Category: Physics

Exploring the Fascinating Properties of Glass | November 21 2025, 23:58

I got carried away with the topic of glass and learned so many interesting things, so I’m sharing. It all started when I read about the supercritical state of matter – it turns out that the line separating liquid and gaseous states on a pressure and temperature graph at some point breaks off, and beyond that lies a state of matter that is neither here nor there. I started reading about states (phases) of matter and stumbled upon the fact that glass is essentially a state between liquid and solid. It flows, just very slowly. This myth is popular thanks to observations of medieval windows, where the glass is often thicker at the bottom, which was attributed to “flowing” under the influence of gravity, and it was even mentioned in school textbooks. In reality, glass is an amorphous solid with extremely high viscosity at room temperature, and it does not flow noticeably even over billions of years; the uneven thickness of old glass panes is explained by production technologies, when the thicker edge was installed at the bottom for stability.

I delved into the topic of glass further. It turned out that the reason why glass can be transparent is rooted in quantum mechanics, specifically in the electronic structure of the material, not because of the density of particles. The essence is that for an electron to absorb a photon, it must transition from one energy level to another, but in silicon dioxide, the width of the band gap is so large that the energy of visible light photons is physically insufficient to make this “jump.” As a result, light simply cannot interact with the electrons and goes straight through the material, while higher-energy ultraviolet radiation can overcome this barrier and is thus absorbed by glass.

It also turned out that melted glass conducts electricity. Moreover, the mechanism of conductivity fundamentally differs from how metals conduct electricity. In a copper wire, current is a flow of free electrons. In cold glass (an insulator), electrons are tightly bound, and ions are locked in the solid lattice. But when you heat glass to the molten state (usually above 1000 degrees for silicates), thermal energy breaks the rigid bonds of the lattice, and glass becomes a liquid, with ions gaining freedom of movement. The current in molten glass is the physical movement of charged atoms (ionic conductivity), not just “flowing” electrons.

The green tint you see on the edge of regular glass (as seen in the attached picture) turns out to be caused by iron ions, present as impurities (~0.1%). Sand is a natural material, and removing all the iron from it is difficult and costly. Low-iron glass, which has tens of times fewer iron ions, is used in solar panels, not just because it is more transparent. Iron greedily absorbs the infrared spectrum (thermal energy), reducing the efficiency of the panel. By removing iron, we allow maximum energy to reach the silicon cells.

And finally, the most “mind-blowing” (literally). There are these things called “Prince Rupert’s drops.” If you drop molten glass into icy water, the outer shell of the drop cools and hardens instantly, while the inner part remains liquid. As it cools, the core tries to contract, but the hardened shell doesn’t allow it. As a result, the inside of the drop preserves colossal mechanical stress (up to 700 MPa).

The physics of this process creates a paradox: the “head” of such a drop can withstand being struck by a hammer because the compression of the surface makes it incredibly strong (the same principle is used in tempered glass for smartphones). But just nick the thin tail, and the balance of forces is disrupted, and a wave of destruction moves through the drop at the speed of a bullet (about 1.5 km/s), turning it into glass dust right in your hands.

There’s also something in physics called “metallic glasses” (amorphous metals). If you cool the molten metal at a rate of a million degrees per second, atoms do not have time to arrange into a crystalline lattice and freeze in chaos. Such “glassy metal” possesses unique magnetic permeability and is stronger than titanium, because it lacks crystal lattice defects, which are usually the points of destruction. So glass is a much broader concept than just transparent substance in our windows 🙂

The only example of an object made from this material, amorphous metal, that I’ve encountered is, believe it or not, the iPhone clip.

By the way, that same amorphous structure of glass, which I mentioned earlier, gives it an unexpected advantage — supernatural sharpness. If you take a scalpel made of the best surgical steel and look at it under an electron microscope, its edge will look like a jagged saw. This is inevitable: steel is made up of crystalline grains, and it’s impossible to sharpen it any smoother than the grain size allows.

But obsidian (volcanic glass) when fractured provides an edge only about 3 nanometers thick (about 1/30000 the thickness of a human hair). There’s no magic here, just that glass lacks a crystalline lattice, which would otherwise prevent achieving a perfectly smooth fracture down to the molecular level. That’s why obsidian scalpels are still used in the most complex eye surgeries — the cut is so clean that tissue cells are minimally traumatized, and healing occurs faster.

And one more powerful engineering case — vitrification (glassification). Mankind has chosen glass as the most reliable “safe” for nuclear waste. Liquid radioactive waste is mixed with special additives, melted, and cooled into blocks. The trick is that dangerous isotopes are not just poured inside, they are chemically embedded into the atomic grid of the glass. Glass is chemically inert, it doesn’t rust like metal or decompose for thousands of years. This is perhaps the only material that engineers trust to store hazardous substances on a geological time scale. Yes, it takes about a million years for a discarded bottle to decompose.

And finally. Digging into history, it turns out that the Romans were engaged in nanotechnology 1600 years before we even invented the word. In the British Museum stands the “Lycurgus Cup” (4th century AD). If you look at it under normal lighting, it’s greenish and opaque. But if you place a light source inside the cup, the glass flashes bright rubin red.

Until the 1990s, scientists could not understand how this was achieved. An electron microscope showed: Roman craftsmen added gold and silver, ground to nanoparticles about 50 nanometers in size (about 1000-1800 times thinner than a hair). This size of particles triggers a quantum effect known as surface plasmon resonance: electrons in the metal begin to oscillate such that they absorb some wavelengths of light and let others pass depending on the angle of incidence. The funniest thing is that the Romans did this empirically, “by eye,” and we’ve only just learned to replicate this consciously in photonics. It’s crazy to think you could handle 50 nm gold dust by eye. This moment required additional googling.

It’s unlikely the Romans mechanically crushed the metal to 50 nanometers — they had no such mills.

More likely, they added gold and silver in the form of salts or foil to the molten glass mass. The nanoparticles formed not by crushing, but by crystallization and sedimentation from the melt under very precise temperature conditions (“glass prescription”). This is even more complex chemistry than simple grinding.

The most astonishing thing is not that they did it, but that the ratio of gold to silver was maintained perfectly. Changing the concentration of gold by just 1% would alter the color to something other than pure ruby red. This indicates that the craftsmen mastered the technology incredibly accurately, although they likely did not understand the mechanism. And that they had a heck of a lot of time for all kinds of nonsense;) probably many generations dedicated their lives to experimenting. Because it’s hard to see why all this was necessary.

There’s a beautiful hypothesis (unproven, but popular) that the cup could have been used as a detector. If you pour a different liquid into it (for example, alcohol with impurities or poison), the refractive index changes, and the color of the “flash” might vary.

Exploring the Chaos Game: Creating Fractals From Randomness | October 04 2025, 15:32

I read something interesting today. About fractals. If you take any three points that form a triangle, and then a fourth point anywhere, and subsequently throw a dice, the faces of which are assigned to the first three points. Next, you move from the current point towards the point corresponding to the result on the dice and place a new point halfway; this becomes the new current point. After many iterations, the points start to form the Sierpinski triangle – the one shown in the attached picture. Intuitively, you would think the triangle should be fully filled because it involves random movements in three directions from a randomly chosen point, but no. Moreover, it works even if the starting point is inside the future empty triangle (yes, a few points will disrupt the picture, but that’s it). If you start our experiment with five or six points instead of three, different shapes will form – see the attached picture. This graphical method is called the Chaos Game.

By the way, it may seem obvious, but in case you wondered — all the presented figures have zero area.

If you take two triangles and with a probability p move towards random vertices of the first, and with (1-p) towards random vertices of the second, you end up forming a Barnsley fern (picture №2).

I love such things because they seem like magic at first glance 🙂

(It’s a kind of problem from the same class as the synchronization of metronomes)

The Optical Illusion of the Changing Purple Dots | September 27 2025, 23:44

An interesting trick. To color the circle dark purple, you simply need to look at it and it will instantly change color. However, to revert it back, you just need to stop looking at it, and it will return to its original appearance (though you’re likely to look at another circle instead)

The Maunder Minimum’s Impact on Stradivari’s Unique Violins | September 18 2025, 21:20

I stumbled upon an interesting scientific hypothesis from 2003 regarding why Stradivari violins (and those of his contemporaries) are so unique. Traditional hypotheses—about the secrets of the varnish or the aging of the wood—prove insufficient. According to this hypothesis, the entire blame lies with the Maunder Minimum, a period of reduced solar activity occurring from 1645–1715, during which the tree growth rate slowed down due to the climate, meaning the wood was denser. The hypothesis suggests that amidst the perfect combination of altitude, humidity, and temperature, this environmental shift provided material with unique properties, ideal for resonant soundboards.

Stradivari was born a year before the Maunder Minimum began. His “Amati Period” (1666–1690), “Experimentation Period” (1690–1700), and “Golden Period” (1700–1720), during which he perfected and produced his best instruments (see Henley 1961), all coincided with the Maunder Minimum. Cremona’s craftsmen during this period used the only wood available to them, i.e., from trees growing during the Maunder Minimum. Neither before nor after this period was such wood available. And, probably, it is nowhere to be found in the world even now.

But really, modern violins are also quite something. Two-three hundred years ago, musicians extracted the maximum from an instrument through trial and error, whereas now it is done through meticulous calculation of sound. It is almost impossible to differentiate violins by their sound anymore, and the difference lies in the realm of individual preferences, rather than an undisputed objective worse-better.

Debunking Kelvin: The Dynamics of Wake Angles at Different Speeds | September 10 2025, 12:03

I look from the boat at the water and wonder whether the divergence angle of the waves depends on speed or not? Started Googling. Turns out, according to Kelvin, it’s constant at any speed, and amounts to 39 degrees (or 19.47 =arcsin(1/3) from the axis). But then I found a paper where the authors studied satellite images and disproved Kelvin, stating that with increasing speed, the wedge indeed narrows slightly (“Ship wakes: Kelvin or Mach angle?”, authors: Marc Rabaud and Frédéric Moisy)

Exploring Airport Security: How Baggage Scanners Work | September 02 2025, 20:29

The day after tomorrow, I am flying to Amsterdam (and then to Turkey), and I remembered that I had an unanswered question to myself about how baggage scanners work at the airport. Of course, I knew that it was essentially computer tomography, X-rays and all that, but I wanted more details. And below is the response as to why they ask you to take out water, and why sometimes they do not.

It turns out that modern scanners can not only see the shape of objects but also determine what material they are made of. How does a regular scanner work? Dense materials (such as metal) absorb a lot of radiation and appear bright or opaque in images. Less dense materials absorb little radiation and appear dark. Hence laptops, for example, had to be taken out — not because the scanner couldn’t recognize them, but because their dense components (battery, boards) could be used to hide other prohibited items behind them. So, it has long been not just scanners, but computer tomography — in essence, the bag or suitcase is scanned from all sides, then a 3D image is created. It seems like everyone knows this.

But I mentioned that they understand the materials items are made from. How?

It turns out that the scanner uses dual-energy X-ray technology. It scans the object with two beams of rays of different energy levels (high and low). Since materials absorb radiation differently depending on the energy of the ray and their atomic composition, the system analyzes this difference. Based on the absorption ratio of the two beams, the effective atomic number Z — a key characteristic, a kind of “elemental fingerprint” of the substance, is calculated.

The problem is that this “fingerprint” of water (~7.4) and many explosives are almost identical. This is precisely why water was banned. Relying only on this parameter would mean receiving a huge number of false alarms.

Here is where computer tomography (CT) comes into play. The scanner creates an accurate three-dimensional (3D) model of the contents of the bag. From the 3D model, the system obtains the exact volume (V) of each object. Based on data on the absorption of X-rays, its mass (m) is calculated. Then it’s simple: ρ=m/V.

That is, the system does not make a decision based on one parameter. It plots each detected substance on a two-dimensional graph with axes “Z — density.” On this graph, water and explosives, having almost the same atomic number, occupy completely different positions due to different densities.

And that’s precisely why water can sometimes be carried through. Smart machines simply do not mark it as something significant, but still identify it as water. Then procedures follow. If the airport has updated the machines, but not the procedures, they will ask to dispose of the water. But also, not all machines are updated everywhere, and at the same airport, it depends on which line is open at the moment.

The cost of such a scanner is $300-400 thousand.

The scanners for people work differently. They use millimeter waves. They pass through clothing and reflect back from the skin. Water absorbs them significantly, so they penetrate only a couple of millimeters. The system registers the reflected signal and constructs a three-dimensional map of the body surface and objects under the clothing. But it does not show this — instead, it displays a simplified contour of a person and shows on it what ML found unusual. Therefore, by the way, many try to carry various items inside themselves, knowing that such a scanner absolutely cannot see it.

Exploring the Boundless Spectrum: The World of Animal Hearing | August 29 2025, 17:56

From my notes as I read Ed Yong’s Immense World—

“..It is known that the range of audible frequencies for animals is different from that of humans, but I didn’t realize just how different. Imagine the highest pitch in the world—it would be just under 20 kHz, as it’s considered the upper limit of the audible range. Both the upper and lower limits tend to decrease with age. Most adults can’t hear sounds over 16 kHz. Anything above 20 kHz we call ultrasound.

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So, it turns out that our closest relatives, chimpanzees, can hear up to 30 kHz, dogs up to 45 kHz, cats up to 85 kHz, mice up to 100 kHz, and moths even up to 300 kHz. Imagine, there are so many high-frequency sounds around us, and how rich their sound world is compared to our limited one. It would be interesting to wear headphones that compress the range from 20-40000 Hz to 20-15000 Hz. Many animals, such as mice, actively use ultrasound for internal communication, beyond the hearing range of their predators.

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And when the topic of ultrasound comes up, it’s impossible not to mention bats with their echolocation. Turns out, it’s a wildly interesting topic.”

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Probably everyone knows that bats successfully hunt in caves, where no light penetrates at all, and they don’t crash into stalactites and stalagmites. There’s an English saying, blind as a bat, but actually, they can see. Some species see better, others worse. But let’s talk about echolocation.

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In general, it’s just radar. The bat screams, the sound bounces off a tree, comes back into its ears, and it gets information about how far away the tree is and whether to slow down or not. But the devil, as they say, is in the details. “Engineering” ones.

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Firstly, high-frequency sound attenuates quickly, so you need to shout very loudly for something to bounce back from a few meters away. Beyond that, bats simply don’t “see.” So, they do indeed shout very loudly, and it’s a directed scream. Specifically, they measured 138 decibels, the sound level of a jet engine if you stand next to it. But in the ultrasonic range.

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Secondly, when they scream so loudly, they need to plug their own ears so as not to kill their sensitive apparatus. It turned out that they have special muscles that block the inner ear during the scream.

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Thirdly, both they and their prey are on the move, very fast and erratic. Meanwhile, the speed of sound is about 343 meters per second. The bat’s brain must calculate the difference between the signal and the echo, taking into account both its own movement through space and the movement of the prey. It turned out that the bat’s vocal muscles can contract up to 200 times a second. Moreover, the frequency depends on the phase of the hunt. 200 times—that’s the final phase, when the moth is right in front of the nose, and tiny movements need to be tracked.

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Fourthly, the bat’s brain also has to cope with creating interference between what was shouted out two moments ago and what was shouted out a moment ago. Considering that the sound can echo off the far wall and the near branch. Plus there are waves from the cries of other bats, and they’re usually very numerous in caves. To manage this, they seem to throw a bit different modulation, plus this musculature allows them to “fire” very short pulses—a few milliseconds—and to renew pulses at their own frequency through very short intervals. Imagine what kind of computer in their brains performs the inverse Fourier transform.”

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So, all this works pretty well in small groups. But for example, the Brazilian free-tailed bats live in groups of millions. Really, together 20 million mouths shout something and wait for their echo from the walls and each other. You can’t just pick modulation and frequencies that easily, but somehow they manage. Not perfectly, and if they gather in a really big bunch in the cave, then they perform their commute to the hunt and back to the cave “by memory” – probably due to issues with echolocation. When a “door” was placed at the entrance to the cave, a bunch of bats crashed into it.

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Fifth, consider how they determine distance. It’s necessary to calculate the difference between the signal sent and the signal received (amid a bunch of noise from other bats), and for hunting, it needs to be calculated very precisely. And sound of course isn’t light, but 343 meters per second is also a lot. So studies have shown that bats can recognize differences as little as 1-2 millionths of a second, which allows them to determine distance to fractions of a millimeter. In other words, our eyes are significantly less accurate than their ears.

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Plus, a moth is actually a fairly complex 3D creation that reflects sound differently with its different parts. Otherwise, bats would eat everything that moves. They recognize. In complete darkness. A mouse’s scream contains a whole palette of frequencies, which reflect differently off parts of a moth, and the mouse’s brain somehow manages to translate this into a coherent picture. Moreover, for each of the constituent frequencies, the delay will be its own.

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Then, all this information is layered over time. Roughly speaking, a snapshot from one point is combined with a snapshot from a point a half meter to the right, then from a point half a meter forward, and so on many, many times, which enhances “sharpness” and detail. Overall, it’s the same with us – we only see the spot in front of us clearly while the rest is constructed by the brain. But the brain of a bat weighs 1-2 grams against our half kilogram.

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Think about it, you’re flying with such a built-in radar, and in front of you are two branches at the same distance, which produce essentially the same echo for their ears. And to distinguish them and understand that it’s not one object but two, you really need an advanced brain.

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So, they send pulses lasting 1-20 ms, plus longer pauses between pulses. The pulses are complex in terms of frequencies, so such bats are called frequency modulation (FM) bats. But there are about 160 species that have a much longer cry—many tens of milliseconds but with short pauses, and instead of a complex gamma of frequencies, these use a pure “note.” These bats are called CF—constant frequency. So here’s the thing with these bats—there’s a problem with the Doppler effect, which is an increase in frequency as the distance decreases. Since their brain is tuned to a strict frequency, like 87 kHz for example, they might lose their prey if the echo that reaches their ears is shifted in frequency. And what they do—they shout at a sound speed lower, so that after the Doppler effect it arrives at the correct frequency for the brain.”

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Incidentally, their radar has two modes—forward and downward, the echoes from which are processed separately. The downward radar provides information about position in space, and the forward radar—about the position in space of the prey.

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When I researched the subject, I found that yes, after 20 kHz humans hear nothing, with one exception—frequencies of 2.4 GHz and 10 GHz, which actually belong to the microwave range. Yes, humans can “hear” these frequencies, but not with the ear, but “hear.” This phenomenon is called the microwave auditory effect or the Frey effect. Initially, this effect was registered by people working near radars during World War II, and the sounds they perceived were not heard by others. It turned out that when pulsed or modulated microwave radiation was applied to areas around the cochlea, it was absorbed by the tissues of the inner ear, accompanied by their thermal expansion. In the course of this process, shockwaves are produced, perceived by humans as sound, which no one else hears. It was also discovered that with the appropriate choice of the modulating signal, it is possible to transmit information to a person in the form of individual words, phrases, and other sounds. Depending on the radiation parameters, the sound created in the head can be irritating, cause nausea, and even disable. The volume of the perceived sound can be changed, but acoustic trauma is not possible, as the eardrum does not participate in the process at all. Generally speaking, the method of specifically transmitting sonic messages that are absolutely inaudible to others opens up a whole bouquet of possibilities. I wonder if research is still being conducted on this topic. Google shows that they used to be pretty intense.”

I once published this along with a video, and Facebook reckons that if you publish a video, the text should be one, at most two lines. And in the end, almost no one saw this text. Everyone just watched the video of a bat flying around my apartment 🙂

Inside Apple AirPods: Design, Battery, and Antenna Secrets Revealed | August 23 2025, 01:52

Very interesting video about how Apple Airpods headphones work (in the comments). You can read about it, or you can just like this post and go check out the original video in the comments. It has pictures!

Battery. 6 hours of operation, but the capacity is only 2% of the iPhone battery capacity. “Dead zones” in the battery, which lead to reduced operating time, can occur due to sudden temperature changes or even just dropping the headphones on the floor. There is a very dense “layered cake” made from a couple dozen layers of anode-cathode. Batteries of fake AirPods or cheap analogs are much worse. Physics: Poor packaging means less active material and fewer lithium ions moving with each cycle => reduced energy density and increased internal resistance => more energy is lost as heat => battery wears out faster.

Antenna. It is located in the stem because the human head significantly dampens the signal. But there is little space in the stem. Metal strip antenna, size 2 mm by 10 microns(!). That’s thinner than human hair. At such size, it cannot maintain shape on its own. In other consumer electronics, antennas can be etched on the printed circuit board, but this limits them to two dimensions. For the AirPod stem, there isn’t enough space. Therefore, Apple uses a clever solution. They embedded the antenna in the surface of a molded plastic cylindrical part. There, clever conductive plastic is used, with added metal. A laser engraves the exact shape of the antenna in the form of small channels with a rough surface. Then, this groove is subjected to electroplating, first with copper, then covered with gold to protect against corrosion. As a result, a durable conductive track is formed, which matches the 3D geometry of the molded part, which would be impossible to create using traditional machining methods. The plastic not only structurally supports the antenna. Other components are attached to it, such as the cable wrapping around the stem to connect the antenna to the Bluetooth chip, the pressure sensor in the stem.

Microphone. In AirPods, not electret microphones, but MEMS: a microelectronic” version of the condenser type. Well, actually, this is not only Apple – any modern TWS headphones, unless they are the cheapest ones. That is to say, modern microphones are made using the same technology as types – photolithography, layer by layer, only in this case it’s a mechanical device, with calculated cavities and flexible layers. Separately interesting is how they make the cavities – they make holes through which etching solution penetrates inside and dissolves the sacrificial layers of silicon dioxide.

Because of such microscopic size, there are several microphones. But why more than one microphone is needed? At the bottom of the AirPods, you will see a small mesh that allows air to enter the second microphone. When you talk, your voice reaches both microphones, but not at the same time. With a difference of only a few millimeters, the chip can detect a delay of six microseconds between when your voice reaches each microphone. This is enough to determine where the sound is coming from and focus on it. Since it precisely knows the distance the microphones are from one another, the chip can compare each signal and amplify your voice during calls.

The third microphone is for noise cancellation. It is located right in front of the speaker, inside your ear.

The microphones consume about 130 mA, which would quickly drain the battery if they were always active. That’s why they are only turned on when you make a call or use noise cancellation. But AirPods are always waiting for a Siri request. How is this possible without constantly active microphones? Here’s a clever solution. Inside the part that is in your ear, there is a small sensor—an accelerometer. It’s the same type of sensor used in phones to determine orientation. But here it serves a different purpose. Instead of measuring orientation, it senses vibration. When you talk, your voice moves through your jawbone. And this vibration is detected by the accelerometer. This low-power consumption signal is enough to wake up the system and activate the microphones when it senses you want to activate Siri. Imagine that, eh?

The sound in AirPods is tuned not “by ear,” but based on a scientific model of the “ideal sound” (Harman curve), which describes the combination of frequencies most people find most pleasing. For this, there is a complicated system of calculated vents and meshes — to control the air flow, which prevents the occurrence of unpleasant “humming” or sharp sounds inside the ear canal. The larger the cells — more air passes through, smaller — less. Such is the mesh, visible as black things on the white earphone—I thought it was for beauty. No, this is exactly that mesh. But at the same time, some kind of moisture protection must be made, and here the mesh is porous. It is claimed that there is some sort of nano-coating that repels water.

Bluetooth. Why it is so immune to interference. Turns out, it uses frequency-hopping spread spectrum technology (Frequency Hopping). Bluetooth devices quickly switch between different channels many times a second and adapt accordingly.

Decoding “Carboy”: A Journey Through Language and Autobiography | August 20 2025, 04:02

Rereading Feynman’s autobiography, this time in English, and my eyes stuck on the word carboy. It turns out that it’s the same as lady jeanne, and the same as demijohn – essentially lady jeanne in French (dame joanne). In short, it’s just a bottle.

Aluminum: From Precious Metal to Everyday Marvel | August 03 2025, 01:09

The USA imports aluminum mainly from Canada because aluminum leaves Canada and arrives in the USA. And from Europe, it would be alumin𝒊um!

Also, sapphires and rubies are essentially rusty aluminum, where in the process the new material becomes much harder than the original. In interaction with oxygen, different varieties of the mineral corundum are formed, which chemically is crystalline aluminum oxide (formula Al₂O₃). And bulletproof glass is essentially transparent rusty aluminum, aluminum oxide, but with aluminum nitride.

Also, aluminum was the most valuable metal on Earth until the 20th century. When Napoleon III entertained guests, they ate with golden spoons, while he used an aluminum one. And the “cap” of our Washington Monument is made of aluminum for that very reason.