Light's Journey From The Sun To The Earth

The sun is the main source of energy in our solar system. The light from the sun gives us warmth, light, rain, and enables photosynthesis, which enables life. It also powers our solar panels, gives us vitamin D, and bleaches your favorite blouse. 

And when the sun finally exhausts its fuel and dies—not so fast, probably in another several billion years—it will bring us all together with it.

Everything we know about the sun comes from the single, albeit intangible, proof of its existence: light. So we're gonna talk about light today.

Sunrise captured at Redang Bay Resort, Redang Island.

In physics, we quantify light as photons—packets of energy with discrete amount of energy—so we'll refer to light as photons of light henceforth.

A photon's journey from the sun to the surface of our skin starts in the middle of the sun, i.e. the core, where the temperature and pressure are so intense—up to 15,000,000 degree Celsius—it enables hydrogen atoms to collide with one another and fuse into helium while releasing photons of energy. This punishing environment is made even more punishing by the sheer number of atoms packed together in a highly dense condition due to the immense pressure—just imagine yourself trying to extend your arms in a sea of crowd. In order to escape from the sun to become sunlight on Earth, a photon needs to first make its way from the core to the surface of the sun, 695,500 km away!

But hold on, you say, photons travel at the speed of light, which is 300,000,000 meters per second, which translates to 300,000 km per second. So all it takes is just two seconds, which is pretty straight forward, right?

No.
Here's the thing: the inner part of the sun is a very dense place. Atoms are everywhere, so it's highly unlikely for a photon to travel unhindered all the way from the core to the surface.
But how dense, exactly? Well no body knows for sure, but scientists have estimated that the mean free path of a photon in the sun—the average distance traveled by a particle between successive collisions -- is about a tenth of a millimeter (0.1 mm), which is like moving 0.1 mm at a time, stop, and move again, until you complete the whole journey of 695,500 km. To add to this woe, we have to consider the fact that when the photons collide, they will probably bounce around in random directions; towards the surface, towards the side, or worst of all: backward.

Luckily for us, mathematicians have a name for this: a drunkard's walk.

Now imagine a scenario, there's a guy so drunk that he needs to hold on to a light post to stand. He wants to get to the next light post, just 10 steps away, but he's so drunk that he can't walk in a straight line. The question is, how long will it take for that guy to get from one lamp post to the next? 

The answer is that if his starting point and ending point are separated by 10 steps, it will take him — on average — 100 steps to get there — that's 10 squared. 
--Richard Gaughan.

Okay. Now let's do some math.

If the mean free path of a photon at the center of the sun is 0.1 mm, and the total distance that needs to be traveled is 695,500 km, then the photon needs to take 6.96 trillion steps.
And factor in the randomness of its motion—the drunkard's walk -- by squaring 6.96 trillion steps, we get 4.84E19 steps, which is 48,400,000,000,000,000,000 steps.
Even moving at the speed of light, a photon would take half a million years just to reach the surface of the sun—which means that the sunlight that hit your skin this morning was generated half a million years ago.

On the contrary, the time needed for the light on the surface of the sun to reach the Earth is only around 7 minutes.
Works its way out for 500,000 years to enjoy a 7-minute unobstructed ride.
What a way to end the journey.

Malcolm