Wacky Physics: Are Entangled Particles Connected by Wormholes?

Wacky Physics: Are Entangled Particles Connected by Wormholes?

A simulation of entangled particles (Credit: John Jost and Jason Amini – via Livescience)

Quantum entanglement (also known as “spooky action at a distance”) is one of the most bizarre things we see happening with particle interactions on a microscale. Instead of acting as one solitary particle, certain pairs act as one – always knowing what the other is doing (and changing based on the characteristics of its partner) – despite being located vast distances apart. Obviously, this is problematic. Relativity says that nothing can travel faster than the speed of light. Yet, that’s exactly what entangled particles are doing – passing along information at speeds far exceeding light-speed travel – the universal speed limit. We shouldn’t rush to make adjustments to general relativity though, as one hypothesis has been put forth that combines quantum entanglement with a darling (yet highly theoretical) concept – Einstein-Rosen bridges (commonly known as wormholes).

According to a paper, published by Juan Maldacena and Leonard Susskind: entangled particles may be connected to one another by infinitesimally small wormholes – tunnel-like portals that connect two distant regions of space. This is how they are able to exchange signals almost instantaneously – even when they are located on opposite ends of the universe. The whole thing centers on a concept called an eternal black hole – another highly theoretical concept that postulates an entirely different universe can be found on the “other side” of a black hole (to get to it, one must delve into the black hole’s event horizon – the point of no return – before traveling into the singularity. Assuming you survive the spaghettification process – you would hypothetically pop back out into a different universe than the one you originated from). In layman terms, this indicates black holes are actually bridges that connect separate universes. (Or to put it another way, one single black hole exists in two universes)

Credit: Getty Images

Assuming you are still following me: in this scenario – with entangled black holes – any change to one of them would automatically effect the other as well. Hence the correlation between the two phenomena. As stated: these ideas, which are not new, are highly theoretical (perhaps even a little bit speculative). They will remain as such until we find definitive evidence of the existence of the so-called wormholes, but they are a mathematical prediction of general relativity. Therefore, one should expect this evidence to manifest eventually. In any case – the entanglement/wormhole hypothesis offers an explanation for noted instances of entangled particles becoming spontaneously disentangled – the wormholes connecting them collapse.

It also provides insight into several other perplexing concepts, dealing with a disconnect between general relativity and quantum mechanics. One deals with black holes and virtual particles.

Click to see a larger image (Source)

Typically, they cancel one another out (and annihilate one another), but on some occasions, a black hole will consume one member of a pair of virtual particles – causing the other to physically manifest – before it drifts off into the abyss of space. We call this hawking radiation. In order for information about the objects the black hole consumed to remain intact – we believe that these particles must all be entangled with one another – meaning that the state of each individual particles depend of the state of similarly entangled particles of hawking radiation.

This presents us with a sticky paradox, called the black hole firewall paradox. It clearly indicates that each particle is entangled with not one, but multiple other particles at the same time – something the laws of physics frown upon. So, to avoid this – physicists developed a concept that says that after a particle crosses the event horizon – into the singularity – the quantum bond breaks. Subsequently producing a huge burst of energy that acts like a wall of fire.

Credit: Newscientist

This is where the wormhole/entanglement idea comes in to play. According to Susskind and Maldacena (who built on a paper published a few years prior to theirs) the wormholes connecting the particles from the interior and exterior of the event horizon act as a buffer to smooth out the entanglement issues – avoiding the need for a firewall. Going a bit further with that, we can say that even when a virtual particle “pops” into existence – before going on its merry way – it is still intimately connected not only to the interior of the black hole it came from, but it also has a palatable connection to its fellow brethren. They quite literally become interconnected by a slew of tiny, spaghetti-like strings. They may even remain as such after leaking hawking radiation causes the black hole to dry up, before evaporating – after the bulk of its mass is lost to space.

Of course – these quantum constructs are much to small for humans to traverse. That, paired with questions about their overall stability – mean that there is no need to get excited about the possibility of teleportation. Or anything else, for that matter. However, this could have a profound effect on how we view the overall structure of spacetime. One physicist – working separate from Susskind and Maldacena – even suggested that spacetime is a manifestation of quantum entanglement. Interesting, indeed.

Tauon – The Supermassive Lepton!

Tauon – The Supermassive Lepton!

The tau particle, you can buy this little guy at the Particle Zoo

We all like hearing about the biggest and the smallest, the heaviest and the lightest, as these categories represent the extremes of the universe…and they usually they are great for comparisons. Today, we’re going to discuss the heaviest of all the leptons, the Tauon (also known as the Tau Lepton or Tau Particle). The Tau lepton has a mass of 1777 MeV/c^2, to put this lepton into perspective, it is several thousand times heavier than the smallest lepton – the electron – and is even heavier than a proton. But before we get into a thorough discussion of these particles, let’s have a bit of background in how particles function, just for a bit of context.

Virtually all of the visible matter in the universe is made up of only several particles.  The standard model of particle physics (a theory related to the electromagnetic, weak, and strong nuclear interactions that outlines the dynamics of the known subatomic particles) contains many particles, but only a few of these make matter. It appears that the universe favours the smaller of the particles; the smallest lepton, the electron, and the two smaller of the quarks (the Up and Down). From these three particles you, me, the the Earth, the Sun… everything in the cosmos is made! The tauon then, being so large, isn’t favoured. Unfortunately, this means that this big guy doesn’t exist for long in the universe. In fact, it only exists for 2.95×10^-13 seconds or 295 femtoseconds (one femtosecond is one quadrillionth [one millionth of one billionth] of a second). But the lepton is actually able to break down into a hadron with the use of a W Boson, or a quark anti-quark pair, or lepton anti-lepton pair, through the use of a Z Boson.

But don’t feel too bad about its paltry existence, the Tau particle does have a few claims to fame. For example, the decay of the Tau particle has been used in the detection of the Higgs Boson, but ultimately the Higgs wasn’t found through this method (alas); however, it was able to determine that the Higgs Boson should lie below the 160 GeV region. As the Tauon is the most unstable of all the leptons, as it is the largest, it doesn’t occur naturally in the universe like the electron. The Tauon, which exists for such a short period of time, only exists in places where there is high energy particle collisions like in the core of stars, supernova, black holes, neutron stars, or our humble particle accelerators.

As previously mentioned, it has a mass of approximately 1777 MeV/c^2, and as it is a lepto,n it is negatively charged and has a spin of 1/2. Like other particles, it has an anti-lepton, which is a 1/2 spin but is positively charged (this is known as the antitau). The Tau Neutrino is also the largest of the neutrinos with a mass of ~15.5 MeV/c^2 which is still some 30 times the mass of an electron and incredibly larger than the electron neutrino.

So, to sum the Tauon: It is the heaviest lepton in the whole particle zoo at nearly 3,500 times larger than the smallest of the lepton, the electron. The tau neutrino is the heaviest of the neutrino family and is heavier than an electron! Compared to the other neutrinos, the tau neutrino is truly a massive particle. Tauons are large enough that they are actually capable of decaying into hadrons, quark antiquark pairs and lepton pairs. Because of how heavy they are they are incredibly unstable and tend to decay very quickly.

New Discovery Simplifies Quantum Physics

New Discovery Simplifies Quantum Physics

Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated — the probabilities of outcomes of particle interactions.
Illustration by Andy Gilmore

That’s right ladies and gentlemen, quantum mechanics just got easier to understand. A team of physicists have released a paper showing their discovery of a jewel-like geometric structure that takes equations, which can be thousands of terms long, and simplifies them to a single term. This discovery is poised to dramatically simplify the equations particle physicists use when calculating particle interactions. It also proposes the uncomfortable idea that space and time are not fundamental aspects of our reality, and it brings us much closer to unifying gravity and quantum theory under one comprehensive model.

The discovery comes on the heels of decades of research in particle interactions. Particle interactions are some of the most basic and common events found in nature. Traditionally, these interactions have been very difficult or even impossible to calculate. Scientists required the use of the world’s most powerful computers to calculate even the simplest interactions. This new geometric structure, called the amplituhedron, is so simple that a particle physicist could calculate these interactions, by hand, on a single sheet of paper.

That, in case you were wondering, is insanely impressive. Harvard University theoretical physicist, Jacob Boujaily, and founder of this idea, said, “The degree of efficiency is mind-boggling. You can easily do, on paper, computations that were unfeasible even with a computer before.”

The Basic Idea

This theory is revolutionary on a number of fronts. At the moment, it’s being catapulted into the forefront of grand unified theory research. Some physicists suspect that a geometric object similar to the amplituhedron could eventually lead to a bridge that connects the physics of the very large with the physics of the very small. To date, all of the unified theories that are proposed are riddled with serious and deep-rooted problems, such as paradoxes and infinities. To unify macro and micro physics, the amplituhedron is paving the way to eliminate two of physics deeply rooted points and some of quantum theory’s central pillars: locality and unitarity.

Image Credit: Georg Johann

Simply put, unitarity is the idea that the sum of all probabilities describing every potential outcome of any quantum event is always equal to one (yes, that was the simple was of saying it). This places an inherent restriction on the amount of evolution that is allowed in any quantum system. Following the same “simple” trend, locality is basically the idea that particles can only interact with, and be influenced by, particles occupying space immediately surrounding them. It’s important to note that locality exists in quantum mechanics largely because special relativity insists upon it. Experimentally, we have shown through quantum entanglement that there seems to be a way to get around locality in the quantum world. In contrast, unitarity is a mathematical construction that helps to make nice round equations. In quantum field theory, both locality and unitarity are central concepts, but there is a catch. When attempting to add gravity to quantum theory, under certain situations, these two pillars (locality and unitarity) break down and stop working. This presents some amount of evidence that neither principle is a fundamental aspect of nature.

This is where the amplituhedron comes in. This geometric shape isn’t constructed by using the probabilities innate to spacetime, but instead suggests that the nature of spacetime is an attribute of the geometry of the amplituhedron. Our idea about the fabric of reality is just that– fabricated, an imaginary construct we have laying over the deeper and more fundamental construction of spacetime. According to David Skinner, a theoretical physicist who calls the Cambridge University home, “It’s a better formulation that makes you think about everything in a completely different way.”

The Complicated World of Particle Interactions

The amplituhedron is a very menacing, beautiful, complicated, multifaceted object that exists in higher dimensions. In principle, you can use the volume of this object to calculate all of the most basic features of reality, known in quantum mechanics as “scattering amplitudes.” This computation describes the probabilities of particles changing into other particles when colliding. These types of calculations are routinely made and tested at particle colliders such as the Large Hadron Collider (LHC). To understand the importance of the amplituhedron, we must first look at where it all began, 60-years ago with the development of Feynman diagrams.

Image source

Named after the Nobel winning Richard Feynman, these diagrams describe all of the ways a particle could scatter, and then the likelihood of any given outcome actually occurring. Feynman diagrams range from the trivially simple to the impossibly difficult. The simplest Feynman diagrams resemble trees, while the more complicated ones have one or more loops that explain particles turning into a virtual particle. A virtual particle is interesting because they aren’t observed in nature, but many physicists have regarded them as a mathematical necessity because they were required to achieve unitarity.

Though Feynman’s diagrams were a stroke of genius , they were simply the wrong tool to use to calculate nuclear particle interactions. In fact, the fact that we are able to compute anything at all is the prime discovery of the computer age; the number of diagrams required to describe something as simple as the 2-gluon to 4-gluon interaction gets so explosively large that scientists didn’t start those computations until the age of computers.  You see, to describe the collision of two gluons that result in four gluons in a lower energy state, particle physicists at the LHC require the use of 220 Feynman diagrams. Together, these diagrams represent thousands of terms involved in the computation that are necessary to determine the scattering amplitude. In short, scientists have realized that Feynman diagrams, though beautiful, are effective ways to calculate a single mathematical object–they are laborious, require many different pieces, and are so numerous that it makes it difficult to do computations even with computers. Physicists are trying to move from that “incalculable” process to a single calculation that (thought difficult) is possible for humans to do (and certainly much easier for computers).

This started with theoretical work preparing for the completion of the Superconducting Super Collider (SSC) that was to be built in Texas (but eventually canceled). Physicists wanted to create a background framework describing scattering amplitudes with which to test the SSC and look for exotic or interesting signals. Physicists quickly determined that creating such a framework for even simple 2-gluon to 4-gluon interactions was so complicated that “they may not be evaluated in the foreseeable future.” Then, in the 1980s, this gluon interaction was simplified from an equation containing several billion terms to a single formula 9-pages long. This was an expression computers of the time could handle, and quantum field theory got a little more manageable. This type of simplifying laid the groundwork for the amplituhedron.

Enter: The Amplituhedron

Though the gluon simplification was achieved in the mid-1980s, it took a couple of decades for particle physicists to really start putting that revolution to use. This started in the mid-2000s when physicists started to find patterns in the scattering amplitudes – and you know how much physicists like patterns. This started the general trend of thought that an underlying mathematical structure might be supporting quantum field theory.

Twistor diagrams
Credit: Arkani-Hamed et al.

Eventually, twistor variables and their corresponding diagrams were developed, which attempted to simplify Feynman diagrams even further. These diagrams moved away from describing particle interactions in familiar variables, such as time and position, and used twistor variables instead. These diagrams worked, and gained rapid acceptance among particle physicists, but scientists didn’t understand how they worked, why they worked, or what made them so simple. Arkani-Hamed provides a colorful description by saying, “The terms in these relations were coming from a different world, and we wanted to understand what that world was.”

The amplituhedron didn’t start coming to light until December of 2012 with the discovery of the positive Grassmannian. This geometric object is the result from studying the relationship between recursion relations and their corresponding twistor diagrams. According to the paper, these diagrams act as an instruction manual for calculating the volume of portions of the positive Grassmannian. This object consists of a region of N-dimensional space bounded intersecting planes (where N is the number of interacting particles).

This geometric structure was exciting, but incomplete. The positive Grassmannian’s construction was being restricted by locality and unitarity. Instead of falling together as eloquent things tend to fall together, something was missing. The prevailing idea was that determining the scattering amplitude had to be the answer to some other mathematical question. It turns out, that idea was right.

Credit: Nima Arkani-Hamed

The scattering amplitude was determined to be the volume of the amplituhedron. Natalie Wolchover from the Simon Foundation best describes this mathematical structure,”The details of a particular scattering process dictate the dimensionality and facets of the corresponding amplituhedron. The pieces of the positive Grassmannian that were being calculated with twistor diagrams and then added together by hand were building blocks that fit together inside this jewel, just as triangles fit together to form a polygon.”

To reiterate the awesomeness of this achievement, the diagram pictured here is a sketch of an amplituhedron depicting an 8-gluon particle interaction. If you were to attempt to use Feynman diagrams to represent this, you’d be dealing with about 500 pages of algebra.

If the discovery of the amplituhedron wasn’t cool enough, physicists have also discovered a “master amplituhedron.” This object has an infinite number of sides (similar to how a circle has an infinite number of sides in two dimensions) and it can, in theory, describe every possible physical process. All of the amplituhedra that exist in lower dimensions should exist on one of the master’s facets. Skinner describes this structure as having powerful calculational ability and talks of it’s incredible suggestiveness since “they suggest that thinking in terms of spacetime was not the right way of going about this.”

Quantum Gravity: The Future of Physics

This idea has very profound implications. Thus far, all of our theories attempting to unify gravity with quantum mechanics have failed. Because of this, scientists have an impossible time describing the internal workings of black holes, the singularity that started the big bang, and other important objects and events. Ideas like string theory are at the forefront of this research, but they tend to be confusing or unproven/unprovable (or both). According to Arkani-Hamed, ” We can’t rely on the usual familiar quantum mechanical space-time pictures of describing physics. We have to learn new ways of talking about it. This work is a baby step in that direction.”

Image Credit: Charles Imes

It’s very important to note that the amplituhedron, even though it doesn’t include unitarity and locality, also doesn’t include gravity. Physicists are in the middle of working on that very problem. It’s possible the amplituhedron contains the answer to quantum gravity, finally unifying the four fundamental forces of physics, or it’s possible the final geometric shape we seek is a little different.

This work is fantastic, very exciting, and moving along very quickly. As physicists seek to understand the meaning of the amplituhedron the rest of the world gets to wait with bated breath to learn of their findings. It’s possible we could have another Einsteinian-type revolution of our understanding of the nature of reality within our lifetimes. Wouldn’t that be exciting?

Light: Particle or Wave?

Light: Particle or Wave?

Classically, light can be thought of in two ways: either as a particle or a wave. But what is it really? Well, the ‘observer effect’ makes that question kind of difficult to answer. So before we get too far into it, what is the observer effect?

Simply put, the observer effect is a principle that states simply observing (or measuring) something can change its value. This effect is vastly more important in quantum mechanics than in everyday life, though it appears in a great many places. This means that – like most things in the quantum world – the phrase “what you see is what you get” doesn’t really apply. Therefore measuring what light is, in a way, can defeat the purpose. However the observer effect does very nicely explain why we have made tests that conclusively prove that light is a particle, and we have made tests that conclusively prove that light is a wave. Logic dictates that it can’t be both, or does it?

Source

First, let me explain why this is confusing. If you aren’t familiar with particle physics – or wave dynamics, in particular – you might simply be wondering what the big deal is. Why can’t it be both? Well the fact of the matter is that particles act in a very specific, ordered manner. As do waves. Yet, for the most part, each constituent part acts completely different from the other. Therefore, if something were to be both wave and particle, it wouldn’t make any sense from a certain standpoint. I mean, If you had to go somewhere, but you had to go east AND west to get there (not eastwestern or westeastern), you’d probably be left scratching you head as to which direction you need to take.

As we mentioned earlier, we have conclusively proven that light is a particle by giving it tests that only a particle will react to. We have also proven that light is a wave to giving it tests that only a wave will react to. Unfortunately, it have been proven that there is no test that can simultaneously test for both wave nature and particle nature, so in a way, light is whatever you want it to be. This goes back to the observer effect. By testing light, we make it whatever we want it to be. Either particle, or wave, which begs an interesting question: what is light before we test it? This is where stuff gets interesting.

Source; WikiCommons

There are many interpretations of wave-particle duality, but the most commonly accepted interpretation is the Copenhagen Interpretation. Erwin Schrödinger has credit for the thought experiment that makes this easiest to explain. To simplify the environment of Schrödinger’s cat, lets say that you are observing a box. You know exactly one thing about this box – that there is a cat inside. Now the cat can exist in two states: either alive or dead. Like a wave and particle, being alive and dead are largely contradictory so the analogy works well. According to the Copenhagen Interpretation of quantum mechanics, until you observe the cat, it is both alive and dead simultaneously.

This is referred to as a state of quantum superposition. Even things that are direct opposites can both be true simultaneously. That is, until the object in question is observed. When this occurs, it results in decoherence, which forces an object to “snap” into one state of being.

This happens, in part, due to the uncertainty principle of quantum mechanics (Sometimes confused with the Observer Effect, this is a different, but related concept). This is pretty simple to explain. The core of the principle is that the more you know about one thing, the less you are capable of knowing about another. This is also why it is impossible to know both the location and momentum of an electron, but that is a topic for another time.

The annoying thing about light is that we can conclusively prove it is a particle, or we can conclusively prove it is a wave. If we test light to see if it is a wave, we prove with 100% certainty that it is a wave, and due to the uncertainty principle, we can know 0% about the particle aspect of light. To test one aspect is to make it impossible to demonstrate the other. So to answer to question “Is light particles or waves”, you have to observe light. But to observe light it to change it. So from a philosophical point of view, the question has no meaning. Who knew science could be so Zen?

I’d like to sum this up with a quote from Lewis Carroll, who in his book “Alice’s Adventures in Wonderland” wrote:

”Ever since her last science class, Alice had been deeply puzzled by something, and she hoped one of her new acquaintances [the mad hatter and march hair] might straighten out the confusion. Putting down her cup of tea, she asked in a timid voice, “Is light made of waves, or is it made of particles:” “Yes, exactly so,” replied the Mad Hatter. Somewhat irritated, Alice asked in a more forceful voice, “what kind of answer is that: I will repeat my question: Is light particles or is it waves:” That’s right,” said the Mad Hatter.”

Are Atoms Mostly Empty?

Are Atoms Mostly Empty?

Image via ScienceLearn

The emptiness of the universe: This is the kind of stuff that the early pioneers in quantum mechanics believed in. In the 1920′s, researchers thought that emptiness — an absence of stuff — is what quantum mechanics was talking about. Arthur Eddington’s “The Two Tables” is a really nice treatment of the subject. In this piece, Eddington essentially argues that there are two tables: First, there is the table of everyday experience. It is a table that we can see and interact with. It is comparatively permanent, it is coloured, and (above all) it is substantial. Second, there is the table of science. This is something that is intangible. It is mostly emptiness with numerous, sparsely-scattered electric charges rushing about with great speed.


However, this metaphor happens to be wrong. The atom is a crazy soup of electrons, positrons, quarks, photons, gluons, and so on. These are popping about and annihilating one another. It just happens that they are so evenly cancelled out that the “empty space” picture, which was given to us by the 1920′s quantum mechanics, describes it extremely well. However, this emptiness is not an accurate depiction of what is actually going on. The deviations, that we can test, go into Quantum Field Theory.

What people living in the 1920′s did not realize is that the “empty space + Coulomb’s potential” is actually not empty space at all. In short, “empty space” is not what we think it is — it is a soup of a lot of things that average out to zero. Like thermodynamic equilibrium, i.e. “no net flow” is nowhere near the same as “no flow” at all!

Quantum Electrodynamics (QED) is the one quantum field theory (QFT) that is so well-tested that it truly is mind-blowing. It has more than 10 significant digits. No other enterprise of human ingenuity comes close to QED in terms of experimental testing and predictive power/closeness to predictions. It does this so well that the Standard Model is actually built on top of QED.

So, if you read a textbook that gave you the empty space version of the universe, that textbook needs updating. I am very sorry that the scientific community is not overly adept at distributing the truths that we have discovered, even if that truth is an inconsequential modification (or clarification) of what had been said earlier.

Superstring Theory

http://www.superstringtheory.com/index.html

What is String Theory?

What is String Theory?

Via Museum of Natural History D.C.

Stop. Look around. All things, visible or not, are made of particles so tiny that many find their sizes difficult to comprehend. Far removed from our everyday experiences, they move at rapid speeds and can only be observed with some of the most powerful technology known to science.

They are atoms.

Most people have at least heard of atoms, and many know that they are made of a nucleus containing protons (positively charged) and neutrons (no charge). Surrounding the nucleus is the electron cloud, containing negatively charged electrons.  However, these subatomic particles are not the smallest constituents of matter.


For instance, protons and neutrons are made of particles known as quarks. If we were to zoom in and dissect these tiny particles, which make up all matter in our universe, many believe that we would eventually come to something surprisingly, perhaps even charmingly familiar– a string.

Diagram of an idealized Lithium atom, primarily useful to illustrate the nucleus of an atom. via WikiMedia

This is the fundamental idea of superstring theory (“string theory” for short)– that the electrons and quarks that make up all the matter in our universe are not zero-dimensional objects, but one-dimensional strings. These strings oscillate, giving the aforementioned particles their charge, mass, spin, and flavor. Just as the different vibrations from a guitar string produce different frequencies of pitch, different oscillations of superstrings produce different qualities for subatomic particles.

Beneath the poetic overview of string theory lies the use of the most advanced mathematics in the world. Those who wish to pursue studying string theory must first study calculus (single and multivariable), analytic geometry, trigonometry, partial differential equations, probability and statistics, and the list keeps growing. Despite the complexity, string theory has proven to be mathematically consistent when tested. Because of this consistency, string theory is a primary contender for the Theory of Everything or M Theory- a theory long sought after by Albert Einstein himself- which explains all known physical phenomena in the universe and could predict the outcome of all experiments that could be carried out in theory. If string theory proves to be accurate, we will be able to explain all known physical events in our universe– from the generation of the tiniest subatomic particles to the events that take place in the abyssal of black holes.

Alongside string theory’s explanation of the generation of subatomic particles is another idea often found in science-fiction novels: the concept of extra dimensions. The idea may sound crazy at first, as do many scientific theories in their early years, but the mathematics behind these other dimensions has proven to be true thus far. We live in a three-dimensional universe (four if we include the dimension of time). However, string theory proposes that there are a total ten different dimensions (11 total, including time). As far-fetched as this may seem at first, the mathematical tests that have been done show this to be true. If this were not the case, string theory would have been abandoned long ago, for the idea of a multidimensional universe is necessary for string theory to be accurate. One other thing that String Theory does is predict gravity. In other theories, gravity is a “given.”

String theory may seem complicated– that is to be expected from a theory that attempts to describe all known physical occurrences in our universe. However, there are those who strive to bring String Theory to those who aren’t necessarily the most scientifically literate or mathematically inclined. Physicists Michio Kaku, co-creator of string field theory, and Brian Greene (author of “The Elegant Universe,”) are both leading theoretical physicists who partake in the development of string theory. They are both popularizers of science, and aim to describe string theory in simpler terms for those who wish to understand the inner workings of our universe; without having to endure the years (and the price) of schooling required to perform the mathematics behind the theory.

Kaku and Greene do more than simply explain to us the ways of string theory, along with other complexities in our world. They show us a beautiful lesson that can be applied to all aspects of life. No matter how daunting a situation may be, no matter how absolutely complex an idea, one can almost always travel to the core to find a beautifully simple solution. And sometimes, if one looks deep enough, the solution may be as simple and as elegant as a string.