Cosmos 10: The Edge of Forever

by Shane L. Larson

My parents are both natural scientists — my mother is a forester, and my father is a plant ecologist. As kids, we would spend long weeks in the summer camping doing “field research” in the wild backwoods of the Rockies.  Tents were optional, and at night I would often lie in my sleeping bag staring up into the blackest night you can imagine.  

The Milky Way, rising over a campsite near Crater Lake, Oregon. [Image by Shane Black, Website]

From the dark valleys and meadows of the Rockies, the sky is a seemingly endless tapestry of black velvet, studded with a sparkling horde of stars converging on the vast gossamer seam of the Milky Way.  It is impossible to scan that deep darkness, as you slowly drift into that fuzzy netherworld between wakefulness and sleep, and not feel like you are falling into an infinitely deep sea that goes on forever.

And for all we know, it does go on forever! The vastness of the Cosmos, especially compared to the typical scales of our everyday lives, is mind-bogglingly large. It is a fact that we have always been cognizant of — our stories, our legends, even our everyday experiences place the sky very far away, beyond the simple reach of human hands. The glitter of distant stars provide an ideal tapestry upon which we can paint our wonderings about the Universe and our place within it. Where did the stars come from? Where did the Earth come from? Where did we come from?  These are the oldest questions we know of, uttered around campfires and over late night dinners and in scholarly classrooms for countless generations.  The answers to these questions are part of an exquisitely interlinked puzzle that starts with the birth of the Universe, and leads ultimately to me and you.  The study of that puzzle is called cosmology.

Cosmology is a branch of science that is a bit like history — we are reconstructing the past history of the Cosmos as a way to understand what we see around us today, and to predict what the ultimate future and fate of Everything might be.  We reconstruct that past history by looking deep into the Cosmos, and with the Laws of Nature in hand, attempt to explain what we see.  As we have talked about before, looking out into the Cosmos is a kind of Wayback Machine — looking across space is looking back in time.  Today, we can see farther across the Universe than at any other time in human history; we have discovered and know more than all the 40,000 generations of humans who have come before us.  And we’ve discovered something remarkable; we’ve discovered that in the beginning, something happened.  Cosmologists call that something, “The Big Bang,” the origin of Everything that Is.

When studying cosmology, you will often read a sentence about the Big Bang and the Origin of the Universe.  The Origin Statement goes something like this: everything in the Universe began in an infinitely dense point smaller than the period at the end of this sentence.  What does that mean?  The answer is the basis for our current understanding of all of the Cosmos.  Let’s parse that question into several smaller questions.

The first obvious question is what do we mean by Universe?  Here, we will take the fundamental definition of Universe to be “everything that exists.”  But there is an unspoken subtlety in the Origin Statement as we wrote it here — in this case, the use of the word “Universe” actually means “Observable Universe.”  What’s the difference between “The Universe” and “The Observable Universe?”

My favorite lunch dive, in Logan, UT.

Consider an example from your everyday life — lunchtime.  Imagine one sunny day you decide to forego the sack lunch you brought with you and instead decide to go out to lunch with some of your friends.  You only have 1.5 hours before you have to be back, and you are walking on foot.  You can only walk so fast, so where are you going to go?  Perhaps Guy Fieri has pointed you toward an excellent BBQ joint on a late night episode of “Diners, Drive-Ins and Dives,” but that would require either a plane flight or a very long road trip, both of which will take far longer than the 1.5 hours you have. Instead, you confine your attention to restaurants within a certain distance — reachable if you walk as fast as you can for a limited amount of time.

The Universe is kind of the same way — there is a maximum speed that anything can attain, namely the speed of light. Thus, in the age of the Universe, there is a maximum distance over which any information can come to the shores of Earth — the distance that light can travel in the age of the Universe!  The “Observable Universe” is that part of the Universe from which we could have received some light that started travelling at the moment the Universe was born, and is just now reaching Earth today (analogous to how far you can walk during your lunch hour).  It is a small part of the “Entire Universe,” most of which we know nothing about because the light from there has not had the chance to reach us (analogous to the entire vast world full of restaurants, which you cannot reach during your lunch hour!).

The Observable Universe is just a small part of the Entire Universe. It is bounded by the farthest distance light could have travelled in the age of the Cosmos. If Earth is at the center of this boundary, then light from outside the blue boundary (such as from the yellow galaxy on the right) hasn’t had time to reach us yet. [Illustration by S. Larson]

In the beginning, the Entire Universe was just a vast (possibly infinite) collection of the ultra-dense points mentioned in the Origin Statement.  The Big Bang was not really an explosion, not in the sense of an exploding stick of dynamite; the Big Bang was the apparently spontaneous and rapid expansion of every single point in the Entire Universe.  What is expanding?  The fabric that makes up the Universe itself is expanding, carrying everything that would become stars, galaxies, trees, kangaroos and people along with it.  Cosmologists call that fabric spacetime.  The very stuff that the Universe is made of — spacetime — is stretching.

Now if that doesn’t immediately make sense, don’t worry! It is a disconcerting and unfamiliar idea. The contemplation of big ideas is always a bit uncomfortable, because we’re stretching our brains in ways that it is not used to; that’s the way science works.  One way to help settle your mind around unfamiliar concepts and to build intuition is to appeal to analogies.  Analogies and metaphors are not perfect, but they help connect the ideas that need to be connected.  One of the classic analogies to understand the Big Bang is to imagine other things that stretch and expand.

Consider a large piece of spandex, with a checkerboard on it, as in the figure shown here.  The checkerboard pattern is not necessary, but it provides a quick and easy way for us to see and talk about distances. This checkered fabric is an analogy, a metaphor that we use to think about the Universe, and in this picture imagine it stretches far beyond the boundaries of the page of your computer screen.  For the moment, I have made the checkers large enough to see, but you could easily imagine them being smaller than what is drawn here, even much smaller (perhaps as small as the proverbial period at the end of the Origin Statement).

Imagine I have two ants sitting on the spandex, one named Xeno (the black ant) and one named Scarlett (the red ant).  They have both staked out a square they like, and are staying put, watching closely that the other ant does not move off their chosen territory.  This is the case shown in the first figure.

(L) Consider two ants, Xeno and Scarlett, on a stretchy sheet representeding the spacetime fabric of the Cosmos. (R) When the Cosmos expands in every direction and at every point, the two ants get farther apart. [Illustration by S. Larson]

Now, unbeknownst to our ants, the very fabric of the Universe is expanding around them, as shown in the second figure. It expands uniformly, in every direction. The result of that, in the context of my spandex checkers, is that every square gets larger (though our ants remain the same size, comfortably bound together by the biological goop and intermolecular forces that give their bodies form).  What are the observational consequence for our ants, keeping their beady little ant eyes on each other?  Much to their surprise, they find themselves slowly getting farther apart!  Scarlett looks around, and clearly she is not moving — she has not moved at all since our little experiment began. Never-the-less, it is quite clear that Xeno is receding from her. Meanwhile, Xeno is thinking the same thing. He has not shifted nor moved at all, but Scarlett is inexorably getting farther away.  The explanation? The very space between them, the stuff that the Universe is made of, is expanding.

What is interesting is that every square in the fabric of our Universe is expanding — the squares are getting larger, and everything is getting farther apart.  No matter how tiny every square started, if we wait long enough, it gets bigger.  The consequence is that from the perspective of anyone anywhere in the Universe, every other point is flying away from them.  Consider a few more ants: Xeno, Scarlett, Kermit (the green ant) and Indigo (the blue ant). If each one of them measures the distance to every other ant, they find that if they wait a while, the distance to every other ant increases.  From  the perspective of any ant, firmly rooted to their little territory in the Cosmos, every other point in the Universe is slowly getting farther and farther away, no matter what direction they look.

Imagine an army of ants (clockwise from the top: Kermit, Scarlett, Indigo, and Xeno). If they all watch each other as the Universe expands, they think ALL other ants are moving away from them, no matter what direction they are. [Illustration by S. Larson]

This is how we think about the Big Bang.  Everything that you can see (the Observable Universe) was once contained in a dot smaller than the period at the end of this sentence; it was like a teeny, tiny square on our spandex.  Then the Big Bang happened, and every point in the Entire Universe — every point on the spandex — started to expand.  The part of the Universe you can see is only one small part of the vast fabric that is everything, but it all started long ago in a very tiny spot.  Everything you can see in the Universe began in an infinitely dense point smaller than the period at the end of this sentence!

On the surface, this story sounds fantastical, almost beyond belief. We can always make up fantastical ideas about the nature of the Cosmos, but for those ideas to move beyond mere speculation and into the realm of science, we must be able to test those ideas.  There must be something we can look for, something that we can observe. In the case of cosmology, there is.

One of the things that physicists know about the world is that if you compress things they get hot. This is the principle behind pressure cookers, this is why it is hot in the core of the Earth, and this is why the Sun burns hydrogen in its core. When the pressure goes up, things get hot!  If the Universe is expanding today, we can imagine running the movie backward in time, watching everything run backward toward the Big Bang.  Because we see everything flying apart now, when we run the movie backward what we see is the entire Observable Universe being compressed down into a small point. The pressure in that point would have been enormous, which means it would have been tremendously hot.  If that were true, there should be some thermal signature of that early, hot, dense state of the Cosmos.

There is such a signature. Arriving on Earth from every direction on the sky, is a faint fog of microwave radiation, known as the Cosmic Microwave Background. It is the light that was released from the birth of all the atoms in the Cosmos, 400,000 years after the Big Bang.  Before this time, the Universe was so hot and dense that atoms could not hold together; they would constantly crash together and break apart into the fluff from which they are made, melting back into the primordial soup of light and sub-atomic particles. But as the Universe expands, it cools slowly until atoms could hold together. The moment that happened, the soup immediately thinned and the light flew free, carrying the message of the birth of the atoms.

The Planck map of the Cosmic Microwave Background. [ESA/Planck Collaboration]

This picture of the Cosmic Microwave Background is the most accurate map every made of the microwave sky; it is the youngest picture of the Cosmos we have ever taken, and the strongest piece of evidence we have that the Big Bang unfolded in the way we have just discussed. This picture, an image of the Cosmos very shortly after its birth, is one of the greatest legacies of our race. It captures, in an exquisite map of subtle patterns and colors, the ability of our species to reduce our ignorance, to become more enlightened about the Cosmos and our place in it.

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This post is part of an ongoing series, celebrating the forthcoming science series, Cosmos: A Spacetime Odyssey by revisiting the themes of Carl Sagan’s classic series, Cosmos: A Personal Voyage.  The introductory post of the series, with links to all other posts may be found here:  http://wp.me/p19G0g-dE

Quantum Mechanics, the Bangles, and Another Manic Monday

by Shane L. Larson

At the opening of Harry Potter and the Deathly Hallows, Part 1 we find Professor Snape stalking up to the imposing wrought-iron gate of Malfoy Manor.  With a casual flick of his wand, he passes through the gate, unimpeded.  If you look quickly around the theatre, you can spot every physicist in the crowd because they are all nodding sagely: magic is just science, and Snape just quantum tunneled through the Malfoy Manor Gate.

Quantum tunneling. The name evokes little trills of excitement, wonder, and possibly confusion because it uses the magic “q” word from the Twentieth Century: quantum.  No aspect of fundamental physics challenged our understanding of Nature more than the ideas of quantum mechanics.  At the start of the 1900s, we were for the first time using our wits and our technology to attempt to understand Nature on scales that had been unaccessible to us since the dawn of time –– the scales of atoms.  The consequence of those explorations and discoveries is all the wonder and convenience of our modern technological society.

Every one of us encounters quantum mechanics everyday.  This morning at 6:21am my alarm clock went off, blaring the dulcet admonitions of the Bangles that this Monday, like last Monday, is just another Manic Monday.  That doleful message was enabled by quantum mechanics.   Deep down inside most devices of modern convenience is one of the great marvels of our time –– the integrated circuit. They are small and innocuous, little black squares of ceramic and rare earth metals with small metal legs splayed out, giving them the appearance of some strange robotic bug. But deep inside they are machines if wonder. They have no moving parts, but their job is to corral and gate billions of tiny electronic denizens that we have dispatched to do our bidding (in the case of your clock radio, to wake you up). The beasts of burden in the world of electronics are electrons, fundamental particles if Nature with a mass 0.000 000 000 000 000 000 000 000 000 006 times the mass of a regulation baseball. Electrons are very small!  It is only in the last 100 years that we have truly understood the laws of physics for the very small –– we call those laws “quantum mechanics.” If you want to herd electrons around a semiconductor and make them do your bidding, then you have to be a master if quantum mechanics.

So what are the laws of quantum mechanics? At its most rudimentary level it is just mechanics, that branch of physics that tells us about the motion of objects. The purpose of mechanics is to determine the location and position of objects as a function of time.  If I throw a baseball, how long does it take to cross home plate? If I slam on my brakes in an attempt to prevent my 1979 Yugo from rear-ending a Lexus that is sitting at a green light, how far do I skid?  How fast does a rocket have to go to break the bonds of Earth, heading outbound through the solar system?  These questions are the purview of mechanics. Quantum mechanics is about these same kinds of questions, but applied to the sub-atomic world.

Many of the axioms of life that you learned as a child provide equally good advice for doing science. An important one is “there is more than one way to skin a cat.”  For every problem in physics, there is more than one way to solve it. In mechanics, there are often many ways to think about problems.  One of the most common ways to think about mechanics is in terms of speed and acceleration –– how fast an object is moving and how that motion is changing. Another common way to think about mechanics is in terms of energy.  Energy has an intuitive foundation you can imagine, characterizing how much effort you had to expend to get an object moving, or the potential an object has to do something.  For instance, a Mack truck rolling down the highway at 65 mph has a lot of energy; it takes a lot of effort to get such a large object moving so fast! In a similar way, an anvil perched precariously on the edge of a cliff must have some energy stored in it, because it has the potential to do a lot of damage to someone far below (as Wile E. Coyote knows well).

Fundamentally, quantum mechanics is an approach to mechanics that thinks about energy. The “quantum” part of the name comes from a discovery of the physicist, Max Planck.  Planck stumbled on the fact that when you look at the energy of sub-atomic systems, the energy comes in discrete packets that he called quanta.  Planck argued that you could not have any energy, but you had to have a specific energy that was a discrete number of quanta added together.  These quanta are tiny, like the objects Planck was trying to describe.  For typical atoms, a quantum of energy is about a hundred billion-billion times smaller the energy of a Major League fastball.

This simple prediction, borne out to high precision in laboratory experiments, has famously non-intuitive consequences for the world.  Perhaps the most renowned is the Heisenberg Uncertainty Principle, which tells us that precision knowledge of all the physical properties of a quantum mechanical system is not possible.  Suppose I wanted to look at the electrons in my alarm clock, scurrying around their integrated circuits in their quest to insure the Bangles get me out of bed at the right time. If the electrons were little cars on highways (like in the Tron movies), I might be tempted to ask “where is each electron and how fast is it moving?”  But the Heisenberg Uncertainty Principle tells me this is not possible; if I want to I can measure where the electron is or how fast it is moving, but I can’t know both accurately.  The more well known the position is, the more uncertain the speed is, and vice versa.

This is disturbing to say the least because it sounds completely counter-intuitive to our everyday experience.  But more importantly to scientists, it suggests a deadly conundrum for our deepest held passions about how the world should work: we believe that there should be a consistent set of physical laws that apply to everything, whether they are baseballs or electrons!  As hundreds of thousands of Major League Baseball replays have shown, we can know where a baseball is (over the outside corner of the plate) and the speed at the same time (it’s printed right there on the screen!).  But Heisenberg says this is not possible.  How is this conundrum resolved?

One way to ask the question is to apply quantum mechanics to a system that is not small.  One could ask “Is a cow a quantum mechanical system?”  When you are first exposed to quantum mechanics, this is the obvious question to ask.  Neils Bohr, one of the early architects of quantum mechanics, pondered the same question.  How could it be that quantum mechanics governs how electrons move around in a semiconductor, but not how a cow walks around a corral?  The resolution to this is that the classical world, on the scale of meatballs and Boeing passenger jets and wallabies, is a gigantic quantum system operating on scales much different than those of an individual atom.  The physical properties of a cow, say its energy or its angular momentum (how fast it is spinning –– imagine a cow on ice skates, if that helps), are 10³⁰ larger than those of a hydrogen atom.  When we look at the quantum world, what we observe are changes in quantum states.  We give each state a name to keep track of a quantity called the principle quantum number, n.  For a hydrogen atom, the n values typically have very small numbers: n = 1, n = 2.  A cow has very large quantum numbers, like 10³⁰.  The quantum nature of a cow is very hard to detect because the difference between two quantum states, say n_cow = 1000000000000000000000000000000 and n_cow = 1000000000000000000000000000002 is much harder to detect than the quantum states of a hydrogen atom, say n_hydrogen = 2 and n_hydrogen = 4.

“But wait!” says the Hermione Granger in the back of the room.  “Both of those are still just different by a factor of 2!” Yes, that’s true.  But identifying the quantum state is about counting the values and then noting the differences.  If I lay 5 Oreos on the table, and you sneak one when you think I’m not looking, I’ll probably notice.  If I lay even a moderately large number of Oreos on the table, say 50 (let alone 10³⁰), it is far less likely I’ll notice that you snarfed one.  The same is true of measuring the quantum nature of everyday objects –– it’s hard to notice the small, quantum mechanical changes.

And so it seems physics is saved –– we could use quantum mechanics to describe a cow because in the macroscopic world, the more convenient physical laws we use to describe the mechanics of cows, passed down to us from Galileo and Newton, are derived from quantum mechanics itself; we just don’t notice the small, quantum mechanical changes in the state of the system.  We call this the classical or the continuum limit.  This is the great lesson of science –– our knowledge of the world is continuously changing, and when it does change, our goal is to understand how our old knowledge fits in the new framework.  Sometimes it requires us to discard long held passions and beliefs, and other times it requires us to bend and stretch our minds to encompass a larger world view than we had before.  Either way, the process is confusing, exhilarating, painful, but ultimately rewarding.  It’s what gets a scientist out of bed after a long weekend –– the promise that your job is going to be just another Manic Monday.