# Speed of light is hard...

Ever since the speed of light became the universal speed limit, there has been the counter argument: if I’m taveling at almost the speed of light, and I turn on my flashlight do the photons emit at less than light speed? I know this argument is almost as viable as the airplane on the treamill one, but it escapes me why that’s the case.

I guess my question is, is the speed limit relative to a starting point? or some other fixed point in space? or am I really not thinking about it in the right way?

The speed limit is the only absolute thing in a universe where everything else is relative. If you drive by me in your car at almost the speed of light, we’ll both measure the photons your flash-light emits as moving at the speed of light. To me that will be because your time is slowed down by special relativity, to you that will be because you have an equal claim that I’m the one moving at almost the speed of light and that I’m the one whose clock is running slow.

Special relativity all the way!

In your frame of reference, they appear to be traveling at “the speed of light” - 186,000 mi/sec. In a stationary frame of reference, they also appear to be traveling at the same speed. Which is why the speed of light is invariant.

The point is that the statement, “if A sees B moving at velocity U, and B sees C moving at velocity V, then A sees C moving at velocity U + V”, is true by every intuition we have, but nevertheless is wrong. In actuality, A sees C moving at (U + V)/(1 + UV/cc).

Bolding mine. I thought this was demonstrated by Maxwell’s equations. Wasn’t this established prior to the publication of Einstein’s paper?

It doesn’t matter if you are traveling at .000000000001c or .9999999999999c. The speed of the photons will be c.

Think about it. If it* doesn’t happen at low speeds, what would be the “magic” speed at which it suddenly started happening?

*“It” being the speed of the photon affected by the speed of the source.

It’s not exactly a “counter argument” (it would require decades of experimental proof to gain that status, and there is none, given that it’s not true).

It’s a question, though, for sure, and a common one.

The answer is that - and this has been proven time and time again both mathematically and in practice for over a hundred years; there’s no dispute that this is the case - the speed of light is the same for all observers whatever speed they’re moving at. This is known as “relativity” and, yes, it’s counter-intuitive, like much of our universe is. It “gets around” that by doing wacky things like actually slowing time down and stuff.

The speed of light is the same relative to all observers.

I still don’t get it.

If Inigo is driving past me at nearly the speed of light, am I going to see his high beams all squished just in front of his car?

I believe the:

(1) High beams would be blueshifted considerably (you though HID headlights were annoying? How about X-ray headlights?),

(2) Inigo’s entire car would be squished (in the direction of travel) quite a bit due to length contraction, from your perspective.

(3) From your perspective (at least for the fraction of a second it takes him to whiz by) Inigo will also appear to have time slowed down to a crawl.

whoops, nevermind about the X-ray thing. They’d still be blueshifted, but not to that degree.

Yes, but the speed of propagation is independent of the wavelength.

I still don’t get it either.

Explain it to a four year old.

Time passes at different rates and distances are warped for observers moving with a nonzero velocity with respect to each other such that they both observe a given photon move at exactly the speed of light through a vacuum.

Can’t. Relativity ain’t an easy concept.

Some of the popular science books do a good job of it.

What, exactly, don’t you get?

So, I’m parked and light from my headlights is coming out of the bulbs at C.

Now I’m traveling at 100 KPH and light is still coming out of my headlights at C, because it can’t travel at C + 100 KPH.

Now I’m travelling at 0.5 C and light is still coming out at C.

Now I’m travelling at C, therefore no light can be emitted.

But I know that’s not correct.