I once had a friend after a long night of drinking consult me on his living room couch, “What does quantum mechanics really mean?” I was taken aback for this particular friend and I had never discussed physics—let alone quantum mechanics—in our entire five year relationship. He was a former UCSB frat boy and he was the friend I turned to when I needed a break from my intellectual studies to indulge in the simpler pleasures of life such as women and beer. He was also so heavily inebriated that I was pretty sure he wasn’t even going to remember asking the question in the morning (which I was indeed later proven right).
I answered casually, “Well, it’s the physics of atoms and atoms make up everything, so I guess it means everything.” Not satisfied with my answer he replied slurredly, “No really, what does it mean? We can’t really see what goes on in an atom so how do we really know? What if it’s just some guys too smart for their own good making it all up? Can we really trust it? From what I know we still don’t completely understand it so how do we know if it’s really real? Maybe there’s just some things as humans were not supposed to understand.”
I’ll be honest I was in shock for I had never heard my friend express this type of existential thinking before. Not to paint him one-sidedly, we had had many intelligent discussions on finances, the economy, politics, but never physics and philosophy. Maybe it had something to do with the marijuana joint I just passed to him. Anyways, after a few moments of contemplation I answered, “Everything from your smartphone to the latest advances in medicine, computer and materials technology, to the fact you’re changing channels on the TV with that remote in your hand is a result of understanding quantum mechanics. But you’re right; we still don’t fully understand it and it’s continually showing us that the universe is probably a place we’ll never fully grasp, but that doesn’t mean we should give up…” I then continued with what might’ve been too highbrow of an explanation of quantum mechanics for an extremely drunk person at 3 a.m. because halfway through he fell asleep.
As my friend snored beside me, I couldn’t help but be bothered that he and so many others still considered quantum mechanics such an abstract thing more than a hundred years after its discovery. I thought if only I could ground it in some way to make people realize that they interact with quantum mechanics every day; that it really was rooted in reality and not a part of some abstract world only understood by physicists. I myself being a layperson with no university-level education in science learned to understand it with nothing more than some old physics books and free online classes. Granted it wasn’t easy and took a lot of work—work I’m still continuing, but it’s an extremely rewarding work because the more I understand, the more exciting and wonderful the world around me becomes.
This was my inspiration behind The Party Trick Physicist blog; to teach others about the extraordinary world of science and physics in a format that drunk people at 3 a.m. might understand. I make no promises and do at times offer more in-depth posts, but I do my best. With this said, as unimaginative as a post about at-home physics experiments felt to me initially, there’s probably no better way to ground quantum mechanics—to even a drunk person at 3 a.m.—than some hands on experience. Below are four simple quantum mechanical experiments that anyone can do at home, or even at a party.
1. See Electron Footprints
For this experiment you’ll be building an easy to make spectroscope/ spectrograph to capture or photograph light spectra. For the step-by-step tutorial on how to build one click here. After following the instructions you should end up with, or see a partial emission spectrum like this one below.
Now what exactly do these colored lines have to do with electrons? Detailed in a previous post, The Layman’s Guide to Quantum Mechanics- Part 2: Let’s Get Weird, they are electron footprints! You see, electrons can only occupy certain orbital paths within an atom and in order to move up to a higher orbital path, they need energy and they get it by absorbing light—but only the right portions of light. They need specific ranges of energy, or colors, to make these jumps. Then when they jump back down, they emit the light they absorbed and that’s what you’re seeing above; an emission spectrum. An emission spectrum is the specific energies, or colors an electron needs—in this case mercury electrons within the florescent light bulb—to make these orbital, or ‘quantum’ leaps. Every element has a unique emission spectrum and that’s how we identify the chemical composition of something, or know what faraway planets and stars are made of; just by looking at the light they emit.
2. Measure The Speed of Light With a Chocolate Bar
This is probably the easiest experiment as it only requires a chocolate bar, a microwave oven, a ruler and calculator. I’ve actually done this one myself at a party and while you’ll come off as a nerd, you’ll be the coolest one there. Click here for a great step-by-step tutorial and explanation from planet-science.com
3. Prove Light Acts as a Wave
This is how you can replicate Thomas Young’s famous double slit experiment that definitively proved (for about 100 years) that light acts as a wave. All you need is a laser pointer, electrical tape, wire and scissors. Click here for a step-by-step video tutorial.
4. Prove Light Also Acts as a Particle
This experiment is probably only for the most ambitious at-home physicists because it is the most labor and materials extensive. However this was the experiment that started it all; the one that gave birth to quantum mechanics and eventually led to our modern view of the subatomic world; that particles, whether they be of light or matter, act as both a wave and a particle. Explained in detail in my previous post The Layman’s Guide to Quantum Mechanics- Part I: The Beginning, this was the experiment that proved Einstein’s photoelectric effect theory, for which he won his only Nobel Prize. Click here to learn how to make your own photoelectric effect experiment.
Good luck my fellow party trick physicists and until next time, stay curious.
A great way to understand the continuous-wave and the quantized-particle duality of quantum physics is to look at the differences between today’s digital technology and its predecessor, analog technology. All analog means is that something is continuous and all digital means is that something is granular, or comes in identifiable chunks. For example the hand of an analog clock must sweep over every possible increment of time as it progresses; it’s continuous. But a digital clock, even if it’s displaying every increment down to milliseconds, has to change according to quantifiable bits of time; it’s granular. Analog recording equipment transfers entire, continuous sound waves to tape, while digital cuts up that signal into small, sloping steps so that it can fit into a file (and why many audiophiles will profess vinyl is always better). Digital cameras and televisions now produce pictures that instead of having a continuum of colors, have pixels and a finite number of colors. This granularity of the digital music we hear, the television we watch, or the pictures we browse online often goes unnoticed; they appear to be continuous to our eyes. Our physical reality is much the same. It appears to be continuous, but in fact went digital about 14 billion years ago. Space, time, energy and momentum are all granular and the only way we can see this granularity is through the eyes of quantum mechanics.
Although the discovery of the wave-particle duality of light was shocking at the turn of the 20th century, things in the subatomic world—and the greater world for that matter, were about to get a whole lot stranger. While it was known at the time that protons were grouped within a central region of an atom, called the nucleus, and electrons were arranged at large distances outside the nucleus, scientists were stumped in trying to figure out a stable arrangement of the hydrogen atom, which consists of one proton and one electron. The reason being if the electron was stationary, it would fall into the nucleus since the opposite charges would cause them to attract. On the other hand, an electron couldn’t be orbiting the nucleus as circular motion requires consistent acceleration to keep the circling body (the electron) from flying away. Since the electron has charge, it would radiate light, or energy, when it is accelerated and the loss of that energy would cause the electron to go spiraling into the nucleus.
In 1913, Niels Bohr proposed the first working model of the hydrogen atom. Borrowing from Max Planck’s solution to the UV catastrophe we mentioned previously, Bohr used energy quantization to partially solve the electron radiation catastrophe (not the actual name, just me having a fun play on words), or the model in which an orbiting electron goes spiraling into the nucleus due to energy loss. Just like the way in which a black body radiates energy in discrete values, so did the electron. These discrete values of energy radiation would therefore determine discrete orbits around the nucleus the electron was allowed to occupy. In lieu of experimental evidence we’ll soon get to, he decided to put aside the problem of an electron radiating away all its energy by just saying it didn’t happen. Instead he stated that an electron only radiated energy when it would jump from one orbit to another.
So what was this strong evidence that made Niels Bohr so confident that these electron orbits really existed? Something called absorption and emission spectrums, which were discovered in the early 19th century and were used to identify chemical compounds of various materials, but had never been truly understood. When white light is shined upon an element, certain portions of that light are absorbed and also re-radiated, creating a spectral barcode, so to speak, for that element. By looking at what parts of the white light (or what frequencies) were absorbed and radiated, chemists can identify the chemical composition of something. This is how were able to tell what faraway planets and stars are made of by looking at the absorption lines in the light they radiate. When the energy differences between these absorbed and emitted sections of light were analyzed, they agreed exactly to the energy differences between Bohr’s electron orbits in a hydrogen atom. Talk about the subatomic world coming out to smack you in the face! Every time light is shown upon an element, its electrons eat up this light and use the energy to jump up an orbit then spit it back out to jump down an orbit. When you are looking at the absorption, or emission spectrum of an element, you are literally looking at the footprints left behind by their electrons!
Left- The coordinating energy differences between electron orbits and emitted and absorbed light frequencies. Right- A hydrogen absorption and emission spectrum.
As always, this discovery only led to more questions. The quantum approached worked well in explaining the allowable electron orbits of hydrogen, but why were only those specific orbits allowed? In 1924 Louis de Broglie put forward sort of a ‘duh’ idea that would finally rip the lid off the can of worms quantum mechanics was becoming. As mentioned previously, Einstein and Planck had firmly established that light had characteristics of both a particle and a wave, so all de Broglie suggested was that matter particles, such as electrons and protons, could also exhibit this behavior. This was proven with the very experiment that had so definitively proven light as a wave, the now famous double slit experiment. It proved that an electron also exhibited properties of a wave—unless you actually observe that electron, then it begins acting like a particle again. To find out more about this experiment, watch this videohere.
As crazy as this all sounds, when the wave-like behavior of electrons was applied to Bohr’s atom, it answered many questions. First it meant that the allowed orbits had to be exact multiples of the wavelengths calculated for electrons. Orbits outside these multiples would produce interfering waves and basically cancel the electrons out of existence. The circumference of an electron orbit must equal its wavelength, or twice its wavelength, or three times its wavelength and so forth. Secondly if an electron is now also a wave, these orbits weren’t really orbits in the conventional sense, rather a standing wave that surrounded the nucleus entirely, making the exact position and momentum of the particle part of an electron impossible to determine at any given moment.
This is where a physicist by the name of Werner Heisenberg (yes the same Heisenberg that inspired Walter White’s alter ego in Breaking Bad) stepped in. From de Broglie’s standing wave orbits, he postulated sort of the golden rule of quantum mechanics: the uncertainty principle. It stated the more precisely the position of an object is known, the less precisely the momentum is known and vice versa. Basically it meant that subatomic particles can exist in more than one place at a time, disappear and reappear in another place without existing in the intervening space—and yeah, it basically just took quantum mechanics to another level of strange. While this may be hard to wrap your head around, instead imagine wrapping a wavy line around the entire circumference of the earth. Now can you tell me a singular coordinate of where this wavy line is? Of course not, it’s a wavy line not a point. It touches numerous places at the same time. But what you can tell me is the speed in which this wavy line is orbiting the earth by analyzing how fast its crests and troughs are cycling. On the other hand, if we crumple this wavy line up into a ball—or into a point, you could now tell me the exact coordinates of where it is, but there are no longer any crests and troughs to judge its momentum. Hopefully this elucidates the conundrum these physicists felt in having something that is both a particle and a wave at the same time.
Like you probably are right now, the physicists of that time were struggling to adjust to this. You see, physicists like precision. They like to say exhibit A has such and such mass and moves with such and such momentum and therefore at such and such time it will arrive at such and such place. This was turning out to be impossible to do within the subatomic world and required a change in their rigid moral fiber from certainty to probability. This was too much for some, including Einstein, who simply could not accept that “God would play dice with the universe.” But probability is at the heart of quantum mechanics and it is the only way it can produce testable results. I like to compare it to a well-trained composer hearing a song for the first time. While he may not know the exact direction the song is going to take—anything and everything is possible, he can take certain factors like the key, the genre, the subject matter and the artist’s previous work to make probabilistic guesses as to what the next note, chord, or lyric might be. When physicists use quantum mechanics to predict the behavior of subatomic particles they do very much the same thing. In fact the precision of quantum mechanics has now become so accurate that Richard Feynman (here’s my obligatory Feynman quote) compared it to “predicting a distance as great as the width of North America to an accuracy of one human hair’s breadth.”
So why exactly is quantum mechanics a very precise game of probability? Because when something is both a particle and wave it has the possibility to exist everywhere at every time. Simply, it just means a subatomic particle’s existence is wavy. The wave-like behavior of a particle is essentially a map of its existence. When the wave changes, so does the particle. And by wavy, this doesn’t mean random. Most of the time a particle will materialize into existence where the wave crests are at a maximum and avoid the areas where the wave troughs are at a minimum—again I emphasize most of the time. There’s nothing in the laws of physics saying it has to follow this rule. The equation that describes this motion and behavior of all things tiny is called a wave equation, developed by Erwin Schrödinger (who you may know him for his famous cat which I’ll get to soon). This equation not only correctly described the motion and behavior of particles within a hydrogen atom, but every element in the periodic table.
Heisenberg did more than just put forth the uncertainty principle—he of course wrote an equation for it. This equation quantified the relationship between position and momentum. This equation combined with Schrodinger’s gives us a comprehensive image of the atom and the designated areas in which a particle can materialize into existence. Without getting too complex, let’s look at a simple hydrogen atom in its lowest energy state with one proton and one electron. Since the electron has a very tiny mass, it can occupy a comparatively large area of space. A proton however has a mass 200 times that of an electron and therefore can only occupy a very small area of space. The result is a tiny region in which the proton can materialize (the nucleus), surrounded by a much larger region in which the electron can materialize (the electron cloud). If you could draw a line graph that travels outward from the nucleus that represents the probability of finding the electron within its region, you’ll see it peaks right where the first electron orbit is located from the Bohr model of the hydrogen atom we mentioned earlier. The primary difference between this model and Bohr’s though, is an electron occupies a cloud, or shell, instead of a definitive orbit. Now this is a great picture of a hydrogen atom in its lowest energy state, but of course an atom is not always found in its lowest energy state. Just like there are multiple orbits allowed in the Bohr model, there higher energy states, or clouds, within a quantum mechanical hydrogen atom. And not all these clouds look like a symmetrical sphere like the first energy state. For example the second energy state can have a cloud that comes in two forms: one that is double spherical (one sphere inside a larger one) and the other is shaped like a dumbbell. For higher energy states, the electron clouds can start to look pretty outrageous.
Left- Actual direct observations of a hydrogen atom changing energy states. Right- The many shapes of hydrogen electron clouds, or shells as they progress to higher energy states. Each shape is representative of the area in which an electron can be found. The highest probability areas are in violet.
The way in which these electron clouds transform from one energy state to the next is also similar to the Bohr model. If a photon is absorbed by an atom, the energy state jumps up and if an atom emits a photon, it jumps down. The color of these absorbed and emitted photons determines how many energy states the electron has moved up or down. If you’ve thrown something into a campfire, or a Bunsen burner in chemistry class and seen the flames turn a strange color like green, pink, or blue, the electrons within the material of whatever you threw in the flames are changing energy states and the frequencies of those colors are reflective of how much energy the changes took. Again this explains in further detail what we are seeing when we look at absorption and emission spectrums. An absorption spectrum is all the colors in white light minus those colors that were absorbed by the element, and an emission spectrum contains only the colors that match the difference in energy between the electron energy states.
Another important feature of the quantum mechanical atom, is that only two electrons can occupy each energy state, or electron cloud. This is because of something inherent within the electrons called spin. You can think of the electrons as spinning tops that can only spin in two ways, either upright or upside down. When these electrons spin, like the earth, they create a magnetic field and these fields have to be 180 degrees out of phase with each other to exist. So in the end, each electron cloud can only have two electrons; one with spin up and one with spin down. This is called the exclusion principle, created by Wolfgang Pauli. Spin is not something that is inherent in only electrons, but in all subatomic particles. Therefore this property is quantized as well according to the particle and all particles fall into one of two families defined by their spin. Particles that have spin equal to 1/2, 3/2, 5/2 (for an explanation on what these spin numbers mean, click here) and so on, form a family called fermions. Electrons, quarks, protons and neutrons all fall in this family. Particles with spin equal to 0, 1, 2, 3, and so on belong to a family called bosons, which include photons, gluons and the hypothetical graviton. Bosons, unlike fermions don’t have to obey the Pauli exclusion principle and all gather together in the lowest possible energy state. An example of this is a laser, which requires a large number of photons to all be in the same energy state at the same time.
Since subatomic particles all look the same compared to one another and are constantly phasing in and out of existence, they can be pretty hard to keep track of. Spin however provides a way for physicists to distinguish the little guys from one another. Once they realized this though, they happened upon probably the strangest and most debated feature of quantum mechanics called quantum entanglement. To understand entanglement, let’s imagine two electrons happily existing together in the same electron cloud. As stated above, one is spinning upright and the other is spinning upside down. Because of their out of phase magnetic fields they can coexist in the same energy state, but this also means their properties, like spin, are dependent on one another. If electron A’s spin is up, electron B’s spin is down; they’ve become entangled. If say these two electrons are suddenly emitted from the atom simultaneously and travel in opposite directions, they are now flip-flopping between a state of being up and a state of being down. One could say they are in both states at the same time. When Erwin Schrödinger was pondering this over and subsequently coined the term entanglement, he somewhat jokingly used a thought experiment about a cat in a box which was both in a state of being alive and being dead and it wasn’t until someone opened this box that the cat settled into one state or the other. This is exactly what happens to one of these electrons as soon as someone measures them (or observes them), the electron settles into a spin state of either up or down. Now here’s where it gets weird. As soon as this electron settles into its state, the other electron which was previously entangled with it, settles instantaneously into the opposite state, whether it’s right next to it or on the opposite side of the world. This ‘instantaneous’ emission of information from one electron to another defies the golden rule of relativity that states nothing can travel faster than the speed of light. Logic probably tells you that the two electrons never changed states to begin with and one was always in an up state and the other was always in a down. People on the other side of this debate would agree with you. However very recent experiments are proving the former scenario to be true and they’ve done these experiments with entangled electrons at over 100 km a part. Quantum entanglement is also playing an integral role in emerging technologies such as quantum computing, quantum cryptography and quantum teleportation.
For as much as I use the words strange and weird to describe quantum mechanics, I actually want to dispel this perception. Labeling something as strange, or weird creates a frictional division that I’m personally uncomfortable with. In a field that seeks to find unity in the universe and a theory to prove it, I feel it’s counterintuitive to focus on strange differences. Just like someone else’s culture may seem strange to you at first, after some time of immersing yourself in it, you begin to see it’s not so strange after all; just a different way of operating. Quantum mechanics is much the same (give it some time I promise). We also have to remember that although reality within an atom may seem strange to us, it is in fact our reality that is strange—not the atom’s. Because without the atom, our reality would not exist. A way I like to put quantum mechanics in perspective is to think of what some vastly more macroscopic being, blindly probing into our reality might think of it. He/she/it would probably look at something like spacetime for example, the fabric from which our universe is constructed, and think it too exhibits some odd properties—some that are very similar to the wave-particle duality of the quantum world. While Einstein’s relativity has taught us that space and time are unquestioningly woven together into a singular, four dimensional entity, there’s an unquestionable duality just like we find in subatomic particles. Time exhibits a similar behavior to that of a wave in that it has a definite momentum, but no definable position (after all it exists everywhere). And space on the other hand has a definable, three dimensional position, but no definable momentum, yet both make up our singular experience of this universe. See if you look hard enough, both of our realities—the big and small, are indeed weird yet fascinating at the same time. Until next time my friends, stay curious.
My next blog topic was scheduled to be a crash course in String Theory as it seemed like a logical follow-up to a previous post, A Crash Course in Relativity and Quantum Mechanics. However as I was trying to put together this crash course on String Theory, I realized that while my previous post did an excellent job of explaining the basics of relativity, it was far too brief on the basics of quantum mechanics (so much so that you should just regard it as a crash course on relativity). It could also be that I’m just procrastinating in writing a blog post on String Theory because, as you can probably assume, it’s not exactly the simplest of tasks. So in the name of procrastination I’ve decided to write a comprehensive overview on something much easier (in comparison): quantum mechanics. I not only want to explain it, but to also tell the dramatic story behind its development and how it has not only revolutionized all of physics, but made the modern world possible. While you may think of quantum mechanics as an abstract concept unrelated to your life, without it there would be no computers, smartphones, or any of the modern electronic devices the world has become so dependent on today. Before we begin, unless you’re already familiar with the electromagnetic spectrum, I recommend reading my post, Why We Are Tone Deaf to the Music of Light before reading this. While it’s not necessary, if you begin to feel lost while reading, it will make this post much easier to swallow.
In 1900 the physicist Lord Kelvin (who is so famous there’s a unit of measurement for temperature named after him) stated, “There is nothing new to be discovered in physics now. All that remains is more and more precise measurement.” As history now tells he couldn’t have been any more wrong. But this sentiment was not one he shared alone; the physics community as a whole agreed. The incredible leaps we (the human race) made in science during the 19th century had us feeling pretty cocky in thinking we had Mother Nature pretty much figured out. There were a few little discrepancies, but they were sure to smooth out with just some ‘more precise measurement’. To paraphrase Richard Feynman (as I so often do), Mother Nature’s imagination is much greater than our own; she’s never going to let us relax.
The shortest summary I can give of quantum mechanics is that all matter exhibits properties of a particle and a wave on a subatomic scale. To find out how we came to such a silly conclusion, let’s begin with one of the above referenced discrepancies which was later called the ultraviolet catastrophe. The UV catastrophe is associated with something called black body radiation. A black body is an ‘ideal’ body that has a constant temperature, or is in what is called thermal equilibrium and radiates light according to that body’s temperature. An example of a body in thermal equilibrium would be a pot of cold water mixed into a pot of hot water and after some time it settles down into a pot with room temperature water. On the atomic level, the emission of electron energy is matched by the absorption of electron energy. The hot, high energy water molecules emit energy to cold ones making the hot ones cool down and the cold ones warm up. This happens until all the molecules reach a consistent temperature throughout the body. Another easily relatable example of a black body is us, as in humans. We and all other warm-blooded mammals radiate light in the infrared spectrum; which is why we glow when we are viewed through an infrared camera.
As you are aware, we cannot see the infrared light we emit with the naked eye because the frequency is too low for our eyes to detect. But what if we were to raise our body’s temperature to far higher than the 98.6 degrees F we’re familiar with? Won’t those emitted light waves eventually have a high enough frequency to become visible? The answer is yes, but unfortunately you’d kill yourself in the process. Let’s use a more sustainable example such as a kiln used for hardening clay pottery. If you were to peer through a small hole into the inside of the kiln, you’ll notice that when it’s not running it is completely black. Light waves are being emitted by the walls of the kiln but they are far too low in frequency for you to see them. As the kiln heats up you notice the walls are turning red. This is because they are now emitting light waves with a high enough frequency for your eyes to detect. As the temperature continues to rise the colors emitted move up the color spectrum as the light wave frequency continues to increase: red, orange, yellow, white (a combination of red, orange, yellow, green and blue produces white), blue and maybe some purple.
Now according to this logic of thinking, and classical physics of the time, if we were to continue to increase the temperature we should be able to push the emitted light from the visible spectrum into the ultraviolet spectrum and beyond. However this would also mean the total energy carried by the electromagnetic radiation inside the kiln would be infinite for any chosen temperature. So what happens in real life when you try to heat this hypothetical kiln to emit light waves beyond the visible spectrum? It stops emitting any light at all, visible or not.
The infinitely increasing dotted represents what the accepted classical theory of the time said should happen in regards to black body radiation. The solid line represents experimental results. Reference these graphed lines from right to left since I refered to light waves increasing in frequency not length.
This was our first glimpse into the strange order of the subatomic world. The person who was able to solve this problem was a physicist by the name of Max Planck who had to ‘tweak’ the rules of classical wave mechanics in order to explain the phenomenon. What he said, put simply, is that the atoms which make up the black body, or in our case the kiln, oscillate to absorb and emit energy. Think of the atoms as tiny springs that stretch and contract to absorb and emit energy. The more energy they absorb (stretch) the more energy they emit (contract). The reason no light is emitted at high energies is that these atoms (springs) have a limit to the energy they can absorb (stretch) and consequently emit. Once that limit is reached they can no longer absorb or emit energies of higher frequencies. However what this implied is that energy cannot be any arbitrary value, as a wave would suggest, when it is absorbed and emitted; it must be absorbed and emitted in distinct whole number values (or in Latin quanta) for each color. Why whole number values? Because each absorption and emission (stretch and contraction) by an atom can only be counted in whole number values. There could be no such thing as a half or a quarter of an emission. It would sort of be like asking to push someone on swing a half or a quarter of the way but no farther. Planck was fervent in stating though that energy only became ‘quantized’, or came in chunks, when it was being absorbed and emitted but still acted like a wave otherwise. The notion of energy as a wave was long established experimentally and was something no one would question—unless you’re Einstein as we’ll see later. How did Planck come to this conclusion? Through exhausting trial and error calculating, he found that when the number 6.63 ×10−34 (that’s point 33 zeros then 663) was multiplied against the frequency of the wave, it could determine the individual amounts of energy that were absorbed and emitted by the black body on each oscillation. When calculated this way, it matched the experimental results beautifully. Whether he truly believed that energy came in quantifiable chunks, even temporary ones, is left to question. He was quoted as stating his magical number (later to become Planck’s constant) was nothing more than a ‘mathematical trick’.
If you’re a little lost, that’s okay. The second discrepancy I’ll address will make sense of it all called the photoelectric effect. To summarize plainly, when light is casted upon many metals they emit electrons. The energy from the light is transferred to the electron until it becomes so energetic that it is ejected from the metal. At high rates, this is seen to the naked eye as sparks. According to the classical view of light as a wave, changing the amplitude (the brightness) should change the speed in which these electrons are ejected. Think of the light as a bat and the electron as a baseball on a tee. The harder you whack the metal with light the faster those electrons are going to speed away. However the experimental results done by Heinrich Hertz in 1887 showed nature didn’t actually work the way classical physics said it should.
At higher frequencies (higher temperatures) of light, electrons were emitted at the same speed from the metal no matter how bright or how dim the light was. This would be like whacking the baseball off the tee and seeing it fly away at the same speed whether you took a full swing or gently tapped it. However as the intensity (brightness) of the light increased, so did the amount of electrons ejected. On the other hand, at lower frequencies, regardless of how intense the light was, no electrons were ejected. This would be like taking a full swing and not even dislodging the baseball from the tee. While it was expected that lower frequency light waves should take longer to eject electrons because they carry less energy, to not eject any electrons at all regardless of the intensity seemed to laugh in the face of well-established and experimentally proven light wave mechanics. Think of it this way, if you were to have a vertical cylindrical tube with an opening at the top end and a water spigot at the bottom end then placed a ping pong ball inside (representative of an electron lodged in metal), no matter how quickly or slowing the tube filled with water (low or high frequency light waves), eventually the ball will come shooting out of the top—obviously with varying velocities according to how fast the tube was filled. If energy is a continuous wave, or stream, ejecting electrons with light should follow the same principles.
Finally in 1905 somebody, that somebody being Albert Einstein, was able to make sense of all this wackiness and consequently opened Pandora’s box on wackiness which would later be called quantum mechanics. In his ‘miracle year’ which included papers on special relativity and the size and proof of atoms (yes the existence of the atom was still debatable at the time), Einstein stated that quantization of light waves (dividing light into chunks) was not a mechanic of energy absorption and emission like Planck said in regards to black body radiation, but a characteristic of light, or energy, itself—and the photoelectric effect proved it! Einstein realized that Planck’s magical number (Planck’s constant) wasn’t just a ‘mathematical trick’ to solve the UV catastrophe, it in fact determined the energy capacity (the size) of these individual light quanta. It was for this he’d later earn his only Nobel Prize.
So how did Einstein conclude this? Well let’s imagine a ball in a ditch. This will represent our electron lodged in metal. We want to get this ball out of the ditch but the only way to do it is by throwing another ball at it. This other ball will represent a quantum of light (later known as a photon). In order to do this you must exert a certain amount of force (energy) to give the ball a high enough velocity to knock the ball in the ditch out. So you call upon your friend to help you who happens to be an MLB pitcher. He’ll represent our high frequency (high energy) light source. Let’s say he can ‘consistently’ throw the ball with 10 units of energy (the units are called electron volts calculated by Planck’s constant times the frequency) and it takes 2 units of this energy just to dislodge the ball from the pit. 2 represents something called the work function in physics. Since it takes 2 units of energy to dislodge the ball, when the ball comes flying out of the ditch it will do so with 8 units of energy (10 – 2 = 8). This energy is called kinetic energy. Now let’s imagine there is ten balls in the pit so we clone our friend ten times (anything is possible in thought experiments). This is representative of turning up the light’s intensity. No matter how many balls are ejected from the pit they all leave with 8 units of energy. This is how we get a result of seeing an electron fly away from the metal at the same speed whether we smacked it or gently tapped it with high frequency light. Seeing your dilemma, your sweet grandmother also wants to help you dislodge balls from this pit. She’ll represent our low frequency light source. Unfortunately she can only throw with a force of 2 units of energy and while she may get the balls to roll a little bit, there isn’t enough kinetic energy left to dislodge them from the pit, no matter how many times we clone her (2 – 2 = 0). This is how we get the result of smacking the metal with a full swing of low frequency light and not see any electrons become ejected.
At the time, Einstein was still nothing more than a struggling physicist working at a patent office and his paper on the photoelectric effect took a while to get traction. However in 1914 his solution was experimentally tested and it matched the results to a tee. Proof that light had properties of a particle was hard to swallow because it had been so definitively proven as a wave during the previous two hundred plus years or so (something we’ll discuss more in part two of this series). In fact many of the forefathers of quantum mechanics, including Einstein and Planck, would spend the rest of their careers trying to disprove what they started. Truthfully, compared to our perception of reality, quantum mechanics is outrageous, but it is an undeniable proven feature of our world. How we figured this out is something we’ll continue with in the next part of this series. Until then, stay curious my friends.
In this post, I’m going to attempt to highlight the basics of the two most successful theories in all of physics, relativity and quantum mechanics. Relativity governs objects on astronomic scales; planets, stars, galaxies and so forth, while quantum mechanics governs objects on subatomic scales; particles smaller than an atom. I’m also going to address why while these theories have been proven beyond a doubt, when combined together they are completely incompatible. A theory that successfully combines the two, a theory of quantum gravity, aka “the theory of everything”, is the holy grail of physics because it holds the key to the origins of our universe.
Relativity describes gravity and the universe in a beautifully simplistic way. Think of nothing more than a ball sitting atop a blanket stretched out between two people. The tautness of the blanket between the two people always remains constant. In the language of physics, this is the gravitational constant. The blanket is the fabric of the universe, called spacetime and as the name suggests, not only is it made of space, but also time. This is why the blanket analogy isn’t exactly accurate, because technically spacetime is four dimensional; three dimensions of space and one of time. However the analogy makes the concept easier to comprehend. The ball represents an object in space. The more massive an object, the more it depresses, or distorts the blanket. The distortion is what is known as a gravitational field. The more massive an object, the greater its gravitational field and ability to attract less massive objects. Say a large ball was placed on the blanket with some smaller ones. The smaller balls would naturally gravitate towards the larger one, like planets in our solar system to the sun.
Now one logical question probably came to mind when visualizing this, what keeps those smaller objects from falling completely into the larger one? Or what keeps our planets in orbit instead of falling into the sun? The answer is angular momentum. Objects in space are always moving. If it wasn’t for the gravitational pull of more massive objects, these objects would travel in straight lines. It is this inertia that keeps them in orbit instead of being pulled in completely. Think of a skateboarder riding the walls of an empty bowl-shaped pool. The skateboarder’s momentum keeps him glued to the walls and if he were to stop, he’d roll into the center of the pool. The planets are doing the same thing. They are riding the walls of the depression the sun makes in the fabric of spacetime.
Gravity keeps everything very orderly and very predictable because it obeys certain laws. This is how astronomers are able to predict the timing of cosmic events with amazing accuracy. Isaac Newton was the first to recognize these regularities and calculate them. He believed gravity was the attractive forces between objects in space. This theory survived for over two hundred years until Einstein realized gravity’s close connection to time. Gravity was not an attraction, but a distortion in the fabric of space, spacetime. And when this fabric is distorted, not only is space distorted but so is time. Time is relative to the observer and how distorted spacetime is at his, or her position. Time moves slower the closer you are to an object of mass because the distortion of spacetime is greater. This is called gravitational time dilation. For example, if you were to stand atop Mount Everest, time would move faster (an unperceivably small amount) for you than say someone standing at sea level because those standing at sea level are closer to the gravitational source (the earth) and deeper within the ‘gravity well’. This has been measured in experiments with atomic clocks at differing altitudes and clocks on GPS satellites have to be regularly adjusted because of this. So technically your head ages faster than your feet.
Gravitational time dilation however only applies to relatively stationary objects. Since you atop Mount Everest and the person standing at sea level are both standing on Earth, you both are traveling through spacetime at the same speed. If you or the other person begins to move, another form of time dilation needs to be applied to receive a correct calculation called relative velocity time dilation. According to relative velocity time dilation, the faster an object moves through spacetime, relative to another object, the slower time moves. Time dilation of relative velocity is much stronger than that of gravity. This can be observed with astronauts aboard the International Space Station. According to gravitational time dilation, because of their higher altitude, the astronauts should age faster than humans on Earth. But because they are moving much faster than humans on Earth, they actually age slower—about .007 seconds per six months. As strange as this all sounds, not only has this effect been proven by atomic clocks, but a measurable difference in brain activity has also been observed.
Gravity and time can be counteracted by velocity and this is a key component to the wackiness of quantum mechanics. As I said previously, according to relativity, the faster an object moves through spacetime relative to another object, the more time slows down for that object because the effects of gravity are less until time and gravity become completely irrelevant at the speed of light. To understand this better, let’s go back to the blanket and balls analogy. Think about one of the smaller balls in orbit stuck at the same speed going around the larger ball. Gravity and angular momentum regulate this orbit and speed. But again, gravity is not a strong force; it can be beaten. Let’s say you take another ball and skip it across the surface of the blanket. The effects of gravity, which include time, are less on the ball you threw than the idly orbiting one. Time, compared to the idle ball, moves slower for the one you threw because gravity doesn’t have the same grasp on it. If you were somehow able to throw a ball at the speed of light it would travel so fast that it would catch up to the point before you ever threw it, like a jetfighter catching its own sound waves. However unlike the jetfighter which can break the sound barrier and outpace its sound, it is impossible for the ball to outpace the speed of light, at least as far as we know. At the speed of light the ball is stuck in the light barrier; its future, present and past existences become piled on top of one another and it has now entered the strange world of quantum mechanics. The ball exists at every time in every place. This is what existence is like within an atom because everything within it moves at, or nearly at the speed of light. This is where the term quantum mechanics comes from. The position and time of particles on a subatomic scale can’t be predicted to an absolute certainty. They can only be ‘quantized’ into approximate probabilities.
Let’s go back to our theoretical ball traveling at the speed of light across our spacetime blanket. I’m going to say this ball is a particle of light, a photon, because a photon is massless and only massless particles are able to travel at the speed of light. The reason being, if the ball had any mass it would distort spacetime and therefore has to play by the rules of gravity and consequently time. As we learned in my previous post, a photon is timeless. It is timeless because it has no mass and without mass, time and gravity have no grasp on you. Even if the ball had massive (pun intended) amounts of energy, it could never reach the speed of light because the energy needed would require an infinite amount of mass. As we also learned in my previous post, mass equals energy. The more energy required, the more mass required so the two counteract each other.
Light from a star being bent by the curvature of spacetime around the sun so that it appears to be in a different position. Einstein’s Theory of Relativity was proven by comparing the known positions of stars with their positions behind the sun during a solar eclipse. Light travels over the contours of spacetime which are created by massive objects within it. The star’s light bends around the distortion the sun’s mass creates in spacetime and appears to be in a different position when viewed from Earth.
However there are places in the universe where even massless matter, like light, has to give into gravity and the worlds of relativity and quantum mechanics come crashing together. Those places are called black holes. Although light can escape the grasp of gravity, it still has to travel along the contours of spacetime that gravity creates. Imagine our theoretical photon ball traveling across the dips and dents of the blanket created by the mass of the other balls. Now imagine if it were to encounter a hole in the blanket; there would be no escape. A black hole, the afterbirth of a collapsed massive star, is something so massive it completely rips through the fabric of spacetime. This is where the theory of relativity fails. The most dreaded symbol in physics is an infinity sign. If your calculations end in infinity, it means your theory has failed. When calculating the gravitational field of a black hole using relativity it ends in infinity; an impossible amount of mass has to be compressed into an impossibly small area, called a singularity. A spacetime singularity is where the quantities normally used to measure gravitational fields become so strong they curve in on themselves. They become looped much like the wacky world of quantum mechanics. Naturally you’d think a combination of the two, a theory of quantum gravity, would solve this. However it produces an answer that is infinity plus infinity for an infinite amount of times. It is an infinitely bigger failure than relativity at predicting the mechanics of a black hole. String Theory is the closest we’ve come to solving this, but it has yet to be definitively proven. If we could find a successful theory of quantum gravity, we’d most likely discover the origins of our own universe. The reason being, our universe has been continually expanding for the last 13 billion years from a singularity much like the one found inside a black hole. Our universe could be the answer for what’s inside a black hole—well at least one black hole. Pretty trippy to think about, right? Until next time, stay curious my friends!
One of my favorite stories in all of physics is the story of sunlight because it touches on such a wide range of concepts. I apologize for the length of this post, but I guarantee you’ll be enlightened on many terms you probably hear thrown around a lot, but not a lot of people understand. Also, we learned in my previous post some of the important uses of light, but didn’t address the most important use of all, life!
Sunlight’s story, along with almost everything in the universe (we’ll ignore something called dark matter for now), begins with a hydrogen atom. Hydrogen is the most elementary and abundant element in the universe, hence the reason it is element one on the periodic table. Also because it’s comprised of one positively charged particle called a proton, which makes up its nucleus, and one negatively charged particle called an electron, which orbits around that single-proton nucleus. Within the sun, or any star, there is a process called nuclear fusion which transforms hydrogen into all 92 elements found in nature. Every grain of matter that makes up our physical world is forged in the heart of stars and is released when they begin to die. Not all stars produce all 92 elements however, like our sun will never get hot enough to fuse enough atoms together to produce heavy metals like gold. When I say heavy, what I am referring to is the element’s mass. The more sub-atomic particles shoved into an element’s nucleus, the heavier it is. Stars of different sizes produce different elements, but all stars begin with fusing hydrogen into helium as our sun is currently doing.
Within the sun’s core, hydrogen atoms are sped up from high amounts of energy, or heat, created by the force of the star’s mass on itself and collide at very high speeds, fusing them together to make helium. The sun has to smash four hydrogen atoms together to make one helium atom. The radioactive elements created in the steps in between are called hydrogen isotopes. Two hydrogen atoms make the stable isotope deuterium, three, the unstable isotope tritium, and four a helium atom. The difference between a stable and an unstable isotope is the even pairing of protons and neutrons (we’ll get to what a neutron is soon) in the nucleus. An even pairing, like one proton and one neutron (deuterium), is stable, but an uneven pairing, like one proton and two neutrons (tritium) is not and eventually falls apart into stable isotopes because it is too energetic to stay together. This ‘falling apart’ is known as radioactive decay.
Two hydrogen atoms make the stable isotope deuterium, three, the unstable isotope tritium, and four a helium atom.
If you’re a fan of The Simpsons, you may remember the Springfield baseball team was called The Isotopes. This was in reference to the town’s nuclear power plant, in which a forced and more violent version of this process occurs called nuclear fission. Typically uranium nuclei are loaded up with extra neutrons until it reaches what is called critical mass. Once critical mass is reached, the nuclei split and large amounts of energy are released because they can’t hold this new influx of neutrons. It’s kind of like your friend who drinks too much at a bar then spews all over the place. This neutron ‘spewing’ is what provides us with electrical power. While the process releases energy, it also leaves varying forms of unstable uranium isotopes that decay naturally into stable isotopes over sometimes hundreds of years. This is because uranium is such a heavier element in comparison to hydrogen, which its isotopes decay rather quickly. These radioactive leftovers are still highly energetic and emit damaging gamma and x-ray waves (we learned what these were in my previous post) and that is why containment is so crucial. My apologies for this nuclear fission tangent, but one should know the difference between fusion and fission. Fusion brings atoms together, fission rips them apart.
So back to the story of sunlight. When the sun does finally manage to smash four hydrogen atoms together, two of the hydrogen’s protons lose mass in the process and become neutrally charged particles called neutrons, making a total of two protons and two neutrons in the new helium nucleus with two orbiting electrons, one for each proton. The expelled proton mass, which eventually will become our beloved sunlight, is given off as energy in the form of highly energetic electromagnetic radiation (a.k.a. light) known as gamma rays. This is an excellent example of Einstein’s famous equation for energy, E=mc2, at work. What this equation says is mass (m) can be converted to energy (E). If you’ve ever tried to lose weight, the same concept applies. You’re trying to convert your mass into energy to lose it. However things on a quantum level work in funny ways. The neutron instead of being less massive actually becomes more massive than it was when it was a proton. This can be blamed on particles within protons and neutrons called quarks and how they behave; something I’ll leave for another post. The ‘C’ part of the equation stands for the speed of light constant which is just something that needs to be added formulaically in order to receive a correct calculation and we’ll get to why later.
We learned in my previous post that electromagnetic radiation is made of particles called photons. These newly created gamma ray photons are at first far too dangerous for earthly consumption. However after tens of thousands of years of being passed around between densely packed atoms within the sun, the photons tire out a bit until they become less energetic visible light photons, or what we call sunshine. Even traveling at the speed of light, photons can take up to a million years to escape the sun; a distance of 432,000 miles from core to surface. While this may seem like a long distance, compare it to the 93 million miles photons travel in only 8 minutes and it becomes apparent how abated those photons are by being continually absorbed and emitted by the soup of atoms within the sun. However once they hit the empty vacuum of space, they have a straight shot to Earth.
When photons finally enter Earth’s atmosphere, some of them are absorbed by tiny pores on plants’ leaves called stomata that convert those photons into chemical energy. This is done by the synthesizing of hydrogen atoms from water in the plant with carbon dioxide in the air to create sugars. This process, I’m sure you’re familiar with, is called photosynthesis. Since plants only use the hydrogen from water, they emit the remaining oxygen as a waste product and we literally breathe their shit. The sugar is stored and later converted into kinetic energy to allow the plant to function. This sugar however can be transferred to a creature that eats the plant and a creature that eats that creature and so forth. Animals (including us) extract energy from these sugars by reacting them with the oxygen they breathe and exhale the remaining carbon dioxide from the sugars so that another plant can use it to create more sugar and oxygen for them to consume.
So next time you look up at the sun (not directly!), think about what’s going on inside there. Think about everything nuclear fusion gives you; air, food— the very matter you’re made of, and say thanks. And as the sunlight warms your skin, think about the tens of thousands of years it took for those photons to reach it. And here’s another interesting fact to blow your mind on; for those photons, you are their entire existence! Well at least within our idea of existence. This is where the ‘C’ (the speed of light constant) in E=mc2 comes into play. The photon, which is energy, travels at the speed of light and that is why that speed needs to be figured into every calculation for energy. It is ‘constant’. And according to Einstein’s theory of relativity, time slows down the faster you move relative to another object until it completely stops at the speed of light. The photon’s time, relative to ours, doesn’t exist. The photon is considered timeless . . . well at least until it’s brought into our reality when you absorbed it as heat. I’ll segue this into my next post which will be on the theory of relativity and quantum mechanics. Until then, stay curious my friends!
When I sit down at a piano I see a lot more than keys; I see an immense sonic spectrum ranging from sound frequencies of 27 hertz to over 4,000. A hertz, if you’re unaware, is one cycle of a wave per second, in this case a sound wave. When I press a C4 key, a vibrating string is displacing waves of air molecules at 260 times per second against my eardrum and my brain interprets those fluctuations as a middle C. And our amazing brain can do that with a range of frequencies about five times the size of a piano’s. It’s too bad our eyes are so limited in comparison.
While a human eye is an incredibly complex organ, it is severely tone deaf when it comes to the music of light. To understand what I mean by this, we must first change how you view light. On a sub-atomic level, light is made up of little spiraling packets of energy called photons. When these twisted little guys interact with one another they dance in a synchronized wave pattern and form light waves. This is how particles behave on a quantum-scale; they exhibit features both of a particle and of a wave. The varying energies of these photons, or how fast the little guys are spinning, produce differing light wave frequencies that our eyes detect as colors. For example the light waves that make up the color red cycle slower than the light waves that make up the color blue.
Just like there are sounds we can’t hear, either the sound waves are too fast or too slow for our brain to detect, there are also colors, or light waves, we can’t see. Of course just because we can’t see them doesn’t mean they don’t exist. In fact we interact with these colors all the time. When you tune into a radio station, you’re tuning into a signal being transmitted over a light wave called a radio wave. A radio station such as 95.5 KLOS is broadcasting their signal over a light wave with a frequency of roughly 95.5 megahertz; that’s 95.5 million oscillations per second, which is actually quite low. The lower the frequency, the longer the wavelength. That is how radio signals travel over long distances. Infrared light waves, just outside the lower end of visible light, is what your body emits as heat and changes the channel on your television when they are transmitted from your remote. If you’ve ever had a sunburn, that is the result of light waves just outside the higher end of visible light, called ultraviolet waves, overexciting the DNA that creates your skin tissue. If you’ve ever had an x-ray image taken, that is an inverted visual display of the high frequency waves, known as x-rays, which were shot through your body that weren’t absorbed by dense objects like your bones. A low energy wave called a microwave excites molecules of water inside your food to produce heat when you zap your leftovers. These are all things you’re familiar with and they all involve light, or in the language of physics, electromagnetic radiation.
Now just to give you a perspective of how limited our eyes are at detecting light I’m going to transpose the electromagnetic spectrum, the known frequencies of light from 1,000 hertz to one zettahertz (that’s 1 with 21 zeros after it), onto the sound frequencies found on an 88-key piano (this sounds more impressive than it actually is—only simple algebra involved). Radio waves, like the ones radio and TV stations use, take up the lowest 26 keys from A0 to A#2. Microwaves take up the next 16, B2 to D4. Infrared waves the next 14, D#4 to E5. Then visible light, which makes up our entire visual reality, takes up only one key, F5. The next eleven keys, F#5 to E6 are ultraviolet waves. The following ten, F6 to D7 are x-ray waves and the remaining ten are called gamma waves; D#7 to C8.*
*These proportions aren’t exact because where one type of wave begins and ends is debatable and I had to approximate for demonstration purposes. But it does accurately show the limited perspective of our vision.