report of superluminal whatever, it's another illustration of Phase vs Group velocity. The pattern indeed moves, but by pre-arrangement not by communication at that speed. A wonderful illustration is from Greg Egan: http://gregegan.customer.netspace.net.au/APPLETS/20/20.html So playing with that applet is the way to explain it.


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In a word: yes. (Edit: in rereading your question, I see you didn't specify which direction the light pulse travels (front-to-back or back-to-front). I'm going to assume front-to-back in order to have a definite answer as the other way depends on how fast the spaceship is traveling.) The first thing to notice is that the light pulse will be traveling at ...


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If we ignore the motion along with the spacecraft, then most motions inside a relativistic spacecraft are slow-motion motions. So an observer observing a moving spacecraft sees light beams move inside the spacecraft like this: From the floor to the ceiling: Motion slowed down by amount: The time dilation factor. From the front to the tail and then back to ...


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Yeah the satellite wouldn't stay in orbit :) But ignoring that... Time dilation comes into play at relativistic speeds. The faster you go, the slower time goes. As such an astronaut on the IIS will age a tiny bit slower than someone on Earth. So for your example, time on the satellite will appear to slow down as observed by someone on Earth. This means ...


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Maybe the explanations you got until now were sufficient, but I would just want to add something simple. Let's represent a light-wave traveling in the direction $x$ as $Ae^{i\phi}$ where the phase of the wave is $(\text i) \ \phi = kx - \omega t = 2\pi\left(\frac {x}{\lambda} - \nu t\right).$ Consider a wave-front (a surface on which the phase is ...


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There are a lot of intertwined ideas here. Let me try to tackle just part of it. When a photon interacts with a medium, it causes local polarization - that is, electrons are displaced by the E/M field of the photon. This interaction leads to a slowing down of the wave - and, as you pointed out, a shortening of the wavelength. However, at this point the wave ...


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I think it is the "back and forth" that you should home in on. You do not say what sort of "level" you want the answer at, but Faraday's law tells you that a changing magnetic field (as you wave the magnet, the B-field changes at a point in pace) begets some sort of electric field. If the rate of change of magnetic field is not constant - i.e. there is a ...


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I'm not sure if I'm missing something here, but is the answer not c, the speed of light, 186000mph? A photon is a particle of light, but as it has no mass it can travel at the speed of light. As for the second part, yes it can be influenced by gravity. As an example, gravitational lensing (the bending of light) around galaxies, making objects behind appear ...


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If you bring an object from infinity to a distance $R$ then the potential energy change is: $$ \Delta U = -\frac{GMm}{R} $$ Assuming your object starts at rest, the potential energy change is equal to the change in kinetic energy, so we have: $$ \frac{GMm}{R} = \tfrac{1}{2}mv^2 $$ so: $$ v^2 = \frac{2GM}{R} $$ You want $v \ge c$, so: $$ \frac{2GM}{R} ...


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Time is what an ideal clock measures. So what's an ideal clock? It's something that measures time. In other words, physicists don't quite know what time is. That's okay. They don't quite know what space is, either. What they do know, and know very, very well, is how to measure both, and how the two (time and space) relate to one another. That the speed of ...


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Being able to sense phenomenon and being able to explain them are different animals. Consider how many millions of magnetic coils we employ in our daily lives. "Science" still cannot give a single, congruent, fully observable at every level, without referring to other phenomenon, explanation of WHY they work. Obviously they do, and we have figured out that ...


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The space-time distortion gets greatly amplified near the limit because thats a mathematical property of the lorentz factor or the swcharzschild factor. Physically it means that it becomes progressively difficult to reach or surpass that limit. The concept of negative mass to me should accompany its own concepts of velocity and kinetic energy which implies ...



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