Bayes theorem and the anthropic principle

Years ago I used to teach Bayes theorem to informatics grad students.

I was reassigned to other lectures though. Truth is, I had a hard time focusing on the boring stuff we were doing with Bayes. It just seemed like there was a deep weirdness about the Bayesian model of probability, but I couldn't quite put my finger on it. I was sure someone who understood it deeply would justify my queasiness.

Since then there's been a bit of a renaissance in thinking about Bayes. In Our Time even did a recent programme with a good bit of Bayes. Physicists are all over Bayes these days, and the Bayesian vs. Frequentist combat is out in the open (I knew this stuff was weird).

These days, I could assign students this essay to read:

PHYS771 Lecture 17: Fun With the Anthropic Principle

... So if Bayes' Theorem seems unobjectionable, then I want to make you feel queasy about it. That's my goal. The way to do that is to take the theorem very, very seriously as an account of how we should reason about the state of the world...

Of course that assignment might also shrink the class size ...

State of the universe: flat, 72% vacuum energy

CV provides the recipe for our universe from the most recent analysis of the echoes of the big bang:

WMAP 5-Year Results Released | Cosmic Variance:

...The WMAP folks have produced an elaborate cosmological parameters table that runs the numbers for different sets of assumptions (with and without spatial curvature, running spectral index, etc), and for different sets of data (not just WMAP but also supernovae, lensing, etc). Everything is basically consistent with a flat universe comprised of 72% vacuum energy, 23% dark matter, and 5% ordinary matter....

Of course the human brain is 70% water, so we shouldn't feel entirely bad that most of what we know is only 5% of the universe.

Here's what Wikipedia has on "vacuum energy":

... Two proposed forms for dark energy are the cosmological constant, a constant energy density filling space homogeneously,^[2] and scalar fields such as quintessence or moduli, dynamic quantities whose energy density can vary in time and space. In fact, contributions from scalar fields, which are constant in space, are usually also included in the cosmological constant. The cosmological constant is thought to arise from the vacuum energy...

and

...Vacuum energy is an underlying background energy that exists in space even when devoid of matter ...

So the recipe is basically definitional. Take away dark and ordinary matter and you get, by definition vacuum energy. Vacuum energy may arise largely from "smooth tension" (aka "dark energy"), but perhaps that's an interpretation of the results, not a statement of the results.

PS. Please note I'm not physicist in any form, I just like learning this stuff.

Update 3/8/2008: A little more detail on bad astronomy. Age - 13.73 billion years (middle aged in terms of a universe in which we can live). The average temperature of the universe is 2.725 degrees Kelvin -- just a smidgin above nothing.

Dark energy is not a force, and another take on fermions and bosons

This December post by CV has been in my queue for a while. He starts out complaining about the popular depiction of Dark Energy as a "force", but soon digresses into lots of basic physics I have trouble remembering.

Here are the parts I particularly liked:

A Dark, Misleading Force | Cosmic Variance

... The wrong part is referring to dark energy as a “force,” which it’s not...

... quantum field theory implies that the ingredients of a four-dimensional universe are divided neatly into two types: fermions, which cannot pile on top of each other due to the exclusion principle, and bosons, which can. That’s extremely close to the stuff/force distinction, and indeed we tend to associate the known bosonic fields — gravity, electromagnetism, gluons, and weak vector bosons — with the “forces of nature.” Personally I like to count the Higgs boson as a fifth force rather than a new matter particle, but that’s just because I’m especially fastidious....

...dark energy is definitely “stuff.” It’s not a new force. (There might be a force associated with it, if the dark energy is a light scalar field, but that force is so weak that it’s not been detected, and certainly isn’t responsible for the acceleration of the universe.) In fact, the relevant force is a pretty old one — gravity! Cosmologists consider all kinds of crazy ideas in their efforts to account for dark energy, but in all the sensible theories I’ve heard of, it’s gravity that is the operative force. The dark energy is causing a gravitational field, and an interesting kind of field that causes distant objects to appear to accelerate away from us rather than toward us, but it’s definitely gravity that is doing the forcing here...

...Anyone who has spoken about “energy” or “dimensions” to a non-specialist audience has come across this language barrier. Just recently it was finally beaten into me how bad “dark” is for describing “dark matter” and “dark energy.” What we mean by “dark” in these cases is “completely transparent to light.” To your average non-physicist, it turns out, “dark” might mean “completely absorbs light.” Which is the opposite! Who knew? That’s why I prefer calling it “smooth tension,” which sounds more Barry White than Public Enemy.

What I would really like to get rid of is any discussion of “negative pressure.” The important thing about dark energy is that it’s persistent — the density (energy per cubic centimeter) remains roughly constant, even as the universe expands. Therefore, according to general relativity, it imparts a perpetual impulse to the expansion of the universe, not one that gradually dilutes away. A constant density leads to a constant expansion rate, which means that the time it takes the universe to double in size is a constant. But if the universe doubles in size every ten billion years or so, what we see is distant galaxies accelerating away — first they are X parsecs away, then they are 2X parsecs away, then 4X parsecs away, then 8X, etc. The distance grows faster and faster, which we observe as acceleration...

Italics mine. I left out his further discussion on negative pressure, he persuaded me that it's a dumb concept (sort of like "centrifugal force").

Boltzmann's brain hits the big Times

The New York Times that is.

In a reprise of John Tierney's NYT interview with Nick (we're in a simulation) Bostrum  Dennis Overbye writes about a topic featured in some of my favorite physics blogs - Boltzmann's brain ...

Big Brain Theory: Have Cosmologists Lost Theirs? - New York Times

...cosmologists try to square the predictions of their cherished theories with their convictions that we and the universe are real. The basic problem is that across the eons of time, the standard theories suggest, the universe can recur over and over again in an endless cycle of big bangs, but it’s hard for nature to make a whole universe. It’s much easier to make fragments of one, like planets, yourself maybe in a spacesuit or even — in the most absurd and troubling example — a naked brain floating in space. Nature tends to do what is easiest, from the standpoint of energy and probability. And so these fragments — in particular the brains — would appear far more frequently than real full-fledged universes, or than us. Or they might be us.

CV fills in some more background

... The point about Boltzmann’s Brains is not that they are a fascinating prediction of an exciting new picture of the multiverse. On the contrary, the point is that they constitute a reductio ad absurdum that is meant to show the silliness of a certain kind of cosmology — one in which the low-entropy universe we see is a statistical fluctuation around an equilibrium state of maximal entropy...

In other words, the silliness of the naked flying space brain demonstrates that we don't understand entropy and the arrow of time.

CV uses the same Bayesian logic used by Bostrum to point out that if our current model of entropy were correct then it would be overwhelmingly likely that you are a Boltzmann's Brain and I don't exist...

... In the set of all such fluctuations, some brains would be embedded in universes like ours, but an enormously larger number would be all by themselves. This theory, therefore, predicts that a typical conscious observer is overwhelmingly likely to be such a brain...

CV concludes today's essay with a, to me, tantalizing comment ...

...So what are we to conclude? That our observed universe is not a statistical fluctuation around a thermal equilibrium state. That’s very important to know, but doesn’t pin down the truth. If the universe is eternal, and has a maximum value for its entropy, then we it would (almost always) be in thermal equilibrium. Therefore, either it’s not eternal, or there is no state of maximum entropy. I personally believe the latter, but there’s plenty of work to be done before we have any of this pinned down..

That last link is to an 207 CV article on how it all began.

Mathematical universe: the softly spoken premise of string theory

Why are mathematical models so insanely good at making predictions about the physical universe?

Is this a testament to the general modeling power of mathematics to describe any internally consistent system, or is the universe in some sense fundamentally mathematical?

These are the sorts of questions that used to come up in my undergraduate days. I don't recall a good answer, though I was certainly on the dim side of that student body. It may be that the answers were simply over my head.

I wonder about those questions again as I, very slowly, read Brian Greene's The Fabric of the Cosmos (See also: BBC IOT - Theories of Everything With Brian Greene). It's a good book; I'll have more to say on it when I'm done - sometime in the spring of 2008. For now I will say I like the substantial non-string chapters better than the string theory portion.

There are a few reasons for this preference. Greene is a string theorist, and I think most specialists do best describing things outside of their core passion. It's easier to be neutral about things that you haven't poured your heart into. More interestingly, the old question, "Is the universe fundamentally mathematical?", plays a role as well.

Most new physics seems, to a hobbyist like me, to make a reasonable bet that the implausible success of mathematical models will hold in new domains. It's a bit like tossing a plank off the end of a pier, assuming that when one walks to the end of the plank a supporting pillar will be found.

String theory tosses a breathtakingly long plank. It's a daring bet indeed. If we're ever to find out that it holds (proof of those necessary 10 space dimensions?) then we do have to take seriously the old whimsy that the universe, at its heart, is purely mathematical.

Until that day, it sure does feel to the physics hobbyist more like an exercise in mathematical brilliance than even traditional theoretical physics ...

Physics Feast: Sean Carroll's favorite posts

Sean "Cosmic Varience" Carroll has indexed his personal favorite posts. A true feast for the physics fan.

In Our Time: Symmetry, Moonshine, String Theory and E8

It's good to stretch one's mind on the way in to the office. It makes modeling relationships between arcane procedural descriptions and CPT codes seem pleasantly relaxing.

Today's stretch is courtesy of an In Our Time podcast [1] on symmetry. The professors do discuss Galois, but so far they've missed Emily Noether. Excellent anyway.

I'm not quite done, but I've learned about Galois, a bit of history, and, for the first time, I have a vague understanding of what Group Theory is about and it's relationship to geometry and topology. Not bad for free.

Towards the end of the podcast they talk about mysterious relationships between one "monstrous" element in an "atlas" of "Groups", where a Group is a collection of mathematical objects with shared symmetric transformations. One of them, the "monster", is described as having a mysterious relationship with mathematical physics.

Cue Wikipedia:

Monstrous moonshine - Wikipedia, the free encyclopedia

Specifically, Conway and Norton, following an initial observation by John McKay, found that the Fourier expansion of j(τ) ... could be expressed in terms of linear combinations of the dimensions of the irreducible representations of M ...

... lying behind monstrous moonshine is a certain string theory having the Monster group as symmetries; the conjectures made by Conway and Norton were proven by Richard Ewen Borcherds in 1992 using the no-ghost theorem from string theory and the theory of vertex operator algebras and generalized Kac-Moody superalgebras.

... Igor Frenkel, James Lepowsky and Arne Meurman explicitly constructed this representation using vertex operators in conformal field theory describing bosonic string theory compactified on a 24-dimensional torus generated by the Leech lattice and orbifolded by a reflection. The resulting module is called the Monster module...

Well, ok, so I didn't exactly follow all of that. Impressive at a cocktail party no doubt, but we don't do that sort of thing.

All quite exciting in a geeky sort of way, except bosonic string theory seems to have been a bit of a dead end. Again, from Wikipedia (emphases mine, I thought this was a lovely explanation btw_:

Bosonic String theory is the original version of string theory, developed in the late 1960s. Although it has many attractive features, it has a pair of features that render it unattractive as a physical model. Firstly it predicts only the existence of bosons whereas we know many physical particles are fermions. Secondly, it predicts the existence of a particle whose mass is imaginary implying that it travels faster than light. The existence of such a particle, commonly known as a tachyon, would conflict with much of what we know about physics, and such particles have never been observed.

Another feature of bosonic string theory is that in general the theory displays inconsistencies due to the conformal anomaly. In a spacetime of 26 dimensions, however, with 25 dimensions of space and one of time, the inconsistencies cancel. Another way to look at this is that in general bosonic string theory predicts unphysical particle states called 'ghosts'. In 26 dimensions the no-ghost theorem predicts that these ghost states have no interaction whatsoever with any other states and hence that they can be ignored leaving a consistent theory. So bosonic string theory predicts a 26 dimensional spacetime. This high dimensionality isn't a problem for bosonic string theory because it can be formulated in such a way that along the 22 excess dimensions, spacetime is folded up to form a small torus. This would leave only the familiar four dimensions of spacetime visible.

In the early 1970s, supersymmetry was discovered in the context of string theory, and a new version of string theory called superstring theory (supersymmetric string theory) became the real focus. Nevertheless, bosonic string theory remains a very useful "toy model" to understand many general features of perturbative string theory, and string theory textbooks usually start with the bosonic string...

So why does Time always get only one dimension? Space seems awfully greedy.

So the monster/physics connection didn't quite hold up, but one supposes Supersymmetry might have some familial connection to the Monster.

Or perhaps there's another step up?

... E8 is the symmetries of a geometric object that is 57-dimensional. E8 itself is 248-dimensional...

...Hermann Nicolai, Director of the Albert Einstein Institute in Potsdam, Germany. "While mathematicians have known for a long time about the beauty and the uniqueness of E8, we physicists have come to appreciate its exceptional role only more recently - yet, in our attempts to unify gravity with the other fundamental forces into a consistent theory of quantum gravity, we now encounter it at almost every corner."

Or a step down?

... Since 1997, physicists have proposed countless variations on Maldacena's theme, all of which interpret a string as a swarm of particles living in a small number of dimensions. Perhaps the easiest case to visualize is when that number is two. In such a scenario, anything that takes place in your many-dimensional, stringy universe has a sort of shadow representation in terms of particles moving on that universe's 'sphere at infinity.' This esoteric-sounding concept is actually similar to the familiar celestial sphere of the night sky as seen from Earth: It's the two-dimensional surface spanning all possible directions one can point to infinitely far in space..

I probably need to stop now. Work beckons, and my furhter inquires on relationship between E8 and the Monster Group started running into "alternative physics" posts. I have enough trouble with "conventional" physics, thanks.

Ok, one last comment. In the nice, sane, quiet world of the humble Higgs (God) particle CV tells us:

... if you impose upon our relativistic, complex, quantum-mechanical wavefunctions the requirement that they be invariant under these U(1) transformations, then you get electromagnetism. Conservation of electric charge. A massless photon. QED - quantum electrodynamics, in all its 12-digit precision glory. Electromagnetism is a simple consequence of the U(1) symmetry of any wavefunction....

It's all relative (sorry). QED seems perfectly pedestrian now.

[1] From a prior post:

Melvyn Bragg's BBC show, In Our Time, has begun a new season. I'm a fan.

The bad news is that the BBC is sticking with its execrable latest-episode-only download policy. So if you want to listen to the superb Opium War episode on your MP3 player you need to either use Audio Hijack Pro to capture the RealAudio stream or (if you know me) ask me for a DVD with the entire series [1]. Incidentally, this is a good time to write a quick email to set IOT free.

The good news is there's a new page that makes it easy to subscribe to a feed. I used to subscribe via iTunes, but if I went a week without using iTunes I missed the show. Now I subscribe via iTunes and Bloglines; I use Bloglines at least daily so it's easy for me to save the MP3 and email it to myself.

Two dimensional string theory

Promotion has sapped the output of my favorite physics bloggers, so I'm grateful to FMH for my physics fix:

Shadow World: Science News Online, Nov. 17, 2007

....Since 1997, physicists have proposed countless variations on Maldacena's theme, all of which interpret a string as a swarm of particles living in a small number of dimensions. Perhaps the easiest case to visualize is when that number is two. In such a scenario, anything that takes place in your many-dimensional, stringy universe has a sort of shadow representation in terms of particles moving on that universe's 'sphere at infinity.' This esoteric-sounding concept is actually similar to the familiar celestial sphere of the night sky as seen from Earth: It's the two-dimensional surface spanning all possible directions one can point to infinitely far in space...

So this re-representation of string theory has been popular for 10 years -- but I don't recall reading about it.

Annoying.

Sciam did cover this in Nov 2005 ("The Illusion of Gravity"), but I wasn't a subscriber then. (SciAm is the only periodical I subscribe to does not give archival access to current print subscribers. It's their right, but I do hold it against them.)

Wikipedia presents the theory more technically:

Juan Martín Maldacena (born September 10, 1968) is a theoretical physicist born in Buenos Aires, Argentina. Among his many discoveries, the most famous one is the most reliable realization of the holographic principle - namely the AdS/CFT correspondence, the successfully tested conjecture about the equivalence of string theory or supergravity on Anti de Sitter (AdS) space, and a conformal field theory defined on the boundary of the AdS space.

and on AdS/CFT correspondence:

In physics, the AdS/CFT correspondence (anti-de-Sitter space/conformal field theory correspondence), sometimes called the Maldacena duality, is the conjectured equivalence between a string theory defined on one space, and a quantum field theory without gravity defined on the conformal boundary of this space, whose dimension is lower by one or more...

Now, as we all know one of the primary challenges of the last 80 or so years of physics has been quantizing gravity. So, as a hobbyist reading this, I'm thinking the mathematical trick is to make the problem more tractable (and perhaps more constrained?) by taking gravity out of the picture. Hence the SciAm title - the "illusion of gravity".

This might be a bit like the old polar vs. cartesian coordinate transformation in Physics 101. Neither is "truer" than the other, but in some problems solutions are much easier. Or maybe the the Maldacena view will turn out to be the "better" model of "reality" (whatever that slippery beast might be).

I'll have to look around for some other popular summaries ...

Relativity + QM + symmetry = QED

After a series of posts with only a marginal connection to physics, CV has returned with a nice discussion of the Higgs particle:

Higgs 101 | Cosmic Variance

...Here comes the miracle: if you impose upon our relativistic, complex, quantum-mechanical wavefunctions the requirement that they be invariant under these U(1) transformations, then you get electromagnetism. Conservation of electric charge. A massless photon. QED - quantum electrodynamics, in all its 12-digit precision glory. Electromagnetism is a simple consequence of the U(1) symmetry of any wavefunction....

Symmetry, in this case the U(1) transformation invariance, is given a natural place in this discussion of the Higgs.

Nice summary!

BBC IOT - Theories of Everything With Brian Greene

Even In Our Time has its limits. I wrote last April that Lord Bragg was struggling with the Poincare Conjecture, and compared it to my physics reading then ...

... Which brings me to my recent readings in physics. I'm reading Gribbins on Quantum Mechanics (1994) and Brian Greene with another cosmology/string theory overview, the Gribbins book is my personal favorite, but it's a bit dated now. Together though, they make it hard to overlook that physics seems to be getting harder and harder. We have more physicists than ever, and I'd wager there's a Feynman or two in the bunch, but we've been stuck for decades now...

I've been savoring Greene's The Fabric of the Cosmos ever since, reading a few pages every day. It's rich stuff! I'll have a post on the book soon, but I confess I'd underestimated the progress of the 90s; quantum speckles on the microwave echoes of Higgs driven inflation is darned impressive.

Which brings me to the podcast I'm listening to now -- Theories of Everything, feature none other than ...

Brian Greene, Professor of Physics and Mathematics at Columbia University and author of The Fabric of the Cosmos (Allen Lane, 2004)

John Barrow, Professor of Mathematical Sciences at the University of Cambridge and author of The Constants of Nature (Vintage, 2003)

Dr Val Gibson, particle physicist from the Cavendish Laboratory and Fellow of Trinity College, Cambridge

Further reading
The Elegant Universe by Brian Greene (Vintage, 2000)
[jf: odd choice, they should have recommended The Fabric of the Cosmos, his current book]
Theories of Everything by John Barrow (Vintage, 1992)

Now that's ambitious. Alas, Bragg is weakest when he ventures into math and physics, and his guests seemed to be struggling as well. At one point Gibson and Green talk about the relationship of extra dimensions to string theory, but they just miss making the key point -- that while finding extra dimensions won't prove string theory, not finding them will severely weaken string theory.

I was also left with the impression that the "string" metaphor is overdone. Maybe it would work better if Green were to say something like "we've developed very fancy maths that allow us to model both the jittery quantum world and the continuous world of cosmology", and one way to imagine the mathematics is to think that it's describing wee little bits of strings ...

Full points to IOT for courage, but Lord Bragg was traveling in alien territory ...

Update 9/30/07: I wrote this post pretty quickly -- like all my posts. Melvynn stayed lost, but his guests warmed up around the half way mark, so it did turn into a strong episode.

Blah, blah, quantum entanglement, yawn, hacking reality, zzzzz

I'm almost caught up with modern physics, but it's taken a toll.

It's started my reading a few months ago when I realized I'd fallen hopelessly out of date, but I'm now only a few chapters from finishing Greenes latest tome. Alas, between Gribbin and Greenes, I'm a broken man. Modern physics is so consistently and cumulatively weird that a steady diet has eliminated my critical capacity. No wonder science fiction writers feel beaten down -- no work of fiction can be as mind-bending as today's physics. It's enough to make the idea that we're all living in a simulation seem comforting by comparison.

Which is to say that latest proof that the universe is every bit as weird as predicted is a bit of a yawner ...

'Spooky' science points to quantum internet - Internet - www.itnews.com.au

Physicists at the University of Michigan have demonstrated how two separate atoms can communicate with a sort of 'quantum intuition' ...

The scientists used light to establish an "entanglement" between two atoms, which were trapped one metre apart in separate enclosures...

... David Moehring, the lead author of the paper who performed the research as a University of Michigan graduate student, explained that the most important aspect of the experiment is the distance between the two atoms.

"The separation of the quantum bits [qubits] in our entangled state is the most important feature," he said.

"Localised entanglement has been performed in ion trap qubits in the past, but to build a scalable quantum computer network (or a quantum internet) the creation of entanglement schemes between remotely entangled qubit memories is necessary."

The researchers used two atoms to function as qubits storing a piece of information in their electron configuration. They then excited each atom, inducing electrons to fall into a lower energy state and emit one photon, or one particle of light, in the process.

The atoms, which were actually ions of the rare-earth element ytterbium, are capable of emitting two different types of photons of different wavelengths.

The type of photon released by each atom indicates the particular state of the atom. Because of this, each photon was entangled with its atom.

By manipulating the photons emitted from each of the two atoms and guiding them to interact along a fibre-optic thread, the researchers were able to detect the resulting photon clicks and entangle the atoms.

Professor Monroe explained that the fibre-optic thread was necessary to establish entanglement of the atoms. But the fibre could be severed and the two atoms would remain entangled, even if one were "carefully taken to Jupiter"...

I wasn't being entirely supercilious. My reading suggests this is a perfectly prosaic result, indeed anything different would have been shocking. The reason the paper was published is because of the experimental genius required, and perhaps because it suggests new ways to build a quantum computer.

Physicist bloggers getting cranky

I read a few physics blogs, and lately I think I'm seeing a bit of irritability. CV (Sean)'s post today hints at the trend ...

Ask a String Theorist! Or an Atomic Physicist. | Cosmic Variance.

..Aaron has begun to talk a little about the multiverse — here, here. He has thereby earned grumpy mutterings, rolled eyes, and “help” from some sensible physicists, some crackpots, some curmudgeons, his guest co-blogger, and even himself. I don’t quite understand what all the angst is about...

Bio-blogger crankiness is usually related to creationists. Creationists seem to leave physics alone (an interesting phenomena); the "crank" and the "crackpot" are the bane of physics bloggers. I think biologists have a legitimate complaint, but physicists protest too much. In the case of physics, the cranks have a case.

It's not that cranks are a good guide to physics, it's rather that physics is so weird that to an outsider the cranks are hardly less plausible than the science. Entanglement across the multiverse? Seems almost plausible.

It doesn't help that by nature and practice physicists are driven to contemplate the forbidden. Tests for "life in a simulation"? Answers to the Fermi Paradox? Rules for the least harmful use of the Bayesian anthropic principle (ok, so maybe the creationists do show up)? Physicists can't stay away -- but the very questions make even them irritable. Cranks like me only darken their mood.

Relax gang. Ignore your cranks and embrace your fundamental weirdness. It's a weird universe, and the crackpots are at home ...

CV is hurting my head again: The anthropic principle and our peculiar relation to the arrow of time ...

Things were odd enough when we seemed to live peculiarly close the mid-life of the universe. But now it seems we live infinitesimally close to the birth of the universe ...

Unusual Features of Our Place In the Universe That Have Obvious Anthropic Explanations | Cosmic Variance

...

Most of the energy in the universe is dark energy. And yet, we are made of matter.

The post-Big-Bang lifespan of the universe is very plausibly infinite. And yet, we find ourselves living within the first few tens of billions of years (a finite interval) after the Bang.

which produced a motley range of comments varying from funny to thoughtful to eccentric. One of them was particularly hard to characterize ...

Jonathan Vos Post on Aug 8th, 2007 at 11:52 am

.... As to the far future, my article on this, which cited Freeman Dyson and others, which first published the idea that we are most likely simulations by a far future dilute electron positron plasma civilization, and which served as the extensively quoted basis (quotation marks accidently omitted) of some Greg Benford novels, is:

“Human Destiny and the End of Time” [Quantum, No.39, Winter 1991/1992, Thrust Publications, 8217 Langport Terrace, Gaithersburg, MD 20877] ISSN 0198-6686

In fairness to Benford, who I think is being criticized here [update 12/7/07: see comment by Vos Post -- this is not a criticism of Benford], science fiction writers have been talking about 'life in a simulation' at least since the early 1980s and I dimly recall Dyson as talking about it eons ago.

For related discussions, see:

• Ten cosmologies and Theory 10
• Life seem absurd? Maybe it is.
• George Bush; Deity of the Computer Simulation?
• http://www.faughnan.com/setifail.html#[9] (Footnote - Are You Living in a Computer Simulation? Nick Bostrom, Department of Philosophy, Oxford University. Philosophical Quarterly (2003), Vol. 53, No. 211, pp. 243-255.)
  
• In Our Time: Common Sense Philosophy: Descartes and Hume try to get out of their heads, and mostly fail to persuade anyone that they're not living in a simulation. Hume in particular seems to have struggled with the impossibility of proving he wasn't a "brain in a bottle", though it's easy to argue that Plato (and probably "Thog") was talking about a similar problem.
  

CV reviews the mutual constraints of cosmology and particle physics

A delightful post for amateur physics junkies: Constraints and Signatures in Particle Cosmology | Cosmic Variance. CV reviews the constraints cosmology places on modeling particle physics, and conversely suggests some cosmologic puzzles that might inspire new particle physics. This one was knew to me:

... There are a number of hints that the highest energy cosmic rays may require exotic new physics for a complete understanding. Above a certain energy (the Greisen-Zatsepin-Kuzmin (GZK) cutoff), particles from cosmological distances shouldn’t reach us at all, because they would scatter off the CMB. This has led people to speculate that any ultra high-energy cosmic rays (UHECRs) may be a signature of new particle physics. Does your theory contain any particles or phenomena that could allow this to happen, and what spectrum of UHECRs should we expect? Some of those topological defects I mentioned above may be an example...

"Topological defects". A rather significant hint I'd say. Mark is referring to:

... Does your theory contain any new topological defects, such as monopoles, domain walls or cosmic strings? If the vacuum structure of your particle physics theory is sufficiently topologically complex, then any symmetry breakings that occur may lead to trapped regions of false vacuum that cannot decay. If so, then many of the constraints mentioned for long-lived elementary particles may apply to these objects. In addition, some topological defects can form networks that redshift more slowly then matter, coming to dominate at a later time in the universe, or can generate a spectrum of gravitational radiation that is in conflict with our detailed measurements of the timing of the millisecond pulsar. If this last constraint is a problem, then it is also possible that the defects unacceptably distort the spectrum of the Cosmic Microwave Background radiation (CMB)...

Keep your eyes open for wandering wrinkles in space-time. Should you happen upon one, email Mark at "once" ...

Cosmic Variance's Sean Carroll on the arrow of time

I've been reading Sean Carroll's posts on Cosmic Variance, not realizing until now that he's a research associate at my alma mater. I guess blogs really are infested by amateurs destroying our culture of knowledge ...

Sean's presentation is pretty readable for the interested layperson ...

Sean Carroll: Why Is the Past Different From the Future?

... In such a universe, everything we think we "remember" ... about the past is ... a mistake.

Dinosaur skeletons arose spontaneously out of dirt.

It's been a busy road to reading material like Sean's. It started when I came across this comment in Wired  last February:

Even the best theories to explain how entanglement gets around this problem seem preposterous. One, for example, speculates that signals are shot back through time. Ultimately, the answer is bound to be unnerving: According to a famous doctrine called Bell’s Inequality, for entanglement to square with relativity, either we have no free will or reality is an illusion. Some choice.
- Lucas Graves, New York City-based writer

As near as I can tell Lucas was simplifying a bit. The complete absence of free will (aka. life in God's movie or the Tralfamadorian perspective) goes back originally to Newton (determination by mechanics) then to Einstein (determination by time slice perspectives) and returned with the transactional interpretation of QM. The good news for the non-Calvinists among us is that the evidence (as I read of it) favors the non-existence of independent reality over the kind of absolute determinism where not only dinosaurs arise from dirt, but all of space and time arise spontaneously and (seemingly) coherently.

So what does all this have to do with Carroll's talk? Well, it seems plausible that the "arrow of time" has something to do with predetermination or non-determination and that it should also have equivalences in both cosmology and quantum mechanics. Here's Carroll's conclusion about where time comes from in the view cosmology - it involves the infinite multiverse ...

...If the universe lasts forever but has no equilibrium
state, we naturally obtain an arrow of time.

It’s crucial that the way in which the multiverse
creates more entropy is to make universes like ours...

Further I cannot go! So where does the arrow of time come from in QM? I'm imagining at the moment that it comes from decoherence...*

* Ok, how did I know that "Decoherence, Quantum Measurement and the Arrow of Time" existed? I didn't, of course. I hypothesized that the arrow of time emerges as a universe of infinite possibilities collapses as the past interacts with it -- an idea that's appeared in at least one science fiction story I've read. I knew decoherence is the technical term used for the interpretation of QM most consistent with this model, so I searched on "decoherence" and "arrow of time". Easy. (The alternate explanation, of course, is that the conference didn't really exist until I thought of it, which led the quantum chaos of the past to collapse.... :-)

The breaking of modern physics: space with non-zero energy

I came across this older article via a blog comment. Shame that this article doesn't have a date on it (a common web page error), but I think it's probably from 2006. It's not news, but I liked the overview of what it's meant to find that empty space has non-zero energy (or equivalently, non-zero mass):

Edge: THE ENERGY OF EMPTY SPACE THAT ISN'T ZERO: A Talk with Lawrence Krauss

.... The energy of empty space had to be precisely zero. Why? Because you've got these virtual particles that are apparently contributing huge amounts of energy, you can imagine in physics, how underlying symmetries in nature can produce exact cancellations — that happens all the time. Symmetries produce two numbers that are exactly equal and opposite because somewhere there's an underlying mathematical symmetry of equations. So that you can understand how symmetries could somehow cause an exact cancellation of the energy of empty space.

But what you couldn't understand was how to cancel a number to a hundred and twenty decimal places and leave something finite left over. You can't take two numbers that are very large and expect them to almost exactly cancel leaving something that's 120 orders of magnitude smaller left over. And that's what would be required to have an energy that was comparable with the observational upper limits on the energy of empty space....

... every measure we've made right now is completely consistent with a constant energy in the universe over cosmological time. And that's consistent with the cosmological constant, with vacuum energy....

... because of this energy of empty space — which is so inexplicable that if it really is an energy of empty space, the value of that number is so ridiculous that it's driven people to think that maybe, maybe it's an accident of our environment, that physics is an environmental science — that certain fundamental constants in nature may just be accidents, and there may be many different universes, in which the laws of physics are different, and the reasons those constants have the values they have might be — in our universe — might be because we're there to observe them.

This is not intelligent design; it's the opposite of intelligent design. It's a kind of cosmic natural selection....

... Right now we're floundering. We're floundering, in a lot of different areas.

...Fundamental physics is really at kind of a crossroads. The observations have just told us that the universe is crazy, but hasn't told us what direction the universe is crazy in. The theories have been incredibly complex and elaborate, but haven't yet made any compelling inroads.

... On the largest scales, when we look out at the universe, there doesn't seem to be enough structure — not as much as inflation would predict. Now the question is, is that a statistical fluke?

... when you look at CMB [cjf: osmic microwave background] map, you also see that the structure that is observed, is in fact, in a weird way, correlated with the plane of the earth around the sun. Is this Copernicus coming back to haunt us? That's crazy. We're looking out at the whole universe. There's no way there should be a correlation of structure with our motion of the earth around the sun — the plane of the earth around the sun — the ecliptic. That would say we are truly the center of the universe.

The new results are either telling us that all of science is wrong and we're the center of the universe, or maybe the data is imply incorrect, or maybe it's telling us there's something weird about the microwave background results and that maybe, maybe there's something wrong with our theories on the larger scales...

Space isn't what it once was. We used to think space separated things, but now we know it doesn't. If you collapse the probability wave on an electron in Kansas, then the probability wave on its entangled partner 200 billion light years away collapses at the same "time". (The catch being what is meant by time in this context.)

Physics isn't what it once was. Physicists seem a bit demoralized, and stunned. I don't blame 'em at all. This reality looks less plausible all the time.

In Our Time: light and John Barrow

If you were to enter the black hole at the center of our galaxy ... 'you easily pass into it without disruption and find it had the density of air ... but you would find yourself unable to return ...'. Which is a crude paraphrase of John Barrow speaking on the speed of light for In Our Time. There's lots more like that, such as "information cannot travel faster than the speed of light", which is a bit different from the way that law has been traditionally expressed.

I was thinking that, even for IOT, this was a rather erudite and interesting guest. The wikipedia profile explains things.

Another excellent episode, but of course no longer available as a podcast. If you don't like that, then help liberate In Our Time. In the meantime, maybe you should start collecting the podcasts ...

The single speed universe

For the photon, there is neither time nor distance. Every destination takes no time at all to reach, which is, of course, also true of non-local "transmission" of non-meaning. I've retained that much from Gribbin and my recent readings of popular works on cosmology and quantum physics.

So does that mean that there's only one "space-time speed" for everything, namely to be as motionless as a photon?

After all, the more gravity one feels, and the more history of acceleration one has, the more one moves through time rather than space alone. in other words, as one gets closer to the speed of light the energy input of an accelerating force is diverted into time travel rather than space travel.

So, if one thinks of speed as movement through space and time, is it true to say that everything in the universe has the same "speed"?

I did a quick google on the topic, and found this article. So maybe that is the way physicists think about spacetime velocity. BTW, the article claims that one interpretation of general relativity is consistent with both the transactional interpretation of QM and Tralfamadorian philosophy.

Truly, all of modern physics is an attempt to understand the photon ...

Update 5/15: Turns out I was remembering chapter one (relativity theory) of Greene's overview of cosmology and theoretical physics! I'd skimmed the chapter a few weeks ago and I was basically recalling what he'd written, though the Tralfamadorian bit is mine. Nice to know I wasn't just spouting off! Even Greene mentions how alien and astounding special and general relativity theory feel when he reviews the concepts -- and that's his profession. These are concepts so beyond our everyday existence that they easily slip out of my feeble mind ...

I'm now taking a leisurely slow read through the book and will doubtless have further related comments ..

Boltzmann’s Brain explained

I'd blogged earlier on a Cosmic Variance article about emergent brains in the eternal soup of a senescent universe, but I didn't know the original context of the Boltzmann Brain idea. Another CV article today pointed me to one from last year that filled in the gaps. The Boltzmann Brain comes from a 2004 paper by Albrecht and Sorbo, and it was described in CV last year:

Boltzmann’s Anthropic Brain | Cosmic Variance

...Let’s posit that the universe is typically in thermal equilibrium, with occasional fluctuations down to low-entropy states, and that we live in the midst of one of those fluctuations because that’s the only place hospitable to life. What follows?

The most basic problem has been colorfully labeled “Boltzmann’s Brain” by Albrecht and Sorbo. Remember that the low-entropy fluctuations we are talking about are incredibly rare, and the lower the entropy goes, the rarer they are...
...So if we are explaining our low-entropy universe by appealing to the anthropic criterion that it must be possible for intelligent life to exist, quite a strong prediction follows: we should find ourselves in the minimum possible entropy fluctuation consistent with life’s existence.

And that minimum fluctuation would be “Boltzmann’s Brain.” Out of the background thermal equilibrium, a fluctuation randomly appears that collects some degrees of freedom into the form of a conscious brain, with just enough sensory apparatus to look around and say “Hey! I exist!”, before dissolving back into the equilibrated ooze.

You might object that such a fluctuation is very rare, and indeed it is. But so would be a fluctuation into our whole universe — in fact, quite a bit more rare. The momentary decrease in entropy required to produce such a brain is fantastically less than that required to make our whole universe. Within the infinite ensemble envisioned by Boltzmann, the overwhelming majority of brains will find themselves disembodied and alone, not happily ensconsed in a warm and welcoming universe filled with other souls. (You know, like ours.)

This is the general thrust of argument with which many anthropic claims run into trouble. Our observed universe has something like a hundred billion galaxies with something like a hundred billion stars each. That’s an extremely expansive and profligate universe, if its features are constrained solely by the demand that we exist. Very roughly speaking, anthropic arguments would be more persuasive if our universe was minimally constructed to allow for our existence; e.g. if the vacuum energy were small enough to allow for a single galaxy to arise out of a really rare density fluctuation. Instead we have a hundred billion such galaxies, not to count all of those outside our Hubble radius — an embarassment of riches, really....

Of course there's no end to the anthropic principle, which I tend to think of as an extreme application of Bayes theorem. We can be anthropic ad absurbum, and say that since we live in a rich universe we must exist in a really, really, really big and really, really, rare entropic excursion event.

Or maybe we're a dream of a more modest excursion, which is, after all, more likely.

Hmph. Cosmology is becoming about as satisfying as quantum mechanics.

Time, entropy and baby universes

CV talks about manufacturing universes that vanish as an evaporating black hole....

How Did the Universe Start? | Cosmic Variance

... The baby-universe idea at least has the chance to give rise to a spontaneous violation of time-reversal symmetry and explain the arrow of time. If we start with empty space an evolve it forward, baby universes can (hypothetically) be born; but the same is true if we run it backwards. The increase of entropy doesn’t arise from a fine-tuning at one end of the universe’s history, it’s a natural consequence of the ability of the universe to always increase its entropy. We’re a long way from completely understanding such a picture; ultimately we’ll have to be talking about a Hilbert space of wavefunctions that involve an infinite number of disconnected components of spacetime, which has always been a tricky problem. But the increase of entropy is a fact of life, right here in front of our noses, that is telling us something deep about the universe on the very largest scales.

Where entropy increases, there goes time. Or so it goes.

Update 4/28/07: Infinitely expanding universes birthing within infinitely expanding universes. Requirements for human observation to collapse probability waves. All interpretations of self-consistent mathematics, but way beyond bizarre. Which leads to the scary thought. Could he be right? Brrrr.