# What is the universal speed limit relative to? [duplicate]

If all speeds are relative, then what "governing" force is that speed limit relative to? Is there some sort of fixed or absolute grid with locations everything is compared to?

Does this also mean that we have a "universal speed"? This being from the combined speed from the earth spinning, us orbiting the sun, the sun orbiting the galaxy, etc. If we do, then that would mean we could, in theory, utilize time dilations between an external observer (like a probe) and earth to determine which direction we're currently moving?

• possible duplicate of What is the speed of light relative to? – ACuriousMind Mar 5 '15 at 17:57
• The first paragraph is a reasonable question (although almost certainly a duplicate, and the whole basis of Special Relativity). The second paragraph seems to lose focus and doesn't make much sense. – Sean Mar 5 '15 at 18:08
• @Sean I reworded the second paragraph to hopefully make it clearer. – Daniel Way Mar 5 '15 at 18:40

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 you can measure, in your coordinates, where you think it is.

Here's the basic problem: I (stationary relative to the dust) measure this light as moving away from me at speed $c$. You, moving relative to me at speed $v$, also see it moving away from you at speed $c$. The better your instruments, the better you will find that the light is moving away from you at speed $c$.

Now let's speed you up a bit more. By this point I am far away, so don't count on me to help you: instead, you drop a little marker in space and then accelerate until that marker is moving backwards at speed $c/2$ relative to you. How fast is the laser pulse moving away from you? Still at speed $c$. So you drop another marker and you accelerate to speed $c/2$ relative to that. Still, the light is moving away from you at speed $c$.

You cannot win. That is what the present theory says. Since I will always see the same events as you see, I will never see you outrun that light pulse. So from my perspective, nothing you can do short of magical teleportation will enable you to outrun the light pulse.

Let's say that you can measure the speed of me moving away from you -- or maybe you just measure the speed of the dust. It does not go at speed $(-1/2)c$, then at speed $(-1)c$, then at speed $(-3/2)c$ relative to your spaceship. That is not how velocity addition works in relativity. Rather, it goes at speeds $(-1/2)c,~(-4/5)c, (-13/14)c$. The dust never goes faster than light either.

You'll be heart-warmed to know that there are no paradoxes. We can prove that the mathematics is 100% consistent.

The reason that this all happens is that when you start moving relative to me, we start to disagree on the time that the "present" is at far-off places. These disagreements start to add up pretty quickly as you start to go a significant fraction of the speed of light, and so that when you get close to it we both see each other's clocks as moving slowly, and we both see each other's spaceships appear to become shorter in the direction they're traveling.

This gives you the answer to your second paragraph, too: because there is no "absolute frame of reference" that the speed of light is relative to (everyone sees light move at speed $c$), no, we can't determine our motion relative to that absolute frame of reference. (But, we know something a little similar: we have been able to determine our motion relative to the cosmic microwave background, which is actually pretty significant if you think about it; it basically says "we know how we're moving relative to our local part of the Big Bang.")

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 have a speed of c in all other inertial frames too (this fact can be understood a bit more intuitively in terms of time dilation, length contraction and the relativity of simultaneity, see my answer here). So, the fact that there is an upper limit on speed does not imply any absolute lower limit--although different frames agree on which particles/waves have a velocity of c, they do not agree on which objects have a velocity of 0.

The physical reason for using this transformation is that it seems to be the one that ensures the fundamental laws of physics will obey the same equations regardless of which frame's position and time coordinates they're written in terms of--the laws of physics seem to be "Lorentz-invariant". This means for example that if you are in a windowless lab moving inertially in space far from any source of gravity, and all your measurements are confined to things inside the lab, with positions and times defined using the inertial frame where the lab is at rest, then the results of a given experiment will be the same regardless of the lab's velocity relative to any particular choice of inertial frame.

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 towards the driver, the emitted light travels at c relative to the bus and the same light also travels at c relative to the road.

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 of light) this is not the case, you will actually observe each other moving at 0.882c due to Einstein's laws of relativity. The equation behind this is: $$u'=(u-v)/(1+uvc^2)$$ Because of this, the speed of light is not relative to anything. No matter what speed you're moving at you will always see light moving at the same speed. This basically makes all points of reference equally valid as a perspective to call "stationary".