# Tag Info

26

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 ...

14

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 ...

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 ...

5

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 ...

4

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 ...

4

Fortunately, explosions tend to decay in intensity like $1/r^2$, so no known celestial events (e.g. supernovae) would really be able to do that. In any case, with these sorts of things, we could presumably see that such an event was "about to happen" and had simply not happened yet. There are actually some awesome doomsday cosmologies which are related to ...

3

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 ...

3

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)

3

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 ...

3

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 ...

2

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 ...

2

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 ...

2

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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You have two different concepts intertwined in your question. You begin by asking about the speed of light in a medium varying with color (i.e. wavelength). This phenomenon is called dispersion and it is present in all materials including air. Dispersion shows up in many places in the field of optics, but the case you are probably most familiar with is ...

2

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 ...

2

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 ...

2

A gamma-ray burst is rather more likely than false vacuum - we observe them on a regular (daily) basis. If one happens in our galaxy, and it's pointed at us, we had a good run. The mechanics are fairly simple - massive star collapses, huge amount of energy squirts out in 2 directions, not affected by $1/r^2$ spherical expansion. Anything in the way gets ...

2

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 ...

2

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 ...

2

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 ...

1

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 ...

1

It is true in general that the speed of light in a medium will depend to some extent on the wavelength/frequency of the light itself, but in most (not all) everyday situations this is not apparent or important, and makes the theory of optics much easier mathematically. As for the refractive index of air, it is not quite 1, but slightly larger, 1.0003 IIRC, ...

1

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 ...

1

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 ...

1

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 ...

1

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 ...

1

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 ...

1

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 ...

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 ...

1

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

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