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Archive for May, 2013

When I was young, I once looked at a box of cereal and had an epiphany.  “Why is that cereal there?”  A universe of unfathomable complexity, with 100,000,000,000 galaxies, each with 100,000,000,000 stars, making 10,000,000,000,000,000,000,000 possible solar systems with planets around them—all that, and I’m sitting across from a box of Vanilly Crunch?

Vanilly

Since that existential crisis, I’ve always wondered why there was something instead of nothing.  Why isn’t the universe just one big empty set?  “Emptiness” and “nothingness” have always seemed so perfect to me, so symmetric, that our very existence seems at once both arbitrary and ugly.  And no theologian or philosopher ever gave me an answer I thought was satisfying.  For a while, I thought physicists were on the right track: Hawking and Mlodinow, for example, in The Grand Design, describe how universes can spontaneously appear (from nothing) according to the laws of quantum mechanics.

I have no problem with quantum mechanics: it is arguably the most successful theory devised by mankind.  And I agree that particles can spontaneously create themselves out of a vacuum.  But here’s where I think Hawking and Mlodinow are wrong: the rules of physics themselves do not constitute “nothing”.  The rules are something.  “Nothing” to me implies no space, no time, no Platonic forms, no rules, no physics, no quantum mechanics, no cereal at my breakfast table.  Why isn’t the universe like that?  And if the universe were like that, how could our current universe create itself without any rules for creation?

But wait—don’t look so smug, theologians.  Saying that an omnipotent God created the universe doesn’t help in any way.  That just passes the buck; shifts the stack by one.  For even if you could prove to me that a God existed, I would still feel a sense of existential befuddlement.  Why does God herself exist?  Nothingness still seems more plausible.

Heidegger called “why is there anything?” the fundamental question of philosophy.  Being a physicist, and consequently being full of confidence and hubris, I set out to answer the question myself.  I’d love to blog my conclusions, but the argument runs about 50,000 words…longer than The Great Gatsby.  Luckily for you, however, my book Why Is There Anything? is now available for the Kindle on Amazon.com:

rave book

You can download the book here.

You might wonder if my belief in the many-worlds interpretation (MWI) of quantum mechanics affected my thinking on this matter.  Well, the opposite is true.  In my journey to answer the question “why is there anything?” I became convinced of MWI, in part because of the ability of MWI to partially answer the ultimate question.  My book Why Is There Anything? is a sort of chronicle of my intellectual journey, one that I hope you will find entertaining, enlightening, and challenging.

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HINT: The letters I gave were grouped in a particular way, using a particular criterion.  If I had used a different font…one with serifs, let’s say…the groupings would have been totally different…

Here are the groupings once again…

DO

B

PQ

CGIJLMNSUVWZ

AR

EFTY

HKX

ANSWER: Notice that one of the keywords I gave was “topology”.  That’s it.  The letters are grouped based on topological similarity.

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Many Worlds Puzzle #2

DO

B

PQ

CGIJLMNSUVWZ

AR

EFTY

HKX

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Laser_squirrel_hd

An image from Zynga’s Mafia Wars, obviously.

One way to say it is…

Let’s say we have a bunch of squirrels congregating underneath a tree.  We can startle the squirrels, and they jump up into the branches of the tree.  But these are ground-loving squirrels, so they very quickly jump back down—sometimes to a lower branch, sometimes all the way down to the ground.

An interesting fact: the squirrels scream as they fall.  This isn’t because of fear, so there’s no need to alert PETA; they’re just emitting squeals of delight as they plummet.  And the frequency of their squeals (and hence the musical note produced) depends upon how far they fall.  A larger drop, a higher frequency.

My goal is to have a whole bunch of squirrels scream with the exact same frequency, all at once.  How can this be done?

Clearly, I need a bunch of squirrels all on the same branch, and I have to hope they all jump off that branch all at the same time.  But this is trickier than it sounds.

It turns out that our tree, a northern elm (Ne for short) has lots of branches, most of them slippery.  In most cases a squirrel will jump off such a branch almost immediately.  However—and this is lucky for us—the 8th branch from the bottom is not-so-slippery.  Squirrels actually like to hang out on this branch for a little while.  Squirrels, being squirrels, do succumb to peer pressure, though, so when one squirrel eventually jumps to the next-lowest branch, the rest of the squirrels follow suit—all screaming in unison—producing a nice, loud, resonant scream of 4.7 x 1014 Hz.

Here’s the problem: when we initially scare the squirrels into the tree, they don’t all jump up to that 8th branch.  Why would they?  They jump up at random, and only a fraction land on the branch we want.  Even if a sizeable number then jump down all at once, producing the desired sound, it is drowned out by all the other screams and squeals of all the other jumping squirrels on all the other branches.  This isn’t what we want.

But maybe we can be super clever.  Let’s get another tree, let’s say a hemlock (He for short), and place it next to the Ne tree.  Why hemlock?  The cool thing about hemlock is that there’s basically only one branch that squirrels can reach (the other branches are just too high).  And here’s the luckiest coincidence of all: this single branch of the He tree is at almost the exact same height as the 8th branch of the Ne tree (the branch that the squirrels kind of like).

So here’s what we do.  We scare a bunch of squirrels beneath the He tree, and they all jump up to that lone branch (they don’t have a choice.)  We then slide the He tree next to the Ne tree.  The naturally curious squirrels climb over to the Ne tree, because the branches are at the same height.  And guess what—the conditions are now just right for our squirrels-screaming-in-unison trick!  We have a large population of squirrels on a not-so-slippery branch, and when the peer pressure clicks in—eeeeeeeekkkk!

Another way to say it is…

Let’s say we have a bunch of electrons in atoms in a gas.  We can excite the electrons with an electric field, and they jump up into higher atomic energy levels.  But being electrons, they very quickly jump back down—sometimes to a lower energy level, sometimes all the way down to the ground state.

An interesting fact: the electrons emit photons as they fall.  And the frequency of these photons depends upon how far they fall.  A larger drop, a higher frequency.

My goal is to have a whole bunch of photons emitted with the exact same frequency, all at once and in phase.  How can this be done?

Clearly, I need a bunch of electrons all on the same energy level, and I have to hope they all jump off that level all at the same time.  But this is trickier than it sounds.

It turns out that our gas, neon (Ne for short) has lots of energy levels, most of them “slippery”.  In most cases an electron will jump off such a level almost immediately.  However—and this is lucky for us—the 8th branch from the bottom (the 5s energy level) is metastable.  Electrons actually like to hang out on this level for a little while.  Electrons, being electrons, do succumb to peer pressure, though, so when one electron eventually jumps to the next-lowest branch, the rest of the electrons follow suit—in a process called stimulated emission—producing a nice, intense, in-phase cascade of photons with f=4.7 x 1014 Hz (about 633 nm, which is ruby red).

Here’s the problem: when we initially excite the electrons in Ne, they don’t all jump up to that 5s level.  Why would they?  They jump up at random, and only a fraction land on the level we want.  Even if a sizeable number then jump down all at once, producing the desired lasing frequency, it is drowned out by all the other photons emitted by all the other jumping electrons on all the other levels.  This isn’t what we want.

But maybe we can be super clever.  Let’s get another gas, let’s say helium (He for short), and place it in the same container as the Ne.  Why helium?  The cool thing about helium is that there’s basically only one energy level that electrons can reach (the 1s2s level).  And here’s the luckiest coincidence of all: this single energy level of He is almost the exact same energy as the 5s state of Ne.

So here’s what we do.  We excite a bunch of electrons in He, and they all jump up to the 1s2s level  (they don’t have a choice.)  We then mix the He with Ne.  Through collisions, many of the electrons in the 1s2s level state of He are transferred to the 5s state of Ne.  And guess what—the conditions are now just right for our cascading electrons trick!  We have a large population of electrons in a metastable state (a population inversion), and when stimulated emission clicks in—we get coherent laser light!

Whether or not those electrons raid your bird feeders for sunflower seeds is another issue entirely.

[Note: my book Why Is There Anything? is now available for download on the Kindle!]

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sazon

If you’re ever in Cullowhee, NC, give Sazón a try.

Suppose I agree to meet my wife for dinner at 8 pm.  She goes to El Pacífico (a local Mexican restaurant) whereas I go Sazón (another Mexican restaurant).  The restaurants are a kilometer apart.  I’ve made an error, of course.

The next week, we agree to meet at El Pacífico.  She arrives at 7 pm, I get there at 8 pm.  Oops, I’ve made another error, this time not in location, but in time.

Which error is worse?

Any student of special relativity will be familiar with the terms spacelike, timelike, and lightlike interval.  Surprisingly, these terms are perfect for discussing my dinner date woes.  But what do these terms mean, on an intuitive level?  Are they even comprehensible in the realm of low, non-relativistic velocities?

Imagine two events, such as me clapping my hands, and you clapping yours.  The events are separated in space by a distance ΔR and separated in time by a duration Δt.  It turns out that if you think of the cosmos as being 4-dimensional, there is then a relationship between ΔR and Δt.

This relationship is the 4D distance formula, Δs2 = ΔR2 – c2Δt2.  Think about it as a sort of “Pythagorean theorem” for 4D spacetime.  That is, its square root (Δs) gives the “distance” between two events in spacetime, given that any event has coordinates (x,y,z,ct).  (Unfortunately, sometimes Δs2 is negative, in which case you cannot take the square root.  But that’s OK; we just talk about Δs2 and don’t even worry about what Δs “means”.)

OK, so why is c (the speed of light) in there?  Well, for two reasons.  One, there has to be some velocity as a conversion constant, so that the fourth coordinate ct has dimensions of distance (just like x, y, or z).  Secondly, the 4D distance formula is constructed explicitly so that if you’re travelling at speed c, then your speed will always be c in every other reference frame.  This is done to match experiment, but whether it’s justified or not depends upon whether the final result (the formula for Δs2) also has merit.  In this case it does, and it turns out that the quantity Δs2 is an invariant: it stays the same regardless of the reference frame you’re in.  Distance is relative; time is relative; but the unholy combination of distance and time, Δs2, is not.

But we’re here to talk about intervals Δs, which represent spacetime distances between events.  Let’s call our first event P1;  our second event is P2.  Now, P1 will be “I throw a ball.”  P2 will be “You catch the ball.”  Let’s say we’re separated by ΔR = 10 m and you catch the ball Δt  = 0.4 s later.  Then:

ΔR2 = 102 = 100 m2,

c2Δt2 = (3 x 108)2 (0.4)2 = 1.44 x 1016 m2.

Wow!  The “time term” (in the Δs2 formula) dominates, so that Δs2=100 – 1.44 x 1016 = – 1.44 x 1016m2, which is negative.  In plain English, the events are separated more by time than they are by space.  When this happens, the invariant interval Δs2 is negative.  We call such an interval timelike.  Another way to think of this is that P1 and P2 can influence each other by cause and effect.

Why is the time term so big?  Basically, because light is so fast.  Remember that we had to multiply time by the speed of light to make the fourth 4D spacetime coordinate have units of distance.  So unless events are very, very far apart—or the time difference is very, very small—then Δs2 will be negative and you will have a timelike separation.

Now, in your everyday life, distances are never that great.  The biggest distance you will ever have between you and a friend is the diameter of the Earth; namely, ΔR = 12,700,000 m.  Even at that distance, events will have a timelike separation unless Δt is below a certain threshold:

ΔR2 > c2Δt2

Δt < ΔR/c = (12,700,000 m)/ (3 x 108 m/s) = 0.042 s = 42 ms.

I do something Pin North Carolina; something else Phappens to my friend Rick in Perth, Australia.  In order for these events to be causally connected, at least 42 ms must past between P1 and P2.  If Δt is less than 42 ms, then light doesn’t have enough time to get from me to Rick; the events cannot be causally connected and we have a spacelike interval instead.  In such a case Δs2 is always greater than zero.  In plain English, the events are separated more by space than they are by time.

(Note: 42 ms is a good value to keep in mind.  On the Earth, for an interval between events to be spacelike, they have to be almost simultaneous: Δt has to be less than 42 ms.)

Let’s apply our new terminology to the example that started this post.  The events P1 and P2 are “I arrive at my destination” and “my wife arrives at her destination”.  We arrive at the same time, 8 o’clock, but the restaurants are a kilometer apart.  So:

Δt = 0,

ΔR = 1000 m,

Δs2 = ΔR2 – c2Δt2 = 10002 = 1,000,000 m2.

Seems like a big error!  But the next week I get the time wrong (not the location) and we find:

Δt = 1 hr. = 3600 s,

ΔR = 0,

Δs2 = ΔR2 – c2Δt2 = – c2 (3600)2 = –1,166,400,000,000,000,000,000,000 m2.

That’s worse.  A lot worse.  It represents a much bigger “interval” in spacetime.  And, truth be told, our culture reflects this; it is much worse to be an hour late for dinner then to show up on time but 1 km away.  And this makes sense: if you go to the wrong restaurant you can correct your error fairly easily; it wouldn’t take that long (maybe 1 minute?) to drive 1 km.  If instead you’re an hour late, there’s not much you can do…

[Here’s the website for Sazón: http://www.sazoncullowhee.com/wordpressinstall/]

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