Tag Archive | "quantum mechanics"

Why is the Higgs Boson a Massive Deal?

After around 50 years since the Higgs boson’s existence was proposed in the 1960’s, scientists at CERN have now confirmed at a 4.9 sigma significance level (more than 99.9999% confidence) that a particle that looks like the Higgs boson exists. Evidence from the ATLAS and the CMS experiments at CERN show a particle with the predicted Higgs boson mass of around 125 GeV resulting from the head-on collision of two protons.

Remember from Albert Einstein’s famous E = mc^2 equation that mass is energy divided by the square of the speed of light. Particle masses are measured using the voltage (or energy) of the electron as the standard. At over 125 x 10^9 electrons worth of energy, the Higgs boson is the heaviest particle that has ever been produced at the Large Hadron Collider (LHC). Indeed, finding this particle was one of the main motivations of building a particle accelerator with the size and power of the LHC in the first place.

A boson is a particle whose behavior can be described by a system called Bose-Einstein statistics. The Higgs boson is a special kind of boson called a “gauge” boson. This class of bosons brings about the fundamental forces of nature, with the photon mediating electromagnetism, gluons mediating the strong force (which holds quarks, the building blocks of protons and neutrons, together), and the Z and W bosons mediating the weak force (which is involved in radioactive decay and hydrogen fusion in stars). The as-yet-undetected graviton is not predicted by the Standard Model, but is a gauge boson that mediates the force of gravity in some quantum mechanical descriptions of gravity.

The Higgs boson has been called in the media as the “God particle,” as it will solve a key problem in the current Standard Model of particle physics. The Standard Model describes the nature of matter through dozens of subatomic particles. The initial problem with the model, however, is that it shows that particles initially have zero mass and cannot explain why some particles have mass. If particles don’t have mass, they will whiz through the universe at the speed of light. This is clearly not the universe we live in.

To solve this matter, Peter Higgs, among other independent teams of scientists, proposed what came to be known as the “Higgs mechanism.” Higgs suggested that throughout the universe exists a field, now called the Higgs field. Fields can be described using particles, like how the electromagnetic field can be represented by light particles called photons. The particle of the Higgs field is the legendary Higgs boson.

Peter Higgs (middle) shedding tears, which have masses from a particle that bears his name, at CERN when the ATLAS and CMS results were publicly announced


The Higgs mechanism acts similarly to how photons, or light particles, travel at 299,792,458 m/s in a vacuum, but not when there are particles in the way. Light appears to slow down (and bends) in a medium, such as glass, because it actually travels a longer-than-apparent path.


The black lines represent the true path of the photon as it goes through a medium. At each portion of its journey, it travels at the speed of light. The red line represents its apparent shorter path.


Photons hit glass particles and get deflected from their path, resulting in a longer true distance traveled despite appearing to have traveled a shorter distance. Since speed is distance over time, it appears to us as if the photon has taken a longer travel time, when it actually just traveled a longer distance at the same speed it always does. Higgs bosons act like glass particles on a photon, obstructing the path of Higgs-interacting particles, such as electrons, in the universe. The “God particle” isn’t magical or supernatural as its name suggests it to be, but without the Higgs boson, there would be no people to wonder why particles have mass.

“Why are things so heavy in the future? Is there a problem with the Earth’s gravitational pull?”


Recall from Newton’s first law that inertia is the tendency to remain at rest, if initially at rest, and tendency to remain in motion, if initially in motion. Since mass is simply the measure of inertia and particles naturally have no mass and fly around at the speed of light, all Higgs-interacting particles will be slowed down by the Higgs field and look to us as if they had gained a resistance to change in motion, which we measure as mass. The photon does not interact with the Higgs field, so it retains its speed and lack of mass.

The Higgs mechanism explains how many particles, such as electrons, gain inertia (or mass). Quarks, which make up neutrons and protons, also gain some of their mass through the Higgs mechanism (though most of their mass comes from interacting with gluons). To be clear, the Higgs boson is not the reason for all mass in the universe.

The Higgs boson is hoped to be the final piece of the Standard Model of physics. Further work will be done to establish that the discovered massive 125–126 GeV particle does indeed have the properties that have been predicted for the Higgs boson. However, even just finding a 99.9999% credible Higgs boson candidate makes scientists more confident that we have in the Standard Model a good picture of the universe at its smallest and weirdest scales.


Peter Higgs Image and Tear Metaphor Credit: Reddit

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Quantum Queries: Where’s Amber?

This is a continuation of the story of Amber the electron. Amber’s story is a very important one because it is also the story of physics, the study of the fundamental aspects of our universe. You may learn about the first part of this story by reading ‘Quantum Queries: Is Ours A Clockwork Universe?’


Down In Amber’s World

Last time, we saw that up here in the world of familiar objects — bouncing basketballs, falling apples, orbiting planets — the laws that govern our universe make it tick like clockwork. Down in the world of Amber the electron, things can seem very different. We must use a different set of rules to explain the behavior of Amber the electron and similarly small objects like protons, neutrinos, and positrons. These are the rules of quantum mechanics, and objects governed by these rules can be called “quantum objects”. Amber the electron is a quantum object.

Back to the questions that started this discussion: Where’s Amber? And how fast is she going? Where is she headed? There are two things we must know about Amber before we can reasonably answer these questions.

First, everything we can say about Amber is contained in what is known as her wave function. The wave function is represented by the Greek letter Ψ (psi). Basically, Ψ contains everything that we can say of Amber.

Second, Ψ can be determined using Schrödinger’s equation (named after the colorful German physicist Erwin Schrödinger).

Schrodinger’s equation

Schrödinger’s equation plays the same role in quantum mechanics as Newton’s Second Law does in classical mechanics. Recall that if we know the location and velocity of Bouncy the ball now, we can use Newton’s Second Law to determine his location and velocity at any other time. Likewise, if we know Amber’s wave function Ψ at any given moment, then we can use Schrödinger’s equation to determine Ψ at any later or earlier time. In other words, the way the wave function changes over time is also deterministic.

But wait, where is Amber? And how fast is she going? Where is she headed? Where will we find her at some later time?

To answer these questions, we now turn to the crux of the matter and possibly the source of all the weirdness of quantum mechanics. We turn to the meaning of the wave function, Ψ. What is Ψ anyway and what does it tell us about Amber’s whereabouts and howabouts?

Well, scientists have discovered that Amber’s wave function determines her probability density. Amber’s probability density gives us the likelihood of finding her in some place. To illustrate what this all means, let us use the well-known example of the hydrogen atom.

Suppose Amber is the electron of an atom of hydrogen. We can use Schrödinger’s equation to determine Amber’s wave function Ψ. Once we have determined Ψ, we can then use it to determine Amber’s probability density. In the context of atoms, the probability density of the electron is also called its electron cloud. Why is it called an electron cloud? Well, just take a look at the picture below.

One of Amber’s possible electron clouds. Chemists call this cloud the ‘1s orbital’. [Photo credit: cronodon.com]

The picture shows one of Amber’s possible probability densities, one of her potential electron clouds. (For those who remember their high school chemistry, the electron cloud shown above is what chemists call the ‘1s orbital’.) The darker regions represent regions in space where one is relatively likely to find Amber. Meanwhile, the lighter regions are the regions where finding her is relatively improbable. Notice how Amber’s probability density is diffused throughout space. That is why it’s called an electron cloud– like a cloud, it is not a firm, rigid structure but is instead spread out. Below are more possible electron clouds for Amber. (Chemists call them the 2p, 3p and 3d orbitals, respectively.)

Other possible electron clouds. Chemists call them the 2p, 3d and 3p orbitals, respectively. [Photo credit: cronodon.com]

So, does this mean that Amber is spread out? Well, let us check via experiment. Let us consider again the original electron cloud above. This time, we label some of the points in space. Let’s label them points A, B, C and D. Even before we perform the experiment to determine the whereabouts of Amber, we already know that Amber is more likely to be found in A than in B and less likely to be found in C than in D. Also, Amber is equally likely to be found in A as in D.

However, scientist found that after performing the experiment, they find Amber in a definite location. Say, you perform an experiment and find that Amber is in B. Two questions naturally arise. First, why in B and not A, where she was more likely to be found? Second, does the result imply that Amber was in B all along?

To answer the first question, we note that quantum mechanics is different from classical mechanics in being probabilistic instead of deterministic. In other words, quantum mechanics is about probabilities or likelihood. And in probabilities, an improbable event is still possible and can therefore happen, while a probable event does not have to occur. For example, when you throw a pair of dice, getting a 7 is a likely outcome while getting snake eyes is unlikely. However, when you throw a pair of dice, it is still possible, although unlikely, to get snake eyes instead of a 7. The probabilistic nature of quantum mechanics is what inspired Einstein to compare it to God playing dice with the universe.

Snake eyes: an unlikely but nonetheless possible outcome. [Photo credit: mobilecasino.ie]

Now it’s time to tackle the second and thornier question: If we perform an experiment to locate Amber and, as a result, find her in B, doesn’t that mean she was in B all along? There are three main answers to this question, and they represent the three main interpretations of quantum mechanics. They can be stated as follows:

  1. The realist position says that Amber was in B all along. However, quantum mechanics was not able to tell us this. After all, quantum mechanics says that everything that can be said of Amber is already in Ψ. However, Ψ did not really tell us where we will find Amber, it merely gave us probabilities. Quantum mechanics is therefore incomplete – it does not give us a complete picture of reality. People subscribing to the realist position believe we need to discover what are known as hidden variables. Once these hidden variables are discovered, we can determine that Amber was indeed in B all this time.
  1. The Copenhagen interpretation says that before the experiment, Amber was not in B, nor was she in A, C, D or in some other location. This interpretation tells us that her wave function gives us all we can know about her. This has a very interesting implication: if Amber was not in any place before the search, and was found to be somewhere after the search, that means that the act of looking for her somehow forced her to be somewhere! In the case of our example, that somewhere simply happened to be B, but it could have been A, C, D or some other location.
  1. The agnostic position is to be silent about the whole matter. After all, who are we to say where Amber was before we actually searched for her? And it doesn’t matter whether you take the realist or Copenhagen interpretations because the equations of quantum mechanics give you the correct probabilities anyway.

After decades of furious research, many working physicists find themselves subscribing to the Copenhagen interpretation. (The Copenhagen interpretation got its name from the city of Niels Bohr, one of its main proponents.) And, surprisingly, the agnostic position is already eliminated by a relatively recently discovered theorem known as Bell’s theorem. Bell’s theorem basically says that it does make an observable difference whether Amber was in B all along or whether she was nowhere.  Also, very few working scientists are still hoping to find the hidden variables required by the realist position.

There are, in fact, other interpretations of quantum mechanics currently being considered by scientists. One of the more interesting of them is the many worlds interpretation.

  1. The many worlds interpretation (MWI) says that all possible outcomes (finding Amber in A, B, C, D and all other possible locations) actually happen, but in different worlds! According to the MWI, what is objectively true is the Universe (with a capital U); it is where you find Amber’s electron cloud. When you try to look for Amber, the many worlds of the Universe decohere; that is, they get distinguished from each other. In one of those worlds, you find Amber in B, and in that world, she was in B all along. In another of those worlds, you find her in A, and in that world, she was in A even before you searched for her. And so it goes for the other possible outcomes (finding Amber in C, D, ect.).

Schrödinger’s cat in the many worlds interpretation.

If you are starting to find Amber’s world weird, know that this is only the tip of the iceberg. The world of Amber and her fellow quantum particles is governed by randomness. It is the opposite of the clockwork universe of classical physics.


Quantum vs. Classical

Now, one might think it strange that there are different rules governing the universe at different scales, classical mechanics for big things and quantum mechanics for very small things. How does one decide how big is big, anyway? Or how small should a thing be for it to be ruled by quantum mechanics? The truth is, according to the best scientific evidence we currently have, quantum mechanics governs the behavior of everything. Even Bouncy the basketball is governed by quantum mechanics! After all, Bouncy is also made of electrons, protons and neutrons, which are all quantum objects. Everything around us is made of quantum objects! However, for objects the size of Bouncy, classical mechanics is a good enough approximation. In fact, it is a superb approximation, to the point that we could use classical mechanics to predict Bouncy’s behavior without fear of being wrong. In other words, classical mechanics is an excellent estimate of quantum mechanics that is appropriate in the world of everyday objects. In the scale of things we see and touch, the weirdness that quantum mechanics displays on the small scale disappears.

Given these statements, this article is therefore about the fundamental rules that govern the behavior of everything around and within us. Ours is a quantum universe, and God does indeed throw dice on us all.

God throwing dice with the universe. [Photo credit: zendope.com]

Up Next on Quantum Queries:

  • What is the deal with Schrödinger’s cat?
  • What is Heisenberg’s uncertainty principle all about?
  • What is a ‘quantum’ of anything?
  • Why did Einstein find quantum mechanics so repulsive?
  • What is tunneling and how will it render Moore’s law obsolete?
  • What is entanglement and how is it related to teleportation?
  • Can we test the truth of the many worlds interpretation?

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Quantum Queries: Is Ours A Clockwork Universe?

Quelling Quantum Quackery

Along with ‘energy’ and ‘vibration’, the word ‘quantum’ is one of those scientific terms most dear to charlatans. Furthermore, quantum mechanics itself is home to terms and concepts that are easy target to quacks who like to sound scientific. Here’s a sampler of commonly abused words and concepts: entanglement, coherence and decoherence, the uncertainty principle, the many worlds, Schrödinger’s cat, action-at-a-distance, and quantum teleportation.

The ease at which impostors can abuse the terms and concepts of quantum mechanics cannot be blamed on one thing only. However, there is one factor that looms above the rest, and this is the lack of public understanding of quantum mechanics. In fact, one could say that it is a lack of understanding of physics, or worse, the lack of understanding of science as a whole!

This  is why I have decided to start the series ‘Quantum Queries’.  Through this series of articles, I would like to introduce the uninitiated but interested netizen to the amazing world of quantum mechanics. In this series we would tackle — in a way that I hope is entertaining and enlightening — some of the most vexing questions that surround the workings of the world around us. Below is a sample of some of the quantum queries that we will try to answer in this series:

  • What is the deal with Schrödinger’s cat?
  • What is Heisenberg’s uncertainty principle all about?
  • Is the many worlds theory true? And if it is, where are all these other worlds?
  • What is quantum entanglement? And can it really be used for teleportation?

My hope is that this series will give its readers the skill to discriminate between genuine quantum physics and quantum baloney. What follows is the first article in this series. Enjoy!


The Quantum and the Classical

Meet Amber. She is an electron. Amber masses 9.11×10-31 kilograms, a mass that makes “featherweight” sound really heavy. (Amber’s mass in decimal form is 0.000000000000000000000000000911 grams!)

Where’s Amber? Also, how fast is she going and where is she headed? Where can we find her later?

Well, answering these questions is not as easy as it sounds. This is because Amber’s behavior is governed by the rules of quantum mechanics, which are quite different from the rules that govern the behavior of familiar objects like falling apples, swinging pendulums or flying cannon balls. The objects familiar to us through everyday experience are governed by the rules of classical mechanics, discovered in the 17th century by Galileo Galilei and Isaac Newton.

How different are the rules governing Amber’s behavior from the rules governing the behavior of, say, a basketball? And where in the world is Amber? To answer these and related questions, let us first review the physics behind the behavior of everyday objects. Let us begin with the classics.


Back to the Classics

Meet Bouncy the basketball. Bouncy masses 145 grams. Scientists have discovered that they can describe Bouncy’s behavior using the rules of classical mechanics. When you hear physicists say, “Bouncy behaves classically,” this is what they mean.

So, where’s Bouncy? Also, how fast is he going and where is he headed? There are two things about Bouncy that are relevant in answering these questions. 

First, classical mechanics tells us that at any given moment, we can narrow down the range of Bouncy’s possible locations and speed as much as we want. For instance, it is possible that you at first only know that Bouncy is within Quezon Cityand has a speed somewhere between 1 kph and 4 kph. However, you can always find a way to narrow these ranges so that, after some investigation, you know that Bouncy is in the basketball court of the Araneta Coliseum and is going somewhere between 1.5 kph and 2.5 kph. Finally, it is possible that further investigation will lead you to conclude that Bouncy is, in fact, in the hands of PBA point guard LA Tenorio, and has a speed of 2.00 kph directed 45° from the horizontal. No one could blame you if you say that you have determined exactly where and how fast Bouncy was at that moment – there is practically zero uncertainty in Bouncy’s location and velocity. If you’re wondering how you could’ve known where and how fast bouncy was at a given moment, just imagine watching a replay of a PBA game. By analyzing the video, you can determine Bouncy’s location and velocity at any moment during the game. (For those who forgot their high school physics, velocity is just speed plus the direction.)

Second, classical mechanics allows us to predict where and how fast Bouncy will be at some later time. You can do this by using Bouncy’s classical equation of motion. An equation of motion is an equation that describes, well, the motion of an object. In classical mechanics, the equation of motion, also known as Newton’s Second Law, can be written as follows:

Newton’s Second Law.

So let’s review what’s been said of Bouncy so far. First, we can be more or less certain of Bouncy’s location and velocity at any given moment. Second, if we know Bouncy’s location and velocity now, then we can use Newton’s Second Law to know his location and velocity in the future.

For example, consider the case where LA Tenorio is attempting a shot and Bouncy leaves his hands at the speed of 2.00 kph, projected at an angle of 45°.

Calculations using Newton’s Second Law will allow you to predict, up to a very high precision, where and how fast Bouncy will be after he leaves Tenorio’s hand. This means that you can forecast whether or not Tenorio will make the shot. Of course you can only do it if you are very fast in calculating. A supercomputer watching the basketball game could perform such überfast computation.

Since it is possible to determine and predict the precise location and velocity of everyday objects like Bouncy, classical mechanics is described as deterministic. Note that classical mechanics does not limit you to calculating Bouncy’s future location and velocity; you can also calculate Bouncy’s previous location and velocity. In other words, if you have enough computing capacity and knowledge of the present situation, you can know the location and velocity of classical objects like Bouncy for all time in the history of the universe!

The path of angry birds are classically predetermined. [Photo credit: pamobriensblog.files.wordpress.com]

But the following question will naturally arise in the curious reader’s head: How do we know thatNewton’s Second Law is to be trusted? How do we know that the whole of classical mechanics is correct? As always in science, the ultimate test of correctness is agreement with observation. And hundreds of years of observation have confirmed the accuracy of classical mechanics in describing the behavior of objects ranging from basketballs, cannonballs, and rockets to things the size of planets and stars.

In fact, for centuries the planets and stars themselves became the paragons of Newtonian physics’ sober splendor. The astounding predictability of the dance of the planets made the image of a clockwork universe indelible in the minds of generations of scientists.

A grand orrery: a picture of the clockwork universe. [Photo credit: abyss.uoregon.edu]

One cannot therefore blame scientists for initially thinking that electrons like Amber will also behave like Bouncy and other classical objects, and that the universe will appear to tick like a grandfather clock at all scales. However, the shocking discoveries of the early 20th century revealed to us that in the strange world of Amber and her fellow quantum objects, the clockwork dreams of classical physicists are regularly blown to smithereens.


Up Next on Quantum Queries:

  • So, where is Amber?
  • What is Heisenberg’s uncertainty principle all about?
  • What is the wave function?
  • What does the many worlds theory tell us about our Universe?

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The Eternal Universe

Let’s get back to basics. The following is a case against a cosmological argument for the existence of God.

Intelligent (not “folk”) Christians will repeatedly tell you that faith and reason are both used in their theologies. Unlike the laity and the unwashed masses, they don’t rely completely on faith, or belief without evidence. Indeed, the Christian religion in its many forms has a long history of logical attempts, from Aquinas to Calvin, at trying to prove the existence of God and the plausibility of their doctrines. This is perhaps due to the fact that certain intellectuals in each tradition simply cannot reconcile their rationality with their religion’s doctrines.

Through tireless philosophical refinement of initially primitive and unimpressive doctrines such as the Genesis myth, we get sophisticated logical arguments such as Thomas Aquinas’ Five Ways. Seeing these attempts at logical proof, though, I am personally baffled by the intelligent theist’s recourse to faith. If God is provable through reason, of what use is faith? If faith is sufficient, why use imperfect human reason?

Philosophical arguments for God take various forms, such as the cosmological, ontological, and teleological arguments. There are, of course, many criticisms against most, if not all, of these. The cosmological (first cause) and teleological (purposeful design) arguments are empirical arguments, taking the world as it is and reasoning that there must have been a Creator.

One of the most interesting of these arguments, for me, is the Kalam cosmological argument. Unlike most arguments for God, it intends to at least be scientific in its attempt at proving that a personal God exists. Through its most vocal proponent, theologian William Lane Craig, the Kalam is used to argue that the universe must have had a cause. Formally stated, the Kalam appears as such:

(1) Everything that begins to exist has a cause.
(2) The universe began to exist.
(3) The universe has a cause.


Everything that begins to exist has a cause

Premise (1) asserts that everything that begins to exist has a cause. This statement evades criticisms such as those that Bertrand Russell put forward against Aquinas such as, “Who made God?” Since the Kalam argument states that everything that begins to exist has a cause, God, who is eternal and never began to exist, does not have a cause.

Physicists such as Victor Stenger have argued that not everything that begins to exist has a cause. When an electron increases in energy to an excited state and returns to its ground state, a photon appears. This appearance of the photon occurs spontaneously and is not a deterministic consequence. That is to say, in Stenger’s words, it is “without cause.” The same is true for the radioactive decay of the atomic nucleus. We can know the probability of decay but it is impossible to say exactly when the decay will occur.


Atomic nucleus decaying an alpha particle (helium nucleus)

William Lane Craig readily counters this by saying that that is not true causeless existence since nature, which God presumably made, is necessary for such events. However, Craig must now accept that probabilistic causes, if they are “causes” at all, are possible mechanisms for the beginning of the universe. This severely weakens the notion that a personal God predetermined the moment of creation with a purpose.

However, even accepting Premise (1) as true, we can move forward and still see that the Kalam argument ultimately fails in its misuse of time.


The universe began to exist

The discovery of the Big Bang model of the origin of the universe was very popular among theists. The Big Bang, they suggest, is proof positive that the universe began to exist. When Georges Lemaître first proposed the model, Pope Pius XII saw this as scientific evidence for creation, “it seems that science of today, by going back in one leap millions of centuries, has succeeded in being witness to that primordial Fiat Lux when, out of nothing, there burst forth with matter a sea of light and radiation, while the particles of chemical elements split and reunited in millions of galaxies.”


Timeline of the universe

Theologians and apologists such as Craig and Dinesh D’Souza find that since the universe as we know it began 13.7 billion years ago in the Big Bang, then the universe began to exist and it had a cause for its existence. Craig, in the Islamic tradition of the Kalam, suggests that since the universe began to exist 13.7 billion years ago, then there must have been a “particularizer” to decide to begin the universe at that moment and not a moment before. And since this particularizer has the capability to decide and distinguish between moments, then this must be a personal kind of God with a mind analogous to ours (therefore not the deist’s God).

Remember, though, that Craig can no longer require this decision to create the universe to be particularized by a personal God since he must allow that probabilistic causes are possible causes for the universe. The mechanical circumstances necessary for atomic decay are all already in place, even though the effect of a decayed nucleus is delayed. The nucleus could decay in 2 seconds, it could decay in 100 billion years. This defeats the necessity of a personal God deciding to create the universe 13.7 billion years ago and not 12 or 20.

As James Still has seen, Craig’s view of time results in severe problems for the Kalam. It seems that in his view, time exists not in the physicists’ definition of time. Physicists use time in the relational view, where time exists relative to bodies in motion, like ticking clocks. This is integral to Einstein’s special and general theories of relativity, where the experience of time changes depending on velocity and the presence of mass. This effect has been confirmed and global positioning systems would fail without the corrections predicted by relativity. More importantly, general relativity shows that, if the universe did begin to exist, time itself began along with space, energy, and matter.

It makes no sense in the relational view of time to suggest that the universe could have had begun a moment before since there were no moments “before” the Big Bang, which is when time started ticking. Therefore, Craig seems to see time as absolute in his metaphysics. Personally, his view makes no sense to me. Perhaps he believes that events can be absolutely simultaneous regardless of frame of reference, which goes against special relativity. At the very least, we know that Craig clearly does not mean “time” in the way it is used by scientists.

It has been suggested that it is possible that the universe has simply always existed—a “brute fact,” in Russell’s words. This would remove any need for a creator since the universe did not “begin to exist.” However, Craig counters this by supporting Premise (2) with the following argument:

(4) An actual infinite cannot exist.
(5) An infinite temporal regress of events is an actual infinite.
(6) Therefore, an infinite temporal regress of events cannot exist.

Through this argument, Craig contends that it is impossible for the universe to have always existed since this would require an infinite temporal regress of events. Craig uses the example of Hilbert’s Grand Hotel to show that an actually real infinite would lead to absurdities.

Briefly, David Hilbert’s paradox of the grand hotel shows that if you have a hotel with an infinite number of rooms, it can accommodate an infinite number of guests. It should then be full after checking in an infinite number of guests. But, if another infinite number of guests should wish to stay in the hotel, one would only need to move the first set of guests to odd numbered rooms and the second group into even numbered rooms. You have now accommodated another infinite number of people in a supposedly full hotel. Craig argues that since this is a counter-intuitive result, then an actual infinite must be impossible.

It is important to note, however, that counter-intuitive results show up in science all the time. The greatest example of this is the discovery of wave-particle duality. A particle can be at many places at the same time. A particle can have many states at the same time. It is therefore not true that counter-intuitive results are necessarily impossible. However, we need not reject Craig’s use of Hilbert’s Hotel to see that Premise (2) in the Kalam is problematic.

Contrary to how Craig views the Big Bang model, the standard model of cosmology does not necessarily see the universe as beginning from a single infinitely dense point—a singularity. This prediction that the universe began as a singularity, via the Penrose-Hawking theorems, was because the Big Bang was erroneously viewed purely through the lens of General Relativity. Both Roger Penrose and Stephen Hawking would later revise their position. Taking into account the physics of quantum mechanics, which would dominate at the extremely small scales of the earliest moments of the Big Bang, Hawking says, “There was in fact no singularity at the beginning of the universe.”


Imaginary time can be described as time as if it were like a dimension of space.

It is completely possible, as Hawking suggests in A Brief History of Time, that the universe has no boundary in time. This means that t = 0 (where t = time) is merely in the middle of a continuous line of imaginary time (a concept necessary to describe quantum tunneling), like how the South Pole is not the end of the Earth, but just another point along the longitudes. Trace the longitude going through the poles of the Earth and you get a finite but unbounded geometry—a great circle; the same could be true for four dimensional space-time. It therefore stands to reason that time need not have a beginning, as a singularity would suggest.

In quantum tunneling, a particle can break through a potential energy barrier even if it has less than the energy necessary to overcome the barrier. The very much real physics of the particle when inside the barrier can be described using complex, or imaginary, time.


In any case, singularity or no singularity, the scientific relational view of time avoids the problem of an infinite addition of events leading up to today because, although the age of the universe is finite, it is also true that the universe is eternal and has always existed. There has never been a time when there was no universe.


The universe has a cause

Craig asserts through an absolute view of time that actual infinities cannot exist. This would also apply to God. God cannot have existed through an actual infinite addition of events going back to nowhere. To get around this, theologians can assert that God is eternal not in the infinite number of events sense but because he is timeless. Unfortunately for the theist, since God is timeless, there would also never have been a time when God did not create the universe. The eternal universe would also be timeless in the same sense.

If Craig is to retain his absolute view of time, he must also reject the impossible timelessness of God. God must have begun to exist and himself have a cause. We can repeat Bertrand Russell’s challenge, “Who made God?” If Craig is to accept the physicists’ relational view of time, he must also accept that the universe is “eternal” in the same sense that God is eternal. Premise (2) fails and God is then an unnecessary explanation for the universe’s existence.

As Paul Draper notes, another problem with the Kalam cosmological argument is that it equivocates two senses of the phrase “begin to exist.” The strength of the Kalam cosmological argument is that it purports to be a proof of God from the evidence. It uses inductive reasoning to show that since everything begins to exist from causes, then the universe must also have begun to exist from a cause. However, the things we see to begin to exist begin in time. The universe, if it began to exist, began with time 13.7 billion years ago. We have no experience, no valid intuition, of things, let alone universes, beginning with time. Craig therefore commits the fallacy of equivocation in reasoning from the example of ordinary objects that the universe must also have a cause. Even if we accept Premises (1) and (2), the conclusion of the Kalam cosmological argument remains invalid. The eternal universe remains a brute fact.



The Kalam cosmological argument was a very strong case for the existence of not just a supernatural creator, but a personal one with a mind and thoughts. Because of the supposed impossibility of infinities in the real world, there is indeed a real problem for the naturalistic existence of the universe.

All of these arguments, however, have been fatally challenged by what we know today about the universe. The necessity of a personal creator is refuted by the existence of natural mechanisms for probabilistic causes. This means that naturalistic causes need not have their effects occur immediately after. The eternity of the universe is also supported by the dependence of time on space. In other words, without the universe, there was no time. Without time outside the universe, there was never a time without a universe. Hence, the universe has always existed and a creator is unnecessary to explain its existence.

It was perhaps impossible to have been an intellectually satisfied atheist until the discovery of relativity and quantum mechanics. The refutation of the Kalam heavily depends on the evidence that supports these theories. This did not have to be how nature is. As we learn more about the peculiarities of the universe, the God-shaped hole at the end of the universe is all but plugged.


All images are public domain except image on quantum tunneling by Jean-Christoph Benoist. Licensed under Creative Commons.

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What In The World is Laser? (Part 3 of 3)


[The author would like to thank the geniuses behind the new Microsoft Paint for making the figures in this part possible.]

How are laser beams produced?

Laser beams are the product of stimulated emission of light. But what is stimulated emission of light? Before we can answer this question, we must first discuss how matter interacts with light.


Light absorption

Matter and light interact in two ways: matter can absorb light or it can emit light. When an atom absorbs a photon of light (a photon of light is a quantum of light energy), it takes the energy of that photon and one of its electrons become excited (although not sexually). An electron orbits the nucleus of an atom in one of the possible orbits. Larger orbits (orbits that take the electron farther from the atom) have greater energy. Normally, an electron will orbit the nucleus in the smallest possible orbit. This orbit is called the ground state. When an electron gets excited, it jumps from the ground state to an orbit with a higher energy. Such an orbit is called an “excited state”. An electron is excited when it is on one of the excited states. The excitation of an electron (represented by the symbol e) by a photon is illustrated by Figure 1 below.


Figure 1. A photon of light (red oval with wave inside) is absorbed by an atom, resulting in the excitation of one of its electrons (e-, gray dot).


The ground state and one excited state shown in Figure 1 are just two of the many possible orbits of an electron around the nucleus. From quantum mechanics we know that the possible orbits are quantized. The quantization of electron orbits is important, so let us stray a bit from the main topic to discuss it.

Using the most important equation of quantum mechanics, Schrodinger’s equation, physicist were able to discover that in a given atom, the electron can only have a certain set of energies. This set of energies is called the spectrum of the atom. The possible energies are denoted by E0, E1, E2, E3 and so on. E0 is the smallest energy that an electron can possibly have. This is called the ground state energy. Obviously, this is the energy of an electron when it is in the ground state. (Recall that ground state is the smallest possible orbit.) E1 is the energy of the first excited state, E2 the energy of the second excited state, and so on. The energy of a higher excited state is always greater than the energy of the excited states before it. In other words, E0 is less than E1, which in turn is less than E2, which again in turn is less than E3 and so on. (E0 < E1 < E2 < E3 < …)  Now, here’s the most important bit. An electron in an atom cannot have energy between E0 and E1. It is simply impossible for an electron to have energy greater than E0 but less than E1. Also, an electron can never have energy between E1 ­and E2, or between E2 and E3, and so on. The set {E0, E1, E2, E3, …} gives the only possible energies of the electron.

Now we go back to absorption. Consider an electron initially in the ground state, so that its energy is initially E0. Suppose then that a photon of light having energy Ephoton hits the electron. This photon will be absorbed by the atom and its energy will then be added to the original energy of the electron. The new energy of the electron after absorbing the photon will therefore be:


Enew = E0 + Ephoton.


But take note of this very important fact: Enew must be one of the allowed energies of the electron. That is, Enew must be one of the following: E1, E2, E3 and so on. This means that if the energy of the photon, Ephoton­, is such that Enew is not one of the allowed energies of the electron, then the photon will be totally ignored – the atom will not absorb it. An atom will absorb a photon only if it will make Enew be one of the allowed energies of the electron.

Figure 2 below illustrates a particular example. The red photon is ignored by the electron because its energy is not enough to make the electron jump to the first energy level. The purple photon, however, was absorbed, because its energy is just right to make the electron jump from the ground state (where energy is E0) to the first excited state (where energy is E1). In other words, the sum of the red photon’s energy and the ground state energy (Ered + E0) is not equal an allowed energy level, so electron ignores the photon completely. On the other hand, the sum of the energy of the purple photon and the ground state energy (Epurple + E0) is exactly equal to E1. Since E1 is an allowed energy, the electron will absorb the purple photon.

Figure 2. (a) A red photon is ignored since the sum of its energy (Ered) and E0 is not equal to an allowed energy. (b) A purple photon is absorbed since the sum of its energy Epurple and E0 is exactly equal to E1, which is an allowed energy.

Spontaneous Emission


The emission of light is just the inverse process of the absorption of light. Here, an electron in a certain energy level (that is, a certain excited state) falls down to a lower energy level (a lower excited state or the ground state). When an electron falls down to a lower energy level, we say that it “relaxes”.

Relaxation is just the inverse process of excitation. (Although this is only true for electrons. In humans, it’s certainly not the case.) When an electron relaxes, it loses energy. The energy lost is of course equal to the difference between the original energy and the new energy. This lost energy becomes the energy of an emitted photon. For example, consider an electron initially in the first excited state. This means that its initial energy is E1. Suppose that this electron relaxes to the ground state, so that its final energy is E0. It is not difficult to see that this electron lost energy, and that the lost energy amounts to E1E0. This energy becomes the energy of the emitted photon.


Figure 3. An atom spontaneously emits a photon of light. The energy of the photon is equal to the energy lost by the electron: E1 – E0


Of course, an electron does not have to come from the first excited state. It may come from the second excited state, or form the third excited state, and so on. The higher the electron falls, the greater the energy of the photon it emits.

The situation shown on Figure 3, however, is just one type of emission called spontaneous emission (which does not have to be nocturnal). This is called so because the atom spontaneously emits a photon of light. Most light sources we know produce light by spontaneous emission. In a fluorescent light bulb, for example, electricity is used to excite the electrons of the atoms of a gas (usually the gas is mercury vapor). But the excitations are only momentary, because the electrons spontaneously jump back to the ground state and in the process emit photons of light. (These photons of light, however, are not what we “see” when we look at a fluorescent lamp. The photons produced in the said process have wavelengths in the ultraviolet region. This means that they are invisible to the human eyes. These invisible ultraviolet photons, however, cause the phosphorescent compound coating the inner lining of the lamp to glow. The phosphorescent compound is the white powder that is found inside the bulb.)

Laser beams, however, are not produced by spontaneous emission of light but rather by stimulated emission of light, hence the phrase “stimulated emission of radiation”. The very suggestive and juicy term stimulated emission describes the phenomenon where an atom emits light due to the stimulation of another photon. Basically, stimulated emission is just like spontaneous emission, only that it is not spontaneous.


Why Stimulated Emission is Amazing

Stimulated emission has the following remarkable property: when a photon stimulates an atom to emit another photon of light, the emitted photon will have the same wavelength, phase, polarization and direction as the original photon. In short, the emitted photon is just a Doppelganger of the photon that stimulated its emission!


Figure 4. A photon stimulates an atom with an electron in the excited state to release another photon. The emitted photon has the same wavelength, phase, polarization and direction as the original. One can think of it s a “clone” of the original.


We can now see that when one has enough atoms with electrons in the excited states, then one can use stimulated emission to greatly increase the intensity of a certain light. This is because light intensity can also be measured through the number of photons in a given beam. The more photons there are, the greater the intensity. But notice that stimulated emission has the ability to practically double the number of photons of the given light source. This is illustrated in Figure 5 below, where three atoms with excited electrons are used to double the number of photons from three to six. This is where the “light amplification” part of LASER comes from. (Recall that laser means “light amplification via stimulated emission of radiation”.)


Figure 5. There are initially three excited atoms and three photons. Due to stimulated emission of radiation, the number of photons has been doubled from three to six. After emission, the electrons of the atoms are already in the ground state.


But the light is not merely amplified by stimulated emission. The beam produced due to stimulated emission has the remarkable property of being composed to photons with the same wavelength (and therefore color), phase, polarization and direction. This is the reason why laser beams are highly monochromatic and coherent. Remember that to be monochromatic means to be composed of only one color. Since a laser is practically composed of an army of photon clones, a laser beam is very monochromatic indeed. Also, since the emitted photons have the same phase (which can be thought of as the tempo or vibration rhythm of the photon), polarization and direction, a laser beam has very high spatial and temporal coherence. In short, all the remarkable properties of laser beams are derived from a very remarkable property of stimulated emission!


Laser Devices


But now I hear the result-oriented and practically-minded among you say: “But how do we prepare a collection of atoms with excited electrons? Does this not mean that we also need photons to excite these electrons? And does this not mean that we are cancelling the amplifying effect of stimulated emission because we will be using photons to double the number of photons? Isn’t it like investing 500 pesos to gain 500 pesos?” Well, the answer is that light absorption is not the only way to excite electrons. There are many other ways to cause electrons to become excited, like hitting them with electricity or heating to very high temperatures them. There are many different kinds of lasers and each kind uses a different strategy to prepare atoms with excited electrons. But once such atoms are prepared, stimulated emission can then be exploited to double the number of photons from a certain light source, thereby increasing the intensity of the light.

In fact, in laser devices, the number of photons is not merely doubled, but is increased by several orders of magnitude. This is done by placing the gain medium in an optical resonator, as shown in Figure 6 below. The gain medium is the material that is used to amplify light. An optical resonator is a combination of two mirrors that make light bounce back and forth between them. One of these mirrors is a totally reflective mirror, while the other is a partially reflective and mirror. The partially reflective mirror allows some of the laser beam to pass while it reflects the rest. The beam that is reflected back can again stimulate even more atoms with excited electrons to emit photons. When it reaches the other end, it will be reflected by the totally reflecting mirror, and will then pass through the gain medium again, before reaching the partially reflecting mirror, where the cycle begins again. Notice, however, that once an atom is stimulated to emit radiation, its electron has already relaxed to the ground state. This means that after several rounds of stimulated emission, all the atoms will have ground state electrons only. So that the production of the beam is continuous, a “pumping energy” must be supplied to the gain medium constantly so that the atoms of the gain medium always have excited electrons.


Figure 6. A simple schematic of a generic laser device.




Now let us sum up all that we have discussed in this series. We started this series with a question: What in the world is laser? Well, laser is short for Light Amplification via Stimulated Emission of Radiation. A laser device is a device that produces laser beams via a phenomenon known as stimulated emission. Because of the remarkable properties of stimulated emission, laser beams have the extraordinary property of being monochromatic and coherent. By saying that it is monochromatic, we mean that it only has one wavelength. By saying that it is coherent, we are saying that its photons are oscillating or vibrating “to the same rhythm and beat”.

Now I hear the astute ones among you say, “Wait a minute, I see an inconsistency here. One minute you describe light as being made up of waves; electromagnetic waves, to be precise. But now you are describing them using particle-like entities called photons. What really is light made of, electromagnetic waves or photons?” This is a very good question, and it has a very remarkable answer: Light is made both of electromagnetic waves and photons. But how is that possible?

Now that is a topic for a separate series.


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Teleporting DNA

While it has been stunningly predictive and useful, quantum mechanics, because of its inherent peculiarity, has been a gold mine for new age hucksters such as Deepak Chopra. Albert Einstein himself couldn’t accept the theory which allowed for particles to take all possible paths from point A to point B and for cats to be both dead and alive at the same time. His aversion to this theory was immortalized in the quote, “God doesn’t play dice,” alluding to the strange universe ruled by random events that quantum mechanics was describing. To quote the physicist Richard Feynman, who made great strides in the field of quantum mechanics, “If you think you understand quantum theory, then you don’t understand quantum theory.”

Feynman’s fellow Nobel laureate, Luc Montagnier, who won the prize for establishing that AIDS was caused by HIV, recently published a paper, entitled “DNA waves and water,” which claims that through the use of electromagnetic fields, DNA molecules, the stuff of life, can “teleport” from one test tube to another. The mechanism this takes is, according to the paper, within the “framework of quantum field theory.”

Montagnier’s experimental setup included two test tubes, one containing pure water, and the other containing a highly diluted sample of a fragment of DNA from the human immunodeficiency virus (HIV). After applying a 7 Hz electromagnetic field for 18 hours to both the tube that contained pure water, and the other tube that contained DNA, the tubes were then subjected to a process called polymerase chain reaction (PCR). This procedure takes DNA molecules present in a sample and copies them continuously, based on a particular defined DNA sequence. Their results showed that the pure water miraculously produced DNA, when there should have been none.

Here the two tubes (with DNA on the left, pure water on the right) are shown being exposed to a 7 Hz electromagnetic field inside a µmetal cylinder.

This is a stunning result—so stunning that it seems rather dubious. The claim posited here is that dilute quantities of DNA can somehow emit “DNA waves” via its natural electromagnetic field and that this signal mimics the exact DNA sequence of the source in water. This signal can supposedly imprint itself into water. Such an outlandish declaration just cannot avoid comparisons to homeopathy. The paper’s conclusion also favors a rather convoluted solution (DNA waves) over a much more simple explanation: contamination. The retention of an electromagnetic field in the absence of the signal source is, however, entirely possible within quantum mechanics, though only in the order of picoseconds (one trillionth of a second)—certainly not enough time for a PCR reaction to take place (which usually takes about an hour).

The nature of PCR is that it is so effective at making copies of DNA that even just one molecule of DNA can be amplified. Imagine thousands of photocopiers that randomly take any page in their vicinity and copy them. Even if you just had one page to be copied, such a sheet containing the letter “X”, you could create millions of copies of this letter in no time since the copies of that page will be used by the other photocopiers to make even more copies—a chain reaction. Now, let’s say that just one stray sheet with the letter “Y” accidentally flew into the copier room. By the end of your copying, you’d have yourself billions of sheets with either “X” or “Y”. That’s how even one tiny splatter of contaminating DNA (from instruments used or even one’s own hands) can ruin an experiment.

Messing up a PCR experiment is so easy that Montagnier’s observation has to be reproduced by other scientists before it can even be taken seriously. The only reason it seems to be grabbing headlines is that Montagnier is a Nobel laureate. But, Nobel laureates are vulnerable to the dreaded “Nobel disease,” when noted scientists who have won the prize later support pseudoscientific ideas.

The originator of PCR, Kary Mullis, also won the Nobel prize, only to go on to deny the link between HIV and AIDS. Another laureate, Linus Pauling, who won two Nobel prizes, promoted the quackery that vitamin C treated cancers and prevented colds, late in his career.

However, regardless of accusations of Nobel disease, Montagnier’s ideas shouldn’t be dismissed offhand. If his observations can be consistently replicated by other researchers (and contamination is ruled out), then a revolution will occur in biology and all of science. It’s a prospect one can’t help but be excited about, but wonder should always be coupled with skepticism.

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