The Party Trick Physicist

The Layman’s Guide to Quantum Mechanics- Part 2: Let’s Get Weird

Post author By Bradley Stockwell
Post date February 26, 2015
1 Comment on The Layman’s Guide to Quantum Mechanics- Part 2: Let’s Get Weird

By Bradley Stockwell

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 20^th 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 19^th 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 video here.

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.

Tags analog, color spectrum, digital, electromagnetic radiation, electromagnetic spectrum, electron clouds, electron orbits, electron shells, Erwin Schrodinger, light waves, Louis de Broglie, niels bohr, particle physics, quantum mechanics, spectrometry, technology, Werner Heisenberg, Wolfgang Pauli

particle physics physics science

The Layman’s Guide to Quantum Mechanics- Part I: The Beginning

Post author By Bradley Stockwell
Post date January 8, 2015
1 Comment on The Layman’s Guide to Quantum Mechanics- Part I: The Beginning

By Bradley Stockwell

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 19^th 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.

Tags Albert Einstein, black body radiation, Einstein, electromagnetic radiation, light, light waves, Max Planck, particle physics, photoelectric effect, photon, photons, physics, quantum mechanics, The UV Catastrophe, wave particle duality, wave physics

Astronomy Astrophysics cosmology science

Jupiter and Her Moons: Our Key to The Cosmos

Post author By Bradley Stockwell
Post date November 19, 2014
No Comments on Jupiter and Her Moons: Our Key to The Cosmos

By Bradley Stockwell

Everyone at some point in their lives (or so I hope) has experienced the wonderful reverence of stargazing. That allure to look upon the heavens and ask ‘what the hell is that?’ seems to be what makes us human; what separates us from the almost nine million other life forms we share this planet with. The night sky has inspired legends, religions and philosophies; our ancestors used it to navigate and mark the passage of seasons and animal migration patterns. But in our present day, the union between us and our big starry-spotted buddy has faded in some sense. Its full glory is now often hidden behind city lights and the petty dramas of our daily lives or the ones we find on television.

While I too am not immune to getting caught up in the rigors of daily life or the latest Doctor Who episode, it’s not too often you’ll find me under a clear night sky without my neck craned upwards. There’s something viscerally exciting to me about seeing the cosmos nude. This is why instead of grabbing a beer and the television remote after a stressful day, I’ll typically still grab that beer but I’ll reach for my telescope instead. While admittedly this may seem like a nerdy pastime, I’m going to try my best to convince you it’s not.

If you’ve ever traveled to a foreign land, the first time feels almost as if you’re visiting an alien planet. Suddenly your perspective of the world increases and you come back home changed. Looking through a telescope for the first time is much the same. I know the first time I saw Jupiter or the magnificent rings of Saturn suddenly our place in the solar system became very real. You can read and study about something all you want, but it’s not until you experience it firsthand that it truly becomes real.

The winter sky is my favorite time for stargazing, primarily because the most important astrological sight to the history of astrophysics and arguably modern science is visible: Jupiter and her moons. This sight has been the key to opening up the cosmos and has been crucial in defining our universe. The best thing is it doesn’t require a high-powered telescope to see it either. In fact I recommend using an entry-level telescope (no more than $150) to see Jupiter and her moons much like the great Galileo Galilei did for the first time on January 7, 1610.

When Galileo first pointed his homemade telescope towards Jupiter, he described seeing a linear arrangement of three fixed stars, two to the east and one to the west, cutting through the center of the planet. However the following night all three stars were to the west. Then three days later one disappeared and six days later a fourth one appeared. At first he was baffled, but then it dawned upon him that these were not stars but were orbiting moons! They were in fact Jupiter’s four largest moons, Io, Europa, Ganymede and Callisto, which now bear his namesake as Galilean moons. The discovery would be the beginning of a great change in science, but it did not come without challenges.

At the time, the discovery was highly controversial. You can even say Galileo was putting his life at risk by proposing it. A planet with smaller orbiting bodies was in direct offense to the longstanding view of the Catholic Church which placed Earth at the center of the universe and all celestial bodies orbiting around it. The church had a long history of burning ‘supposed’ heretics at the stake for challenging this model. But upon further observations by other astronomers, the evidence was irrefutable. The church eventually conceded and accepted a model proposed almost 70 years earlier by the astronomer, Nicolaus Copernicus. The model, which Copernicus waited until he was on his deathbed to present in fear of being labeled as a heretic, placed the sun, not the earth, at the center of the universe. Obviously this model, now called the Copernican model, would continue to be updated, but it would lay the foundation for others like Johannes Kepler, Isaac Newton, William Hershel, Edwin Hubble and Albert Einstein to further define our universe. Galileo’s discovery would help ignite a scientific revolution during The Renaissance and finally break down the cage in which the Catholic Church put scientific research in.

Jupiter and her moons would again make history when the astronomer, Giovanni Domenico Cassini, observed them between 1666 and 1668. He was the first to notice discrepancies in their orbits. To explain these discrepancies, he theorized that light coming from them must have a finite speed. Shortly after, another astronomer, Ole Romer, took this concept further when he realized that indeed the time it took for Io, the innermost Galilean moon, to orbit was shorter when Earth was closer to Jupiter and longer when Earth was farther away. From these observations, Romer was able to calculate the speed of light; approximately 186,000 miles per second. Putting a speed limit on light would forever change how we view the universe for when we peer into the cosmos we now know we are looking back in time! In fact we can now look at light as far back as the beginning of the universe. A telescope is not only a ship with which to sail the cosmos but also time.

In addition to aiding our view of the universe, Europa, the second innermost Galilean moon, may be a likely candidate for harboring alien life! This moon is covered in a thick layer of ice made of water. Because of heat generated from the contraction and expansion of the moon by Jupiter’s powerful gravitational force, many astronomers believe there is liquid water below the surface which could possibly host microbial life.

Jupiter and her moons is but one of the many wonders awaiting your gazing eyes. Although I am not religious, spying through my telescope is the closest thing I have to prayer. It gives me a better vantage point on life and puts things, or should I say the earth, into a humble perspective. While I’m certain life exists somewhere else in the universe, the right conditions to produce it are rare; and intelligent life, extremely rare. In fact from research and astronomical observations alone, it’s not a stretch to say that out of the hundreds of billions of other planets in the galaxy, Earth may be the only one with advanced life. Granted our galaxy is but one among 350 billion in the observable universe, but this perspective suddenly increases the value of our existence. How lucky are we that the winds of energy that control the cosmos happened to deposit matter in the form of the human race? Regardless of how you believe that came to be, there’s no need for theology to tell you how special your existence actually is. I think if we as humans realized this more, we’d start behaving differently. We’d start looking out for ourselves and this world better because right now as a species we don’t particularly have a universal view on life. It’s rather shortsighted in my opinion. Well until next time, stay curious my friends!

Tags astronomers, Astronomy, Astrophysics, Callisto, Cassini, Copernicus, Eurpoa, Galilean moons, Galileo, Galileo Galilei, Ganymede, Giovanni Domenico Cassini, Io, jupiter, Nicolaus Copernicus, Ole Romer, Romer, stargazing, telescopes

Brain Science business Business Science entrepreneurship Health Life Lessons small business

5 Things That Separate Successful People From Everyone Else

Post author By Bradley Stockwell
Post date November 11, 2014
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By Bradley Stockwell

Marketing Director Merchant Capital Source

As I’ve said several times before, bettering your business begins with you. Every investment in yourself is an investment in your business. If you’re looking to transform yourself into a successful business owner and entrepreneur, you need to begin acting and thinking like one—and it’s not easy. In some cases it can mean some major life and brain hacking, but once you’ve made these transformations, you’ll wonder how you ever operated any other way. If you don’t know where to begin, you’re in luck. After reading hundreds of articles, biographies, advice columns and using myself as a guinea pig, I’ve narrowed down the five essential things successful people do that others don’t. After all this research and testing you’ll be surprised to learn there’s no great secret. Success comes down to five simple things that you most likely know you should already be doing.

1. They Read More & Watch Less Television

All great thinkers and innovators read and I can’t express the difference it’s made in my life personally as someone who was once a very casual reader. If there’s one thing you take away from this post, I insist it is this. While it may be hard to start, once you’re in the habit you’ll find it’s much more fulfilling than other forms of media because neurologically it’s the healthiest thing you can consume. Numerous studies have shown reading requires, stimulates and strengthens several regions of the brain.

Television on the other hand has shown to decrease brain activity in regions that are particularly important to business owners. When watching television, brain activity switches to the right side of the brain. This is significant because the left side of the brain is responsible for logical thinking and critical analysis. It also decreases activity in your frontal lobes which is responsible for decision making. Brain scans have shown that when people watch television brain activity mirrors that of someone under hypnosis. Maybe all those rumors of television being used as a brainwashing device have some merit. While I’m not saying to stop watching television altogether it’s good to practice moderation and be selective with the programs you consume.

2. They Sleep

While it may be tempting, and sometimes necessary, to tack a few more hours onto your busy day you should calculate the repercussions sleep deprivation can have on productivity, not to mention health.

Studies have shown that reducing sleep by even 1.5 hours for one night can reduce flexible decision-making and innovative thinking by as much as 32%! Also when sleep-deprived your perceived exertion level for the same tasks done while fully awake increases by 17-19%.

I myself have read and tried many methods on supposedly how to operate on less than six hours of sleep and found unless you’re superhuman, they simply don’t work. For me personally, sleep is essential to my creative process. Some of my best ideas have come from my dreams or middle-of-the-night epiphanies. While the amount of sleep needed varies for everyone, sacrificing it for productivity, in my opinion, is counterproductive. So sleep—you’ll be healthier, happier and much more successful.

3. They Learn

Although you may not be in school anymore, there’s no reason why learning should stop. In fact I’ve found learning to be much more enjoyable outside the confines of formal education because I can learn what I want, when I want and how I want. And it doesn’t always have to be a business-related education; learning anything new creates new neural pathways in the brain and as I’ve said previously, the more neural pathways your brain has available the better it works.

Granted this doesn’t mean learning about the latest celebrity gossip is just as valuable as learning how to play an instrument. I’m sorry to tell you, but if it doesn’t feel like your brain is stretching it’s not. The reason why something is perceived as challenging is it requires you to alter your way of thinking, or neurologically speaking, to create new neural pathways.

While this is difficult, finding something you’re curious about is a great motivator. And you’ll find the more you challenge yourself, suddenly the easier and more enjoyable it becomes to learn new things. Intelligence in my opinion is much more an exercise than a gift. While you may think you don’t have enough time to educate yourself, I began dedicating just my lunch break to learning and in the last year I’ve learned how to play the piano and taught myself enough courses in physics to keep a regular blog on it. The world is a wonderful and mysterious place and I encourage you to poke and probe at it as much as possible.

4. They Write

Something you’ve probably noticed if you keep up with business publications is that most successful business owners and CEO’s write. Whether it’s in a journal, book, blog, or guest article, they do this for two reasons. One being that writing is simply a great cathartic release and the other to retain information they’ve learned.

Writing is great for your mental and emotional health. Keeping a journal can give you a safe place to vent stress and process problems. Studies have also shown it improves creativity, self-esteem and memory retention. Like reading, this can be difficult to start but I think what most people get caught up on (or at least I did at first) is that you have to make an entry every day for it to be effective. I’ve found that even one journal entry a week can suffice, however I tend to write more when my life is stressful or eventful.

Writing is also an essential adjunct to learning. It requires you to not only recall something you’ve learned but to also process and analyze its applications. In my opinion, this makes the difference between knowing and understanding something. As Einstein once said, “Any fool can know; the point is to understand.” This is the primary reason I keep regular business and physics blogs whether or not anyone actually reads them.

5. They Exercise & Eat Well

If you want to be a highly productive individual you’re going to need the right fuel. While most people say they don’t have enough time to accomplish the tasks they intend to (so they do counterproductive things like not sleeping enough), the truth most likely is they don’t have the energy to. Just like a race car can’t run off low octane fuel, successful people cannot run off low-grade food. Like any machine, your body is an energy processor and if you input high quality energy, the greater your output will be. As with all these changes it’s difficult at first, but once you make a habit of it you’ll find you’ll actually start craving healthy food over junk.

The second part of this is making your body as energy efficient as possible and that means working out. Once again, don’t get hung up on setting unrealistic goals and think you need to work out every day. You’ll be amazed at what just a little walking, or bicycle riding can do. If you’re close enough to work to commute by these methods, do so. Beginning and ending your day with a little exercise can do wonders.

The biggest nemesis to productivity is stress, hormonally known as cortisol. Your body releases cortisol when stressed and without exercise to burn that cortisol, stress compounds on itself and leads to impulsive behavior and anxiety. Exercise also releases endorphins which help you rationalize problems and increases optimism, energy and memory retention—not to mention you’ll live longer. Also while exercise may be physically exhausting, mentally it is relaxing. Treat it as your alone time to distress from work and home life.

Tags business, business advice, business management, business owners, Einstein, entrepreneurship, happiness, healthy eating, learning, life advice, mental health, reading, sleep, small business, small business ownership, smb, startups, television, writing

business economics entrepreneurship small business

How The Great Recession is Changing American Business For The Better

Post author By Bradley Stockwell
Post date October 8, 2014
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By Bradley Stockwell

Marketing Director Merchant Capital Source

It’s true; money doesn’t make the world go round—conservation of angular momentum does. However, history doesn’t mark itself by Earth’s rotations but by the movements of the economies that create it. So yes, with this perspective, the cyclical movements of history are governed by money. As a physics student, I enjoy drilling things down to their foundations and at the bedrock of every change in history you’ll typically find the economy. Trends, fashion, technology, music, art, politics, war—are all reflections of the economy. Why is that? Because we as a general society identify ourselves with the way in which we earn a living and when that changes, it has a trickledown effect on everything else in our lives.

The recession marked the end of one era and the beginning of a new and (call me optimistic) better era. Adapting to the recession emboldened us to step out and find smarter ways of making a living; to finally change the many things that led us into the recession anyhow. Thanks to the internet, more people are starting businesses and launching new ideas now than ever. Online crowdfunding has given a platform on which to present and fund ideas and the online business is a cost-effective solution to sell that idea. Great things happen when massive amounts of people start pursuing their dreams—new industries are created (including the alternative lending industry in which I’m currently employed in), business practices are improved and technology advances. In the last five years there’s been an explosion of entrepreneurs and small business owners—many of whom were victims of the recession, who are shaping a better and smarter economy. Thanks to social networking, there’s been a great shift towards the empowerment of the individual; whether it be the products we buy, the media we consume, or most importantly the jobs we hold—every facet of our lives is now becoming individualized. Companies are beginning to see the benefit of having an open ear to not only their consumers, but also their employees, giving rise to a new type of entrepreneur; the intrapreneur. In fact entire business models are now shaped around the intrapreneur such as the ‘sharing industries’. Companies like Uber and Airbnb are allowing people to use their existing resources, like their car and home, to earn a part time or full time living; helping the economy boost itself on its own terms. Not to mention they are also improving the taxi and hotel industries by forcing them to adapt to this new influx of competition. These symbiotic business models, where the company, the employees and consumers all benefit, are precursors for how I think American business will look in the next ten years.

It’s an exciting time to be alive. I believe we are at the beginning of a great change in humanity because of changes happening in the business world. As I stated earlier, when the economy changes everything else soon follows. We’re starting to realize the value of open-sourced sharing of information and the empowerment of individuals. While these seem like conflicting concepts, they’re not. Both need each other in order to create a competitive atmosphere and we, especially as Americans, know competition drives advancement. Elon Musk, CEO of Tesla Motors, SpaceX and Solar City, is the embodiment of this idea and I believe the archetype for the 21^st century CEO. Every patent Tesla Motors held was recently released for ‘free use’ to drive the progression of electric car technology. Not only will this certainly spur the success of Tesla, but it will also contribute to the success of a recovering automobile industry and will combat the now present threat of climate change due to carbon emissions. Not to mention Tesla’s direct-sales model is also trying to kill everything we hate about buying a car from a dealership. See everybody wins—the company, the industry, the consumer and humanity.

Astrophysics Biology chemistry Life Lessons particle physics physics religion science spirituality

The Spirituality of Science

Post author By Bradley Stockwell
Post date October 3, 2014
3 Comments on The Spirituality of Science

colonoscopy

An obviously very doped-up me after my colonoscopy

By Bradley Stockwell

To spare you of the intimate details, I’ll just say recently I’ve had some ‘digestive issues’. Two weeks ago I had a colonoscopy to check out these issues. Although I realized the possibility that they may be caused by something serious such as cancer, when my doctor presented me with that reality, it dug in a lot more than I thought. Fortunately, it seems this world is stuck with me a little longer for all my biopsies came out okay. However during the five days in which I had to wait to hear these results, I couldn’t help but contemplate my own mortality and what death means to me as an atheist.

For lack of a better label, I am an atheist but I am not spiritual-less. I find a deep sense of sanctity and humility in the scientific observations of nature. To make clear, this post is not intended to degrade or disprove anyone’s religious faith. The world is richly diverse in beliefs, cultures and opinions and I think that’s a necessary and beautiful thing. What I do have a problem with is the contention surrounding the subject of faith and I in no part want to contribute to it. The reason I love physics so much is it seeks to find unity amongst division and I apply that same philosophy in all facets of my life. Simply, I’m presenting how I sleep at night without believing in a god(s) or an afterlife because it is an honest question I’m frequently asked.

The primary source of my peace of mind comes from the laws of thermodynamics which describes how energy behaves. The first law, the conservation of energy, states energy cannot be created nor destroyed. This law was exampled in a previous post, Flight of The Timeless Photon, on how the photon (aka energy) is transformed from hydrogen proton mass into the life-providing sunshine we all know. The energy we consume, and consequently life, is all sourced from the sun. And the sun’s energy is sourced from the matter within the universe and to find out where the universe’s energy is sourced, we would’ve had to been around during The Big Bang. However according to multiverse theorists, it’s a good chance that it may have come from the matter of a previous universe which was chopped up and scrambled by a black hole into energy. Regardless, the point I’m trying to make is energy is immortal. It is the driver of the circle of life not just here on Earth but in the entire universe. As special as you think you are, you are nothing more than a temporary capsule of mass for energy to inhabit. Death is nothing more than a dispersion of this energy and this is what I take consolation in. When I die, all the energy that was me, my personality—my soul, my body even, still remains in this world. I’m not gone; just less ordered. I am a part of what keeps the arrow of time moving forward as the universe naturally moves from a higher state of order towards a lower—the second law of thermodynamics.

The universe is very cyclical. Life and death are just different stopping points on a grand recycling process. Matter, like our bodies, is created and recycled and energy, like our souls, is immortal and transferred. If you’re familiar with Dharmic beliefs, this probably sounds familiar. It’s funny how the world’s oldest religion, Hinduism, seemed to grasp these concepts thousands of years before science did. While I’m not a practicing Hindu, nor do I plan to be, if forced to choose it would be the closest to my belief system due to the many correlations I find between it and science. One correlation I was most awestruck by was the concept of Brahman to the laws of thermodynamics (aka the laws of energy) mentioned above. According to belief, Brahman is the source of all things in the universe including reality and existence. Everything comes from Brahman and everything returns to Brahman. Brahman is uncreated, external, infinite and all-embracing. You could substitute the word energy for Brahman and get a simple understanding of the applications of the first and second laws of thermodynamics.

If you can’t fathom the thought of an afterlife as some form of your current self, I can understand that. Once again I’m not here to convince you differently, I’m just presenting my viewpoint. However in regards to the value of life, I do hope to convince you that there is no deeper appreciation than through the eyes of science. I only stress this to debunk the perpetuated myth that science somehow devalues the beauty of this world by picking it apart. Once again, the reason I love physics is it widens the perspective of my existence through unifying the universe’s many diverse creations and movements. It connects me to the infinitely larger cosmos above yet also to the infinitely smaller universes below. I have an atomic connection to the stars, a chemical connection to the earth, a biological connection to life and a genetic connection to my fellow humans. When you see the world on so many dimensions, I can personally attest that suddenly everything becomes very interesting. Even the things we don’t give much thought to, like sunshine, weather, the way in which water ripples, or why your friend’s beer overflows when you smack the top of it with yours, become regularly appreciated with a new sense of awe and curiosity. The world becomes much more absorbing than anything a smartphone or television can provide and you find yourself wanting to experience everything it can offer. There’s no greater feeling than the intercourse between knowledge and experience. This perspective is perfectly captured by one of my idols, the great physicist Richard Feynman.

“I have a friend who’s an artist and has sometimes taken a view which I don’t agree with very well. He’ll hold up a flower and say “look how beautiful it is,” and I’ll agree. Then he says “I as an artist can see how beautiful this is but you as a scientist take this all apart and it becomes a dull thing,” and I think that he’s kind of nutty. First of all, the beauty that he sees is available to other people and to me too, I believe. Although I may not be quite as refined aesthetically as he is … I can appreciate the beauty of a flower. At the same time, I see much more about the flower than he sees. I could imagine the cells in there, the complicated actions inside, which also have a beauty. I mean it’s not just beauty at this dimension, at one centimeter; there’s also beauty at smaller dimensions, the inner structure, also the processes. The fact that the colors in the flower evolved in order to attract insects to pollinate it is interesting; it means that insects can see the color. It adds a question: does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting questions which the science knowledge only adds to the excitement, the mystery and the awe of a flower. It only adds. I don’t understand how it subtracts.”

When I finally do say goodbye to this world, I hope my friends and family will realize this is not actually the case. Everything that was me is still very much a part of this world, just partaking in a different dimension of it. The energy contained within my body will go back into the earth so that it can provide new life to the flora and fauna which kept me alive as I dined on them throughout my own life. Every joule of energy that was me will be released back into this world to live life anew. And will the unique combination of matter the winds of energy deposited as Bradley Stockwell be forgotten? Well I hope I will have done something impactful enough to be remembered by history, but if not, I can always depend on my beloved light particle, the photon, to ensure my existence will mean something. Explained in detail in my previous post, A Crash Course in Relativity and Quantum Mechanics, according to relative velocity time dilation, the photon’s existence is timeless relative to ours because it moves at the speed of light. A funny thing happens to time at the speed of light—it ceases to exist, at least relative to our perception of time. That is of course until I interrupt this so-called photon’s path by absorbing it as heat and become that photon’s entire existence; forever altering the universe. And this is not the only way the photon will preserve my existence. I of course don’t absorb all the photons I come into contact with—some of them bounce off me and are collected in the photon detectors (aka the eyes) of my friends and family members. These photons then create electromagnetically charged webs of neurons, better known as memories. Well until next time, stay curious my friends!

Astrophysics particle physics physics science

A Crash Course in Relativity and Quantum Mechanics

Post author By Bradley Stockwell
Post date September 9, 2014
2 Comments on A Crash Course in Relativity and Quantum Mechanics

BH_LMC2

By Bradley Stockwell

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.

spacetime

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!

Tags Albert Einstein, angular momentum, black holes, Einstein, general relativity, gravity, light waves, photons, quantum mechanics, relativity, spacetime, spacetime singularities, special relativity, speed of light, string theory, the universe, theory of relativity, time dilation

Biology chemistry particle physics physics science

Flight of the Timeless Photon

Post author By Bradley Stockwell
Post date August 14, 2014
2 Comments on Flight of the Timeless Photon

By Bradley Stockwell

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!

Tags Einstein, electromagnetic radiation, elements, helium, hydrogen, isotopes, light waves, nuclear fission, nuclear fusion, photon, photosynthesis, quantum mechanics, quarks, radioactive decay, relativity, stars, the sun, uranium

particle physics physics science

Why We Are Tone Deaf to the Music of Light

Post author By Bradley Stockwell
Post date August 1, 2014
5 Comments on Why We Are Tone Deaf to the Music of Light

By Bradley Stockwell

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.

Tags color spectrum, electromagnetic spectrum, gamma rays, infrared, light, light wave, light waves, microwaves, music, music physics, music science, photon, piano, radio waves, sound frequencies, sound waves, ultraviolet, visible light, x-rays

business Business Science entrepreneurship Health Life Lessons

Why You Are More Valuable Than Any Salary

Post author By Bradley Stockwell
Post date March 11, 2014
No Comments on Why You Are More Valuable Than Any Salary

By Bradley Dowies

Marketing Director Merchant Capital Source

Even with surmounting evidence of the importance of a good social life, getting exercise and decreasing stress, people continue to prioritize their salaries over their health. However when you apply monetary values on good health it becomes obvious that money is far from everything. A study from the Journal of Socio-Economics used “shadow pricing” (an economics term to estimate the price paid for increments of addition production) to estimate monetary values of potential life satisfaction gained by interactions with friends and family. Here’s a breakdown of what the study found:

Going from poor to excellent health: +$463,170/ year

Having a better social life: +$131,232/ year

A happy marriage: +$105,000/ year

Seeing friends and family regularly: +$97,265/ year

That means you could potentially be missing out on $796,667 worth of life satisfaction due to your time and social life consuming job. Now ask yourself again, is that long commute, or that 60 hour workweek really worth that high salary? Despite numerous scientific studies in support of this, I personally had to learn on my own and thought it more potent to share my story than to state studies.

I graduated from college in 2009 in the midst of the “Great Recession” at a time when the job market had been decimated. Although my degree was in advertising and I had intended to enter the field, I was left to make suffice with what was available, and what’s available after an occupational apocalypse? The cockroaches of the professional job market: sales positions. It seems no matter how bad things get, there’s always a need for a good salesperson. I had student loan debt and bills to pay, so at the time I felt I had no other choice. Fast forward two years and I had found financial success in my unintended sales career; I had been promoted twice and had a healthy managerial salary. While my finances were healthy, I was not. I had gained 20 pounds, I was working on average 55 hours a week and had to work most Saturdays. Most days I’d have to skip my lunch, or work while eating it and I was drinking heavily on the weekends. This was the type of atmosphere that was bred at my job; you give your life to the company, otherwise there’s hundreds of other saps willing to replace you because there’s nothing else out there and you should consider yourself fortunate to even have a job.

In late 2011, I had a life changing moment, or what I called my quarter life crisis. I had to ask, “Is this really what life is supposed to be?” After 18+ years of schooling, you get a job and learn to do one thing very well and do it everyday until you either retire, or die. While I had gained financial independence, I had lost my life in the process. I was good at my job, but my life was stagnant. I was no longer learning; no longer challenged and the adult world seemed empty. This was when I realized money would never bring me happiness, only buy the drinks I needed to cope with its misery.

The tipping point came when I was offered a very lucrative position in medical device sales in which I’d be making the coveted six-figure salary at 24 years old. After a long life contemplation I decided not only to decline the position, but to quit my career in sales altogether. Although the job offer was admittedly very tempting and everyone thought I was crazy, I knew I’d be committing my future to a life I never intended to have. I wanted to be in advertising and marketing because it was challenging to me; it was my passion, my joy; it fulfilled me.

After quitting I moved in with my grandmother and took several part-time jobs and internships throughout 2012. Also against the advice of many, I took the savings I had accumulated and traveled to Europe—something I told myself I would always do in my twenties. The trip only galvanized my commitment to the value of my life and was my motivation while I rebuilt my career over the next two years. In that time, I was able to go from a minimum wage intern to a marketing director. While I am not quite making a six-figure salary yet, I feel immeasurably richer than I ever have. My career is now based on my talents, knowledge and ideas as opposed to learned repetitive routines. Your job takes up the majority of your waking hours and if you’re miserable, or not challenged, your life will suffer. Simply summed up by Confucius “Choose a job you love, and you will never have to work a day in your life.” When I am getting paid for a passion, the work it takes to be successful seems a lot more effortless.

Along with finding a more fulfilling career path, there are a few simpler choices I’ve made that have also contributed to my success. The first was moving closer to work—close enough that I can walk, or bicycle. I never realized the difference starting your day out with a little exercise as opposed to sitting in traffic could make. Instead of struggling with other drivers on the road, I’m struggling with new ideas and planning out my day and by the time I arrive at work, my first hour of work is done. Secondly, a healthy exercise and diet regimen. Being healthy simply allows me to have the energy and mental focus I need in order to be more productive at work. Thirdly was utilizing my lunch as a time to take my mind off work. Whether it’s reading a book, or learning something new, I’ve found when I get out of the office and away from my desk I come back renewed and the second half of my day is more fruitful than if I had not. Lastly, learning and challenging yourself doesn’t have to stop just because you’re out of school. Creating new synapses in your brain helps with problem solving and creative thinking and while it’s not related to your work, you’ll inadvertently find yourself better at it.

Tags business, happiness, happy work life, job satisfaction, life advice, small business, work life