Why is the sky pink?

On Mars, the sky is pink during the day, shading to blue at sunset. What planet did you think I was talking about?

On Earth, the sky is blue during daytime, turning red at as the sun sinks toward night.

Scattering light

Well, it’s not quite as simple as that: if you ignore your dear sainted mother’s warning and look at the Sun, you’ll see that the sky immediately around the Sun is white, and the sky right at the horizon (if you live in a place where you can get an unobstructed view) is much paler. In between the Sun and the horizon, the sky gradually changes hue, as well as varying through the day. That’s a good clue to help us answer the question every child has asked: why is the sky blue? Or as a Martian child might ask: why is the sky pink?

First of all, light isn’t being absorbed. If you wear a blue shirt, that means the dye in the cotton (or whatever it’s made of) absorbs other colors in light, so only blue is reflected back to your eye. That’s not what’s happening in the air! Instead, light is being bounced off air molecules, a process known as scattering. Air on Earth is about 80% nitrogen, with almost all of the rest being oxygen, so those are the main molecules for us to think about.

As I discussed in my earlier article on fluorescent lights, atoms and molecules can only absorb light of certain colors, based on the laws of quantum mechanics. While oxygen and nitrogen do absorb some of the colors in sunlight, they turn right around and re-emit that light. (I’m oversimplifying slightly, but the main thing is that photons aren’t lost to the world!) However, other colors don’t just pass through atoms as though they aren’t there: they can still interact, and the way we determine how that happens is again the color.

The color of light is determined by its wavelength: how far a wave travels before it repeats itself. Wavelength is also connected to energy: short wavelengths (blue and violet light) have high energy, while long wavelengths (red light) have lower energy. When a photon (a particle of light) hits a nitrogen or oxygen molecule, it might hit one of the electrons inside the molecule. Unless the wavelength is exactly right, the photon doesn’t get absorbed and the electron doesn’t move, so all the photon can do is bounce off, like a pool ball off the rail on a billiards table. Low-energy red photons don’t change direction much after bouncing–they hit the electron too gently for that. Higher-energy blue and violet photons, on the other hand, scatter by quite a bit: they end up moving in a very different direction after hitting an electron than they moving before. This whole process is known technically as Rayleigh scattering, for the physicist John Strutt, Lord Rayleigh.

The blue color of the sky

Not every photon will hit a molecule as it passes through the atmosphere, and light from the Sun contains all the colors mixed together into white light. That means if you look directly at the Sun or the sky right around the Sun during broad daylight, what you see is mostly unscattered light, the photons that pass through the air unmolested, making both Sun and sky look white. (By the way, your body is pretty good at making sure you won’t damage your vision: your reflexes will usually twitch your eyes away before any injury happens. I still don’t recommend looking at the Sun directly for any length of time, especially with sunglasses, which can fool your reflexes into thinking everything is safer than it really is.) In other parts of the sky away from the Sun, scattering is going to be more significant.

The Sun is a long way away, so unlike a light bulb in a house, the light we get from it comes in parallel beams. If you look at a part of the sky away from the Sun, in other words, you’re seeing scattered light! Red light doesn’t get scattered much, so not much of that comes to you, but blue light does, meaning the sky appears blue to our eyes. Bingo! Since there is some green and other colors mixed in as well, the apparent color of the sky is more a blue-white than a pure blue.

(The Sun’s light doesn’t contain as much violet light as it does blue or red, so we won’t see a purple sky. It also helps that our eyes don’t respond strongly to violet light. The cone cells in our retinas are tuned to respond to blue, green, and red, so the other colors are perceived by triggering combinations of the primary cone cells.)

At sunset, light is traveling through a lot more air than it does at noon. That means every ray of light has more of a chance to scatter, removing the blue light before it reaches our eyes. What’s left is red light, making the sky at the horizon near the Sun appear red. In fact, you see more gradations of color too: moving your vision higher in the sky, you’ll note red shades into orange into yellow and so forth, but each color is less intense.

So finally: why is the Martian sky pink? The answer is dust: the surface of Mars is covered in a fine powder, more like talcum than sand. During the frequent windstorms that sweep across the planet, this dust is blown high into the air, where light (yes) scatters off of it. Since the grains are larger than air molecules, the kind of scattering is different, and tends to make the light appear red. (Actually, the sky’s “true” color is very hard to determine, since there is a lot more variation than on Earth.) When there is less dust in the atmosphere, the Martian sky is a deep blue, when the Sun’s light scatters off the carbon dioxide molecules in the air.

By DXS Physics Editor Matthew Francis

Making Light in Electronics

By DXS Physics Editor Matthew Francis 

A while back, I wrote about one of the most common ways of making electric light: fluorescent bulbs. Understanding fluorescent lights requires quantum mechanics! While a lot of quantum physics seems pretty removed from our daily lives, it’s essential to most of our modern technology. In fact, reading what I’m writing requires quantum mechanics, since you are using a computer (maybe a handheld computer like an iPad or smart phone, but it’s still a computer) or a printout from a computer.

Modern electronics, including computers and phones, depend on semiconductors. Conductors (like the copper wire in power cords) let electricity flow easily, but semiconductors conduct electricity more reluctantly—but that very reluctance lets us control the flow. While they can’t sustain large currents like conductors can, we can tinker with the chemistry of semiconductors to make them conduct electricity in very precise ways. One of those ways lets semiconductor devices make light: those are known as light-emitting diodes, or LEDs.

You likely have many LEDs in your home: they’re common as indicator lights on appliances, and you might even have LED light bulbs. While they’re pretty expensive right now, the price of LED lights is getting lower all the time, and they have major advantages over both incandescent (old-style) light bulbs and fluorescents. They won’t burn out even as quickly as fluorescent lights (themselves longer-lived than incandescents), and consume less energy. Since they are based on solids rather than gases, they’re not going to break easily, either! But how do they work?

The Electrons in the Band

When I described fluorescent lights in my earlier post, I described how atoms have distinct energy levels inside them, and light is produced when electrons move between those energy levels. Fluorescent lights use gases (generally mercury vapor), so the atoms are relatively widely separated. In solids, including semiconductors, atoms are tightly packed together, forming bonds that don’t break without high pressures or temperatures. In fact, they may also share electrons with each other; a particularly dramatic example of this is in metals, where the electrons in the highest energy levels of the atoms all form a gas that surrounds the atoms. That’s why metals are such good conductors—a little push from a battery or other power source makes those electrons flow in one direction (on average at least), much as a fan creates currents in the air.

Semiconductors are a bit more complicated: their electrons are loosely bound, but still stuck to their host atoms. The way physicists understand this is something known as the band model: just like atoms have energy levels, solids have energy bands. Low energies correspond to electrons stuck to their atoms, which can’t leave; we call these closed shell electrons (for reasons that aren’t important for this particular post). Moderate energies are known as valence electrons, which stay put ordinarily, but can be persuaded to move if given the right incentive. Finally, high energies are conduction electrons, which aren’t tied to a particular atom at all; as their name suggests, they are the ones that carry electric current.

Whether a solid conducts electricity depends on its band structure, and the size of the energy barrier in between the bands, which is called a gap. Large gaps require large energies for electrons to jump them, while smaller gaps are more easily jumped. Conductors have negligible gaps between their valence and conduction bands, while insulators have huge gaps. Semiconductors lie in between; adding extra atoms to a semiconductor can make the gap smaller (a process known as “doping”, which sometimes makes describing it unintentionally funny).

Cars and Roads and Electrons

At low temperatures, semiconductors may not conduct electricity at all, since no electrons can jump the gap into the conduction band. Either warming them up a bit or applying an external electric current gives the electrons the energy they need to move into the conduction band.

I was pondering analogies about band structures to help us understand them, and thought of this one based on cars and roads. Think of closed shells as like parking spaces along a road: cars (which stand in for electrons) are stationary. Valence bands are the slow lane, which is clogged with traffic, so the cars technically can move, but don’t. The conduction bands are fast lanes: cars can really zip, but there’s a traffic barrier between the slow lane and fast lane. (That barrier is the weakest part of my analogy, so remember that we should be thinking of a barrier as something that can be traversed under some conditions but not others.)

One more complication: there are two types of semiconductors, known as n-type and p-type. In n-type, just a few electrons (cars) have access to the conduction band (fast lane) at a time, but in p-type, enough electrons get in to leave holes in the valence band. Applying a current to the semiconductor shifts another valence electron into the hole, but that leaves another hole, and so forth…so it looks like the hole is moving! In fact, physicists refer to this as “hole conduction”, which also sounds odd if you’re not used to it.

Now we’re finally ready to understand LEDs. If you join an n-type semiconductor to a p-type semiconductor, you make something known as a diode. (The prefix di- refers to the number two. If you join three semiconductors, you get a transistor of either the pnp or npn types, depending on the order you use.) The bands (lanes) don’t line up perfectly at the junction: the conduction band in the n-type is generally only slightly higher than the valence band of the p-type, so just a little nudge is needed to move electrons across. This means when they reach the junction between the materials, electrons from the n-type semiconductor can fill the holes on the p-type, which is a decrease in energy. Just as in individual atoms, moving from a higher energy level to a lower energy level makes a photon—and that’s where the LE in the D comes from!

LEDs tend to produce very pure colors, rather than the mixture of colors our eyes perceive as white light. To create LED light bulbs, generally blue LEDs are coated with a phosphorescent material, much like the kind used in fluorescent bulbs. Unlike fluorescents, though, there’s no gas involved, and less heat is lost (though there is still a little bit). Together these factors make LED light bulbs longer-lasting and more efficient even than fluorescents, though currently they are far more expensive.

Despite how common LEDs and other semiconductors are, they’re considered fairly advanced physics. But guess what: if I did my job right, you should understand LED physics now! What is often thought of as “advanced” is really everyday science, and it’s a part of how quantum mechanics (with all its electrons and fascinating interactions on the microscopic level) has helped create our modern world.

How fluorescent lights work: quantum mechanics in the home

We have a tendency to think that “quantum mechanics” is synonymous with “out of the ordinary.” I do that, too, since there’s so much strange to talk about: the blurring of particles and waves, the apparent randomness that drove Einstein crazy, and so forth. It’s easy to forget that quantum mechanics also is an everyday matter. The odds are pretty good you’re reading this post on a computer screen (as opposed to a printout), and possibly the light you’re using is fluorescent.

The three major types of lights you can buy are incandescent bulbs, fluorescent lights (including compact fluorescent lights), and light-emitting diodes. Incandescent bulbs are the “normal” type (though they are becoming less so): They light up when an electric current runs through a thin wire made of tungsten, which heats up. The wattage of an incandescent is a measure of how much power it consumes, and most of that power goes to heat, not light, which is why you can burn your hand if you touch a bulb that’s been on any length of time. Because of the wasteful nature of that kind of bulb, a lot of people have made the switch to compact fluorescent lights (CFLs), which don’t run hot and use a lot less power for the same amount of light. And they work by using quantum mechanics!

Of course even incandescent bulbs are quantum-mechanical underneath: after all, everything Continue reading

As Seen on TV! Restoring Hair with LASERS!!!!!!

The author’s rapidly-expanding forehead.

Anyone who watches TV, reads magazines, or flips through catalogs has seen some interesting products. Maybe they seem plausible to you, maybe they don’t. However, a little investigation shows they are based less on science and well…actually working, and more on wishful thinking. At worst they’re actual con-jobs, designed to separate you from your money as efficiently as possible (which I guess is a certain standard of success). As a result, we at Double X Science bring you “As Seen on TV!” In these features, we’ll look at some of the products shilled on talk shows and infomercials, items lurking between the articles you read in magazines, or things you might find on the shelves of the stores where you shop.

I admit it, I’m a balding dude. My forehead is gradually taking over my entire scalp, replacing my formerly thick and curly hair with a vast expanse of pink skin. Yes, dear readers: My hair was once so thick and curly that, when I wore it long and in a ponytail, ladies would ask me for my secret. (The answer: Wash it every other day with some brand of cheap shampoo and let it air dry. Don’t tell.) I don’t like the fact of my impending baldness, so I’m sympathetic toward defoliation-sufferers who want to bring their hair back at any cost.

On the other hand, I don’t think I’ll invest in any of the hair restoration products advertised in the SkyMall catalog I picked up on my flight to my brother’s wedding in San Francisco. I counted seven products in this single catalog promising to restore hair in one way or another, either reversing baldness or filling in thin patches on the scalp –- and that doesn’t include hair-coloring, extensions, or other options. I won’t cover all of them, but no fewer than three products pledge to bring hair back through the magic of lasers.

Ah, lasers. They may not have the mystique of magnets or the nous of “natural”, but they are a frequent ingredient in modern snake oil. (Come to think of it, one of the hair-restoration products may have contained snake oil. I don’t want to ask.) But while lasers can help correct nearsightedness in some cases, perform minimally invasive surgeries, and remove hair, color my scalp skeptical about their ability to restore hair.

First, a disclaimer: I’m not a biologist, a doctor, medical researcher, or in any field related to those. I’m a physicist, so the closest I ever get professionally to this topic is the “no-hair” theorem in black hole physics. The “no-hair” theorem says that black holes have very few distinguishing characteristics: only mass and rotational rate (and technically electric charge as well, though it’s hard to build up enough charge to make a difference). The analogy is that, if all humans were completely hairless, we would have a lot fewer ways to tell each other apart. In other words, this ain’t my area, so bear (bare) with me!

Night on Baldhead Mountain

Hair loss can occur for a wide variety of reasons: chemotherapy, a number of unrelated diseases, even stress. However, as humans (both men and women!) age, we all tend to lose our hair to some degree. The effect is most pronounced in male pattern baldness (a bare patch on the top of the head merging over time with the growing forehead to leave a fringe around the edges of the scalp) or female pattern baldness (a general loss of hair at the top of the scalp). However, past the age of 80, nearly everyone starts losing hair, regardless of genetics, diet, or health.

The reasons, as with so many other things, are hormonal. Hair production is governed by sex hormones: most famously testosterone, but also a less well-known cousin known as dihydrotestosterone (DHT). In some people, DHT commands the follicles — the small organs in the skin that produce and feed hair — to shrink, producing ever-finer hair until they cease operating entirely. Thus, gradual hair loss of the usual (as opposed to disease- or circumstance-derived) variety is generally preceded by the hair itself becoming thinner and fuzzier.

My naive understanding of the biology of hair loss leads me to suspect that since hormones are the culprit behind hair loss, then any hair restoration should address those hormones in some way. That alone makes me suspicious of the laser-based products SkyMall peddles. To see why, let’s look at lasers themselves.

Lasers (without sharks)

The word “laser” began as an acronym: Light Amplification by the Stimulated Emission of Radiation. The details could be an Everyday Science or Double Xplainer post in their own right, but here’s the short version. The lasers used in the SkyMall products are LED lasers, meaning they are based on the underlying physics as LED lights. An electric current kicks electrons or other electric charge carriers from one type of material to another across a junction. The excess energy the electric charge sheds during this process is given off in the form of a photon, a particle of light. Since the same amount of energy is involved every time, light from LEDs is nearly monochromatic, meaning it is almost purely one color.

The “amplification” part of the name comes by putting the LED into a special kind of cavity with reflective walls. These walls set up standing waves for the light, which interfere constructively like vibrations in a guitar string, making them brighter. However, unlike guitar strings, the production of the light in lasers is a self-feeding process, resulting in the different parts of the system synchronizing until they emit photons in concert with each other. It’s really interesting stuff, and while it’s somewhat complicated, there’s nothing really mysterious or magical about it, any more than magnets are magical.

In fact, LED lasers are so unmagical that you can buy them as cat toys. LED lasers are the inner workings of laser pointers, which you can buy very inexpensively at any number of shops.

The smell of frying follicles

One of three laser-based hair-restoration products from SkyMall.
This one features built-in headphones, so you can at least listen
to music while you sit around looking like a fool. However,
I recommend a cheaper set of headphones, since the $700
price tag is a bit steep, and you’d get the same result with
regards to hair restoration.
Laser hair removal uses intense lasers to selectively heat the follicles in the skin, hopefully avoiding damage to the rest of the skin. This process can slow down hair growth and cause the hair to fall out of the treated follicles, but it doesn’t always actually stop it: the treatment must be continued for a long term. Basically, the laser is damaging the follicle.

As you can imagine, that also makes me skeptical that lasers can stimulate new hair growth. Lasers produce light…and that’s it! In addition to the usual red lasers like in laser pointers, manufacturers also make infrared lasers, which are useful for surgery. While we perceive infrared as heat (which is why sunshine feels warm), I don’t think merely warming the scalp is going to make hair grow faster, or else you wouldn’t need lasers at all — an electric blanket would do just as well. Too much heating and we’re back at laser hair removal.

Similarly, visible-light lasers like the kind that seem to be in these SkyMall products simply produce red light. Because ordinary light bulbs produce a broad range of colors (white light is a mixture of all the visible-light wavelengths), sitting under a desk lamp would expose your scalp to red light. Yes, it wouldn’t be as intense as lasers, but you could do the same trick with a laser pointer from Schtaples (the Scmoffice Schmupply Schtore), provided you have the patience to hold it against your scalp for long periods of time.

The author engages in home laser hair restoration, while his cats
meow around his feet.
So, to summarize:
  • Hair loss in its most common forms is hormonal, so it’s unclear to me that light (whether laser or otherwise) has anything to do with it. Hair removal can be achieved with lasers, but that involves causing damage to hair follicles, not using anything intrinsic to light.
  • Lasers are simply very monochromatic light sources, that use synchronization of atoms on the microscopic level to do their business. There’s nothing in a laser that isn’t in ordinary light bulbs, though you can make things far more intense with a laser. However, high intensity brings us back to laser hair removal, not restoration.
  • As always, if a product sounds miraculous, it’s probably bunkum. If all it took to regrow hair was a glorified laser pointer, nobody would be bald! LED lasers are cheap and ubiquitous; we could all restore our hair without paying a company $700 (and listen to the music on inexpensive headphones, to boot).
Now if you’ll pardon me, I’ll get back to shining this laser pointer at my scalp.

Why Can You Hear Around Corners But Not See?

As I sit and type this in my study, I can hear my cats crashing around the living room, which is around the corner from me. There’s a wall between us, so I can’t see them or shoot them with my water pistol (which I would be tempted to do if they were in the same room, before they knock over something fragile). So, just like in my earlier post on mirrors, we’ll start with a question: why can I hear my cats around the corner, but not see them?

Both sound and light are waves, but the way we perceive those waves are very different. I don’t just mean the organs we use – eyes and ears do have major biological differences – but how the characteristics of those waves differ. We perceive differences in light through color, and differences in sound through pitch, but in the end these characteristics mean the same thing: they’re a measure of how big the wave is. The technical term for this is its wavelength: the distance it takes for a wave to start repeating itself.

For visible light, red has the longest wavelength, while violet has the shortest. In between you get the other colors of the rainbow, and if you mix them all together you get white light. Visible light wavelengths are between 400 and 700 nanometers, which is smaller than bacteria (which themselves are smaller than cells in our bodies)! Wavelengths smaller than 400 nanometers get into ultraviolet, X-ray, and gamma-ray territory; wavelengths greater than 700 nanometers comprise infrared, microwaves, and radio waves.

For sound, the situation is a little messier, since our ears respond to frequency, not wavelength. The specific wavelength of sound depends on the temperature and humidity of the air, but if we assume dry room-temperature air, a low-pitched sound has a wavelength of about 17 meters and high-pitched sounds have wavelengths around 2 centimeters. That’s a big range, and not all those sounds will travel around corners. Shorter wavelengths are ultrasound, which are probably most familiar for tracking the health of fetuses: these sound waves can penetrate or reflect off tissue, and by measuring the waves that bounce back, doctors can track blood flow and other developmental processes inside your body. (X-rays go right through soft tissues, so they’re better for looking at bones.) Longer wavelengths are infrasound; animals like elephants use these very low-pitched sounds for communication across long distances.

When a wave meets an opening like a door, it can experience something known as diffraction: the wave passing through the opening spreads out on the other side. However, the wave doesn’t just come through the center of the door: it makes a bunch of waves along the length of the opening, and those waves actually interfere with each other. The wider the door, the more of these new waves are made.

The image to the right shows the interference pattern from a red laser shining through a very narrow opening (smaller than a millimeter). The central maximum is where most of the light coming through the opening ends up, but you also have dark spots where the light interferes and cancels out. The secondary spots on either side of the maximum are much less bright, and you also get tertiary and smaller spots that are fainter still. You get the same pattern for sound, though for obvious reasons I can’t show you a picture of it! The only difference is you exchange brightness for loudness, and dark spots for places where the sound is silenced.

The width and intensity (brightness or loudness) of the spots depend on the ratio of the wavelength to the size of the opening. If the wavelength is bigger than the opening, there isn’t diffraction; if the wavelength is about the size of the opening, then you get strong diffraction, and the central maximum is a lot wider than the opening. If the wavelength is much smaller than the opening, then the central maximum is quite small, and since the secondaries, tertiaries, and so forth are fainter still, the pattern may be hard to detect.

So there’s our answer! A typical doorway is around a meter wide (a little less, usually), so sound with its relatively large wavelengths will create a big central maximum and sufficiently-loud secondaries. That can be enough to hear even if you aren’t in a straight line with the hooligan cats in the other room. A corner is just a very wide doorway, so everything I’ve said about doorways carries over to them too.

Visible light has very small wavelengths, so while you do get light diffraction through doorways, you’d need a microscope to see the pattern! If you have a strong light shining through the door, you’ll get a nice rectangular blaze of light on the opposite wall, but it’s not much bigger than the door, and doesn’t go around corners. However, if you have a cell phone or a cordless phone, the signal from those definitely can go around corners: those are based on microwaves or radio waves, which have much larger wavelengths than visible light.

Similarly, elephants communicate via infrasound over huge distances because rocks, trees, and other obstacles are smaller than the wavelengths they use, so the sound just diffracts right around them. Very handy! Tigers use roars to establish territories, and since they live in dense forests, again infrasound lets their growls travel around the trees easily. (We humans may not hear the infrasound part of the roar, but we can definitely feel it. The lowest notes from large pipe organs or tubas are below our normal hearing range, but they still can contribute to the overall sensation of a musical piece.)

There is one place where diffraction does play a role in our vision: our eyes themselves. Doorways are too big for diffraction, but the pupil in a human eye is about 2 millimeters across, varying depending on whether we’re in a bright or dark place. The size of the central maximum of light cast on our retina is part of what determines how well we see. Diffraction also is why radio telescopes need to be very large, but why an ordinary visible light telescope you might have doesn’t need to be huge – yet the larger it is, the more clearly you’ll be able to see distant planets and galaxies. The telescope is like a big window, so you want to match the size of the window to the wavelength of the light you’re viewing.

Now if you’ll excuse me, I need to go make sure my cats haven’t wrecked the living room.

Einstein's most famous equation, sort of. This is the transcription of the chalkboard from a public talk Einstein gave in Pittsburgh in 1934. (Credit: Dwight Vincent and David Topper)

Did Einstein write his most famous equation? Does it matter?

Why all the fuss about E = m c2?

By Matthew R. Francis

Albert Einstein in Pittsburgh, 1934. (Credit: Pittsburgh Sun-Telegraph/Dwight Vincent and David Topper)

The association is strong in our minds: Albert Einstein. Genius. Crazy hair. E = m c2. Maybe many people don’t know what else Einstein did, but they know about the hair and that equation. They may think he flunked math in school (wrong, though he did have conflicts with some teachers), that he was a ladies’ man (true, he had numerous affairs during both of his marriages), and that he was the smartest man who ever lived (debatable, though he certainly is one of the central figures in 20th century physics). Rarely, people will remember that he was a passionate antiracist and advocate for world government as a way of bringing peace.

Obviously whole books have been written about Einstein and E = m c2, but a blog post at io9 caught my attention recently. The post (by George Dvorsky) itself looked back to a scholarly paper by David Topper and Dwight Vincent [1], which reconstructed a public lecture Einstein gave in 1934. (All numbers in square brackets [#] are citations to the references at the end of this post.) This lecture was one of many Einstein presented over the decades, but as Topper and Vincent wrote, “As far as we know [the photograph] is the only extant picture with Einstein and his famous equation.”

Well, kind of. The photograph is really blurry, and the authors had to reconstruct what was written because you can’t actually see any of the equations clearly. Even in the reconstructed version (reproduced below)…there’s no E = m c2. Instead, as I highlighted in the image, the equation is E0 = m. Einstein set the speed of light – usually written as a very large number like 300 million meters per second, or 186,000 miles per second – equal to 1 in his chalkboard talk.

Einstein's most famous equation, sort of. This is the transcription of the chalkboard from a public talk Einstein gave in Pittsburgh in 1934. (Credit: Dwight Vincent and David Topper)

Einstein’s most famous equation, sort of. This is the transcription of the chalkboard from a public talk Einstein gave in Pittsburgh in 1934. (Credit: Dwight Vincent and David Topper)

What’s the meaning of this?

It is customary to express the equivalence of mass and energy (though somewhat inexactly) by the formula E = mc2, in which c represents the velocity of light, about 186,000 miles per second. E is the energy that is contained in a stationary body; m is its mass. The energy that belongs to the mass m is equal to this mass, multiplied by the square of the enormous speed of light – which is to say, a vast amount of energy for every unit of mass. –Albert Einstein [2]

Before I explain why it isn’t a big deal to modify an equation the way Einstein did, it’s good to remember what E = m c2 means. The symbols are simple, but they encode some deep knowledge. E is energy; while colloquially that term gets used for a lot of different things, in physics it’s a measure of the ability of a system to do things. High energy means fast motion, or the ability to make things move fast, or the ability to punch through barriers. Mass m, on the other hand, is a measure of inertia: how hard it is to change an object’s motion. If you kick a rock on the Moon, it will fly farther than it would on Earth, but it’ll hurt your foot just as much – it has the same mass and therefore inertia both places. Finally, c is the speed of light, a fundamental constant of nature. The speed of light is the same for an object of any mass, moving at any velocity.

Mass and energy aren’t independent, even without relativity involved. If you have a heavy car and a light car driving at the same speed, the more massive vehicle carries more energy, in addition to taking more oomph to start or stop it moving. However, E = m c2 means that even if a mass isn’t moving, it has an irreducible amount of energy. Because the speed of light is a big number, and the square of a big number is huge, even a small amount of mass possesses a lot of energy.

The implications of E = m c2 are far-reaching. When a particle of matter and its antimatter partner meet – say, an electron and a positron – they mutually annihilate, turning all of their mass into energy in the form of gamma rays. The process also works in reverse: under certain circumstances, if you have enough excess energy in a collision, you can create new particle-antiparticle pairs. For this reason, physicists often write the mass of a particle in units of energy: the minimum energy required to make it. That’s why we say the Higgs boson mass is 126 GeV – 126 billion electron-volts, where 1 electron-volt is the energy gained by an electron moved by 1 volt of electricity. For comparison, an electron’s mass is about 511 thousand electron-volts, and a proton is 938 million electron-volts.

In our ordinary units the velocity of light is not unity, and a rather artificial distinction between mass and energy is introduced. They are measured by different units, and energy E has a mass E/C2 where C is the velocity of light in the units used. But it seems very probable that mass and energy are two ways of measuring what is essentially the same thing, in the same sense that the parallax and distance of a star are two ways of expressing the same property of location. –Arthur Eddington [3]

Another side of the equation E = m c2 appears when we probe the structure of atomic nuclei. An atomic nucleus is built of protons and neutrons, but the total nuclear mass is different than the sum of the masses of the constituent particles: part of the mass is converted into binding energy to hold everything together. The case is even more dramatic for protons and neutrons themselves, which are made of smaller particles knowns as quarks – but the total mass of the quarks is much smaller than the proton or neutron mass. The extra mass comes from the strong nuclear force gluing the particles together. (In fact, the binding particles are known as gluons for that reason, but that’s a story for another day.)

A brief history of an idea

The E0 = m version of the equation Einstein used in his chalk-talk might seem like it’s a completely different thing. You might be surprised to know that he almost never used the famous form of his own discovery: He preferred either the chalkboard version or the form m = E/c2. In fact, in his first scientific paper on the subject (which was also his second paper on relativity), he wrote [4]:

If a body gives off the energy L in the form of radiation, its mass diminishes by L/c2. The fact that the energy withdrawn from the body becomes energy of radiation evidently makes no difference, so that we are led to the more general conclusion that … the mass of a body is a measure of its energy-content …

In other words, he originally used L for energy instead of E. However, it’s equally obvious that the meaning of E = m c2 is present in the paper. Equations, like sentences in English, can often be written in many different ways and still convey the same meaning. By 1911 (possibly earlier), Einstein was using E for energy [5], but we can use E or L or U for energy, as long as we make it clear that’s what we’re doing.

The same idea goes for setting c equal to one. Many of us are familiar with the concept of space-time: that time is joined with space (thanks to the fact that the speed of light is the same, no matter who measures it). We see the blurring of the boundary between space and time when astronomers speak of light-years: the distance light travels in one year. Because c – and therefore c2 – is a fixed number, it means the difference between mass and energy is more like the difference between pounds and kilograms: one is reachable from the other by a simple calculation. Many physicists, including me, love to use c = 1 because it makes equations much easier to write.

In fact, physicists (including Einstein) rarely use E = m c2 or even m = E/c2 directly. When you study relativity, you find those equations are specific forms of more general expressions and concepts. To wit: The energy of a particle is only proportional to its mass if you take the measurement while moving at the same speed as the particle. Physical quantities in relativity are measured relative to their state of motion – hence the name.

That’s the reason I don’t care that we don’t have a photo of Einstein with his most famous equation, or that he didn’t write it in its familiar form in the chalk-talk. The meaning of the equation doesn’t depend on its form; its usefulness doesn’t derive from Einstein’s way of writing it, or even from Einstein writing it.

A small representative sample of my relativity books, with my cats Pascal and Harriet for scale.

A small representative sample of my relativity books, with my cats Pascal and Harriet for scale.

Even more: Einstein is not the last authority on relativity, but the first. I counted 64 books on my shelves that deal with the theory of relativity somewhere in their pages, and it’s possible I missed a few. The earliest copyright is 1916 [6]; the most recent are 2012, more than 50 years after Einstein’s death. The level runs from popular science books (such as a couple of biographies) up to graduate-level textbooks. Admittedly, the discussion of relativity may not take up much space in many of those books – the astronomy and math books in particular – but the truth is that relativity permeates modern physics. Like vanilla in a cake, it flavors many branches of physics subtly; in its absence, things just aren’t the same.


  1. David Topper and Dwight Vincent, Einstein’s 1934 two-blackboard derivation of energy-mass equivalence. American Journal of Physics75 (2007), 978. DOI: 10.1119/1.2772277 . Also available freely in PDF format.
  2. Albert Einstein, E = mc2. Science Illustrated (April 1946). Republished in Ideas and Opinions (Bonanza, 1954).
  3. Arthur Eddington, Space, Time, and Gravitation (Cambridge University Press, 1920).
  4. Albert Einstein, Does the inertia of a body depend upon its energy-content? (translated from Ist die Trägheit eines Körpers von seinem Energiegehalt abhängig?). Annalen der Physic17 (1905). Republished in the collection of papers titled The Principle of Relativity (Dover Books, 1953).
  5. Albert Einstein, On the influence of gravitation on the propagation of light (translated from Über den Einfluss der Schwerkraft auf die Ausbreitung des Lichtes). Annalen der Physic35 (1911). Republished in The Principle of Relativity.
  6. Albert Einstein, Relativity: The Special and the General Theory (1916; English translation published by Crown Books, 1961).

Backyard Brains: Affordable neuroscience

Mouse neurons. Image via Wikimedia Commons.
Originally published in PLoS Biology.

Nerve cells, called neurons, are special cells. They interact with each other and with other tissues in part by using electrical impulses. The cool thing about these cells is that thanks to their electrical signaling, we can measure when they’re sending their messages. A neuroscientist friend of mine once poetically described as “exquisite” the ability to measure the firing of a single neuron in a finch brain. There is something special about being able to observe that usually hidden process of signaling that underlies every move you make, every thought you have, and every sensation you detect.

The very word “neuroscience” sounds expensive. Measuring the signaling of nerves? That sounds pretty fancy. But with some wires and basic neuroscience tools, anyone can give it a try, measuring the nerve signaling, for example, in an insect. Which, do you think, would be the more memorable learning experience, a full-on sensory exposure to the sights and sounds of neuron signaling, or this? 

Now, a company called Backyard Brains is really bringing the neuroscience to the people. You don’t have to use their affordable kits in your backyard, but as neuroscientist and writer Mo Costandi highlights today in an interview with Tim Marzullo, co-founder of Backyard Brains, this level of technology can become available to high-school students anywhere. In the interview, Marzullo notes that the goal is to produce kits that lower the fiscal and resource requirements for making neuroscience available to people who aren’t graduate students in neuroscience.

As part of their bringing the neuroscience to the people, the Backyard Brains scientists have created the Spiker Box kit, which lets students listen to neurons firing in a de-legged cockroach. These kits are friendly with computers, iPhones, and iPads, so students can use these devices to record and listen to the Zzzzzzztt! of a firing neuron (see video below). Electrophysiology in action, made accessible. 

An even fancier introduction to science awaits. Some proteins are especially made to change their shape in response to a light trigger. Scientists have produced animals–mostly fruit flies–that make these proteins in some neurons, where they don’t usually occur. With light-reactive proteins present in the neurons, researchers can actually make the neurons fire by giving them a shot of laser light. In other words, they can make the animals move using light. Wouldn’t it be cool if classroom students could see that kind of neuroscience in action?

Backyard Brains is on the case. They’re working on a product that will allow students to use blue light emitted from an iPad to trigger light-reactive proteins in nerves that communicate with muscle cells. Because the process involves light and organisms with introduced genes, it’s called optogenetics. That sounds even more swanky than neuroscience, but Backyard Brains is working on making it accessible.

Other Backyard Brains products include RoboRoach (you’ll have to read that one for yourself), soldering kits, and the roaches themselves

Emily Willingham