# How can light travel at a speed greater than the speed of light

I now know that the sentence ''the speed of light is always constant in vacuum'' is just an oversimplification, for example light travel at the speed greater than the speed of light (non-locally) sometime and also can travel at the speed less than the speed of light (non-locally).

Its just when in special relativity the metric tensor take its simple form light travel at the speed of light.(SR is local). [sir John Rennie's example: if you were hovering just outside the event horizon you'd observe the speed of light to be less than $c$ everywhere nearer the black hole than you, but faster than $c$ everywhere farther from the black hole than you.]

Doesn't it mean information travelling faster than light (at least non-locally)? Is it possible? And also how much local is local?

• The speed of light (in vacuum) is constant in any unaccelerated frame of reference. Acceleration, including that due to gravity, changes everything. – pyramids Apr 5 '15 at 9:22
• Vacuum is the one that is oversimplified, space is a vacuum but it can be blended to your liking... Actually no it is your mass that cause the space around you to bend and light just move along this space so speed will be affected... Sounds weird too... The distance is compressed... Anyway matter tells space how to bend and space tells light how to move. – user6760 Apr 5 '15 at 9:28
• Nothing, including information, can travel faster than light. But information can travel faster than $c$ if light can travel faster than $c$ along the same path. I'm not sure what answer there is to your question other than this simple statement. Maybe you could update your question to clarify what further info you need to answer your question. – John Rennie Apr 5 '15 at 12:26
• @John Rennie :I think this is relevant here?physics.stackexchange.com/questions/60519/… – Paul Apr 5 '15 at 15:03
• Well yes, but that doesn't help me understand what answers you are looking for. – John Rennie Apr 5 '15 at 15:14

The local speed of light is always $c$. Local in this sense could mean that for each observer there exists a neigborhood of that observer such that, if we call $v_c$ the "observed speed of light",

$|v_c - c| < a$

where $a$ is arbitrarily small.

However $v_c$ is a slightly nebulous concept as beyond the inertial frames in special relativity, there isn't a general way to define the observed speed of light for a given observer. $v_c$ will depend entirely on how we choose to define $v_c$ for a given observer in a given spacetime and the above limitation on $v_c$ is merely expression of that, whatever the definition of $v_c$, we want it to match the local measurements of the observer.

• @Paul the link you provided actually and specifically only indicate space expanding can exceeds the speed of light, it is a misconception that speed of light scales proportional to expansion of space now this statement is untrue. Photon can never exceed c however space stretches or expands. No worry I learnt it the hard way when my rep falls a lot through this site, drinks on me. – user6760 Apr 6 '15 at 1:46

What matters in principle is not if information can travel faster than c, rather if this leads to causality violations. As pointed out in this article, the Scharnhorst effect is the only known effect where light is expected to travel faster than c. However, in that case you cannot use this to create a causality paradox.

If light(to be taken here) travels @ a velocity >c, you won't be able to see or apprehend it. So, you need an observer having a relative velocity =

• It looks like you hit submit before finishing your last thought. – Kyle Kanos Apr 13 '15 at 17:52

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