A reader sent me a really wonderfully wacko link. It’s a fundamentalist islamic site, which tries to use relativity to argue for the divinity of the Koran. It’s remarkably silly. (I also recently got a link to something similar, but from a Jewish perspective – claiming that the Torah disproves relativity. Alas, I screwed up and lost the link; if whoever sent me that link could re-send it, I’d really appreciate it!)

The claim that relativity proves the Koran is true. See, they claim that the Koran tells you what the speed of light was, and that the *real* absolute speed of light as described by relativity is stated in the Koran, and that it’s tied to the muslim Koranic lunar calendar.

Now, most of us think that the speed of light is an absolute constant – roughly 3×10^{8}m/s. But according to our new wacko pals,

that’s not true! That speed of light isn’t really constant.

Their argument is based on the idea that the speed of light can vary in

certain accelerated reference frames – and that, therefore, the speed of light

is not a fixed quantity based on the speed of light in a vacuum – because the

speed of light in a vacuum can vary! But the Koran says that angels travel in

one day the same distance that the moon travels in 100 lunar years. Since in

the Islamic calendar, a lunar year consists of 12 lunar months, where each

month is a lunar orbit, that’s 12,000 lunar orbits per day. And since

*obviously*, angels move at the speed of light, and 12,000 lunar orbits

per day works out to *roughly* 3×10^{8}m/s, the real absolute fixed, unvarying speed of light is 12,000 lunar orbits per day.

Let’s start by checking their figures. The moons orbit is pretty close to circular – it’s got a very low eccentricity of around 1/20th. According to Wikipedia, its average orbital radius is about 384,403 km; and its average orbital speed is 1.022 km/s.

Now, we come to our first problem. The moons orbital period around the earth is about 27.3 days long – 2358720 seconds. (This is the *orbital lunar month*). But because of the earths orbit around the sun, the *apparent* orbital period is 29.5 days – or 2548800 seconds. (This is the *synodic lunar month*.). In the month where the moon orbits the earth, the earth moves in its orbit. The direction that the the earth is facing at noon has shifted because of the earths motion in its orbit. So the moon has to go a bit further to appear to have completed a circle.

So we’ll compute two different versions of the speed of light according to our new friends – the orbital month, and the synodic month. Using our two different months, we get slightly different answers for how far the moon moves in a month.

In the synodic month, the moon travels about 2,605,000 kilometers. In the orbital month, the moon travels about 2,411,000 kilometers. So, by our friends count, that means that the speed of light predicted by the synodic month is about 28,927,342,080 kilometers/day – or 334,800 kilometers/second.

In an orbital month, the moon travels about 2,411,000 kilometers – for

a predicted light speed of 28,932,000,000 kilometers/day – or about 335,000 km/sec. The actual speed of light is around 299,800 km/sec. So the “Koranic” speed of light is close, but not *very* close – assuming the best possibly estimate (the synodic), it’s off by around 10%. That’s actually pretty damned poor – an experimental apparatus built in 1849, using very mediocre measurements of distance, came closer than that.

But that’s not the half of the problems with our new friends!

See, the reason that they care about this is because they don’t understand relativity. It’s like I always say: the worst math is no math. These guys have heard about how relativity says that time slows down under certain circumstances, and from that they conclude that the speed of light must *change*. But the Koran fixes all that! Because no matter what,

from earth, the speed of light will always be the same: 12,000 lunar orbits/day.

n observer outside gravitational fields measures the speed of light locally (in his location) at 299792.458 km/s but when he looks towards a black hole he sees the speed of light there to be as slow as a few meters/s. At the same time an observer freefalling into that black hole measures the speed of light locally (in his location) at 299792.458 km/s; when he looks towards the black hole he sees the speed of light there much slower; when he looks away from the black hole he sees the speed of light there much faster. When he looks towards outside gravitational fields he sees the speed of light there a zillion km/s. In 1915 (10 years after Special Relativity) Einstein developed another theory called General Relativity that deals with gravitational fields and according to this latest theory the speed of light appears to vary with the intensity of the gravitational field.

This is what happens when you try to use words instead of math. The whole point of relativity and time dilation is that it makes the speed of light be the same everywhere. If I’m moving towards you, the light coming from me towards you is moving at the same speed as the light from a stationary object

the same distance away. No matter what viewpoint you consider, the speed of light is always the same. The speed of light doesn’t slow down when someone is falling into a black hole. It stays *exactly the same*; what relativity does is explain *how* it can be the same.

What our friends are doing is playing with a poor understanding

of general relativity. It’s true that Einstein, when he formulated

general relativity, was uncertain about this. The idea of the speed of

light changing in a non-inertial frame of reference is consistent with – but not necessary to – general relativity. Modern interpretations of

relativity, based on the continuing research and extensive experimentation by physicists, conclude that it doesn’t.

Where does this confusion come from? There’s a nice explanation of it here.

The basic idea is that velocity can only be measured relative to something

that provides a system of coordinates. Velocity is measured in terms of

coordinates applied to space-time. But the coordinates are dependent on the

shape of space-time. So when we’re trying to measure coordinates in an area

where space-time is heavily bent by a gravity well, measuring coordinates

becomes tricky – in fact, it becomes ambiguous, because there are

multiple different ways of applying coordinates that are, arguably, correct.

In some of those coordinate systems, used within a reference frame where there is a significant gravitational gradient, you can observe varying speeds of

light.

What we end up with when we work through the math is that for any

*freely falling* frame of reference, the speed of light in that frame

of reference is the well-known, unchanging speed of light. But if you use a

frame of reference which is in a fixed position relative to a gravity well,

then you can create the appearance of a varying speed of light. But that is

because of the fact that you’ve created a very artificial frame of reference:

a non-accelerated frame that isn’t free-falling into a gravity well. So the

frame of reference is subject to the time-dilation effect of the gravity well,

but *not* to the acceleration. It’s ignoring the warp of space-time

while simultaneously being affected by it.

What does this mean? Well – from the perspective of someone in the

kind of reference frame that creates the appearance of varying lightspeed – that is a fixed frame in a large gravity well – the speed of the moon

revolving around the earth *also* appears to vary. In other words,

the supposedly *corrected* Koranic absolute speed of light doesn’t

fix the problem that it’s supposed to correct. Because, you see, they didn’t

do the math.