The Push of Light, Part 1: Crooks, Crookes and Pushes

[Note: In this post I’m going to use the terms “light”, “electromagnetic waves” and “electromagnetic radiation” interchangeably and take them all to mean the same thing. The color red is light in the visible range, but microwaves are also light just in the microwave range. If this seems strange, I would recommend this previous post of mine, though it’s not really necessary to understand what I’m talking about here.]

In everyday life it’s pretty clear that light carries energy. We go out in the sun, and our skin tans. The energy of the UV sunlight both directly and indirectly drives the production of melanin in our skin. Stay out too long, we burn. Leave a chocolate bar out in the sun and it melts. We use lasers to engrave and even to cut things like metal. Microwaves heat our food. Light causes plants to grow big and strong through photosynthesis. Likely the most obvious demonstration of the fact that light carries energy is solar panels, where we directly convert light into power. So I’m not going to spend any time here justifying the fact that light carries energy, but something that is perhaps less appreciated is the fact that light also carries *momentum*. Light pushes (seriously, click the link, it’s pretty cool)

In this and a number of follow-up posts, we’re going to explore some of the very cool consequences of this simple reality, called “radiation pressure” (remember, light = “electromagnetic radiation”). We’ll look at how we can use the momentum of light to sail to other stars. How it spins and spirals the objects in our solar system. How it keeps the stars themselves alive. We’ll even look at how the momentum of light can, pretty counter-intuitively, be exploited to actually steal motion from something else and how we can use this to cool things towards absolute zero, the coldest possible temperature.

If you’ve taken a basic physics class or two, the notion that light has momentum may seem impossible. (If you haven’t taken a physics class, by the way, then there’s no problem and you can happily read forward.) In those classes you might remember momentum as being equal to velocity times mass, and you might also remembering that the particle associated with light, the photon, has no mass. Thus, there would seem to be a contradiction. How can light have momentum? Is the momentum equation wrong? Do photons have mass?

In this series of posts I will address that… but not immediately. Instead I want to talk about what it means for light to have momentum and how that plays out in the world around us; the consequences and effects. Only after that, will I talk about *why*/*how* light can have momentum. So I’ll get there, and if you’re skeptical I’d ask you to hold that skepticism until we address it.

However, before we can even get into any of that it’s worth taking a bit of time to talk about momentum in general, in order to make sure we’re all on the same page. It’ll also be useful for later posts. If you feel that you already understand momentum and collisions very well then you can safely skip this section if you like, but you’ll be missing out on some of my best jokes (Note: this is a total lie. All my jokes are my best jokes.).

Momentum. How to Hit Things with Other Things… But like, well.

If I take a ball of something sticky, like let’s say putty, and hurl it at something like a cardboard box – and by saying it’s sticky I’m assuming that the putty sticks to the side of the box – the box-with-putty-stuck-to-it will go flying. Initially the box had no motion and the putty did and after the sticking collision the whole box + putty system has some motion. Intuitively, we also have an expectation that for an identical putty ball thrown at an identical speed, how fast the final box + putty system is moving – how hard it goes flying – depends on how heavy the box is. If the box is very heavy, it barely moves at all. It’s the same if we kept the weight of the box the same but threw smaller and smaller pieces of putty. Now, besides from demonstrating that I either have anger management issues or just some pretty strange hobbies, this set-up plays to our intuitive understanding that our ball of putty carries momentum and when it sticks and collides with the box, the final box+putty system inherits this momentum. Obviously, this is hardly the most rigorous of arguments but it at least motivates the idea that in a “sticking” or “absorbing” (i.e. we imagine the box “absorbing” the putty) collision, the momentum of the final combined object is equal to the momentum of the initial putty – if we assume the box is initially motionless. However, because the box is so much heavier than the initial putty, the final speed or motion of the combined object is much less than the speed of the initial putty. For light we then expect that if something absorbs light, it inherits the momentum of that light.

 

This whole thing works in reverse too. If you fire a gun, the force used to accelerate the bullet is also visited upon you (Newton’s laws an all that). Thus, “emitting” or “shooting” something also gives you momentum. How much? Exactly as much as you gave the thing you emitted. You plus the emitting object were initially at rest and then, let’s say, you shoot the object to the right, you will experience an equal momentum to the left such that the total momentum of you+object has been unchanged. For light we then expect that if something emits light, it receives an equal amount of momentum in the opposite direction from “radiation/light recoil”. It’s the exact same amount of momentum you get from the “absorbing” case except in the opposite direction to what was emitted.

I can also think of a different “experiment”; one where I throw a tennis ball against a wall. (A fun thing about being a scientist is you can always claim whatever dumb thing you’re doing is “an experiment”.) A tennis ball is kind of like a spring. As it hits the wall, all the energy of its motion is channeled into compressing and squishing the ball, but as things progress all this stored up potential energy is returned back to the ball’s motion as it rebounds and goes back in the opposite direction from the one it came. In a real tennis ball, like a real-world spring, not all of the energy that was diverted away from motion is recovered. Some is lost forever to things like heat, to permanently deforming the ball, to exciting sound waves that carry away that distinctive “thud” sound and so on. However for our purposes, we’ll just assume the tennis ball is perfect. In that case all the energy of motion is perfectly returned and after the bounce the tennis ball seemingly is going exactly as fast as it was initially, just in the opposite direction.

Why do I say “seemingly” going exactly as fast? When we think of bouncing a ball against a wall, we generally don’t think of the wall itself as being set into motion by the collision. But really, it is. However, not only is the wall itself very heavy, but it’s also rigidly integrated into a building, which has some concrete foundation inset into the ground and so on. In a very real sense, like the crappiest of Greek Titans (just don’t shrug), by bouncing a tennis ball against a wall, you are imparting momentum, and thus motion, to the entirety of the Earth. However, the wall+building+entire-planet system is, obviously, very, very, very heavy (just like your… nevermind). Thus, just like our putty thrown at a very heavy box, the speed you’re giving the wall in the opposite direction to the rebounded tennis ball is unbelievably, outrageously, imperceptibly small. So for all intents and purposes we can approximate it as zero.

In this case of a very heavy wall then the tennis ball leaves the bounce with basically the exact same speed it came in with, but in the opposite direction. It might seem then that the momentum of the tennis ball hasn’t changed. After all, its speed hasn’t. If that were the case we’d also expect that we’re imparting no momentum to the wall, since momentum is conserved. In reality, it’s quite the opposite. The wall has to impart a force sufficient to bring the speed of the ball from its starting speed to zero and then it needs to additionally give just as much momentum in the opposite direction. So rather than the momentum transferred to the wall being zero, it is in fact the initial momentum of the ball times two. More concretely, we can say that under the assumption of bouncing off something that is infinitely heavy – so we can ignore the motion of the wall – a “reflecting” collision imparts twice the initial momentum of the reflecting object onto the heavy object. Thus, “reflecting” collisions deliver *twice* the momentum to the final heavy object as “sticking”/”absorbing” collisions. (Note: in the absorbing case, the final heavy object also includes the mass of the thrown object, which is now stuck to it.)

So just to recap the key things I’m trying to argue here. If you are initially at rest (i.e. you have no momentum yourself) and are hit by an object and you “absorb” it, or it sticks to you, the you+object system inherits the momentum of the object. If the object is very small we can basically just say that you inherit the momentum of the object and we don’t really have to make a big deal of always saying it’s the you+object system. If instead the object perfectly “reflects” off of you, you are given twice the momentum of the object. If you “emit” an object, you get the same momentum as the final emitted object, but in the opposite direction. So if we take as given that light has a momentum then all this comes down to: if you absorb light that is moving to the left, you go to the left with a certain momentum; if you emit identical light to the right, you go to the left with that same momentum; and if identical light perfectly reflects off you, you will go to the left with twice the momentum of the previous two cases.

Back to Light

Okay, let’s get back on track. Based on our discussion of objects like putty and tennis balls, from everyday experience it may seem implausible that light should carry momentum. If you think it’s doubly implausible because you remember from your physics class that momentum is supposed to be proportional to mass and light has no mass, then hold on. Does that mean that when I open my fridge and that little fridge light goes on that it’s basically throwing waves of light “putty” or “tennis balls” at me? (No, I don’t know what a light tennis ball is either, it’s just something I said and now we have to live with it.) Am I being pushed away from the fridge by this light? If I take a mirror, which light collides with “reflectively”, and lay it on a scale and then shine a flashlight onto the mirror, does that mean the downward force, the “weight”, registered by the scale increases? If instead of a mirror, I lay something very black on the scale – a black object absorbs light, and thus we have an “absorbing” collision – does the scale also read a higher number, but only half the increase when compared to the mirror? Is my car antennae being deflected and pushed as it absorbs radio waves so I can listen to my favorite station (I would totally list an actual radio station here if I actually listened to radio). Does a microwave oven “compress” my day old pizza while it cooks it? Does shooting a laser pointer, which “emits” light push back on me?

YES! On all accounts. Yes, it really does.

However, the reason this might raise an eyebrow is because in everyday situations the effect is suuupppppeeeerrrr tiny. Our great omniscient watcher and keeper, the sun, on a typical bright day, hits every square meter of the illuminated Earth’s surface with about 1,000 Watts of power, or a thousand Joules of energy every second. If we throw the laws of thermodynamics out the window (bye, bye, sucker!) and just assume that we could turn 100% of that energy into useful work, I could power 10 incandescent light bulbs with 1 square meter of sunlight, or 60 LED lightbulbs (if you’re still using incandescent bulbs, by the way, you should really think about switching!). That’s a Big Mac and a half of energy deposited every hour. If it seems weird to use a Big Mac as a measure of energy, just remember that a food Calorie, capital C, or kilocalorie, is simply a unit of energy. 1 kcal is approximately 4,000 Joules.

However, for all that energy, the resulting downward pressure on this square meter, due to this 1,000 Watts of light, is only 0.0000045 Newtons (if we assume, for simplicity, that the Earth’s surface is completely black and a perfect absorber of light). For context, a single human hair would push down, due to its weight, by about 0.000001 Newtons, and imagine that weight spread over the whole area. So for this square meter of area (about a square yard), being blasted with 1,000 Watts of light, there also comes an accompanying *radiation pressure* that really only amounts to pushing down with the extra weight of 4 strands of human hair. So…. not much. But the key thing is, it isn’t zero.

Why is it So Small?

If you want to figure out the radiation pressure that results from a certain incident irradiance (power per unit area) of light it’s actually very, very simple. If the object is a perfect absorber then the resulting pressure is just the irradiance divided by the speed of light: P= I/c (c is the speed of light). For a perfect reflector of light, like an ideal mirror, it’s twice that (P = 2I/c). For a more general opaque object that reflects some light and absorbs some light, it’s somewhere in between those two numbers.

So you see then why the pressure is very small, because the speed of light is a very, very big number. It’s approximately 300,000,000 m/s and if you have a 1 Watt per squared meter irradiance you have 1/300,000,000 = 0.000000003 Pascals of radiation pressure, or a thousand times less than the weight of a single human hair distributed over the entire square meter.

The Search for a Teeny, Tiny Push

With our discussion of radiation pressure, it is important to understand that we are talking about fairly old physics. This isn’t cutting edge stuff, or one of those new crazy things that came with the development of quantum mechanics. Rather, the first suggestions that light carries momentum traces back four centuries to the storied astronomy Johannes Kepler who suspected light must be capable of pushing. We’ll talk about him and why he though that later. However, jumping forward, in the 1860s James Clerk Maxwell wrote down his all-important “Maxwell’s equations” that describe the behavior of electric and magnetic fields, unified them as one object, and concretely described light as an electromagnetic wave – which in and of itself was something that had been expected for a while. (For more on how light is an electromagnetic wave, see this previous post) At that point it was an unavoidable prediction. Or as he himself said in 1873 [J. C. Maxwell, A Treatise on Electricity and Magnetism , II., p. 39I, 1873]:

“Hence in a medium in which waves are propagated there is a pressure in the direction normal to the waves and numerically equal to the energy in unit volume. ”

However, after doing some very similar calculations to what we’ve just done, and realizing how paltry it was, he suggested:

“It is probable that a much greater energy of radiation might be obtained by means of the concentrated rays from an electric lamp. Such rays falling on a thin metallic disc, delicately suspended in a vacuum, might perhaps produce an observable mechanical effect.”

So, right from the beginning people knew the effect would be small and hard to demonstrate. This is because if you have any real air pressure, any wind, any errant electric or magnetic effects (other than light), any vibrations, or sound, then the influence of these things could easily swamp the effect of radiation pressure. Thus, the push to demonstrate this predicted phenomenon ended up involving a tour-de-force of theory and experiment involving a veritable who’s-who of famous physicists of the late 19th century.

For example, you have Svante Arrhenius, who won the 1903 Nobel Prize in Chemistry and was actually a physicist by training, was deeply interested by the role that radiation pressure must play in the cosmos. He was sure it was a key player in the formation of the Aurora Borealis (i.e. the Northern Lights), the corona of the Sun and that faint glow of daylight you see at night even before the sun has arrived (called Zodiacal Light). Now, Arrhenius wasn’t specifically correct on many of these accounts but it was an important step in the right direction and the beginnings of a recognition that light and electromagnetism can play just as important a role in the behavior of the cosmos as gravity. Arrhenius, by the way, is probably a more interesting and complicated character than is often realized. He didn’t just work in chemistry, nor in physics, but also in physiology, geology, and… um… eugenics. He was an important member of the “Swedish Society for Racial Hygiene”. Hey, I didn’t say it was all *good* stuff. But it at least an interesting read.

Another recognizable character in the story for radiation pressure was the physicist Karl Schwarzschild. He’s most famous for being the guy who predicted the existence of black-holes in 1916, using Einstein’s newly developed Theory of General Relativity. Though it’s probably more accurate to say he “started the ball rolling” on black-holes, it would take at least another 20-30 years for people to really realize what they were seeing in the theory. No, Einstein wasn’t the guy who theorized black-holes, it was Schwarzschild and he did it, believe it or not, from within the trenches of World War I where he was an officer in the German artillery. He died in those trenches a year later.

In addition, to people like Maxwell, Schwarzschild and Arrhenius, you also had recognizable names like Ludwig Boltzmann (the founding father of kinetic theory and an early architect of quantum mechanics) and Oliver Heaviside (the man who predicted the existence of the Earth’s ionosphere, among many other things) who threw their hats into the ring in one form of the other. However, a person of particular note, who thought he had it all figured out and in the bag the very same year (1873) that Maxwell made the above proclamation, was the chemist Sir William Crookes.

His idea to demonstrate the existence of radiation pressure was as brilliant as it was simple. He developed what we now call the Crookes Radiometer which is basically just a very sensitive pin-wheel encased in a vacuum-sealed glass bulb (see diagram).

 

Then, what he did was to make the pin-wheel out of reflective material and paint the back of each fin with black paint (or just cover it with black soot). Based on the theory of momentum we developed we then expect light that reflects off the reflective part to impart twice the momentum that it does if it is absorbed by the black part. So, if you look at the diagram, you can see that if you shine a light on the fin you will have an unequal force and it will start to spin!

So what happened when he shone light on it? It did spin! Awesome! Like super fast! Yay! Like, way faster than it should for radiation pressure! Huh? And in totally the wrong direction! Wait what? It would take almost a decade of additional scientific work and debate to find out what was really going on in Crookes’ device but the big clue was that, especially in the late 19th century, no vacuum pump was perfect and thus the pin-wheel was not in a perfect vacuum, but as you improved the quality of the vacuum, the wheel spun slower. If the wheel was spinning because of radiation pressure, it should spin faster the better a vacuum you make (less friction and drag), not slower. Now, you can actually buy Crookes Radiometer at geeky stores and science museum gift shops and they really do spin when illuminated. However, the reason is actually due to the heating caused by the light on the black paint, and the effect that has on gas particles that are still sticking around in the not-perfectly-evacuated vacuum chamber which collide with it. Maybe we can talk about this more fully in a later post, but the key thing is that a Crookes Radiometer doesn’t spin because of radiation pressure.

However, Crookes idea was totally solid and when the first people eventually did demonstrate its existence (Lebedew in Moscow in 1901 and Nichols and Hull in the UK in 1903) their approach really wasn’t that different. In fact it’s largely a mixture of Crookes’ ideas and the device Maxwell suggested above, so I won’t go into detail, but you can google “Nichols radiometer” if you’re curious. Basically, the big, brilliant innovation was to use a better vacuum pump and make a more sensitive pin-wheel – actually a super thin piece of metal suspended from an extremely thin wire to make a torsional pendulum.

After these experiments the cat was out of the box. Maxwell’s equations predicted it and it had been found. But what did it matter? In the next posts in this series we’re going to talk about the ways that radiation pressure shapes the cosmos. We’re going to talk about how it can allow us to explore the stars. We’re even going to talk about how we can use it as a way of stealing momentum from atoms and molecules.

See ya then.