The Meandering Journey Of Photons
In two previous posts, we saw the emergence of radicals naturally — with examples from Economics and Game Theory. In this third installment of the series, let’s see how they emerge in stochastic (or random) processes in nature. The star of this show is a photon — the emergence of low-entropy infra-red photons responsible for all life on planet earth.
We Didn’t Build That!
All organic life is carbon-based. The biochemical magic of a human body is the clockwork of a little over thirty-seven trillion cells, each with an infinity of carbon atoms. No lab has forged a single carbon atom yet. It begs the obvious question:
If we didn’t, who did?
A tantalizing clue lies in what Mr. Tyson so eloquently states:
The four most common chemically active elements in the universe — hydrogen, oxygen, carbon, and nitrogen — are the four most common elements of life on Earth. We are not simply in the universe. The universe is in us
— Neil deGrasse Tyson
Or should we instead ask What did? Stars! Pause a moment to ponder this. It is not far-fetched to posit the earth formed from enriched gut fragments spewed over eons by many dying stars. All organic life has a cosmic signature. That includes you, me, and anyone that has ever lived or will ever live on this earth. That an entire cosmos gets implicated in the gaze of their open palm is humbling as it is awe-inspiring.
Hydrogen, with a lone proton for a nucleus, is the ingredient created by the Big Bang. A carbon nucleus has six positively charged protons glued and held against their will by the strong nuclear force. Left to their devices, they would fly apart due to the repulsive electromagnetic force. An average star is an oven that can cook carbon starting from a cloud of hydrogen atoms. It requires a recipe. But our focus is its by-product — the twinkle of a star, where radicals, and more importantly, organic biodiversity in all its glory emerges. But first, the recipe.
A nebula is a stellar nursery where gravity heralds a star-birth as it scoops up the molecular gas cloud around seeds (protostars). Once kick-started, they condense, accrete mass, and they grow into giant glowing balls. A nebula can seed billions of stars that blossom into an entire galaxy.
Consider our sun — a garden-variety star among a trillion others in our Milky Way galaxy. We enjoy its warmth comfortably inhabited in the Goldilocks zone — a balmy ninety-three million miles away.
Going inward radially from its surface to core, one encounters successively denser annular crucibles reaching staggering temperatures and pressures due to gravity — an unrelenting vice that crushes and packs protons kicking and screaming. For sustenance, the sun must steadily (every second) detonate an equivalent of a trillion megaton hydrogen bombs simultaneously. Unfathomable to us, but just another day (or a second!) in its office. It burns clean and is more efficient than any hydrogen bomb ever conceived by humanity.
Thermonuclear processes consisting of a cascade of chain reactions shave off a smidgen from each proton, which gets converted into energy (Fig. 1). Emitted gamma-rays put the twinkle in every star that toes the famed E=mc² line. The star burns throughout its life lasting anywhere from a few million to billions of years. Successively heavier elements, including carbon, get synthesized in a lopsided tug-of-war between gravity and the strong force. Gravity ultimately (and always) emerges victorious.
A star is no exception to death. Its core collapses under its enormous weight after exhausting most of its fuel. All that remains is a corpse of a black-hole, white dwarf, or neutron star. But not before a spectacular show in its death throes, going supernova. The result is brilliant expulsion of its guts containing various elements of the periodic table.
Price Of Freedom
I’m looking for freedom,
Looking for freedom;
And to find it, cost me everything I have.
Well I’m looking for freedom,
I’m looking for freedom…
And to find it may take everything I have!
— By Kelvin Wooten, Anthony Hamilton, Elayna Boynton, Django Unchained
Let’s focus on the star of the show — the gamma rays produced in the fusion reactions. Emitted by the most violent events in the universe, they pack the most punch, have the shortest wavelengths, and therefore the highest frequencies in the electromagnetic spectrum.
E = h𝑓 = hc/λ
where 𝑓 is frequency, λ is wavelength, E is energy, h is the Planck’s constant and c = vacuum-speed of light
On earth, they occur in natural radioactive decay, nuclear explosions, and lightning. In the sun, they are a by-product of thermonuclear fusion. If not for our atmosphere absorbing gamma radiation, they can render the earth sterile, as they can kill living cells. But the sun seems to have taken kindly to mother earth despite being tormented by violent opposition within — where gamma-rays first need to get past some stiff resistance.
Resistance is in the form of electrons, protons, and other atoms. With a wavelength matching the size of an atomic nucleus, their fate gets dictated by electrons. A single gamma-ray can be absorbed and re-emitted in generations of x-rays (lower energy photons). Each x-ray begets a thousand infra-red photons with even lower energy. All the while getting flung in random directions, but on average, generally outward and away from the core.
Upon escaping the leaky sieve of the inner core, they must make their way past an additional hurdle. The sun’s outer convection zone is like a giant pot with an ocean of plasma. Forces and magnetic fields stir, sink, swirl, or fling the broth. A photon that does make it to the sun’s surface is an emaciated descendant of generations of convicts who all embarked on a treacherous journey to escape, only to sacrifice their lives betrothed to an unachievable ideal. The photon’s journey can be modeled as a Random Walk.
After drowning his sorrows, the drunkard can’t get very far staggering away from a lamp post. In fact, after N-steps, he can’t be outside a circle with a radius r=√N centered on the lamp post. There are several amazing posts describing Random Walk, but a radical emerges naturally!
r = √N
Mean Free Path
The mean-free-path (𝓁) is the typical distance a particle (photon or any other) travels between interactions. At the sun’s core, its density and opacity dictate how frequently it gets scattered by electrons. Estimates range from 1 mm to 30 μm. It is akin to the step-size of the drunkard’s walk.
𝓁 ≈ 1 mm → 30 μm
Time To Step
A photon travels at light-speed! The time for a single step is.
t = 𝓁 / c where c = speed of light
As The Crow Flies
Its linear distance from the center to the surface is the sun’s radius, R. The number of random-walk steps as the crow flies times the step size must equal its radius!
R = 𝓁 · √N
Time To Escape
The total time elapsed from inception to escape is simply the number of steps times the duration of each step.
𝞽 = t · N = (𝓁/c) · (R/𝓁)² = R²/(c𝓁)
All told, time to escape the hell realm turns out to be … (🥁🥁🥁)
𝞽 = 52 thousand years → 1.7 million years
A staggering number by any stretch of the imagination! Once they hit the interstellar space, not all photons make it to the earth. A tiny sliver does.
A sliver that gets out, makes up for the lost time in the sun. It hastily treks ninety-three million miles in about five hundred seconds, eager to breathe fire into life on planet earth. When you enjoy a sunny day, close your eyes and meditate on this.
The photons warming your body are ancient. They started their journey long before our primate ancestors arrived in caves or even earlier than our species (homo sapiens) made an appearance! Dwell on that as you enjoy the warmth.
We are lucky to be alive and to be able to wonder. Life on earth owes its existence to low-entropy (infra-red) sunlight that sustains photosynthesis. It could have been otherwise. In the fight between the bear and the lion, the fox wins! Earth likewise emerges winner in the bitter struggle between matter and radiation ensuing in the sun. And the fruit of its Herculean effort to escape is mind-blowing!
I will leave you with a masterpiece of astronomical literature. Sir Arthur Eddington waxes eloquent its struggle:
A large proportion, sometimes more than half the total heat, consists of imprisoned radiant energy — ether-waves traveling in all directions trying to break through the material which encages them. The star is like a sieve, which can only retain them temporarily; they are turned aside, scattered, absorbed for a moment, and flung out again in a new direction. An element of energy may thread the maze for hundreds of years before it attains the freedom of outer space.
Nevertheless, the sieve leaks, and a steady stream permeates outwards, supplying the light and heat which the star radiates all round.
The inside of a star is a hurly-burly of atoms, electrons and æther waves. Dishevelled atoms tear along at 50 miles a second with only a few tatters left of their elaborate cloaks of electrons torn from them in the scrimmage. The lost electrons are speeding a hundred times faster to find new resting-places. Look out! there is nearly a collision as an electron approaches an atomic nucleus; but putting on speed it sweeps round it in a sharp curve. A thousand narrow shaves happen to the electron in 1/10¹⁰ of a second; sometimes there is a slide-slip at the curve, but the electron still goes on with increased or decreased energy …
As we watch this scene, we ask ourselves, Can this be the stately drama of stellar evolution? It is more like the jolly crockery-smashing turn of a music-hall. The knockabout comedy of atomic physics is not very considerate towards our æsthetic ideals… The atoms and electrons for all their hurry never get anywhere. They only change places. The æther waves are the only part of the population which do actually accomplish something; although apparently darting about in all directions without purpose in spite of themselves make a slow general progress outwards.
— The Internal Constitution Of The Stars, Sir. Arthur Eddington, 1920
- Forged in the Stars: Natural History Magazine, Neil deGrasse Tyson, 1996
- The Internal Constitution of The Stars, Nature, Sir. Arthur Eddington, 1920
- The Sun Fact Sheet, NASA
©️ Dr. VK, 2021. All Rights Reserved.