Tag: electromagnetism

  • Why is glass transparent?

    Why is glass transparent?


    Imagine transparent materials didn’t exist. What would cars look like? How would you be able to look at the cold Winter Moon from your bedroom window without getting cold yourself? Would air be opaque too? What about the lenses in our eyes? And if all materials consist of molecules, how is it that the molecules of glass are transparent while others aren’t? This last question was asked by the oldest(beginfootnote)If I’m not mistaken, thirteen at the time I’m writing this.(endfootnote) son of one of my best friends last week.

    Firstly, I’ll try to give an answer as short as possible. If you’d like to know more, you can read on. Be warned, however: the article is quite possibly a bit long. It’s just that the answer to this seemingly easy question asks for quite some background knowledge. On the other hand, with a brilliant question like this one—let’s just say, you’re asking for it.

    Short answer

    Sometimes the composition of a molecule is such that its electrons will hardly respond to passing photons. For all intents and purposes, they will leave them be. At most, they will change their course a little. To our eyes, the material is then transparent.

    If electrons do react to incoming photons, they might reflect them or absorb all of their energy, making the photons disappear. Sometimes they just vibrate a little bit and make the entire atoms vibrate a little bit too (phonon), but nothing much else happens. The material just increases temperature for a minuscule amount. Sometimes the electrons vibrate so much that they’ll radiate that energy very soon after, causing new photons to be created, which then move on to the rest of the universe. To us, that material is then opaque; the photons radiated from the material end up in our eyes.

    So, this was the short version. If you’d like to know more, do read on!

    Molecules, atoms, elementary particles

    Perhaps you know this but just to be sure: all solids, liquids, and gasses consist of molecules. Here you see a photo of a bunch of so-called pentacene molecules made by Canadian scientists[1]. These molecules aren’t present in glass, however, it does give an impression of what molecules can look like.

    caterpillar-like pentacene molecules

    Every caterpillar-like thingy is a molecule. When they stick close enough together, they form a solid. If they are capable of sliding past each other, it’s a liquid. And if they’re capable of jiggling a lot more away from each other, it’s a gas.

    It’s possible to look more closely. Those molecules consist of atoms. Do have a look at this cool photo of one such molecule which Swiss physicists and one physicist at Utrecht University were able to snap in 2009[2].

    a pentacene molecule, consisting of five benzene rings

    You might be able to distinguish five hexagonal shapes with protrusions. At every corner and every protrusion, an atom is present. You don’t see the individual atoms – they’re too small for that. However, you can see the structure formed by the chain of atoms, thereby shaping the molecule into existence.

    Back to glass. The window in your bedroom is composed of different types of molecules. There are a lot of silicon dioxide molecules, sodium carbonate molecules, calcium oxide molecules, magnesium oxide molecules, and some aluminium oxide molecules. Here you see a drawing of one such silicon dioxide molecule.

    a molecule of silicon dioxide

    Do they look like that for real? No, absolutely not. It’s just a conceptual model. In science, a model is meant to be a tool and never an exact copy of reality. And yet, we use models as they are quite helpful for imagining what we’re working with and for doing calculations on them. You have to keep in mind, though, it’s not what it really looks like.

    From (the model of) the silicon dioxide molecule you can see that it is comprised of three atoms: one silicon atom (grey) and two oxygen atoms(beginfootnote)‘Oxygen’ and ‘oxide’ stem from the ancient-Greek words for ‘sharp’ (ὀξύς, oxús), and ‘birth’ (γένος, génos), and the Latin word for ‘acid’, which is acidus. Lastly, the word ‘di’ stems from the ancient-Greek δίς (dís), meaning ‘twice’. As the molecule consists of two oxygen atoms, the official chemical name of the molecule is thus silicon dioxide.(endfootnote) (red). You may also wonder what these two little bars on each side are supposed to be. They symbolise the electrons which are shared by all the atoms amongst each other. Atoms can stick together when they share electrons with each other. In other words, it refers to how strong the atomic bond is. More bars equals a stronger bond.

    Every atom consists of yet smaller parts. Apart from one(beginfootnote)the hydrogen atom(endfootnote), atoms are made up of three types of particles: electrons, protons, and neutrons. At the core of the atom are all the protons and neutrons. The electrons kind of swirl around them in a cloud-like type of existence. As electrons don’t themselves consist of smaller things, they are said to be elementary(beginfootnote)‘Elementary’ stems from the Latin word elementum, carrying a meaning like ‘first principle’. There is nothing that goes further down than what is elementary. Elements always form the basis for other things.(endfootnote) particles. Here you see a model of an atom.

    a model of an atom

    The core (or ‘nucleus’) with all the protons and neutrons is so small that it’s usually drawn as a point or a little ball. However, if you were to zoom in, you’d see a lump of protons and neutrons. Around it there is the cloud-like electron or multiple electrons. (If you’d like to know exactly why a cloud is the model for one or more electrons, you can read This is not an atom.)

    It’s quite possible that an electron is further removed from the nucleus than shown here. If an electron receives energy, it’ll jump further away from the nucleus. After a very short period, the electron might jump back to its old position. If it does so, its energy leaves the atom again in the form of light. One of the ways in which the electron receives energy is light.

    Light

    What is light? Is it a wave, does it consist of particles? For a long time, physicists had no idea what light was exactly. Since the seventeenth century, great debates went on between physicists supporting Sir Isaac Newton and physicists supporting Christiaan Huygens. I fear a little that some science teachers at high schools still think it’s a big mystery. One of my science teachers in high school told us he was still on the fence whether it’s particles or waves. Unfortunately for him, since slightly less than a hundred years ago, we know.

    Isaac Newton (left): light = particles (tiny balls). Christiaan Huygens (right): light = waves. The correct quantum mechanical answer is: light = a disturbance in the Universe-pervading electromagnetic field. Depending on what is practical, one uses the mathematics of classical waves or the mathematics of photons (wave packets, not balls!) to work with. Physics students learn to use both approaches.

    What I’m about to tell you is not something you’ll likely learn in high school. I’m not sure why but it may have to do with textbook authors finding the mathematics too complicated. So, what you’re about to read is more or less what you’ll learn at university as a physics student, only without the mathematics.

    The problem with the question ‘wave or particle’ is that it suggests there’s only one choice. This is incorrect. The question should be: What is light? The answer is: a field(beginfootnote)In mathematics and physics, we call this a gauge field. It’s quite abstract mathematics. However, no matter how abstract, it has proven to be highly applicable in practice. Mobile phones would not have existed without these abstract mathematics.(endfootnote), one of the many Universe-pervading fields present, in this case the electromagnetic field. And to be even more precise: light is a disturbance of this electromagnetic field. One can describe this disturbance as either a wave or a particle, depending on what is more practical for the matter at hand.

    Besides, in modern physics the meaning of the word ‘particle’ differs from what you’d normally expect. In physics a particle is actually a packet, a wave packet. It’s not a pellet, it’s not a tiny ball or even a point. It’s a tiny packet of information which we mathematically describe as a tiny wave (a disturbance).

    Richard Feynman was an important, Nobel Prize-winning physicist who made enormous contributions to quantum electrodynamics.

    According to one of the best theories we have of our Universe to date, so-called quantum electrodynamics(beginfootnote)‘Quantum’ is Latin for ‘how much’. Physicists have been using the word as a synonym for ‘particle’. Plural is quanta. ‘Dynamics’ stems from the ancient-Greek δυναμικός, dunamikós, ‘powerful’ en refers to the theory describing forces and change of forces.(endfootnote) (QED), the Universe is pervaded by a mostly invisible – yet sometimes visible! – electromagnetic field. In most cases, that field does nothing at all. You can’t smell it, you can’t touch it, you can’t see it.

    However, when the electromagnetic field is being disturbed at a specific place in the Universe – e.g. on the inside of the LED lamp in your lavatory – then that disturbance will propagate in all directions, from that specific spot in the Universe towards the very rest of the Universe – i.e. the space of your lavatory. This disturbance you can see! I’m not sure how your pets might call this disturbance, however, humans call it light.

    Albert Einstein
    Albert Einstein

    If your eyes were able to zoom in immensely, you would see that light actually consists of billions and billions and billions of tiny disturbances. Light is a bundle of tiny disturbances in the omnipresent electromagnetic field. Those tiny disturbances used to be called ‘light quanta’ by Albert Einstein and others. However, since 1928, we call them photons(beginfootnote)This stems from the ancient-Greek φῶς, phôs, which ironically means ‘light’.(endfootnote). In popular books and magazines and even by physicists they are called ‘particles’. Again, they’re not pellets or tiny balls or anything. The word ‘particle’ refers to them being very tiny but it doesn’t say anything about what they look like. As model, tiny pellets or points are sometimes used, however, it’s not what they are. Photons are, just like electrons, elementary, however.

    In high school and at university, to do calculations on light, the wave model of light is used rather often. The great mathematician and physicist James Clerk Maxwell was one of the founders of the mathematical framework of the wave model of light. He and others before him are responsible for us still talking about ‘light waves’ instead of photons. The classical electromagnetic theory of Maxwell works so well that it’s compulsory for physics students to study this wonderful theory. So, it’s not at all wrong to speak of light waves.

    James Clerk Maxwell
    James Clerk Maxwell

    In the twentieth century, however, physicists found that quantum electrodynamics was able to predict and describe more phenomena than Maxwell’s classical electromagnetic theory, so the first kind of replaced the latter. Put differently, Maxwell’s theory is still highly useful in industrial applications, however, with QED, you can do what Maxwell’s theory can do plus a lot more.

    This is the way it usually goes in physics. The law of universal gravitation of Sir Isaac Newton works brilliantly. You can even apply it to Mars landings. However, the theory of gravity by Albert Einstein, so-called general relativity, can do what Newton’s theory does and a lot more, more precisely. So, general relativity has kind of replaced Newton’s law of universal gravitation. And yet, the latter is compulsory in high school and at university. It’s not wrong. It’s very useful, even! However, it does have its limitations. That’s why we first learn about Newton’s gravity and only later do physics students have to learn about Einstein’s gravity. Without Einstein’s general relativity, Google Maps and GPS-systems inside cars would not have worked properly.

    Hence, physics students learn everything about Maxwell’s wave theory and only later do they learn about quantum electrodynamics. And without quantum electrodynamics you would not have had computer processors, there would have been no internet, no mobile phones, no touchscreens.

    Light and energy

    The great physicist Max Planck came up with the idea that every photon has a specific energy level. He also showed that with every energy level comes a particular light colour. Bright blue light carries more energy than deep-dark red light. Sometimes light (photons) has (have) so much energy that it has (they have) become invisible to our human eyes. High-energy ultraviolet(beginfootnote)‘Ultra’ is Latin for ‘beyond’. So, ultraviolet means beyond violet.(endfootnote) light (UV light) is invisible to us. However, if your eyes were much more sensitive than they are now, you would see a very bright ‘more violet than violet-coloured’ light. Conversely, light can have very little energy. So little even, we won’t be able to see it anymore. Hence, infrared(beginfootnote)‘Infra’ is Latin for ‘below’. So, infrared is ‘below’ or ‘less than’ red.(endfootnote) light is invisible to us. However, if our eyes were slightly more sensitive, we would see ‘less red than red-coloured’ light.

    This cheery looking fellow was a physicist and a genius. His name was Max Planck. A photograph from 1933.
    This cheery looking fellow was a physicist and a genius. His name was Max Planck. A photograph from 1933.

    WiFi and 4/5G are light too. The photons have very little energy compared to the photons in your lavatory. If our eyes had been thousands of times more sensitive than they are now, you would have seen that the antennas of the WiFi router and the mobile phones are basically lamps radiating ‘less than less than less than (thousands of times ‘less than’) red-coloured’ light.

    The electromagnetic field pervading our Universe can thus be disturbed at various energy levels. Depending on that, light looks differently. It has varying colours or is invisible – which it is most of the time. Our eyes aren’t the best instruments to look around with. Of all possible energy levels the electromagnetic field can be at, we can only discern just a few. That energy portion is what we call visible light.

    Another word for disturbances of the electromagnetic field is electromagnetic radiation. Depending on the energy level of the radiation, we have different terms for it, such as ‘radioactive radiation’ or ‘gamma radiation’. However, all these things – the lavatory light, the WiFi, 4/5G for the mobile phone, the head lights of the car, the radio waves from the neighbour, the Bluetooth speaker in the kitchen, the x-ray images at the dentist, the microwave – are all light, are all electromagnetic radiation, are all disturbances of the one and the same electromagnetic field. The only difference is the energy level of that disturbance.

    The correct order going from very little to deadly amounts of energy is the following: radio, WiFi, microwave(beginfootnote)If you want to know whether microwave radiation is deadly or not, do give my article Is microwave oven radiation unhealthy? a read.(endfootnote), 4/5G >> infrared light (TV remote) >> visible light (lavatory light, club lights) >> UV light (take care, apply sunscreen) >> x-rays (only operated by professional medical workers) >> gamma radiation (deadly, except for Bruce Banner) >> cosmic radiation (deadly, except for Captain Marvel).

    As most electrons inside of walls of houses won’t respond much to electromagnetic disturbances (photons) at the energy level of WiFi (very little energy), to WiFi photons, the walls are almost transparent. This is why you can receive WiFi straight through the walls. If your eyes were sensitive enough, you would be able to see the light coming from the router, straight through the walls. Those same electrons, however, do react to photons at the much higher energy level corresponding to visible light. This is why those photons do not fly through the wall. And this is why we find walls to be quite the opaque type objects. Nevertheless, the electrons do not respond again to photons at the even higher – much higher – energy levels of x-rays. This is exactly why walls are perfectly transparent to Superman.

    Depending on the composition of the molecules and atoms do electrons more or less react to the presence of photons at varying energy levels. If electrons of the material do not respond to photons at the energy level corresponding to visible light, then the material is transparent to us.

    Below you see a diagram of the full spectrum(beginfootnote)‘Spectrum’ is Latin for ‘appearance’. So, if you speak of the spectrum of something, such as electromagnetism, then you’re referring to all of its appearances.(endfootnote) of electromagnetic radiation (click to enlarge). As you can see, only a small portion is visible to us.

    A diagram of electromagnetic radiation. Far right, we see the dangerous types of radiation: cosmic rays, x-rays, gamma rays, UV-light. In the middle, we see visible light. Far left, we see the lowest energy photons: WiFi, mobile phones, microwave ovens.
    A diagram (not to scale) of electromagnetic radiation, or photons, if you will. The mentioned values are the frequencies of the photons, expressed in gigahertz (GHz). The higher the frequency, the higher the energy of the photon.

    GHz refers to the frequency of the photon and is a measure for the photon’s energy level. The higher the frequency, the higher the energy level. Ultraviolet radiation is where it’s starting to become dangerous to us. This is where our cells become damaged (‘DNA damage’). As long as you’re not exposed to the Sun for too long and x-ray photography is done in very short amounts of time, it’s going to be fine. But be careful. Again, gamma radiation and cosmic radiation are deadly. I understand, it doesn’t feel comfortable at all, but please, please do listen to your parents when you’re going out for a space walk. Put on that spacesuit.

    Impressionable electrons

    In the previous century, physicists such as Albert Einstein discovered that electrons can be influenced by incoming photons(beginfootnote)This is what he received the Nobel Prize for. You can read more about that in my article The formula that got Albert Einstein the Nobel Prize and should stop us getting sunburn all the time.(endfootnote). It very much depends on the way the electrons are captured inside the molecules – which depends on the type of atoms – at which energy level photons they will start reacting.

    In the case of glass, the electrons do feel electromagnetic disturbances slightly. This is why they do start to jiggle differently just a notch. That jiggling causes changes in the part of the electromagnetic field that is inside of the glass. And these changes will influence the photons (disturbances in that same electromagnetic field) in such a way that they’ll change course slightly.

    There's a bear swimming in a pool in a zoo. The pool is visible from the side through a large window. Due to refraction, the head of the bear above the surface seems to be located at a different place than the rest of its submerged body. The bear seems beheaded and yet, it lives.

    This is why the image behind glass can seem to be slightly warped. The same happens when light goes from air to water (as water, too, contains electrons which react to incoming photons). The electrons don’t do too much so that photons can just pass through, however, they do enough so that the photons do change course slightly. Or a lot as you can see by the water in the photo above. In my article Why, exactly, do glass and liquids refract light? we take a deep dive into this phenomenon.

    Why is glass transparent?

    And so, glass is transparent as the electrons in glass molecules aren’t capable of reacting very much to incoming electromagnetic disturbances (photons). Just a little. So, they do bend the original trajectory of the photons slightly.

    There are materials containing electrons responding to all energy levels except those corresponding to blue light, for example. This means that blue light can just pass through while the rest is being absorbed. To us, this material seems to be a blue filter.

    It’s also possible to produce materials carrying electrons which react to all photons in the visible part of the spectrum. They do this so strongly that photons will be reflected completely. We call that a mirror.

    closeup photo of primate looking in a mirror

    Note that we’re talking mostly about photons we can see. To us most glass is transparent. However, we can also produce glass which seems transparent as it lets visible light pass through, while they are much less transparent to birds at the same time.

    We are incapable of seeing UV light. Birds can, however. So, if glass is produced in such a way that they will let visible light pass through but not UV light, they seem less transparent to birds, preventing them to bump into it.

    So, the answer to the question, ‘And if all materials consist of molecules, how is it that the molecules of glass are transparent while others aren’t?’, should rather be: ‘Transparent to whom? To birds? Or to humans?’

    References

    [1] Dinca, L. E. et al. (2015) “Pentacene on Ni(111): Room-Temperature Molecular Packing and Temperature-Activated Conversion to Graphene,” Nanoscale, 7(7), pp. 3263–3269. doi: 10.1039/C4NR07057G.

    [2] Gross, L. et al. (2009) “The Chemical Structure of a Molecule Resolved by Atomic Force Microscopy,” Science, 325(5944), pp. 1110–1114. doi: 10.1126/science.1176210.

  • Einstein’s special relativity in under 6.999 minutes for people on the move

    Einstein’s special relativity in under 6.999 minutes for people on the move


    In 1905, Albert Einstein published an article on moving bodies and electrodynamics. He noticed that Newton’s mechanics of moving bodies weren’t compatible with Maxwell’s equations of electromagnetism. In this article, he reconciled the two by modifying the first. These ideas and mathematical derivations became what we now know as Einstein’s special (theory of) relativity. In this post, we will describe some of its important bits. We start with two fundamental propositions. For the geeks, we will end with answering why special relativity is special.

    Einstein’s postulates

    His first postulate is basically that, whether or not you’re standing on a moving object, such as a ship, a train, or in your car, the same laws of physics apply. If you’re standing on a platform at the train station and you throw a ball in the air, the laws of physics ensure your ball comes down again. If you’re standing in a moving train, that ball still comes down again because the same laws of physics apply. The fact that you’re in motion doesn’t change anything to the rules of the Universe.

    Einstein’s second postulate is basically that, by extension of the first one, the speed of light is the same for everyone. He recognised that Maxwell and colleagues correctly describe light as an electromagnetic disturbance propagating according to the electromagnetic laws of physics. He also recognised that the velocity of the light source plays no role in Maxwell’s equations. And so, if the first postulate is correct, then irrespective of the velocity of an observer relative to the light source, light travels at the same speed $c$ ($c$ is about 300 000 000 m/s) and nothing can go faster.

    An image of the interior of an underground train. Passengers are sitting across each other.
    Whether you’re on the train or standing on the platform, the laws of physics are the same. The propagation of light is a law of electrodynamics not involving the velocity of its source. Hence, its velocity is the same on the train as on the platform, irrespective of its source or the train’s velocity.

    Intuition works mostly, just not really

    Suppose, you’re standing on a train station’s platform. A train passes at a speed of 30 metre per second. From inside the train, our friend throws a tennis ball out the window but in the direction of where the train is headed, at 2 metre per second, right at you. You catch it. At what speed does the ball hit your hand?

    Intuitively, you might say, that’s 30 + 2 = 32 metre per second. This way of calculating is very useful, most of the time. Instinctively, you would simply add the train’s speed and the throwing speed together. This is how Isaac Newton(beginfootnote)And Galileo Galilei before him as this is the so-called Galilean transformation.(endfootnote) would want you to do it. And, mostly, he’s not wrong. Except, well, he is kinda.

    Let’s wonder what would happen if our friend didn’t throw a ball, but, instead, switched on a pocket torch. The train still passes at 30 m/s. Light, however, flies out the torch at a speed of about 300 000 000 m/s. You lift up your hand. It ‘catches’ the light. At what speed does it hit your hand?

    You might say, that’s 30 + 300 000 000 = 300 000 030 m/s. But no. That’s wrong. Remember Einstein’s second postulate? Irrespective of the motion of the observer, light always travels at 300 000 000 m/s and nothing goes faster, full stop. So, by our simple addition, we would have invented a way for light to go faster than light! We would be Nobel Prize winners, surely. Except, it doesn’t, and we’re not.

    Something’s gotta give

    So, if the speed of light is the same to our friend, on the moving train, as it is to us, standing on the platform (do read this again and realise how bonkers this is), then how the Helheim does the Universe achieve this? After he did some relatively simple mathematics – which a student in secondary education can do – Einstein realised that something was up with metres and seconds. He proved that what is a metre to us isn’t a metre to our friend and vice versa. Furthermore, what is a second to us isn’t a second to our friend either.

    Basically, since we, on the platform, measure light to be going at 300 000 000 metre per second, and so does our friend on the train, well, that means that our understanding of what metres and seconds are is wrong.

    The point

    Here’s what’s happening. If two ‘things’, people, ‘objects’, or reference frames as physicists call them, move with respect to each other, weird things happen to space and time. Yes, the actual space and time. They are weird. We thought they were just there. Static. Always and everywhere the same. Two unchanging entities. Well, they’re not.

    In the Dutch town of Leiden, the project Leiden Wall Formulas have scattered physics equations throughout the town centre. This is the Lorentz contraction, aptly placed alongside a train track: it describes how space (in this case, a one-dimensional length) is contracted, according to Einstein’s special relativity. Click here for Google Street View.

    Suppose, we are on the train this time. We are in motion relative to our friend on the platform. Our friend then observes that space along our direction of motion becomes smaller, it contracts. They will actually measure our train to be shorter as compared to when it was standing still relative to our friend. They will also observe that our time is being stretched, i.e. our clock slows down. If one second goes by on their clock, they see only 0.9999999995… seconds have past on ours(beginfootnote)This number is a metaphor. The real time difference is too small for my calculator to show.(endfootnote).

    And to us, being on the train, it’s our friend who is travelling (backwards!) relative to us, in fact, the whole world is travelling relative to us, backwards. So, indeed, we measure the world to be shorter in the opposite direction of our motion as well as their time being slowed down.

    Twin paradox

    Now, you might say, hold on: if both of us see each other’s clock slow down, then surely, there is no difference between our clocks. However, when we ride back to our friend, stop at the platform, and compare our clock to our friend’s clock, we do see that our clock is behind. This is the so-called twin paradox. If both can state the same thing, how do their clocks still differ in the end, causing one half of the twin (on the train) to be younger than the half who stayed behind (on the platform)?

    This is due to the switching of reference frames: we were on a moving frame (the train), switched to a moving frame in the opposite direction (returning to our friend), and, lastly, switched to the platform’s frame, standing next to our friend, to compare clocks, while our friend never switched – he stayed on the platform(beginfootnote)Contrary to many popular and even introductory physics texts, this has less to do with acceleration, even though this does plays a role – without it, in the real world, one wouldn’t be able to switch reference frames. However, mathematically, acceleration isn’t necessary for solving the so-called twin paradox, switching frames is.(endfootnote). So, the situation isn’t symmetric.

    Length contraction and time dilation. They’re not illusory, they’re real. Many experiments showed that space contracts and time dilates for things in motion as observed by things with a different motion.

    Newton vs Einstein

    To summarise in a slightly more mathematical way – Newton taught us that one platform metre equals one train metre and that the same is true for seconds:

    1 platform metre = 1 train metre,
    1 platform second = 1 train second.

    Einstein, however, taught us that:

    1 platform metre $\equiv \dfrac{1\text{ train metre}}{\gamma}$,
    1 platform second $\equiv \dfrac{1\text{ train second}}{\gamma}$.

    This $\gamma$ (Greek letter gamma) is crucial. It’s a factor necessary to make sure that the speed of light doesn’t get any faster than the speed of light, even if it’s on-board a moving train. This factor is called the Lorentz factor(beginfootnote)Named after Hendrik Lorentz. The expression for his Lorentz factor is as follows: \[ \gamma = \dfrac{1}{\sqrt{1-\dfrac{v^2}{c^2}}}, \] where $v$ is the speed of the other relative to us and $c$ is the speed of light.(endfootnote).

    We never notice these things though. Usually, our speeds are way to slow for the effects of special relativity to be noticeable. Except for things that do go fast. Without Einstein’s special relativity, GPS satellites wouldn’t work(beginfootnote)Of course, we also need Einstein’s General Relativity for that, but that’s for another time.(endfootnote). Research institutes such as CERN and Fermilab also need to take special relativity in account for the high-energy, fast-flying particles.

    So, our intuition (Newton) is mostly just fine though not precisely right.

    What’s so special about special relativity

    This is a somewhat technical question, requiring a somewhat technical answer, our apologies. Contrary to what is being said in many popular science texts, special relativity isn’t really about constant speeds as opposed to general relativity dealing with acceleration. In fact, special relativity is able to deal with acceleration. It’s just that it works fine as long as we’re assuming things exist in so-called Euclidean space, adhering to Euclidean geometry(beginfootnote)Named after Euclid.(endfootnote). However, after ample deliberation, Einstein concluded through his general relativity that we’re not living in Euclidean-geometric reality at all. We’re living in a Riemannian manifold(beginfootnote)Named after Bernhard Riemann.(endfootnote). In short, Euclidean space is a special case of the more general Riemannian manifold(beginfootnote)If we’re being precise, Hermann Minkowski developed a modified version of Euclidean space which we now call Minkowski space, while Riemannian manifold should actually be named pseudo-Riemannian manifold but many physicists simply call this Riemannian manifold anyway, perhaps because they’re not mathematicians.(endfootnote). Hence, we have special relativity as opposed to general relativity.


    Featured image by StockSnap from Pixabay, modified by @kjrunia (added equations).


  • Just a minute: how do polarized sunglasses work?

    Just a minute: how do polarized sunglasses work?


    According to our best understanding of the observable Universe, it is filled with an omnipresent electromagnetic field. Certain perturbations of that field correspond to what we call (electromagnetic) radiation, the visible part of which we call light or light particles, or photons. These disturbances can have specific but differing frequencies, which, when visible, we may perceive as red, yellow, green, blue or violet. Every photon has a frequency: some value is going up and down over time. It turns out that discovering what it is that is changing over time, is the key to unlocking the answer to how polarized sunglasses work.


    Traditionally, it’s useful to mathematically separate the electromagnetic field into two components: the magnetic and the electric subfield. For a slightly more in-depth discussion of this topic, have a look at Why, exactly, do glass and liquids refract light? Geometrically, these subfields are orientated perpendicularly to one another. Have a look at Figure 1.

    Figure 1. A cartoon of the electromagnetic field. It consists of five parts. Their descriptions are given in the main text.
    Figure 1. A cartoon of the electromagnetic field.

    Part a. A three-dimensional electromagnetic field (EM-field) pervades the observable Universe. Here, it is depicted as a finite block but that’s just a cartoony metaphor. In reality, it has the shape of the Universe, and it’s seemingly infinite, or, to be more precise, it’s everywhere you can possibly look.

    Part b. As said before, it turns out to be very useful to mathematically separate the EM-field into two components: the magnetic and electric subfields, depicted here as two planes orientated perpendicularly.

    Part c. When a photon passes through space, this is where the EM-field is disturbed. It is a local change of electric and magnetic values back-and-forth over time. Very important to note: there is nothing in space going up and down or left or right, it is just a cartoon depicting changing values of the respective subfields. The only thing that is actually spanning through space is the trajectory of the photon, depicted by an orange arrow.

    Part d. For our polarized sunglasses, only the electric subfield is relevant, so, we’ve left out the magnetic arrows, just the electric arrows are shown.

    Part e. Of course, no light beam consists of merely one photon. In reality, a bundle of billions of photons are whizzing through space. The orientation of their EM-components will be at all sorts of angles.

    Inside the glasses

    Figure 2. A cartoon of atoms in the polarized filter of sunglasses. On average, they are lined up in a chain in a way as to allow the electron cloud to mainly move up and down, not left and right. The material is said to be vertically polarized.
    Figure 2. A cartoon of atoms in the polarized filter of sunglasses. On average, they are lined up in a chain in way as to allow the electron cloud to mainly move up and down, not left and right. The material is said to be vertically polarized.

    The atoms of polarized sunglasses are lined up in a chain of atoms in such a way that the most wiggle room they have is in the vertical direction as depicted by Figure 2. Incoming photons transfer their energy, through the EM-field, to the wiggling electron cloud, which starts wiggling even more but only in the vertical direction. The latter will activate the EM-field with a vertically orientated electric subfield component, thereby propagating the vertically polarized parts of the incoming light beam.

    Photons with a horizontal polarization, i.e. with a horizontally orientated electric subfield, wiggle the long chains of the sunglasses’ atoms in the horizontal direction. Their energy gets distributed over billions of atoms, horizontally, and is merely dissipated as heat: too low for light propagation. So, basically, these type of photons disappear and the sunglasses heat up a little bit.

    Lastly, photons with an electric subfield perturbation at an angle in between the horizontal and vertical direction will sometimes pass through, sometimes will dissipate.

    Why are polarized sunglasses vertically polarized?

    When light hits a surface, the outgoing or reflected light mostly consists of photons with the same electric orientation as that of the reflecting surface. So, roads and water mainly reflect horizontally polarized light. When you’re navigating a vehicle, you would definitely want to prevent blindness from reflections off of the road or water.

    Pilots

    Computer screens also emit polarized light. If you hold polarized sunglasses in front of it and turn them, at some point, a computer screen’s light will be blocked.

    A pair of polarized sunglasses are held in front of a computer screen. They are rotated at an angle of 90 degrees. The image of the computer screen disappears as the sunglasses turn black, blocking every light coming off of the screen.

    This is also why pilots don’t wear polarized sunglasses: a slight turn of the head would make it impossible to quickly and reliably read vital information off of their instruments. So, despite what expensive brands would like you to believe, a set of polarized sunglasses called something like ‘aviator sunglasses’ are useless in real-life aviation.

    To check if your sunglasses have genuine polarized filters, tilt them in front of a working computer screen. This way you’ll know which pair to leave at home before flying an aircraft.

    Cinema

    Watching a 3D film in the cinema requires a different type of polarized glasses. So, despite what many people may have told you, it’s not that one glass has been vertically polarized and the other horizontally. True, your left eye needs to receive slightly different images from your right eye but this is achieved in a far more ingenious way.

    As you would want the audience to be able to watch the film despite their (sometimes involuntary) head movements, both the film projector and the 3D glasses are cleverly exploiting circular polarization. Otherwise, the moment you would lovingly tilt your head towards your company’s shoulder, a simplistic left-right combination of horizontal and vertical polarization would render any film star on the big silver screen into a vague and flat character.