String Theory in 1000 Words (Kind Of)

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By Bradley Stockwell

Because my last two posts were quite lengthy, I’ve decided to limit myself to 1000 words on this one. Before I begin, I must credit the physicist Brian Greene for much of the insight and some of the examples I’m going to use. Without his book The Elegant Universe, I wouldn’t know where to begin in trying to explain string theory.

In short, string theory is the leading candidate for a theory of everything; a solution to the problem of trying to connect quantum mechanics to relativity. Because it has yet to be proven experimentally, many physicists have a hard time accepting it and think of it as nothing more than a mathematical contrivance. However, I must emphasize, it has also yet to be disproven; in fact many of the recent discoveries made in particle physics and cosmology were first predicted by string theory. Like quantum mechanics when it was first conceived, it has divided the physics community in two. Although the theory has enlightened us to some features of our universe and is arguably the most beautiful theory since Einstein’s general relativity, it still lacks definitive evidence for reasons that’ll be obvious later. But there is some hope on the horizon. After two years of upgrades, in the upcoming month, the LHC—the particle accelerator that discovered the Higgs Boson (the God Particle), will be starting up again to dive deeper into some of these enlightenments that string theory has given us and may further serve as evidence for it.

So now that you have a general overview, let’s get to the nitty gritty. According to the theory, our universe is made up of ten to eleven dimensions, however we only experience four of them. Think about the way in which you give someone your location. You tell them you’re on the corner of Main and Broadway on the second floor of such-and-such building. These coordinates represent the three spatial dimensions: left and right, forward and back and up and down that we’re familiar with. Of course you also give a time in which you’ll be at this three dimensional location and that is dimension number four.

Where are these other six to seven dimensions hiding then? They’re rolled up into tiny six dimensional shapes called Calabi-Yau shapes, named after the mathematicians who created them, that are woven into the fabric of the universe. You can sort of imagine them as knots that hold the threads of the universe together. The seventh possible dimension comes from an extension of string theory called M-theory, which basically adds another height dimension, but we can ignore that for now. These Calabi-Yau ‘knots’ are unfathomably small; as small as you can possibly get. This is why string theory has remained unproven, and consequently saves it from being disproven. With all the technology we currently possess, we just can’t probe down that far; down to something called the Planck length. To give you a reference point of the Planck length, imagine if an atom were the size of our entire universe, this length would be about as long as your average tree here on Earth.

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Calabi-Yau shapes, or ‘knots’ that hold the fabric of the universe together.

The exact shape of these six dimensional knots is unknown, but it is important because it has a profound impact on our universe. At its core, string theory imagines everything in our universe as being made of the same material, microscopic strings of energy. And just the way air being funneled through a French horn has vibrational patterns that create various musical notes, strings that are funneled through these six dimensional knots have vibrational patterns that create various particle properties, such as mass, charge and something called spin. These properties dictate how a particle will influence our universe and how it will interact with other particles. Some particles become gravity, others become the forces that attract, glue and pull apart matter particles. This sets the stage for particles like quarks to coalesce into protons and neutrons, which interact with electrons to become atoms. Atoms interact with other atoms to become molecules and molecules interact with other molecules to become matter, until eventually you have this thing we call the universe. Amazing isn’t it? The reality we perceive could be nothing more than a grand symphony of vibrating strings.

Many string theorists have tried to pin down the exact Calabi-Yau shape that created our universe, but the mathematics seems to say it’s not possible; that there is an infinite amount of possibilities. This leads us down an existential rabbit hole of sorts and opens up possibilities that the human brain may never comprehend about reality. Multiverse theorists (the cosmology counterparts to string theorists) have proposed that because there is an infinite number of possible shapes that there is an infinite variety of universes that could all exist within one giant multidimensional form called the multiverse. This ties in with another component of the multiverse theory I’ve mention previously; that behind every black hole is another universe. Because the gravitational pull within a black hole is so great, it would cause these Calabi-Yau ‘knots’ to become detangled and reform into another shape. Changing this shape would change string energy vibrations, which would change particle properties and create an entirely new universe with a new set of laws for physics. Some may be sustainable—such as in the case of our universe—or unsustainable. Trying to guess the exact Calabi-Yau shape a black hole would form would kind of be like trying to calculate the innumerable factors that make up the unique shape of a single snowflake.

The multiverse theory along with M-theory also leads to the possibility that forces in other universes, or dimensions, may be stronger or weaker than within ours. For example gravity, the weakest of the four fundamental forces in our universe, may be sourced in a neighboring universe or dimension where it is stronger and we are just experiencing the residual effect of what bleeds through. Sort of like muffled music from a neighbor’s house party bleeding through the walls of your house. The importance of this possibility is gravity may be a communication link to other universes or dimensions—something that the movie Interstellar played off of.

Well I’ve gone over by 52 words now (sorry I tried my best!), so until next time, stay curious my friends.

 

A Crash Course in Relativity and Quantum Mechanics

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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.

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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!

Flight of the Timeless Photon

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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.

 

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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!