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A quantity or geometric relation being called "proper" can be understood as "referring to those participants who are thereby (directly, intrinsically) characterized". Consequently we can consider for instance the "proper length of a given train", as the distance of its two ends ("tip of the locomotive, $A$" and "ETD, $B$") between each other, provided ...


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It's a mixture of $c_\infty = c_0 = c$ and "the question doesn't make sense". So, first, how it does not make sense: What's the "speed" of a quantum object? It has, in general, no well-defined position, so $v = \frac{\mathrm{d}x}{\mathrm{d}t}$ is rather ill-defined. Instead, we should probably look at the mass of the photon, since all massless objects ...


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As far as I know for a photon that's moving at the speed of light (obviously) time comes to a halt and space contracts to a point, making all travels instant from its perspective. Now this is the part I might have understood wrong, so please correct me if what I've said isn't true. It isn't true I'm afraid. Imagine you were travelling though this universe ...


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There is no contradiction. From your quote: The proper length of an object is the length of the object in the frame in which the object is at rest. and The proper time between two events - such as the event of light being emitted on the vehicle and the event of light being received on the vehicle - is the time between the two events in a frame ...


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Could gravitational waves and electromagnetic waves/light be the same thing? I think most physicists would say they aren't, in that gravitational waves are thought to be quadrupole waves, whilst electromagnetic waves are thought to be dipole waves. However it's worth noting that the photon can be considered to be a singleton electromagnetic wave, and that ...


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which should not be possible. Indeed, uniform coordinate acceleration $a$ is inconsistent with special relativity however, uniform proper acceleration $\alpha$ is consistent. The proper acceleration is the acceleration of the object according to an attached accelerometer. For 1D motion, the relationship between $\alpha$ and $a$ is given by $$\alpha = ...


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Have a look at the article by Phil Gibbs on the relativistic rocket. This describes the motion of a rocket that is accelerating with a constant acceleration. In this context constant acceleration means the crew of the rocket feel a constant acceleration. Technically the rocket has a constant four-acceleration. Anyhow, the velocity of the rocket as observed ...


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Look at sparknotes.com/physics/specialrelativity/dynamics/…, you can see $dE/dx=F$ - if your force is constant, it is the energy that increases constantly. $E=\gamma(v)m_0c^2$, you can deduce the $v$. Beacause of laziness I used mathomatic, and it gives me something like this: $v=c\sqrt{1-\frac{m_0 c^2}{(F\cdot x + m_0 c^2)^2}}$ If you check it for x=0 and ...


6

Is there some other formula ... which ... does not allow the speed ... to surpass the speed of light? That would be the equations of special relativity mentioned by sahin in a comment. Image from Loodog? Another factor you have to take into account with classical mechanics is to work out how a constant force can be applied to your object over 11 ...


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Even if what you said were true (which seems not to be the case, see comments on your question), it would have no practical application. If the angle is always the same, it means that it is not related to other variables that could be of interest.


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suppose it is possible to accelerate matter at speed of light By this you must mean suppose that relativistic mechanics is, at its root, wrong. What will the time reflects on these two clocks? Since you've stipulated that relativistic mechanics is wrong, which incorrect, non-relativistic mechanics would you like to apply to this problem?


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There is no limit to the velocity that a person may travel. However, there is a limit to the acceleration that a person can handle. This is complicated as that maximum acceleration depends on how long the person is at that acceleration, how fast they got there, their muscular structure etc. The shorter time you have an acceleration the greater that ...


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Index of refraction depends on frequency of the light. Indices can be very high in the far infrared. CO2 lasers operate at a wavelength of 10.6 um. This is about 20 times longer than visible light. The highest index I know of is GE, n = 4. See this for more. It is possible to "stop" light in a Pr-doped crystal. But this really sets the state of the crystal ...


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You can store light up to one minute so far. Basically you make a crystal transparent (low OD) at a predefined desired wavelength. When the light pulse goes in, you turn the crystal opaque (high OD). You retrieve the pulse by making it transparent again at the right time. The material is some Pr-doped crystal. For this purpose, it is hard to find a material ...


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Light speed is something of a cosmic speed limit. Nothing can exceed the speed of light, and only massless particles can travel at light speed. Any particle with mass would require an infinite amount of energy to accelerate to the speed of light.


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I quite sure it's not theoretically possible. Without doing any actual calculations, I recall that accelerating a massive object to light speed would require an infinite amount of energy. Some energy certainly can be gained with the "slingshot" method, but definitely not an infinite amount. Specifically, it's the Lorentz factor that prevents objects from ...


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First of all to achieve speed of light the energy requirement tends to infinite, which is only possible by entire mass conversion, as if there will be not much to percieve as you wouldnt be alive to achieve speed of light, as in case of zero rest mass particles there is no mass, hence they achieve light of speed that is zero rest mass particle are not ...


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One of the main effect that would be affecting how this man would see is the contraction of length that are not in its referential(travelling with him). If a referential is moving at the speed v close to c in the +x direction. Then every object that are not in its referential will be shorten along the x axis by a factor $\gamma$ such that : ...


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You could do that, but if you did, you'd best not call the new unit "meter" in order to avoid confusion. That is why we don't define the meter as the length traveled during 1/300 000 000 th of a second, for instance: such a definition would cause confusion with older precision measurements that used previous definitions of the meter. You can only ...


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The wavelength of harmonic EM wave changes in medium, but saying "the phase velocity of the wave changes in the medium, while frequency stays the same" is no explanation, since then we have the question why phase velocity changes in the medium. The explanation is based on the wave theory of light, not photon theory. Essentially, primary EM wave from the ...


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I saw a some videos about the information paradox aka Hawking paradox. My understanding of it was that as soon as something is unable to leave a black hole (the event horizon where light cannot escape) that it's information is then represented as surface area (2d) on the outside of the black hole rather than our standard idea of volume (3d) and believing ...


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A black hole does not have an infinitely strong 'gravitational pull'; the spacetime curvature is finite at the horizon. However, the proper acceleration required to hover above the horizon diverges at the horizon. That is to say, the weight of an observer, hovering above the horizon, goes to infinity at the horizon. Nonetheless, to an observer hovering ...


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does it mean that at a blackhole, an object will fall at an infinite speed because of the infinitely strong gravitational pull of the blackhole? No. Actually, defining exactly what you mean by the speed an object falls into a black hole is a tricky problem. In relativity you generally find that different observers observe different things. But we can ...


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Quick short answer, someone else will give you a better one Nobody, not the best people we have, nobody, knows what goes on inside a black hole. There is no way to look inside because no light comes out. So we can guess anything we want about infinite speeds etc.... till the cows come home, but no measure means no proof of your guess being correct. Hope ...


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I believe that the vertical leg could differ from the horizontal leg. If the vertical leg is long enough, then the difference in air pressure would change the time the beam took to complete the path.


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There are a couple of Einstein's papers that talk about the constancy of the velocity of light, the most important of them, in my opinion, is the one called On the Influence of Gravitation on the Propagation of Light. In this paper he notices that the velocity of the light depends on the potential gravitation, yes! The velocity of light shall be regarded ...


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even though John puts it down quite nicely, I don't think that was the answer you sought? Yes, the Michelson-Morley experiment has, to my knowledge, only been done in accelerating reference frames, because of the rotation and gravity of the earth, some with precision high enough to measure both gravity or the rotation velocity. Unfortunately I can't ...


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You say: I found out that the speed of light is NOT invariant in an accelerated reference frame but things are more complicated than this. The local speed of light measured by an observer is always equal to $c$, and this remains the case whether the observer is stationary, moving, accelerating or anything else you might think of. So if your Michelson ...


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Your whole question relies on the fact that you can define a rest-frame for light. Assuming that the constant c appearing in special relativity is indeed the speed of light, there is no such thing as a rest frame for light. More specifically it is trivial to check that Lorentz factor tends to $\infty$ as you get closer and closer to light speed, hence the ...


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In a non-accelerated reference frame, a point or a particle cannot be motionless wrt. light, for the reason that busukxuan mentions: All observers will measure the speed of light to the same value, c. But in an accelerated frame, such as an expanding universe, it is possible. For instance, galaxies that are farther away than about 14 billion lightyears, ...


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The first to do something equivalent to that were Pound and Rebka who first measured the gravitational redshift in 1959. I'm not aware of anyone who actually used a Michelson interferometer in a upright orientation.


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from wikipedia "The speed of gravitational waves in the general theory of relativity is equal to the speed of light in vacuum, c." so the time taken to feel the effects of the star is the distance you are from the star divided by the speed of light. so you should feel it at exactly the same time as its light reaches your eyes (20 sec)


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So far the only experiments done are “near” Earth. There, objects that are in lower gravity, underwent acceleration and high speed have shown time dilation as predicted by special and general relativity. Gravity at least does seem to be a factor here but exactly how much is unclear. I am afraid we would have to go ask Jack and Jill to answer this question. ...


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The clock isn't slowed by any force, the clock is only slow from Jill's perspective due to his immense speed. From Jack's point of reference he is not moving and Jill is speeding away from him and her clock is slow.


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As the influence of gravity is infinite throughout the universe. The influence of gravity is not infinite. If you mean roughly the 1/r potential of the Newtonian gravitation, you should learn that it is an approximation. General relativity is the validated theory for cosmological distances, and observations show the effects of gravity are confined and ...


0

To answer the main question, yes. Black Holes have such a gravity influence that not even light can escape.


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Light will always be measured to move at c in a "local inertial frame", see this article on the equivalence principle for a discussion of what that means. If you use a non-inertial coordinate system, there is no requirement that light always moves at constant coordinate speed, so if you don't want to restrict things to inertial frames then the answer to your ...


1

No, the wavelength will grow due to gravity, look up "gravitational red shift"


1

Its a good thing you're asking such questions. At the age of 16, Einstein asked himself such questions. But he later realised such insights are redundant. Travelling at the speed of light, as Einstein enlightened us, is something impossible. But since we're looking at a hypothetical scenario, why not turn to Sci-Fi? "The Fastest Man Alive" or The Flash can ...


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Let me address the part about virtual particles, since the speed of light has been well covered by John. Virtual particles that arise and disappear within a certain timeframe, is There a relationship between how long those particles appear before they disappear in some way geared to the speed of light? Virtual particles are a mathematical formulation ...


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I believe that Paul's (http://www.mathpages.com/home/kmath210/kmath210.htm) source answers it brilliantly. "The main bunch of riders - may be moving at a constant speed. But within the bunch an individual rider may moving more slowly, dropping back for a rest or a drink." Coupled with Mr. Witthoft's response "What you're missing, Dirk, is that there is no ...


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No, the photon would still go at c. E = hf for a photon. E is energy, h is a special number called Planck's constant, and f is frequency (also sometimes people use v instead of f). Instead of speeding up the photon, the gravity would increase the frequency of the light. For example, a red beam of light, pulled by gravity, might have its frequency increased ...


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There is no "correct" speed. All speeds are relative to the observer, but this does not mean you can watch something moving faster than light even if you are moving one way at 0.6c (60% the speed of light) and someone else is moving the other way at 0.6c. Even though typical logic would dictate that you see each other move at 1.2c (20% faster than the speed ...


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Short answer : the same light goes at the same speed (c) relative to any observer. There is no grid. This is counter-intuitive : if you're standing in a bus traveling at 30 mph and you walk at 3 mph towards the driver, you walk at 30 + 3 = 33 mph relative to the road. But that doesn't work for light : if the bus travels at c/2 and you shine a flashlight ...


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Suppose we play a racing game. I scatter a little bit of dust around space, then you come by me in your spaceship at some speed $v$. Let's start with $v = c/2$, just so we're not contentious. Right as you pass, I fire a really bright laser pulse in the direction you're going. You're racing the laser light. The dust means that you see reflections of it, so ...


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It's relative to all inertial reference frames--in special relativity the coordinates of one inertial frame are related to the coordinates of another by the Lorentz transformation, and this transformation has the property that anything with a coordinate speed (change in coordinate position divided by change in coordinate time) of c in one inertial frame will ...


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Even when the Earth is further away, the moon will be seen to appear later, sure, but it will also disappear later - so the measured times between disappearance and appearance should be the same When the Earth is far away, the moon will be seen to appear late, but it will also seen to disappear late - so the measured time between disappearance and ...


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The answer to your question is that nothing can travel faster than light, and light can't escape through the event horizon. Therefore gravitational waves can't escape either. I give an algebraic proof that light can't escape in my answer to Why is a black hole black?, and a more visual proof in my answer to Would the inside of a black hole be like a giant ...


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First, if you accept that gravitational waves can't travel at fast than the speed of light in regular space, then you can move to the inside of a black hole and then imagine letting the light and the gravitational wave race each other as you fall freely. As you fall freely then over a short time interval and a short distance everything looks normal to ...


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Yes. Light travels slower through diamond than it does through glass, slower in glass than it does through water, slower through water than it does through air, and slower in air than it does through a vacuum. We usually talk not about the speed $v$ of light in a medium, but the refractive index $n = c / v$, which is the ratio of the ...



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