Whether Something Can Come From Nothing, and Quantum Mechanics

It is very popular  in certain circles that place a high value on the classical scholastic arguments for the existence of God to ask "why is there something rather than nothing?"  Ex nihil, nihil fit, is the Latin phrase, that from nothing, nothing comes.  If there is something, then why?  How did it get here?

It is then popular in certain circles that place a high value on scientific understanding --- people who perhaps don't understand math well enough to study it for real, but who nonetheless appreciate human efforts to understand the natural world in terms of rational processes and read as much of it as they can understand --- to make the rebuttal claim that, according to the physical understanding of quantum mechanics, something can come from nothing.


You can see an example of this conversation in the below video:

The idea is that in quantum field theory, study has shown that even in the state representing a vacuum, i.e. a system with zero particles, there is still the constant process of random particle-antiparticle pair creation and annihilation going on all the time.  You start with zero particles, and for brief instances you have two particles.  Or, in higher order interactions, four, or one hundred and twenty four.  Therefore, something -- particle-antiparticle pairs -- can come from nothing -- the quantum vacuum.

This idea is right, and it's wrong.  I think both people are talking past each other, and in this post, I would like to try to clarify.

I'm not a field theorist.  I've had some grad classes in it, but it's not anything in which I'm an expert (in fact, there probably isn't anything in which I'm an expert, but it's a helpful caveat).  Still, what I'm about to say is very basic to field theory (if anything in field theory can be called "basic"), and I'm more or less directly citing the text Field Quantization by Greiner and Reinhardt (available on Amazon for only $\$20$!).  What follows is a very, very brief outline of how quantum field theory leads to the understanding of the quantum vacuum, but also how the results therein do not mean what many people think it means.  I have some wikipedia links throughout, so that hopefully people who do not understand math can at least follow along with what I'm trying to say -- the math isn't important, but the physics is.

The Uncertainty Principle and Energy Non-Conservation, part 2

Quantum mechanics is typically interpreted to mean that the conservation of energy can be violated as long as the time scales involved are short.  An old professor of mine used to summarize it as "there is such a thing as a free lunch, if you can eat it fast enough."

Here's how the argument goes.  From quantum mechanics, we get the uncertainty relation

$$\Delta E \Delta t \geq \hbar,$$

where $\Delta E$ is the uncertainty -- or statistical spread -- of the energy, and $\Delta t$ is the uncertainty of the time.

Following this, physicists reinterpret the uncertainty $\Delta E$.  Rather than representing a quantification of our lack of knowledge about the energy of a system, this is interpreted as being, somehow, the amount of "free" energy that a system can borrow in violation of the First Law of Thermodynamics.  So if we have mean energy $E$ and uncertainty $\Delta E$, it means we "actually have" energy $E$, and then Nature gracefully lends us $\Delta E$ to overcome some energy barrier, which we quickly repay in time $\Delta t$.

However, that puts us at 

$$\Delta E \geq \hbar/\Delta t$$

which puts no limitation how much energy we can borrow.  Or, rather, it puts a lower bound; we must borrow at least $\hbar/\Delta t$ worth of energy.  Or, we could borrow even more!   If this is true, then we have infinite energy forever!

The oil companies will go bankrupt!

What is Spin? A More Simpler Explanation

The Copenhagen interpretation of quantum mechanics wasn't supposed to be mystical.  In fact, it was made precisely to avoid mysticism: "Shut up and calculate!" is probably the best summary of it possible.  Who cares what wavefunctions are or how they collapse, gimme the expectation value.  It's supposed to be practical, simple.  It's logical positivism at it's more rarified.

courtesy SMBC

Somehow, the refusal to address the complications of quantum and to just skate on by, has led to all sorts of weird mysticism stuff like quantum healing.  Today most non-physicists have misunderstandings of entanglement and many-worlds and why Schrodinger hated cats so much.  And very sadly, most physicists have no ability to correct them, as all they can do is draw squiggly tridents and funny S's and say "here is the answer".  That's all we're taught!  "It's a mystery, no one knows so shut up and calculate!"

The result is that no one really knows anything.  Physicists have a blackbox of expectation values and non-physicists have neat anecdotes for cocktail parties.

English Place Pronouns Retain Case

There's often confusion about what "Old English" is.

When people talk about Old English, they typically mean Shakespeare or the King James Bible or any flowery language with "thee"s and "thou"s.  Which isn't Old English at all.  Elizabethan and Jacobean English are both just older forms of Modern English.  The fact that modern speakers of English can read these writings without advanced degrees pretty much says it all.  Sure, the older dialects had more grammatical complexity than we are familiar with (separate personal and familiar second persons, distinct conjugations for first, second, and third person singular, etc.), but overall, Modern English is a pretty simple language, grammatically.

Computer Simulation of a Rift in the Space-Time Continuum Devouring the Universe

Part of my research involves computer simulation of bizarre materials with exotic optical properties; materials that can bend light in almost any manner desired.

I work on the theoretical side of things; I can say that I have in fact touched a beaker and used a pipet to move water from said beaker to another nearly identical beaker (I did this just to feel science-y and say I've done it) but I have no lab experience and would probably destroy everything in your lab if you let me use it.  All this to say, though I can sort of describe these materials (whilst gesticulating with a pipe, and with a dreamy glaze over my eyes and lulling drawl to my voice) I -- me -- am incapable of producing them.  So if I want to convince someone with a lab and knowledge (and a budget) to actually make them, I have to give more than my impressive pipe-gesticulations.

Hence, I use computer algorithms to make simulational models of the bizarre materials, send some simulated light in to them, and can thus prove to these experimental people with labs that the totally awesome sailing ship I just blew through a smoke ring can in fact be built and sailed through physical rings.

Why the Shroud of Turin Can't Possibly Belong to Jesus

A friend of mine recently posted the following picture on facebook.

The caption refers to recent experiments trying to duplicate the image on the Shroud, specifically by bombarding it with electromagnetic radiation.  (This is the closest thing to a reference I could find - it's in Italian, sorry.)

A have a decent number of friends who very earnestly believe the Shroud of Turin to be the very same piece of fabric used to wrap the crucified body of Jesus.  By some unknown process, at the moment of his Resurrection, they believe the Shroud was irradiated to contain a photo negative imprint of Jesus' body; I don't know why the Resurrection should produce radiation, but then I guess I don't know why it shouldn't, either.

Even recently, in late March, one scientist in Italy produced tests tracing the Shroud to within the era of Jesus' lifetime.  This contradicts dozens of other scientific and historical investigations concluding that the Shroud came in to existence sometime in the 12th century AD, but I guess it's something.

Or maybe Poofy-Hair Guy is actually
right about something?

For all I know, the Shroud really was caused by miraculous radiation, and for all I know the Shroud absolutely existed in the first century, before being lost to all record for twelve hundred years, after which time it appeared suddenly and without provenance in France with more carbon-14 in its fibers than a natural piece of fabric should have.  That might very well be the case.  I don't know, and maybe I never will.

What I do know, however, is that the Shroud of Turin was not the piece of fabric that was used to wrap Jesus' body.

The Width of Narnia

As is revealed in Voyage of the Dawn Treader, the world of Narnia is a flat earth.  Characters can literally fall of the edge of the world.

I started wondering, at one point, how thick is that edge?

Characters from our world report no differences in the gravity (or whatever) on Narnia; they don't feel any greater or lesser weight walking around.  Arguably, if Narnia had a lower gravity, then the Pevensies might have had, at least, an easier time crossing through the snow.  And contrariwise, if Narnia had a much higher gravity, then the adventure would have mostly been about aching knee joints.

Further, when the Pevensies stay in Narnia as kings and queens, they eat the food there, and this does not make them sick.  The food they eat they report as tasting equivalent to earth food.  When they grow up, they marry dryads and naiads and other mythological things and have children.  Weird as this is, it all proves pretty much conclusively that Narnia is made of the same kind of "stuff" as Earth; this is important.

So we know three things.  We know Narnia has the same overall downward-pulling force as Earth's gravity, we know that Narnia is made of the same kind of stuff as Earth, and we know that Narnia is a flat earth with a literal edge that you could fall off.

This is enough to calculate, to a very good approximation, how thick Narnia is.

Time Travel is Creepy

The other day, an idea dawned on me.  It took several hours before the full weight of it began to sink in.  It's an idea that has enjoyed constant employment by the human imagination, so much so that the terror of it has been weakened from banality.  When I was forced to take it out of fantasy books and in to reality, I wasn't so sure I liked it.

It occurred to me, that it might be possible to make a device that causes light to travel in closed causal curves.  As in, I could do some calculations and tell you how to make it and someone with a nanolab could build it in a year or so. This would allow communication with the future through radio waves; you broadcast them in to the machine and into the future, the future responds by broadcasting into the past.

Vectors are Not 1-Forms

So, I recently moved in to a new research area.  It's new to my advisor, too.  Actually, generally speaking, it's pretty new period, first appearing some ten years ago or less.  Anyway, this new field deals fairly heavily with Maxwell's Equations in curved spacetime, so to understand it we are needing to review differential geometry and general relativity, two fields which are not in the normal purview of my advisor's expertise.  I was asked to prepare a chalk-talk that would introduce the key concepts of differential geometry to them, and another talk to segue in to Maxwells Equations in curved spacetime.

Not like I'm an expert on differential geometry, but I've studied it some privately and as an undergraduate.

While studying for this, it dawned on me suddenly, like the storm clouds that pile higher and higher until the first bolt of lightning strikes the ground, that vectors and 1-forms are different.

Every thing I have ever read in physics equates them.  Or not really.  Everything I have ever read in physics doesn't even demonstrate that it understands why those two should occupy different semantic domains.

What the heck am I even talking about?

The Uncertainty Principle and Energy Non-Conservation and Why Your Textbook is Wrong

I read this all the time, in physics books and articles and on the internet: Apparent violation of conservation of energy is possible at the quantum scale for very short periods of time due to the Heisenberg uncertainty relation:
∆E∆t ≥h/2π
In that equation, ∆E is the "uncertainty" in the energy and ∆t the "uncertainty" in the time, meaning the accuracy to which we are able to measure these values.  The h in the equation is Planck's constant (which I didn't write as h-bar because I didn't want to encode LaTeX for one equation).  The two are inversely proportional, so as one goes up, the other must go down, so for short times, you can get enough "free" energy to send a particle through an energy barrier.

This is wrong.  Wrong, wrong, wrong.

Why Travel to Hyperspace Would Instantly Kill You

So, I've wondered a lot about a way to construct a "system of magic" (as often appear in modern fantasy works) from a collection of physical laws.  And until I got carried up in classes last semester, that was one of my main focuses of attention.

I was thinking that, in an alternative universe, there's no reason why they should have the same number of spatial dimensions as us.  So why not four, or five, or ten?

Because if you traveled to four-dimensional space, then you would find your skin insufficient to contain all of the air, blood, half-digested food, and maybe even internal organs that now find an extra degree of freedom within which to diffuse.

Five and higher dimensions makes it worse; the many things inside of you that keep you alive would disperse and splatter even faster.

So far I have discovered that to have any sort of meaningful adventure in a parallel universe, it must have the same number of spatial dimensions as we do (namely 3), it must have at least one time-like dimension, the electromagnetic interaction must exist and must recognize and interact with your electrons and protons.  Gravity would be nice, and I don't know enough about weak and strong interactions to know if they would be necessary.

http://abstrusegoose.com/457

There are most likely other limitations and dangers in such fantastic travel that have not yet come to mind.

In short, the inter-universe questing of children from our universe can never be to any world truly alien from our own.  Which is very sad.

Update: spam bots kept specially favoring this multi-year-old post in particular with travel blog advertisements disguised as comments, so I have disabled comments on this post.

What IS Santa?: a proposal for a modern understanding

For as long as I can remember, every Christmas, I have been confused by what exactly Santa Claus is.

Historically, Santa Claus is St. Nicholas of Myra, a Christian archbishop in modern-day Turkey who lived during the Roman persecution of the Church and was present at the Council of Nicea.  He was claimed to be a wonder-worker, and was also well-known for his anonymous gifts to the needy.  He has historically been honored on the 6th of December, and because of his generous reputation convents and monasteries began a tradition of sneaking out at night and delivering gifts to the poor. (see here, here, and here for references, the middle one being especially fantastic)

Among the hundred or so other things of which he was patron saint, one of them was sailors.  For this reason, sailors would often find themselves back home on the 6th, and be able to give a present obtained at sea to their children "from St. Nicholas".

That all makes sense to me.  Santa was a really cool guy who loved the poor and Jesus, and he was such a great guy we still do nice things for children and the poor because of him.  "Here's an extra toy, son, in honor of this really great guy."  Awesome, sign me up!

What doesn't make sense, though, is the weird Santa of American folklore, the guy who lives at the North Pole with a cadre of elves, who flies around in a sleigh pulled by magic reindeer and sneaks in to your chimney to deliver gifts to all the kids all over the world.

I mean, what is he?

goblin --> elf, Great Goblin |-> Santa
This is literally how I understood
this as a child

The Night Before Christmas, arguably the progenitor of the modern mythofigure, describes Santa as a "right jolly old elf".  As a kid, I took that to heart and assumed Santa was like the Elf King by virtue of being the tallest and fattest of the elves, and that makes him in charge (I guess the same way the Great Goblin in the Hobbit is king of the goblins).

In Defense of the Perpetuum Mobile

Somehow, I stumbled on a series of YouTube videos on perpetual motion machines.  They are very fun.  The videos mainly consist of two types:

1. Scammers looking for a laugh trying to trick gullible people into wasting their time building them, though secretly there will be a hidden engine or off-screen fan providing additional torque to the device.
2. The people who fall for these scam designs, and their own self-imposed scam designs, who are honestly trying to build a perpetual motion machine and honestly think they have built a machine that runs forever.

You get a lot of failed designs, obviously.  Technically, you get all failed designs.

How to Prep for Doomsday: You Won't Need Guns or Food When You're Dead.

According to one poll, at least 10% of the international population thinks the world is going to end on the 21st/22nd of this month.

I can't understand why you'd think that, first of all.

The Mayan's had some good knowledge of the position and movements of stars in the sky, sure, and incredible considering how little they apparently knew about much else.  But they also didn't know that the planets moved around the sun in elliptic orbits.  Or what stars were.  Or that gravity was a thing.  Modern astronomers exceed their knowledge on how the planets and stars behave in the same way string theory exceeds doing addition on your fingers.

And ever as he rode, his hart did earne// To prove his puissance in battell brave

                LII
Then freshly up arose the doughtie knight,          
  All healed of his hurts and woundes wide,
  And did himselfe to battell ready dight;
  Whose early foe awaiting him beside
  To have devourd, so soone as day he spyde,
  When now he saw himselfe so freshly reare,          
  As if late fight had nought him damnifyde,
  He woxe dismayd, and gan his fate to feare;
Nathlesse with wonted rage he him advaunced neare.

                    LIII
And in his first encounter, gaping wide,
  He thought attonce him to have swallowd quight,    
  And rusht upon him with outragious pride;
  Who him r'encountring fierce, as hauke in flight
  Perforce rebutted backe. The weapon bright
  Taking advantage of his open jaw,
  Ran through his mouth with so importune might,    
  That deepe emperst his darksome hollow maw,
And back retyrd, his life blood forth with all did draw.
- The Faerie Queene, Edmund Spenser, Book 1, Canto 11


One of the Chinese students was asking me about graduation requirements.  After listing a bunch of things, a friend also listed "slaying a dragon".  The Chinese student was very confused by this, and so I drew this picture on the office whiteboard to illustrate (notice the thermodynamics scribblings on the top).  Then I felt really good about my drawing skills and decided to post it online.  And then I figured a suitably epic quotation was need to go with it.

In my defense, by the way, let me just point out the correlation between the rise of the University system and the decline in reported dragon sightings.  Coincidence?  Hardly.

The Dirac Sea: Turtles All the Way Down

This semester, I am taking a course on relativistic quantum mechanics.  Currently we are covering the "hole interpretation" of negative energy solutions to the Dirac equation.

I've done this stuff before, as an undergraduate, in private study, and in various grad-level courses.  So I'm used to the interpretation being given.  But I decided recently that it is perfectly absurd.

Thought Experiment on Entropic Restrictions in Time Travel

In a discussion of time travel, questions will come up about freewill and causation.  I have always found this conversation frustrating because the common view is just so plainly wrong.

The common view is the one espoused in Back to the Future, which arguably is where most Americans get their understanding of time travel. (I guess as opposed to empirical time travel science?)  Everyone knows this so I don't even have to summarize it, but here goes:  You go back in time but you have to watch out that you don't accidentally change anything, because if you change something because then you will change the future.  In particular, you need to make sure that your introduction to your parents when they were in high school doesn't keep them from falling in love, or else you would undo your own existence, the fact of which alone should point out that there is something screwy here.

source

In this idea, because you can change the future you came from, there are different "timelines".  When you go back in to the past you go to a different timeline or split the universe or whatever and the effects of your meddling will be in the new timeline and not the one you came from.

So why do we think there are multiple timelines?

The Berenstein Bears: We Are Living in Our Own Parallel Universe

When I was growing up, all through elementary school we would watch movies and read books about the Berenstein Bears.  I still even remember the theme song for the TV show, mostly, which wasn't a song so much as a guy in a gruff bear voice speaking in rhyming couplets.  If you don't know who the Berenstein Bears are, they were nuclear family of anthropomorphic bears who lived in a tree out in Bear Country and had family-based situational comedy and taught life lessons.  And Ma Bear always wore a blue shower cap.

These bears appeared in a series of children books by the married Stan and Jan Berenstein, that later became a TV series, that got beamed to 3rd grade classrooms all over the country.  Anyone between the ages of 23-30, and maybe more, will know who the Berenstein Bears are.  And they will remember the flashy cursive bubble-letters on the front of every single book and in the opening credits of the show.  The bubble letters that spelled out "Berenstein Bears".

About a year ago, Jan Berenstein passed on, as had Stan some time before.  And appearing in headlines across the internet, I saw "Jan Berenstain Dies at 88".

BerenstAin.

They misspelled her name.  In her obituary.  Gosh, that's really just morbidly embarrassing.  "Berenstain" doesn't even make sense.

From The Magicians

I recently read The Magicians by Lev Grossman.  The story is sort of a commentary/deconstruction of childhood fantasy novels, especially Harry Potter and Narnia.  I suppose I have more I could say about it, but I was really struck by this quote:

Penny chose Oslo -- not even New Oslo, just Oslo, as if they thought they came up with it first -- for its total lack of anything that might distract him.  He arrived in mid-September and had no trouble renting a small farmhouse on the outskirts of town on a one-lane rural route.  His landlord was a retired schoolteacher who handed him the keys and then fled to his winter in South Carolina.  Penny's nearest neighbors on either side were a congregationless one-shack Pentecostal church and an out-of-session summer camp for disturbed children.  It was perfect.  He had found his Walden.

He had everything he needed: silence; solitude; a U-haul trailer packed with an enviable library of magical codices, monographs, chapbooks, reference books, ad broadsheets.  He had a sturdy desk, a well-lit room, and a window with an unscenic view of an unmown backyard that offered no particular temptation to gaze out at it.  He had a manageable, intriguingly dangerous research project that showed every sign of maturing into a genuinely interesting line if inquiry.  He was in heaven.

But one afternoon a few weeks after he arrived, as he sat at his desk, his watery blue eyes trailing over words of consummate power written centuries ago with a pen made out of a hippogriff feather, Penny found his mind wandering.  His large, usually lineless brow crinkled.  Something was sapping his powers of concentration.  Wa he under attack, maybe by a rival researcher?  Who would dare!  He rubbed his eyes and shook his head and focused harder.  But his attention continued to drift.

It turned out Penny had discovered in himself a weakness, a flaw he never would have suspected himself of in a thousand years, an age to which, with a few careful modifications that he would look into wen he had the time, he had every intention of living.  The flaw was this: he was lonely.

The idea was outrageous.  It was humiliating.  He, Penny, was a stone-cold loner, a depserado.  He was the Han Solo of Oslo.  He knew and loved this about himself.

This describes me almost perfectly.  Sometimes I want cloister myself off and just read and study and solve problems, free from the oppressive burdens of human interactions... but I just can't.  I can go with very little human interaction, but very little still isn't none.  And it has been interesting to learn of my own possession of the weakness of needing human interaction.

Identity Crisis

Sometimes, oftentimes, I wonder if I actually "count" as a scientist.  If I'm really a scientist, or just someone with high-functioning autism and a love of applied mathematics.

I don't find myself fitting in with the rest of the scientific community, or not very well.