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There is a difference between the concept of the speed of light and the velocity of light. are both of them constant ($dc=0$ and $dv_c=0$)? if yes, why?.

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marked as duplicate by Qmechanic Jun 19 '13 at 12:17

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

Possible duplicate of How to bend light. – Mostafa Jun 2 '13 at 20:38

Hint: Velocities include directions. Light can travel in different directions. So...

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The speed of light is constant. The velocity of light should be, unless light changes direction. Speed is the magnitude of velocity, a scalar quantity (has size, but not direction), whereas velocity is a vector, which has both magnitude and direction. c is defined as speed, which has only magnitude. There is no definition of the velocity of light, but if the light was traveling north when last measured, velocity could be negative, positive, or zero based on the direction traveled.

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The last sentence doesn't make much sense. Vectors aren't positive or negative. – Ben Crowell Jun 3 '13 at 3:06
The vector can be defined as negative, positive, or zero depending on the direction and coordinate system. By themselves, vectors are not positive or negative, only in reference to a coordinate system. – cuabanana Jun 5 '13 at 16:53
No, vectors can have positive and negative components. In any coordinate system, there will be vectors whose components are a mixture of positive and negative values. – Ben Crowell Jun 6 '13 at 19:18

The speed of light in vacuum is constant, otherwise is could not be well defined. It is called a Universal Constant for this reason. It does not vary even with your reference frame. That is to say, if you are standing next to your friend who is holding a flash light, the light will appear to be moving the 'same speed' to both of you, even if you are running in one direction. This is different from if your friend were to throw a ball, which would then appear to be traveling at different velocities depending on your reference frame: i.e. it may be moving faster or slower in your reference frame depending on whether you are running in the same or opposite direction as the ball.

The speed of light in vacuum is given by

$c = 299,792,458$ meters per second

Velocity, as cuabanana stated, is just the speed defined with a direction. The magnitude of the velocity (i.e. speed) is constant, given by the same number above.

If light is propagating through a transparent medium, such as glass, it will actually travel slower than the speed of light in vacuum, $c$. The speed of light in a in a medium is given by:

$$v_\text{light} = \frac{c}{n}$$

where $n$ is called the index of refraction of the material. The index of refraction for vacuum is 1: hence the speed of light in vacuum is $c$. The index of refraction for glass is about 1.5, and thus the speed of light in glass is about $c/1.5 \approx 200,000,000$ meters/second.

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The velocity of light changes all the time. If the velocity of light were constant, eveyrtything would be perfectly transparent and you couldn't see anything. So let me list down when, where and how the velocity of light changes.

  1. Reflection.

    Let us choose a convinient orthonormal coordinate system where the reflector is sitting in the $xy$-plane and the $z$-direction is normal (orthogonal, perpendicular) to the reflector. Then, the $y$-direction, let us say, is redundant, so discard it. For convenience, also let the point where the the light ray hits the reflector be the origin of the coordinate system. Now, clearly, then, the $x$ component of the light ray's velocity is negated while the $z$ component remains the same.

  2. Refraction

    The speed and direction are both changed. Let us say the light ray is hitting the refracvtive medium from a vacuum. Then, it will change its speed as $v=r^{-1}c_0$ and its angle will also be affected as $\theta_f=\arcsin\left(r\sin\theta_1\right)$.

  3. Deflection

    Here, light appears to bend due to gravity as per the Geodesic Equation, which can be shown using the Euler-Lagrange Equations. $$\frac{\mbox{d}^2x_\lambda}{\mbox{d}\tau^2}=-\Gamma_{\mu\nu}^\lambda\frac{\mbox{d}x^\mu}{\mbox{d}\tau}\frac{\mbox{d}x^\nu}{\mbox{d}\tau}$$ Of course, switching your coordinate system back to a curved one (using the inverse of the Christoffel symbols $\mathbf{\Gamma}$), the light is still following its geodesic in curved spacetime.

    Luckily, photons are uncharged (electromagnetically) and thus are not deflected by electromagnetism.

    For these reasons, light almost NEVER goes at a constant direction (in a straight line) or at a constant speed. Since there is gravity, opaque objects, non-vacuum media, etc. Also, in case you are talking about a constant being applied to light's direction, then there' is one more.:

  4. Light is emmitted in different directions, and if it were only one, then that would single out a prefered direction,.

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Velocity of light in higher in Casimir vacuum. It is called Scharnhorst effect.

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Higher than what? How high? – Brandon Enright Jun 3 '13 at 2:52
@Brandon Enright higher than the constant c. – Anixx Jun 3 '13 at 2:53
This is a hypothetical effect. There are other effects where the speed of light is higher than $c$, but they don't imply a signal going faster than $c$. – fffred Jun 3 '13 at 2:58
@fffred Scharnhorst effect is propagation of both signal and light faster than c. Anyway, the question did not ask about "signal". Velocity of light depends on the energy of vacuum, this exactly answers the question, I believe. – Anixx Jun 3 '13 at 3:07
That effect is pure fantasy. Shame on wikipedia for even having an article about it. – Chris White Jun 3 '13 at 3:20

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