# What is the speed of light relative to?

Consider the scenario where you measure the time it takes for light to travel to the left 10 meters and to the right 10 meters. Both measurements will take the same time, even though we are moving through space at crazy speeds. This must mean that light is not moving relative to "space" as a whole. What does it move relative to? The light emitter? If so, try shooting two beams of light 10 meters from the wall. The first time the emitter is stationary; the second time it is moving at 100 m/s. Am I mistaken in thinking that it would hit the wall slightly faster? Wouldn't this light be moving faster than the light emitted from the stationary source?

• The speed of light is relative to everything. And yes, that doesn't get along with your understanding of how space and time work, but that intuitive understanding is simply wrong. You haven't defined your thought experiment carefully enough for us to say what the result of each one would be, but there is a unique answer in every case. May 27 '14 at 3:23
• the answers are good. The extra energy given to light by the moving emitter becomes an extra energy in the energy of the photons that compose the light E=h*nu, nu will become larger, the effect of doppler shift on light. May 27 '14 at 4:18

Am I mistaken in thinking that it would hit the wall slightly faster?

THE insight of relativity is that this is not true. No matter whose clocks and rulers you use, you will always measure the speed of light (in vacuum) to be the same.

This has as a consequence the fact that lengths and times are not as absolute as was once thought. If you are looking at a ruler that is moving relative to you, then that ruler will appear to be shorter (along the direction it's moving); and a moving clock will appear to be slower.

This must mean that light is not moving relative to "space" as a whole.

Relativity does away with the idea of absolute space and instead all velocities are relative to some object or frame of reference (hence relativity).

• The idea that all velocities must be relative was around since Galileo, so that actually isn't new. All Einstein did (which isn't little) is find a way to make it work with the velocity of light being absolute. May 27 '14 at 3:36
• Thanks for the correction @JavierBadia. You are correct, the idea of relativity of velocities was from Galileo's time. May 27 '14 at 4:19
• I know that special relativity isn't a simple concept, but could you try to explain it a bit further in layman's terms how my examples act? I will most likely accept this answer but I'm going to wait until tomorrow to give any other answers a chance. May 27 '14 at 4:32
• @Keavon, the two beams of light, one from the stationary emitter and one from the moving emitter, have the same speed according to either emitter; both emitters measure the speed of either beam to be c. Though this sounds impossible, it isn't and, once you become familiar with the Lorentz transformations and spacetime diagrams, this result will seem natural. May 27 '14 at 12:02
• Punk_Physicist: "If you are looking at a ruler that is moving relative to you, then that ruler will appear to be shorter (along the direction it's moving)" -- Presumably: "shorter" than a ruler of equal length (at rest to you); "and a moving clock will appear to be slower." -- Presumably: "slower" than a clock of equal rate (at rest to you). And btw.: Is there anything stopping you (or anyone) from calling for instance the quantity $$c ~ \sqrt{\frac{1 + \beta}{1 - \beta}}$$ an "apparant speed" ?? ... May 28 '14 at 5:05

If an object has velocity $u$ in the frame of reference $O$ and $O$ has velocity $v$ in the frame of reference $O'$, the object has velocity $u' = u + v$ in the $O'$ frame.

But, what if $u$ is infinite? Since $\infty + v = \infty$, an object with infinite velocity relative to some frame of reference has infinite velocity relative to any frame of reference with relative velocity $v$; infinite speed would be an invariant speed.

In the context of special relativity, $c$ is, in a certain sense, like the infinite speed in the context of Galilean relativity; $c$ is an invariant speed. In SR, if a particle has speed $c$ in a frame of reference, it has speed $c$ in any frame of reference.

In fact, if one replaces $c$ with $\infty$ in the Lorentz transformations, one recovers the Galilean transformations.

In this sense, the Lorentz transformations are more general and, in fact, one can derive the form of the Lorentz transformations with just the principle of relativity leaving the determination of the invariant speed as a matter of empirical verification.

We deduce the most general space-time transformation laws consistent with the principle of relativity. Thus, our result contains the results of both Galilean and Einsteinian relativity. The velocity addition law comes as a bi-product [sic] of this analysis. We also argue why Galilean and Einsteinian versions are the only possible embodiments of the principle of relativity.

It's relative to any observer. This is possible because perspectives moving at different speeds experience time differently, which allows for light to be seen moving at the same speed regardless of perspective and the motion of that perspective.

• And what if the observer is a photon?
– user85666
Jul 12 '15 at 7:54
• My theory is that reality "updates" itself at the speed of light. No time progression ever reaches the photon so nothing about the photon or it's perspective would ever experience any progression. Jul 14 '15 at 5:02

What is the speed of light relative to?

It is relative to you and all other objects, in direction and measure.

As mentioned by physicist Brian Greene in his book The Elegant Universe, see The_Elegant_Universe-B.Greene.pdf Motion Through Space-Time pages 26 and 27, all objects are constantly on the move within Space-Time at the speed of light.

This common constant motion of all objects in Space-Time, and the rotation that occurs if they change their direction of travel within that Space-Time environment, changes the measurement instruments in such a manner that the speed of light is always measured as being the speed of light no matter what direction you are traveling in within the environment of Space-Time, thus in turn no matter what percentage of your constant motion(c) is across space only(v).