Friday, September 16, 2011


When I explored the behavior of light in my previous article, I mentioned a strange particle called a positron, and I told you that it is an electron travelling backward through time. I also said that this particle comes into existence quite naturally when a photon of light annihilates into two new particles, an electron and a positron. This was an introduction into the strange world of antimatter, of which positrons are an example.

To keep things as simple as possible I left a few details out of that description of electron-positron annihilation. I will fill you in as we explore antimatter further.

Antimatter is a real mystery to physicists. It is not that they do not know where it comes from or how to create it. The real mystery is where it all went. We will explore that mystery in a little while.

First let me set the scene for you.

Matter is Energy and Energy is Matter

The story begins with Albert Einstein. In 1905, he wrote a now-famous equation E = mc2 or energy equals mass (m) x the speed of light (c) squared. If you think about this, it means that there is a whole lot of energy in even the tiniest bit of mass. A kg of mass (it doesn't matter what kind - it could be an atom-size piece of neutron star matter,  filled with squished neutrons, or a cubic meter of air - both contain about 1 kg of mass) equals about 25 billion kWh of energy. To give you an idea of how much energy that is, it could power 100 medium-sized cities for a year! If we could find a way to simply change matter into energy we would solve our energy crisis flat. Wait a minute, we can change matter into energy!

Nuclear fission occurs in a nuclear power plant, and this reaction turns matter into energy. The atomic nucleus of uranium-235 absorbs a free neutron and spontaneously splits into two or more lighter nuclei, shown here:

When this happens, a tiny fraction of total nuclear mass is converted into energy in the form of kinetic energy and high-energy gamma photons.

Mass and Energy Inside an Atom

Atomic nuclei live in a mass-energy equivalent world: If you add up all the mass of the protons and neutrons inside any nucleus you get a sum that is greater than the actual nuclear mass. Why? This is because a force exists inside nuclei holding the protons and neutrons together like glue. It is called the strong nuclear force and it is one of the four fundamental forces in the universe. The mass equivalence of this force, calculated using Einstein's formula, is exactly equal to the difference in mass you get. Big unwieldy uranium-235 nuclei are unstable because they have less binding energy per proton than medium size nuclei - they have just enough to hold the nucleus together, but not forever. Even if never bombarded by a free neutron, each uranium-235 nucleus eventually spontaneously decays into smaller more stable nuclei. This is called radioactive decay and it eventually happens to every unstable element.

Back inside our nuclear plant, kinetic and gamma ray energy is then converted into thermal energy and that heats water to turn a turbine. At the end you get mechanical energy, which is in turn converted into electrical energy.

We are not converting whole atoms into energy here, just a tiny fraction of their atomic mass. And we don't get to use all of that energy either. There is a lot of energy conversion going on between the fission reaction and, let's say, your vacuum cleaner - and usable energy is lost at every conversion step. Additional energy is lost as unusable heat through dissipation and friction along the way, lots of it from transmission lines. Still, nuclear power plants can put out tremendous energy, and they are significantly more efficient that coal, gas or oil energy.

Mass and Energy are Usually Both Conserved

With the exception of nuclear decay, matter and energy are always conserved in all chemical and physical interactions. Let's look at what happens when the bottom of your car door rusts.

The useful conservation rule I just mentioned tells us that every atom of iron in that rusting door is conserved and every atom of oxygen (from the air) is also conserved. Let's see what the reactions involved look like.

It all starts off when 4 electrons (4e-) interact with oxygen in the air. The electrons can come from an electrolyte such as road salt. Road salt doesn't have to be present for your car to rust but it really speeds up the reactions that follow.

O2 + 4 e- + 2 H2   4 OH-

Iron, in the presence of water, oxygen and road salt, creates, in essence, a battery.

2Fe(s)     2Fe2+(aq) + 4e-

Electrons, produced at the "anode end" (Fe(s)) travel to the "cathode end," (O2). The anode end is where an oxidation reaction happens and the cathode end is where a reduction reaction happens. This is an example of how the electromagnetic force is involved in every chemical reaction.

The iron ions and the hydroxide ions then combine to form ferrous hydroxide:

Fe2+(aq) + 2OH-(aq) ==> Fe(OH)2(s)

Ferrous hydroxide oxidizes once again to form ferric hydroxide:

Fe(OH)2(s) =O2=> Fe(OH)3(s)

This compound then dehydrates into rust:

Fe(OH)3(s) =dehydrates=> Fe2O3.nH2O(s) or rust

The "n" means that you can get different kinds of rust, depending on how many water molecules are attached to each ferric oxide molecule.

As complex as the rusting process might seem, it involves only the transfer of matter and energy. No matter or energy is lost or created.

Mass-Energy is Always Conserved

When we talked about nuclear decay, matter and energy were not conserved. Matter was destroyed and energy was created. However, even nuclear reactions must follow the rules of the universe. One very important rule is that total mass-energy is conserved. This means that even in nuclear reactions the total amount of mass-energy remains the same. This rule extends to the universe itself, and it has been instrumental in helping physicists work out how much total energy and mass exist. It also means that the universe, from its first instant, contained all the mass-energy it would ever have and that amount has remained constant to this day.

We've seen how energy can be created from matter. But do we know how to create matter from energy?

The answer is yes but only in very small amounts. Einstein tells us that E = mc2. "c2" is an enormous value, 300,000 km/s x 300,000 km/s. That gives us a clue to the enormous amount of energy we would need to create matter. That is one practical hurdle. The other hurdle is that we can't just order up whatever matter we want, like using a Star Trek replicator. So, let's say we've used a particle accelerator like the one at CERN to accelerate a proton almost to light speed, and we aim it at a small bit of matter. This collision will supply enough energy, in the form of high-energy photons, to break what is called the pair production threshold. The energy, in this case exceeding twice the rest energy of an electron (2 x mec2), will spontaneously create an electron and its antimatter twin, a positron. You can't make just electrons or protons, etc. You can only make matter/antimatter pairs of particles. Positrons, by the way, are much easier to make than anti-protons or anti-neutrons because electrons have a much lower rest mass, and therefore, a much lower energy hurtle to overcome to make them.

Harnessing the Positron

To make positrons, you can use a high-powered laser to drive electrons into gold nuclei. If the electrons and positrons you make have enough energy, they can undergo scattering with more nuclei, radiate more photons, and make more positrons and electrons (another rule of the universe is that charge is always conserved). You can separate the positrons out using magnets and then store them in a positron trap, shown here:

Credit: ARC Centre of Excellence for Antimatter-Matter Studies

This is a vacuum tube with strong magnetic and electric fields that hold positrons in the middle so they can't contact the sides and annihilate themselves with electrons. You can keep a few million positrons at a time with this device.

Positrons are an Important Part of Nuclear Medicine

Luckily you don't need the above procedure to carry out positron emission tomography (PET) scans. This is what a PET scanner looks like:

This scan is used to produce a three-dimensional picture of the metabolic processes going on inside the body. Among other applications, it is often used to detect cancer tumours. First a patient drinks a tracer, in this case radioactive fluorine bound to glucose. Here, all you need is a very small emission of positrons and they come from the positive beta decay of the fluorine. Fluorine-18 decays very fast and it is not very damaging to healthy tissue. The tracer becomes more concentrated in more metabolically active tissues, and cancer cells are very active. Active cells take up the tracer from the blood stream and from there each positron travels for a short distance (less than 1 mm) through tissue, losing kinetic energy and slowing down until it finally interacts with an electron. When this happens, a pair of annihilation gamma photons are created, and they move in opposite directions. They are detected on a scanning device and this device can use the information to localize a tumour.

It takes a tremendous amount of energy to make even small antiparticles such as positrons. And yet, strangely enough, these particles show up spontaneously all the time all around us. Even light reflecting from a mirror creates the occasional electron-positron pair. We call these virtual particles.

Virtual Particles

Virtual particles exist for a very limited time in a very limited space. They must follow most of the same physics laws as real particles do. But they may not exhibit all of the same phenomena. I will give you an example shortly.

Positrons, and in fact all subatomic particles, spontaneously appear and disappear all the time. As I mentioned in my article about light, quantum uncertainty (a probability function) becomes significant over very small distances, such as the inside of an atom. For individual particles, every quality, from mass to speed to momentum, has a range of possible values. Only when we average those values over many many particles do we get results that agree with classical physics.

Real Particle Annihilation

Remember when I talked about spontaneous photon annihilation in the article on light behaviour? Both the electron and the positron which were created from that are virtual particles. Keep this in mind as we continue.

Here I have a Feynman diagram of positron-electron annihilation. An electron and a positron are annihilated and two gamma photons are created:

Notice that I said two photons are created, not one. Are you wondering why, when I talked about light behavior, I implied that this annihilation event created only one photon? This annihilation process, like everything in physics, must satisfy conservation laws, right? Charge is conserved - the net charge before and after is zero in this case. Angular momentum is also conserved. Linear momentum and energy are conserved. Wait a minute here, what about the single photon case?! Doesn't this last law forbid the creation of a single photon? Well it does, for real particles, and this is exactly what happens inside an accelerator like the one at CERN. Real particles at tremendous energies are smashing into other real particles and real particles come out. This is also why we get two gamma rays, each one going off in opposite directions, when we do PET scans.

Side Note About Energies

In the electron-positron annihilation process I've shown here, what you get out at the end depends on how fast you slam the electron and positron together. At the minimum energy to produce annihilation, you get two high-energy photons called gamma rays. These are the squiggly lines labeled  γ   shown above. At higher energies you can get bigger heavier particles with exotic names like D-mesons, Z-bosons and neutrinos. We will talk more about the Z boson soon but for now, I'll just tell you some cool things about it. It is a force mediator particle just as photons are. However, the Z-boson mediates (carries out) the weak force. This is the fundamental force involved in radioactivity (nuclear decay). Like photons it has no charge but unlike photons, which have no mass, this is a real heavyweight, almost 100 times more massive than protons! Remember that to create any new particle from annihilation you must supply enough energy to match their rest-mass energy equivalent. Z-bosons are massive and that means there's a lot of energy bound up in them that you have to supply.

Let's get back to our comparison between real and virtual particles.

Virtual Particle Annihilation

So far, we have learned that for real particles several conservation laws must be followed. When I was talking about positrons in my article on light, I kept saying that one photon came out of each annihilation event and vice versa. I did not catch myself in a screw-up; this is quite accurate. So what gives? Well, quantum field theory does. The electrons and positrons I was talking about in that article are virtual particles. They don't always have to follow all the same rules. Remember when I said that electrons are held in place away from nuclei inside atoms because of continuous photon exchanges going on between them? A process similar to photon exchange holds the neutrons and protons together inside the nuclei of atoms. In this case, gluons do the job of photons. Gluons are particles that mediate the fundamental strong force.

Side Note About QED versus QCD

The study of gluons and quarks is called quantum chromodynamics, QCD. Unlike the electrically neutral photons of QED, quantum electrodynamics, these particles have different kinds of charge (called colors). This makes the calculations involved even more complicated than the ones for QED (Feynman diagrams are simplified illustrations of this math and they are useful in both theories).

Back to Our Comparison

Gluons are in the same particle family as the Z-bosons I mentioned earlier. For our purposes, the gluon exchange is analogous to the photon exchange. Here's what a Feynman diagram looks like for gluon radiation.

Credit: Joel Holdsworth

Only a single gluon is created, not two. This does not violate linear momentum and energy and this is why: All the particles here are virtual particles. According to quantum theory these particles cannot be isolated or captured. They do not exist as particles! What they are are momentary ripples or excitations within fields, in our case, the strong nuclear force field. We no longer need all the rules for the motion of classical objects, but we do need some rules. I hoped to blow you away when I said in my light behavior article that particles are moving backward through time right under your nose. I cheated a little: These particles, positrons, are not whizzing around you and banging into things, setting off annihilations and emitting gamma radiation all over the place. They are virtual positrons and they reign only inside the quantum world within and closely around atoms. You are safe around reflecting surfaces! However, virtual particles can and do impact our everyday world around us, and if you were reading my last article carefully, you already know this. I have more 'proofs' to share with you shortly. And I promise to revisit this crazy backward time notion, both in this article and in more detail in a new article coming up.

Quantum Foam

Physics on the tiny scale of the atom occurs within an environment called quantum foam. It is on this scale where antiparticles show up and, just as quickly, disappear. Even tiny wormholes and black holes pop in and out of existence. This scale is called Planck length - it is unimaginably short, 1.61 x 10-35 m. The strange things that go on here occur over instants of time as brief as 5.39 x 10-44 s (Planck time). We are now at the extreme limits of space-time. Distance and time cannot be cut into shorter pieces, not even theoretically.  On a larger scale, space-time appears smooth but that appearance breaks down at the Planck scale. We don't have a theory of quantum gravity yet so we don't have a complete picture of what space-time actually looks like at this scale, but for our purposes the term, quantum foam, works just fine.

Energy curves space-time*, so at Planck scale, energy fluctuations are large enough to make it choppy or foamy. Here, virtual particles poof into and out of existence. These virtual particles are themselves space-time! That means that they can and do show up as fluctuations within even perfectly empty vacuums, and these fluctuations mean that vacuums have energy. Physicists don't yet know for sure how much energy this is, but out of necessity pairs of virtual particles cannot pop into existence unless they have 2mparticlec2 energy. This extreme energy, called vacuum energy, also makes tiny wormholes and black holes possible. This is a strange concept: space-time's tiniest components are filled choc-a-block with energy. We are soaked in this energy right now, and yet it is not available to us, for example, to do work. Oh wait a minute, it is!

* Einstein defines energy more specifically as energy-momentum in his theory of general relativity. You might have heard that very massive objects (big stars, black holes) warp space-time. Any mass, even an atom, warps it a little. Recalling that mass and energy are equivalent (right?), we can say that anything with energy, mass or both (momentum) will bend space-time. This means that even photons should be able to generate gravitational fields. There is still some speculation that they can't. Photons have what we call relativistic mass (they are massless but have energy, and they also have a kind of momentum called angular momentum). Electrons and quarks (stuff inside matter) on the other hand have rest mass (we experience them as having mass). Here, again, we find ourselves trying to mix quantum mechanics (electromagnetic field propagation) with general relativity (the bending of space-time, or gravity). And no matter how many ways we keep knocking at that door it just won't budge (yet).

Virtual Particle Behaviours

I invite you to take a look at a phenomenon called the Casimir effect. Wikipedia explains it well for us. Here, virtual photons exert a significant and measurable force on two parallel metal plates. Virtual particles also mediate the static electric force between charges (mediated by photons), magnetic fields (again, photons), the near fields of radio antennas (photons), the strong nuclear force inside atomic nuclei (gluons), the weak force (W and Z bosons) and the list goes on. Virtual particles bubbling in and out of existence create much of the phenomena we see all the time. They don't create all of it. The electromagnetic force is mediated by real photons, and virtual ones, as we will see right now.

Real versus Virtual Particle Behaviour - Near Fields

Remember the near field I just mentioned? At a distance of up to about 1 emission wavelength from an antenna, a special kind of electromagnetic force operates. It is mediated by virtual photons, which create strong inductive and capacitive effects from the current and charge within the antenna. What really sets it apart from the 'real' electromagnetic radiation coming from the antenna, called far-field radiation, is that near-field radiation decreases in power far faster. Depending on how far you are away from the antenna you see the effects or one or the other of the two different "kinds" of electromagnetic (EM) radiation, one mediated by virtual photons and the other mediated by real photons. Virtual photon-mediated near field radiation exhibits some very strange behavior. 'Real' EM radiation consists of an electric field component (E) and a magnetic field component (B), where the values E and B are equal at any point in space. You will see this if you refer back to the first diagram in my last article, "The Behaviour of Light." 'Real' EM radiation is an example of a transverse wave. It can be polarized perpendicular to the direction of travel in one, and only one, of four different ways. Virtual EM radiation behaves differently. First of all, the relationship between E and B is very complex and E doesn't have to equal B at all. Second, it can exhibit all four kinds of polarization simultaneously. I'm not sure if anyone knows exactly how near field EM radiation works but it has a great many practical applications such as wireless communication between smart phones and tablets. For example, soon you will be able to buy an Apple iPhone with an NFC (near field communication) chip in it. You input your credit card information and simply place your smart phone near a store's reader to purchase your items. I'm not sure how they worked out the security on that.

Some Particles Are Their Own Antiparticle

Every virtual particle pops into existence with its own antiparticle. You might be wondering how the virtual photon/antiphoton pairs interact within the strange virtual electromagnetic field I mentioned above. The answer is bit disappointing: some particles are their own antiparticles. Most of them are force carriers and they include photons, Z bosons (mediating the weak nuclear force) and gluons (mediating the strong nuclear force). All antiparticle twins of particles bear opposite charges. Positrons, electron's antimatter twins, are positively charged for example. However, particles that are their own antiparticles, must all, as a rule, be electrically neutral.

Where's the Antimatter?

We now know that antiparticles (recall that subatomic particles make up matter and force) represent one side of the virtual particle pairs that make up quantum, or Planck-sized, spacetime. After some thought, this begs some very fundamental questions. If particle/antiparticle pairs are created everywhere all the time, then why isn't the universe made up of half of each kind? Why is there any matter at all, when every pair that is created almost instantly annihilates itself? To answer these questions we will have to equip ourselves with some pretty challenging theoretical background. We will be exploring some theories still in progress beyond this point, and theories might change a little or a lot over the next few years.  Let's give it a try. (If the following symmetry theory is too confusing, please skip to my Brief Conclusion below. I think you will enjoy the two movies I have included. I found the symmetry theory very challenging and would greatly appreciate any corrective feedback from experts.)

Symmetries Were Broken When the Universe Began

When the universe first exploded into existence it contained nothing but energy and a lot of it. This energy was, at first, homogenous. It was all the same everywhere. Each of the four fundamental forces rapidly settled out of this primal force, one after another, each through a process called symmetry-breaking. All this happened in less than 10-12 second. The process of symmetry-breaking operates much like a phase transition does. Examine a glass of water right at the freezing point. The water is undergoing a phase transition. Water in one phase, ice, settles out of water in another phase, liquid. You can see the separation quite easily and in our application we will call this separation the domain wall. It is difficult to understand how an initially homogenous system, the just-formed universe for example, can evolve into an asymmetrical system when all the forces acting on it should be acting symmetrically. However, much like how ice formation breaks the homogeneity of water (it breaks its symmetry), one phase transition that took place when the universe was just forming may be responsible for creating a surplus of particles over antiparticles. This particular kind of  phase transition allowed the electroweak force to settle out. When it settled out, a special kind of symmetry called P-symmetry (you can think of it as the symmetry of the three coordinates of space, called parity was broken. This meant that another kind of symmetry called C (charge conjugation) symmetry could also be broken. Electromagnetism, gravity and the strong force have already settled out at this point. They settled out when C-symmetry was still intact so these fundamental forces all observe this symmetry. The weak force, however, settled out from the electroweak force just after C symmetry was broken so it does not observe it.

Example: The Weak Force Violates CP Symmetry

Nuclear decay is mediated through the weak force. The weak force only acts on left-handed particles, and right-handed antiparticles. The direction of spin and the direction of motion are opposite each other in left-handed particles and in the same direction in right-handed particles, as shown in the diagram below. Any particle can be either right or left-handed.

Let's say that an atom of the uranium-235 sample we talked about earlier is decaying. The weak force acts on a left-handed Z-boson in our universe. In theory, according to P symmetry, it should also be able to act on an anti Z-boson in a mirror universe. The problem is that the anti-boson is also left-handed, so in this case the weak force can't act on it. This violates both C and P symmetries. It is called a CP violation.

Broken Symmetry May Explain Why Our Universe is Made of Matter

Quarks, Antiquarks and Matter

First of all, let me introduce you to the quark. This particle is a fundamental constituent of matter. Quarks combine to make composite particles called hadrons, two of which are stable and these are the protons and neutrons inside an atom's nucleus. Another result of the CP symmetry-breaking we talked about earlier, is that some probability amplitudes for quarks are not equal to the corresponding amplitudes for antiquarks. By themselves these differences mean that quarks do not observe CP symmetry and yet we know that they do. Let me explain: Time reversal has its own probability, and when we include time (with its own form of symmetry), a larger symmetry, CPT symmetry, is conserved. This means that as long as antiparticles move backward through time, the universe can theoretically have an exact mirror of itself (called parity (P) conservation), including mirror images of all of its forces and particles. All of our laws in physics point to this mirror-ability.

Antiquarks Are Filtered Out . . .

Getting back to our quarks: Both quarks and antiquarks have the same phase and the same positive energy as they move in space-time. However, their phase depends on their mass. Both have identical mass too, but their mass depends on two variables - flavor and something called the Higgs VEV (an expected value of the energy of a vacuum). What's interesting here is that the Higgs VEV isn't homogenous - it varies along the domain wall. The domain wall is the separation line that is created when symmetry is broken. Because of this, some probabilities for quark qualities differ from the corresponding probabilities for antiquarks. This means that quarks and antiquarks may have different reflection and transmission probabilities through the domain wall. And this (finally, bear with me) means that more quarks coming from the unbroken side are transmitted compared to antiquarks. These quarks are then added to the broken-side quarks, which were already there. These are the new quarks of our universe.

. . . And Removed (well, remade into something else)

In the unbroken phase, something called the sphaleron interaction occurs. Here, in the high-energy environment of the new universe, the sphaleron converts all baryons to anitleptons and antibaryons to leptons. Baryons here include the hadron-making quarks that contribute to matter (protons and neutrons). Leptons are electrons and their relatives. The sphaleron interaction almost never happens under ordinary conditions but in the extreme heat and pressure of the new universe it happened a lot, and what it did was wipe off all the, now excess, antiquark content in the unbroken phase by turning them into leptons such as free electrons, etc. This left an excess of quarks in the universe, an excess of matter over antimatter. The same kind of process happened with all the elementary particles, seeding the universe with particles over antiparticles.

A Brief Conclusion

Our universe is almost completely made of matter because of the way it unfolded. Antimatter really does exist but, under ordinary circumstances, it doesn't exist for long. We need to magnetically separate any antimatter we create and we need to keep it held apart from matter using strong magnetic and electric fields. It will be a long time before we can engineer something like an antimatter rocket that can harness the incredible energy that is released when particles collide with their anti-particle twins, or will it? Take a look at what NASA's been up to. Scientists have been looking into whether a positron-fueled rocket could get us to Mars. This is an artist's conception of what it might look like:

This is a proposed design for an antimatter engine that might work:

It is theoretically possible that a universe could unfold on the "other side" of broken symmetries. Perhaps our universe's theoretical mirror twin does indeed exist somehow somewhere, and in that universe, perhaps an antimatter technician is using EEM (electron emission tomography) to scan her antimatter patient for antimatter tumours, the inner doors of an antimatter car are rusting out to the annoyance of an antimatter me, and antimatter scientists are pondering an exotic-sounding matter-fueled rocket. This 3-minutre video sums up our antimatter story very nicely:

This 24 minute Cosmic Journeys video, which aired in August 2011 explores our current knowledge of antimatter in depth. Here you will find out how scientists are looking for antimatter in our universe. It's high def with great imagery, one of my favourites!

A final note: I explore how the universe became seeded with matter over antimatter in my article "Our Universe Part 8: Hadron Epoch." There you will find a similar but slightly different take on this theoretical process.

Sunday, September 11, 2011

The Behaviour of Light

What is Light?

Light is all around us.

We need light. Plants and microorganisms harness the energy in sunlight, providing the basis for Earth's entire web of life. And, as I sit here in my yard enjoying the sunlight, I think about the first light ever created. That light still exists, it is striking the atoms of my skin right now, in the form of cosmic background microwave radiation. And I wonder, what is light, how does it work, what is its nature?

Light is the propagation of energy from one place to another. I don't just mean the light we can see. By "light" I mean all electromagnetic radiation, of which visible light is just a small part. Electromagnetic radiation is a form of energy that exhibits both wave and particle behavior at the same time. We will explore the evidence for this soon enough. Light has both electrical and magnetic field components to it as it propagates from one place to another, and these two components oscillate in phase with, and are perpendicular to, each other, and they are perpendicular to the direction that the energy is moving. This diagram shows what I mean.

Credit: Supermanu, GFDL, CC-BY-uSA

This diagram represents a single unit of electromagnetic radiation, a photon. The Greek letter λ is one wavelength (frequency = 1/ λ). K represents the direction in which the photon is traveling, to the right in this case. The + and - q symbols represent positive and negative charge (q) associated with the photon. E represents the photon's energy propagating along the electrical field and B represents its energy propagating along the magnetic field. This looks complicated, but all light really is a tiny oscillation through electric and magnetic fields, carrying with it energy from one place to another.

Photons all travel at the same speed, the speed of light. The speed of light, however can be slowed when photons travel through various mediums. In a vacuum all photons travel at the same speed, c, which is 299,792,458 m/s. Photons appear to travel slower through ordinary glass, for example. The refractive index (slowing power if you will) of glass is about 1.5 so the speed of light traveling through it is c/1.5 or about 199,861,639 m/s, significantly slower. Yet this is nothing compared to how dramatically light is slowed down when it passes through a state of matter called a Bose-Einstein condensate. In 1999, researchers at Harvard University clocked light traveling through a condensate at 61 km/h! Did you notice that earlier I said "appear to travel slower"? I will explain what I mean by this later on.

Photons can pack different amounts of energy. They do this by increasing their frequency to increase their energy and vice versa.

This diagram compares photons of different energies. It is what we call the electromagnetic spectrum.

Credit: Inductiveload, NASA

Look at the tiny spectrum within the frequency bar. This is visible light and these photons have frequencies between 4 x 1014 Hz (red light) and 7.9 x 1014 Hz (violet light). They are the colours of a rainbow. Violet light has more energy than red light. Gamma ray photons are of extremely high frequency and they pack the highest energy of all. These photons are released from decaying atomic nuclei when a nuclear bomb goes off or when stars explode, and they are very deadly.

How does something act like a wave and a particle at the same time? This is a great conundrum and the answer does not make sense; it comes from direct experimental evidence.

The Science of Light Started with Two Competing Theories

People have been keenly curious about light for millennia. Until the 1800's, most investigators pictured light as a beam of particles. Yet, and this is interesting, back in the 1600's, scientists such as René Descartes, Robert Hooke and Christian Huygens showed that light displayed wave behaviors such as refraction, diffraction and birefringence. However at the same time, Isaac Newton put forth his particle, or corpuscular, theory of light and he held such great sway during this century that the corpuscular theory endured for 200 years (even though he himself verged on resorting to waves to account for the interference patterns he investigated for his famous publication, Opticks). The reign of Newton ended in the early 1800's when Thomas Young and August Fresnel so clearly demonstrated light interference and diffraction that the wave model of light was finally adopted en mass. By then, James Clerk Maxwell was developing his theory of electromagnetism. Heinrich Hertz, another contemporary of this time, bridged these two theories by demonstrating that light is an electromagnetic wave, sealing the deal on the wave theory for another century. But this was not to be the final chapter on light theory . . .

Wave Theory

Let's examine the experimental evidence for the wave nature of light, as demonstrated by Young's elegant slit experiments.

When Thomas Young famously carried out this double-slit experiment in 1803 he showed that light consists of waves. It became the definitive word on light behavior and effectively shut down Isaac Newton's contemporary and competing theory that light behaved like discrete corpuscles.

He aimed a narrow beam of sunlight though an opening in a window onto a card with two slits cut into it and onto a screen placed behind on which he could see the resulting light pattern it created.

If light acts like particles he would expect the beam of light to eventually build up a pattern that corresponds to the size and shape of the slits, like what would happen if paint balls were fired over and over through two similar but larger slits in a wall. He would see something like this:

What he observed was a diffraction pattern, the beam of light passed through the narrow openings and spread out. He saw something like this instead:
Where the waves met crest to crest, constructive interference occurred, creating brighter thicker lines and where they met trough to trough, destructive interference occurred creating dimmer thinner lines.

Diffraction is what happens specifically to waves. The same results could be created with water or sound, for example.

Young performed his experiment using a beam of sunlight. He didn't have the technology to emit photons individually. In 1909, G.I. Taylor was able to reduce down his beam of light until just one photon was emitted at a time, and he got the same results as Young did a century earlier, with the appearance of interference building up with each photon that was fired.

If you are confused by this experiment, check out Dr. Quantum's animation. He describes electrons being shot off one at a time. The results are the same as for photons shot individually:

This is very strange stuff, but wait! He was shooting off individual photons one after another, so how could each subsequent photon know where to land in order to create a wave interference pattern? This result implied that photons could anticipate subsequent photons. That would have to involve some kind of communication backward through time! I will leave you to stew with this for a moment as we turn our attention to the particle nature of light.

Particle Theory

Newton's corpuscular theory of light was based on simple theoretical ideas and experiments. Subsequent and more sophisticated experiments showed very clearly that light has a distinct particle nature. Perhaps the best proof comes from the photoelectric effect. Heinrich Hertz first observed this phenomenon in the late 1880's, but it was not until the early 1900's that Albert Einstein mathematically described the photoelectric effect in terms of discrete quanta or photons. It won him the 1921 Nobel Prize in Physics. This is how the photoelectric effect works:

First of all, a photon in a light beam has a specific energy and that is determined by its frequency. If a sheet of atoms (usually a metal because metal atoms have lots of electrons around their big atoms and the electrons are bound loosely enough to be fairly easily dislodged) is struck by a single photon of sufficient energy, then an electron within the struck atom is ejected and detected on a detector. This happens because the photon's energy is absorbed by the electron and that energy is high enough to overcome the electron's binding energy, sending it flying off. If you increase the intensity of the light beam you increase the number of photons striking the metal sheet and you increase the number of electrons emitted. But you do not increase the energy each electron possesses (some of the energy absorbed by each freed electron also contributes to its increased kinetic energy as it flies off into the detector). There is a way you can increase the energy of the electrons flying off the sheet, however. You increase the frequency of the light used. Higher frequency light has more energy and more energy is transferred to the electrons. They will fly off faster because they have more kinetic energy. The photoelectric effect is explained well at the Hyperphysics site, with really good diagrams.

If light acts like waves, the electron energy would be expected to be proportional to the intensity of the light. As we see, it isn't. The electron energy depends only on the frequency (energy) of the light's photons. This concept - that a low intensity high frequency light source could dislodge many electrons and even an incredibly intense low frequency beam of light could not budge a single electron - flew in the face of well-established wave theories and was not easily accepted. None the less, Einstein managed to usher in the wave/particle theory of light, in which light manifests either its wave or particle nature according to the circumstances it finds itself in. This duality called for a new scientific paradigm, which could embrace it, and that is the concept of quantum mechanics.

Wave-Particle Duality

Quantum mechanics is the mathematical description of the wave-particle duality of matter and energy (yes, matter has this dual nature as well). It was developed in 1925 by Werner Heisenberg. In a nut-shell, it describes the time evolution of a physical system using a mathematical structure called a wave function. The wave function describes the probability that a physical system will be found in a given state at a given time. Light, in this new theoretical construct, is not a wave or a particle. It is a probability of a wave or particle at a given time. This concept describes the behavior of photons, electrons, and in fact all subatomic particle behavior. This video gives you a good idea of how the quantum mechanical model of the atom historically came about:

This is not an easily digestible idea and it might be tempting to simply leave this whole quagmire to the subatomic world where the problem of probabilities has little impact on our macroscopic world. The problem is that it does impact our everyday world. Superconductors, semiconductors, nuclear reactions and even chemical reaction mechanisms cannot be explained with classical mechanics. Cell phones, TV's and computers all rely on quantum effects. And to further convince you that quantum mechanics affects your life, consider that planets, stars, your house, and you could not exist in discrete clumps of matter if it were not for quantum mechanics at work behind the scenes inside every atom.

Quantum Electrodynamic Theory

We now have a theoretical foundation for light. Let's go further by revisiting some everyday light phenomena and testing out an even newer theoretical framework. This new framework is called Quantum Electrodynamics or QED. It describes how light and matter interact with one another using both quantum mechanics and special relativity. In fact, it is the first theory where these two concepts successfully combine and make sense. If you refer back to my unified field theory arguments in the "Universe" series of articles, you will find that the biggest challenge facing physics today is how to combine quantum mechanics with general relativity (which describes the force of gravity).

QED was first formulated in 1920 but it did not receive wide acceptance until the 1960's when, with the help of Richard Feynman and his colleagues, it was developed into the first successful quantum field theory, incorporating particle creation and annihilation into a self-consistent framework. The 1965 Nobel Prize in Physics went to them for this ground-breaking work. It has been used to precisely model such phenomena as the Lamb shift and the anomalous magnetic moment of the electron, which cannot be explained using classical physics. Late in his life, Richard Feynman gave a series of lectures on QED theory that were designed for the lay public. They are written down in the book, "QED - the strange theory of light and matter." I am drawing heavily from this book because it is the most understandable explanation of QED I have found.

Partial Reflection

I took this this photo of my desk while I'm working. In it you can see the reflection of my computer in the glass desktop. You can also see past it to the scissors in the clear plastic box under the glass. Some photons of light are reflecting from the scissors to your eyes while other photons are reflecting off the surface of the glass to your eyes. A reflection that you can see through like this is a partial reflection. The old film noir directors were experts at this kind of shot, usually through a café window.

Wave theory can explain partial reflection as interference when the light source is intense, that is, when many photons are involved, but wave theory breaks down when photons are studied individually. This is reminiscent of Taylor's refinement of Young's slit experiments.

I am going to use Feynman's example in his book to explore this phenomenon, and I urge you to pick up a copy of it for yourself.

Imagine identical red photons striking a block of clear glass straight down at a 90° angle. A device called a photomultiplier (A) is placed above the glass to catch and record any reflected photons. Another photomultiplier (B) is placed inside the glass. I know this experimental set-up is almost impossible but bear with me. This is what it looks like, with the angles altered a bit to help us see what's going on:
If the photons are directed straight down at the glass, an average of 4 photons will reflect back and arrive at detector A and 96 will arrive at detector B inside the glass. This will happen no matter how thick the glass is, as long as detector B is somewhere right below detector A. Here's the mystery with partial reflection: How can identical photons, each one shot out identically to the next, produce different results? 4% of photons decide to reflect and 96% of them decide to go through. With this simple experiment, we have just identified the probability component in quantum dynamics.

Now we will repeat the experiment by replacing the block of glass with a sheet of glass with its top and bottom surfaces exactly parallel to each other. In this case, detector A is in the same place above the glass as before but detector B is placed beneath the glass sheet. Now, photons can reflect from either the top surface or the bottom surface of the glass, so the number of reflected photons should be twice as many, around 8%, 4% of the first 100% reflecting back and 4% of the remaining 96% of photons reflecting back. Here is what the experiment like, again with the angles altered so we can see the photon paths better:
We find that this result happens with some glass sheets and not others, with the only difference between them being their thicknesses. These are our results (it doesn't matter what the real measurements are - all 3 glass sheets are very thin):

Thinnest sheet - 0% photons reflected
Medium thick sheet - 8% photons reflected
Thickest sheet - 16% photons reflected

Now we continue to use thicker and thicker sheets of glass. The amount of reflection does not continue to increase but goes down again gradually to 0%. As we continue to use thicker sheets, the cycle repeats itself. Again, over and over, if the layer of glass is one of many right thicknesses, zero reflection results.

Our prediction of 8% actually turns out to be the correct average result.

How can glass reflect 4% of the light until a back surface is added, and all of the sudden the amount of photons reflected varies from 0% to 16%? How did the photons decide to reflect in differing percentages based on where the back surface was placed, when the reflecting photons themselves never arrive at it?

No one knows how photons decide to reflect or not. But we can use QED, and specifically Richard Feynman's famous diagrams, to calculate the probability of whether a photon will reflect or go through. These diagrams are a way of calculating the probability amplitude of an event happening or not. I will show you some examples of them shortly.

Partial reflection explains why a film of diesel fuel over water is iridescent.

(Credit: John, Wikipedia)

The cycle of 0 to 16% reflection by 2 surfaces repeats more quickly if you increase the frequency of the light, so violet light reflection repeats faster than red light, for example. As a result, some thicknesses might strongly reflect both violet and red, where both of their probability amplitude crests happen to coincide, and at other thicknesses, neither may be reflected at all. The thickness of the diesel film shown above varies minutely, so you see all kinds of colours reflected back to you (this happens because sunlight is almost white light; it is composed of a mixture of frequencies: red, yellow, green and blue light - if you decided to come back at night and view the fuel slick under the light of an old-fashioned sodium street light that shines pure yellow light, you would get only yellow reflections).

Reflection from a Mirror

The established rule for calculating where light will go in this case is the angle of incidence equals the angle of reflection. This might lead you to assume that all the incident photons of light travel in one path to the mirror surface and back up again to a detector. After all, 100% of light is reflected is it not? To test this assumption, we will set up an incident light source, again red photons so they're all the same energy, at an angle of 45° to a strip of mirror and we'll place a detector where the expected path of reflected photons should reach. As you visualize the mirror you might think that the two ends of it, far from where any photons are expected to strike, will have nothing to due with the reflection. But quantum theory has something to say about that assumption. It tells you that a photon has an equal probability of striking the mirror at any point along its length, not just where the point of reflection is. In reality, the incident light does not all travel in one straight beam; it spreads out. If you use Feynman's arrows, you can draw a series of arrows, each representing the probability of a photon striking a specific point along the mirror, each of equal length (equal probability!). Each arrow will point a different direction, however. The arrows turn, like tiny stopwatches, as the photon travels, marking off how long it takes to get from source to mirror and from mirror to detector. All the arrows are then added up head-to-tail like vectors, so that opposite-directed arrows cancel each other out and those going the same direction add together. This calculation gives you, in essence a final arrow of highest probability and that arrow (did you guess it?) corresponds to the classical path of the light you predicted. Because the probability arrows differ only in the time taken by each photon, this final arrow also represents the shortest and, therefore, quickest path the photons can take. You might, very understandably, think that all I have shown you is some fancy trick that comes up with the right answer, that it doesn't prove that reflection is actually going on all over the length of the mirror.

Let's test your argument and the validity of quantum theory.

Let's chop off the mirror leaving one quarter of its length, over to the left. When we add up all the photon arrows now, we get arrows canceling each other out (the vectors actually go in a circle). We don't get any reflection. But this is what you expected of course!

Now let's take this shortened up mirror and scrape away the sections of it where arrows have a bias in one direction. For example, we add up all the arrows that point to the right, more or less. Now we have a substantial final arrow, and a strong reflection! You take a mirror that won't reflect, scrape off strips of it and, voila, it reflects. What we've done here is create a diffraction grating tailor-made for red light. Violet light has a higher frequency (the little stopwatch goes around faster) so we would have to make the strips closer together (or adjust the location of the detector). This experiment proves that light was indeed reflecting along the whole length of the mirror in the reflection experiment. You just didn't see it in that case because it all cancelled out. You can observe diffraction grating for yourself by looking at a CD at an angle.

The tiny grooves in the surface act like mirrors that are scratched in just the right places.

This technique, using Feynman diagrams, can be applied successfully to explain all light phenomena.

If you think about the mirror experiment above, you will see that light in that case was not just traveling in a perfectly straight line. Vector arrows that weren't perfectly aligned still contributed a vector component to the classically correct direction. Light reflecting just to the left and just to the right of the point of reflection significantly contributed to the final arrow of probability. This means that a beam of light does not travel in a perfectly straight line, but rather some of the light travels in a small core of nearby space. Light "smells out the neighbouring paths around it," to use Feynman's phrase in his book. If we took our mirror now and chopped off each side of it, leaving a piece that is too small for this core of light to strike it, we would not get any reflection at all. Light would then be scattered in all directions.

Here is the main point I hope to leave with you: The behavior of light in classical optics reflects not the actual photon's path but the path of greatest probability (and we can fairly accurately call this path the quickest path).

Photons and Electrons Dance Together

When we explored reflection I gave you the impression that photons bounced off the surface of the glass. Photons don't really do this. Instead they interact with electrons in the atoms that make up the glass. This interaction between photons and electrons is the basis of one of the four fundamental forces, called electromagnetism. This force is behind many phenomena we see every day, including all of chemistry and biology. All of these interactions between photons and electrons boil down to 3 basic actions:

a) A photon goes from place to place (this is not quite correct is it? I mean the probability of a photon goes from place to place!).

b) An electron's probability also goes from place to place.

c) And, finally, an electron emits or absorbs a photon.

Each of these actions has a probability amplitude (a final arrow length if you will).

A Closer Look at Refraction

Remember when I was talking about refraction as the appearance of light slowing down? The slowing is actually extra turning of the imaginary stopwatch as photons strike more electrons more often in materials that are dense in outer valence electrons (these are electrons within the atom's outermost orbital. They are more freely available to interact with photons). The photons appear to take longer to travel through such materials because they are busier being absorbed by electrons, which then emit new photons. As this goes on, the travel time for light inside the material grows longer. Bose-Einstein condensates consist of extremely tightly packed, cold and sluggish atoms, extremely dense with electrons, and that is why light takes so long to make some headway through it, as demonstrated here (with some awesome implications of the phenomenon!) in this cool video:

There is an important distinction to keep in mind here: When light is refracted, it appears to slow down, and in classical terms it does. But the individual photons involved in refraction do not slow down. In between electron emission and capture, they are motoring along at light speed. Or are they?

Electrons and photons (and again I should be more correct by calling them wave functions to remind us of their inherent uncertainty) travel a bit differently than we think of travel. They travel in space-time. Yes, this implies that they can (and do!) travel forward and backward through time. Give yourself a moment to digest that. Now, we assume that photons of light all travel at exactly the speed of light. There is a strict rule in physics that says nothing can travel faster than light speed. Well, that isn't entirely correct. Light speed, like everything else in the quantum world, has a probability. A photon can travel faster or slower than light speed, c. I assure you that at any distance appreciably longer than the diameter of an atom, all the possibilities of c cancel each other out and c is very accurately 299,792, 458 m/s. But over the tiny distances that electrons travel within an atom, this built-in variability becomes significant and must be taken into account.

Photons Live In Spacetime

To explore this idea, I will again work with an example I am borrowing straight from Feynman's book.
This is a diagram of a photon going into an electron and a (new) photon coming out, three of countless similar interactions that occur within the mirror when light strikes it. For ease, the three dimensions of space are condensed down and treated like one, so we have a time versus distance graph. The electron's movement is shown by the black arrows and the movement of the two photons involved is shown by the red arrows (these red arrows are conventionally drawn as squiggly lines but I don't have the Photoshop ability to make those). These are just three of countless possible ways this interaction could play out. And in each of these cases, where an electron absorbs a photon, continues on for a bit and then emits a photon, what we see in the everyday world is not a reflection but the scattering of light off the mirror (except in the very unlikely event that the trajectories of the two photons perfectly line up along the three spatial dimensions).

Let's take a closer look at possibility c in the diagram above because it is especially interesting. Here I have redrawn it in just a bit more detail.

I've marked out a timescale going from zero to 10 arbitrary and extremely tiny units, all positive values because we, in our everyday world, can only look at time going forward when we investigate things. From T0 to T4 we see an electron and a photon moving toward each other. At T4 something very weird happens: The photon (bottom left) suddenly disappears and two new particles appear in its place - an electron and a new particle called a positron. The important thing to remember for our purposes here is that a positron is an electron moving backward through time. Here, from our viewpoint, it appears to move towards itself. At T5 the positron and the original electron annihilate themselves and a new photon is produced. The electron created by the earlier photon continues forward in space-time.

This simple (well, not so simple) event sounds like total science fiction but it has been documented in the lab. And remember: This is just one of countless photon-electron interactions that occur every time ordinary light strikes a mirror (or any surface) and scatters. Particles are moving backwards through time right under your nose right now.

Why QED is Important

Feynman goes on to explain how photon exchanges between electrons and protons inside atoms account for how atoms of different elements exhibit different properties, a branch of science called solid-state physics, as well as how magnetism works, and how and why subatomic particles have specific spins. Finally he provides a good introduction to quantum chromodynamics, the science of how subatomic particles called quarks (these make up protons and neutrons inside the nuclei of atoms) get their spins, colours and flavours (physicists dropped the ball here with the naming). QED is an elegant theory with experimental verification to back it up. It is a powerful tool that physicists now have at their disposal and it is a major component of the Standard Model in physics.

The ultimate goal of the Standard Model is nothing short of a complete theory of all fundamental interactions, in other words, a theory of everything. The Standard Model is an example of Quantum Field Theory where each field describes, or is mediated by, a fundamental particle (photons and electrons are fundamental particles). It's not complete. Physicists are still looking for the particle that mediates gravity fields, called the hypothetical graviton, and the Higgs boson, the particle that is believed to give objects mass. Dark energy is not accounted for yet either, all of which are central to the physics of general relativity. The discovery of the Higgs boson alone would be instrumental in bridging the gap between relativity and quantum theory.

A Universe Without Electromagnetic Radiation (Without Light)?

You and everything else are made up of atoms. Within each atom, electrons orbit (within probability clouds called orbitals) around a nucleus made up of protons and neutrons. Each electron is held within a certain range away from the nucleus by photon exchanges between it and a proton. If it were not for these photon exchanges and the fact that electrons are polarized (another phenomenon that can be explained using QED theory), all atoms would have the same properties and electrons would all cluster together near their nucleus. They would not be easily attracted to other atoms, so all chemical and biological reactions would be impossible. Not only that, but all matter in the universe would behave something like, but different from, smeared out neutron star matter. Physicists think that inside neutron stars neutron degenerate matter exists, where electrons under great pressure collapse into the nucleus and merge with protons to form neutrons. Would matter even exist in a universe without electromagnetism? Almost all the elementary particles that mediate the fundamental forces have electrical charges and magnetic moments. There would be no magnetic or electrical forces. Stars, even if they could exist in some neutron star-like form, could not emit energy. A universe without light (electromagnetic force) would be absolutely unrecognizable, and unlivable, to us!

Electromagnetic energy is being propagated by photons and exchanged by electrons inside every atom of you right now. You could say, with some accuracy, that you are infused with light. The warmth you feel and all the processes of life your tissues and cells are busy with, and just about everything going on around you this moment is taking place because energy is being transferred place to place by photons.