Illustration: Jayachandran/Mint
Illustration: Jayachandran/Mint

Measuring all the light there is to see, or not

Scientists have managed to calculate all the light generated throughout the history of the universe by measuring the extragalactic background light

The Clemson University press release says it all, right at the start: “From their laboratories on a rocky planet dwarfed by the vastness of space, Clemson University scientists have managed to measure all of the starlight ever produced throughout the history of the observable universe."

Indeed: we float about on what, if you ponder the enormity of the universe, is essentially a tiny rock. We live our lives because of the light—the energy—we get from a nearby star. We call it the Sun, affording it the pomp of a capital letter, but there are billions upon billions of stars like it out there and there’s absolutely nothing unique about ours. Life has emerged on the third of the Sun’s planets—our little Earth. But while we don’t know for sure, it’s hardly likely, given the sheer number of stars and their planetary systems, that the Sun is unique in that respect either.

Yet sitting on that tiny rock, from the depths of that overwhelming ordinariness, we humans look for ways to comprehend the vastness of space. And so it is that a team of astronomers found one more measure of it.

What could it possibly mean “to measure all of the starlight ever produced"? Well, think of that 11-watt LED light bulb you’re about to replace because it failed. You’re puzzled, because you only bought it two months ago and you turned it on for only about three hours every evening. Why did it fail so quickly, you wonder. Maybe you do a quick calculation: three hours a day for 60 days, that’s 180 hours of 11-watt light, for a total of 1,980 watt-hours, or 1.98 kilowatt-hours (kwh).

That’s one measure of how much light this particular bulb produced through its life. It’s in that spirit that the Clemson University team, headed by astrophysicist Marco Ajello, found a way to measure starlight.

But of course, it’s not quite as easy as the brief calculation I did for the bulb. For one thing, there’s the sheer number of stars around us today. For another, there’s the sheer number of stars that once existed and have died, all through the history of the universe. For a third, there’s the problem of how to measure not just the light that illuminates us today, but all the light that ever illuminated any corner of the universe.

Take just the Sun. There are estimates that it puts out about 4 x 10^26 (4 followed by 26 zeros) watts—that is, it’s like a 400,000,000,000,000,000,000,000,000 watt bulb. But unlike your 11-watt bulb that went out after two months, the Sun has been shining for close to 5 billion years. I’ll leave you the calculation of how many kilowatt-hour that is. But remember that this is a garden-variety star among uncountable billions of stars, and that doesn’t include the ones that have died. Perhaps you’re getting some small sense of the truly gigantic quantity of light that, in a manner of speaking, is out there right now.

However, getting a small sense is one thing. How can we actually calculate how much light is out there and has been out there through the last 14 billion years, the age of the universe? Do we simply multiply the sun’s output by many billion or many trillion, not really knowing exactly how many trillion? Or is there another way we can come up with a reasonable estimate?

You might wonder at the purpose of this pursuit of light and it’s good to wonder. At some point, this becomes another exercise in searching for non-obvious ways to find answers, because the obvious ways are not easy to pursue.

This is true of a lot of things in astronomy. For example, take that mention I tossed out casually above, of the age of the universe. How do we know it is 14 billion years old? After all, nobody has lived quite that long. After all, too, we can only apply carbon-dating techniques to rocks here on Earth. That could tell us the age of our planet, but is that the age of the universe?

Astronomers came to an estimate for the latter age by a process of reasoning that began when Vesto Slipher noticed that light from galaxies is “redshifted". That’s because they are moving away from us and the farther they are from us the faster they are moving away. No need to repeat the explanation from a previous column, here except to say this: the logic leads inexorably to the now generally accepted figure—14 billion years—for how old the universe is. Along the way, we learn plenty about cosmology and galaxies and various intriguing stars.

Think of this calculation of the universe’s lifetime light output in the same spirit. If we want to find it, it’s not as straightforward a task as multiplying the Sun’s output by the number of stars we see. For one thing again, there are plenty of stars we can’t see, though we may be able to detect them. For another, plenty more stars are buried in plenty of galaxies, many of those also hard to detect. For a third, just like bulbs come in 4 watt and 11 watt and 17 watt varieties, stars come in multiple varieties too. It would be naïve to assume they are all like the Sun. For a fourth, what about all the stars that have lived full lives and died over the last 14 billion years?

In other words, we need to find some alternative way to make this calculation. (And along the way, the promise is that we will learn plenty about other aspects of astronomy). That is what the Clemson University team has done. Though actually, they were trying to estimate star formation rates, and—again like a lot of things in astronomy—this intriguing calculation was a byproduct.

A small clarification here. The calculation is done not in terms of watts, but of photons. The best way to think of photons is as tiny particles that flood through the universe. Each carries a minuscule quantity of light energy. That is, it helps this thought experiment to think of light from any star—any bulb, for that matter—as streams of photons, coursing in every direction through space, colliding with just-as-energetic photons from other bulbs and stars—and some fraction landing on us here on Earth.

If we think in terms of photons, how do we relate them to the watts I used above? That involves Planck’s constant (see my column “No eyelashes please: The kilogram, redefined", which tells us about the energy a photon carries. I won’t get into the calculations, but will instead say this much: when it worked, your 11-watt bulb emitted about 3x10^19 photons per second. The sun? It emits about 10^45 photons per second.

Huge numbers both, but hold on for a wilder ride.

Why consider photons at all? Because they can leave an imprint.

If you stand on a terrace in a big city at night and look out at the sky, you’ve seen the glow of the city. I don’t mean all the individual lamps, but the overall thin curtain of light that spreads because it hasn’t been blocked by buildings or bridges, poles or people.

Astronomers speak of something analogous that permeates the universe, that they call “extragalactic background light" (EBL)—light that spreads because it hasn’t been blocked by dust or stars, comets or asteroids. Now on the terrace, you can look through the curtain and see distant car headlights, say. Think of them as leaving an imprint on the curtain. Similarly, photons from distant stars and galaxies can leave an imprint on the EBL. We can measure those imprints.

There’s your alternative way to calculate the light output.

This is a greatly simplified explanation of what Marco Ajello, his Clemson colleagues Vaidehi Paliya and Abhishek Desai, and three others accomplished. In essence, they were able to track changes in the amount of EBL over the millennia: to “reconstruct the evolution of the EBL", as they describe it in their paper (A gamma-ray determination of the Universe’s star formation history, Science magazine, 30 November 2018. This reconstruction in effect records the formation and life of stars over time and thus of the light generated over time in our universe.

All of which produces, finally, a truly fantastic number. Over the 14 billion years of its existence, they concluded, our universe has produced 4x10^84 photons. 4 with 84 zeros, right there.

I’ll do the arithmetic for you: That’s about 300 billion trillion trillion trillion 11-watt bulbs. That’s about 8 billion trillion Suns.

Take an interest in astronomy, you see, and you can run into and play with all kinds of gargantuan numbers. All the while sitting somewhere on a rocky little planet called Earth.

Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun

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