Finding yourself in the mathematical universe of pi

I’m reading Tegmark’s Our Mathematical Universe. It’s the layperson version of a 2007 paper (downloadable)

I explore physics implications of the External Reality Hypothesis (ERH) that there exists an external physical reality completely independent of us humans. I argue that with a sufficiently broad definition of mathematics, it implies the Mathematical Universe Hypothesis (MUH) that our physical world is an abstract mathematical structure. I discuss various implications of the ERH and MUH, ranging from standard physics topics like symmetries, irreducible representations, units, free parameters, randomness and initial conditions to broader issues like consciousness, parallel universes and Godel incompleteness. I hypothesize that only computable and decidable (in Godel's sense) structures exist, which alleviates the cosmological measure problem and help explain why our physical laws appear so simple. I also comment on the intimate relation between mathematical structures, computations, simulations and physical systems.

As best as I can tell, Tegmark, more or less like Einstein, thinks of spacetime as a static thing; we relate to spacetime as a tune relates to a CD. It is a bit of an illusion that one thing follows another, or that we seem to have a past and a future, or that things are created and end. Rather as a block of granite contains all sculpture, or the alphabet all knowledge, meaning is just an arrangement that fits. “I think therefore I am” indeed.

Which made me wonder if I could find “I am John” in pi. Seems a bit similar. If pi is random then that string should show up somewhere.

Happily the “National Energy Research Scientific Computing Center” will search pi for strings based on a 5bit English character set encoding.

Alas, “I am John” is not in the span they search…

search string = "i_am_john"
45-bit binary equivalent = 010010000000001011010000001010011110100001110
string does not occur in first 4 billion binary digits of pi

My daughter’s name does turn up:

search string = "brinna"
30-bit binary equivalent = 000101001001001011100111000001
search string found at binary index = 872397609 

binary pi : 0010101000010100100100101110011100000101111010011010101101000011
binary string: 000101001001001011100111000001
character pi : aqyfuc_nj_--yjbrinnaoiuma.fvfkbv.bcfgz
character string: brinna

This essay should be in there too, assuming pi digits really are deterministically random. Somewhere. Which I think has something to do with the Mathematical Universe. Somehow.

PS. From the arXiv paper: “… quantum field theory states such as the Hawking-Hartle wave function or the inflationary Bunch-Davies vacuum have very low algorithmic complexity (since they can be de- fined in quite brief physics papers), yet simulating their time evolution would simulate not merely one universe like ours, but a vast decohering ensemble corresponding to the above-mentioned Level III multiverse. It is therefore plausible that our universe could be simulated by quite a short computer program.”

Coming to terms with the multiverse

Like most people, my neurons were rebooted a few times between birth and adulthood. So I don’t remember that much about childhood, but I do remember sitting in a schoolyard, perhaps in grade one or two, trying to get my head around the end of the universe.

I’m not at all sure, but I believe at that time, around 1970, I thought of the universe as infinite. Later it became finite, a theoretically countable number of galaxies somewhere between 10-20 billion light years “across” with an estimated age that didn’t quite add up. Then came inflation and the height of a human defined the mid-point between Neutrino and the Universe. That was six or seven years ago.

Those were the good old days. Now we have the Multiverse, and Tegmark’s taxonomy of multiversi …

Level I: Beyond our cosmological horizon[edit]

… A generic prediction of chaotic inflation is an infinite ergodic universe, which, being infinite, must contain Hubble volumes realizing all initial conditions.

Accordingly, an infinite universe will contain an infinite number of Hubble volumes, all having the same physical laws and physical constants…. 

Level II: Universes with different physical constants…

… In the chaotic inflation theory, a variant of the cosmic inflation theory, the multiverse as a whole is stretching and will continue doing so forever, but some regions of space stop stretching and form distinct bubbles, like gas pockets in a loaf of rising bread….Different bubbles may experience different spontaneous symmetry breaking resulting in different properties such as different physical constants…

Level III: Many-worlds interpretation of quantum mechanics … 

Level IV: Ultimate ensemble …

I’m slowly reading Tegmark’s popular book of which some criticism might be made. That review, however, offers little solace to universe nostalgics (emphases mine)…

Level I [is] just lots of unobservable extensions of what we see, with the same physics, an uncontroversial notion. Level III is the “many-worlds” interpretation of quantum mechanics, which again sticks to our known laws of physics. Level II is where conventional notions of science get left behind, with different physics in other unobservable parts of the universe. This is what has become quite popular the past dozen years …

So an infinite number of universes like the one we observe is “uncontroversial” and the idea that our infinite multiverse is only one extreme instance of vastly larger number (mostly unsuitable for particles, much less life) is “quite popular”.  There are necessarily an infinite number of John Gordon’s typing versions of this post…

Yes, infinity is like that.

I prefer to think that nothing ever happened, and that we are merely granite dreaming, but I try to creep up on the multiverse by way of metaphor. One person standing on a barren planet is inexplicable; 8 billion people on a planet infested with life is relatively easy to understand.

Perhaps so it is with universes.

Why did Sean Carroll write 'From Eternity to Here'?

Newt Gingrich has written many Amazon book reviews. One of them was on a physics book I'd read, maybe Greene's The Fabric of the Cosmos -- though I don't see the review there now.

I don't remember which book, but I remember Gingrich claimed he'd finished it in a few days of easy reading. Given Gingrich's historical record he's either the world's smartest fool or a master of bull poop. Modern physics books are a hard slog for the non-genius, non-physicist. I've read a few of them, and I'm always impressed by how much work it is to integrate the concept space, and how insane the working scientist authors are to write these complex tomes.

Why, for example, did Sean M. Carroll [1], write From Eternity to Here? The guys an untentured Caltech theoretical physicist -- he's supposed to be cranking out grants and papers. I mean, I love the book, but this isn't survival behavior. His blogging is sinful enough, but the book is another level.

Part of the reason might be getting some of his personal theories more attention. Carroll believes cosmological inflation, while "true", simply "begs the question". That is, while cosmological inflation explains some properties of the observable cosmos, it raises even more questions about the state of the pre-inflationary cosmos. Carroll believes the physics of entropy is a possible key to that puzzle. In today's physics community this seems to be mildly heretical and probably not a great way to get tenure. [3]

So frustration with the establishment is probably a part of his compulsion, but it's not all. There's a clue to the rest buried in the footnotes [2] ...

273. What would be even better is if some young person read this book, became convinced this was a serious problem worthy of our attention, and went on to solve it.... if you end up finding an explanation for the arrow of time that becomes widely accepted within the physics community, please let me know if this book had anything to do with it.

The work of puzzle solving goes on, from one mortal generation to the next. That's our little way of poking a stick in the Eye of Entropy.

[1] The unrelated Sean B. Carroll is another working scientist author of popular biology books.
[2]  Consecutively numbered - brilliant. Wish everyone did this instead of renumbering each chapter. After reading the core book, go back and read the footnotes. I made the mistake of borrowing this book from the library -- and blowing through multiple renewal periods and fines and so on. Finally, with 30 pages to go, I gave up and bought the sucker. If Carroll ever does another edition though, he ought to include a concept glossary as well.
[3] Most serious books of lay physics, including Greene's work, has this element. Like Greene and other working physicists, Carroll sticks with establishment physics for 90% of the book, then lays out his own ideas with clear warnings that "dragons are here". It's a good practice and it's part of what distinguishes books by reality-based physicists from the flaky side of the cosmos.  Of course in modern physics "reality" is profoundly unreal.

See also:

• BBC IOT - Theories of Everything With Brian Greene 9/2007
• Mathematical universe: the softly spoken premise of string theory 1/2008
• Carroll on Time: emergent or fundamental? 9/2011
• Entanglement and the realness of time 8/2011
• Sean Carroll: Blog Posts - Carroll's favorites
• Cosmic Variance's Sean Carroll on the arrow of time 6/2007
• Inflation isn't what it used to be (cosmologic version) 10/2011
• A quantum state eternally evolving in an infinite-dimensional Hilbert space 11/2008

Inflation isn't what it used to be (cosmologic version)

I barely got my head around the inflationary universe, and it's already passe.

Sean Carroll starts us off with his debut article in Discover -- Welcome to the Multiverse. That's just a warmup though, his blog digs a lot deeper.  ...

The Eternally Existing, Self-Reproducing, Frequently Puzzling Inflationary Universe | Cosmic Variance | Discover Magazine

... it is crucial to note that in conventional non-inflationary cosmology, our current observable universe was about a centimeter across at the Planck time. That’s a huge size by particle physics standards. In inflation, by contrast, the whole universe could have fit into a Planck volume, 10-33 centimeters across, much tinier indeed...

... “essentially all” — models of inflation lead to the prediction that inflation never completely ends. ... inflation will end in some places, but in other places it keeps going. Where it keeps going, space expands at a fantastic rate. In some parts of that region, inflation eventually ends, but in others it keeps going. And that process continues forever, with some part of the universe perpetually undergoing inflation. That’s how the multiverse gets off the ground — we’re left with a chaotic jumble consisting of numerous “pocket universes” separated by regions of inflating spacetime...

... thinking about black hole entropy has led physicists to propose something called “horizon complementarity” — the idea that one observer can’t sensibly talk about things that are happening outside their horizon. When applied to cosmology, this means we should think locally: talk about one or another pocket universe, but not all of them at the same time. In a very real sense, the implication of complementarity is that things outside our horizon aren’t actually real — all that exists, from our point of view, are degrees of freedom inside the horizon, and on the horizon itself....

Sean ends by sending us back to read a 2007 article than runs through stories of pre-inflationary creation ... How Did the Universe Start? (April 2007)

That's a lot to digest, but the very next day Sean features a rant by Tom Banks, a fierce physicist who must put coffee in his Ritalin ...

Guest Post: Tom Banks Contra Eternal Inflation | Cosmic Variance | Discover Magazine

A lot of research in high energy theory has been devoted to the topic of eternal inflation. More and more, over the last few years, I’ve come to regard this as an enormous waste of intellectual resources and I’ve chosen Cosmic Variance as a very public way to make my objections to this theoretical mistake clear...

... We also discussed a solution to Einstein’s equations which was a black hole with de Sitter interior embedded in this homogeneous isotropic cosmology. In the paper referred to above, we have found an exact quantum model, satisfying all the consistency conditions of HST, which corresponds to that solution. There is a one parameter family of models corresponding to the choice of dS c.c. We can also find approximate solutions of the consistency conditions corresponding to two or more such black holes, separated by a large distance...

... So we can construct models in which there are many values of the c.c. depending on which black hole interior one resides in. Each mini dS universe will be stable, unless it collides with another...

I didn't get much out of Tom Banks essay -- it's aimed at someone who knows something. I'm left with a vague sense that we're on the wrong side of a black hole and we know it as our universe. Of course since we have black holes in our universe, it's presumably holes all the way down. Maybe we're computational ghosts replaying whatever fell in from the other side.

Fortunately I've read Greg Egan's Permutation City so this feels pretty comfortable.

Carroll thinks we'll get this figured out sometime in the next 30 years or so. I hope I live to see it.

Setting aside the "simulation" thesis for the moment, and inspired by Egan but unconstrained by knowledge or data, I'll make a guess as to how it will all turn out. For the fun of it, because, after all, this is my blog.

I think the infinities will go away and that everything everywhere will all sum to zero.

I think when this theory is explained to someone like me, physicists will use the analogy of a granite cube 3 meters on a side. They'll say that in this cube is every shape and form there could ever be, all atop one another, waiting to be revealed by the sculptor.

Or they'll show how two sounds can produce silence, and tell us that in silence is every sound, every word, every signal and thought that could ever be. All at once.

CERN's neutrinos - kudos to the BBC coverage

Amidst a flurry of sensational coverage, the BBC gets special credit for the headline and the quote (emphases mine) ...

BBC News - Speed-of-light experiments give baffling result at Cern:

... Puzzling results from Cern, home of the Large Hadron Collider, have confounded physicists because subatomic particles seem to have beaten the speed of light...

...But for now, he explained, "we are not claiming things, we want just to be helped by the community in understanding our crazy result - because it is crazy".

"Speed of light" is the right headline, not "faster than light". The quote is important too -- they are not claiming things.

It's hard to overstate how outrageous a result this is. By comparison the "cold fusion" claims of 1989 were prosaic. There are many experimental conditions in which various things propagate faster than the speed of light in a vacuum, but those experiments are all consistent with the universe as we model it.

This result is not consistent with our models. True "faster than light" travel implies "causality violation"; a form of time travel where effect precedes cause.

Just based on how science works, rather than any knowledge of physics, I would give 90% odds that this result does not last a month, and 99.9% odds that when all is done the speed of light will survive. Despite that, there is a good chance of normally interesting physics somewhere in there.

If the results hold up, of course, a Nobel would be the least of it.

Carroll on Time: emergent or fundamental?

My favorite part of Sean Carroll's posts on the nature of Time was about emergence vs. fundamental time ...

Time exists...The real question is whether or not time is fundamental, or perhaps emergent. We used to think that “temperature” was a basic category of nature, but now we know it emerges from the motion of atoms. When it comes to whether time is fundamental, the answer is: nobody knows. My bet is “yes,” but we’ll need to understand quantum gravity much better before we can say for sure.

Carroll, my favorite physics blogger, confirmed that I was on the right track when I wrote entanglement and the realness of time. I wasn't just making it up! I'm willing to bet a beer that within fifteen years the consensus will be that time is emergent rather than fundamental. That's easy for me to say, I really have no idea what I'm talking about.

Reading the essay I'm reminded that in classic General Relativity Fate rules; a life history is fixed from death to birth, like the track of an ancient LP. Calvin would approve.

I wonder if Carroll holds that opinion as well, updated for an era of Quantum Gravity perhaps with a twist of the many worlds interpretation of QM.

Modern physics is so weird.

Entanglement and the realness of time

I can't find the post I was looking for.

It was written by a physicist I read. i'm still looking for it, but there were two interesting assertions. One was that "time was not real", the other was that entanglement is deeper than time.

He was being coy, but this is what I think he meant.

By "real" I think he meant "fundamental". So time is real enough, but if we really understood it we'd see it as emerging from other processes.

It's easy to understand this with "pressure". Humans presumably named the "wind" more than a hundred thousand years ago. Much more recently humans named "pressure" as the expansionary force of a heated balloon. Pressure is certainly real. It's not fundamental though. Much more recently humans figured out that "pressure" was the outcome of atoms in motion. Atomic action is more fundamental.

I gather time is thought to be like that -- an emergent outcome of something more fundamental.

So why should entanglement be the key to understanding time?

Well, physicists think quantum entanglement is very fundamental. It's close to the machinery of reality.

Entanglement is weirder than I can imagine. If I understand it correctly, one could (in theory) separate two entangled particles by a billion light years, measure one a "millisecond" apart (a very squirrely concept in this context), and find the measurements were correlated -- even though a light signal would take a billion years to cross that gap.

In other words, "entanglement" may take place outside of time or space. That's kind of interesting. So if you want to probe time and space, and expose its underlying reality, you might as well start with probing entanglement. If you get it right, you might be able to understand entanglement outside of time (and space), and also understand why we are inside of time.

I really do need to find that post ...

Update 9/1/11: I haven't found that post, but a subsequent Carroll essay suggests I'm not just making this up.

The wilfull wastefulness of the Foundational Questions Institute

The "Foundational Questions Institute" (FQXi, don't ask about the acronym) recently sponsored an essay question about the nature of reality, specifically whether it is fundamentally digital or analog. Is there, for example, a smallest slice of time? Or, if you suspect time is not fundamental but is some epiphenomena of entanglement, is there a way in which the quantum world is less digital than it seems?

Sponsored essays on speculative physics! Neat idea, and seems right up my ally. Of course FQXi's mission statement must attract a wide "variety" of thinkers (emphases mine) ...

... FQXi catalyzes, supports, and disseminates research on questions at the foundations of physics and cosmology, particularly new frontiers and innovative ideas integral to a deep understanding of reality, but unlikely to be supported by conventional funding sources...

Still, the advisory council includes Guth, Bostrom, Barrow, Rees, and Smolin. So I would have tagged them as potentially eccentric, but most likely interesting.

Would have tagged them I say - but not after I actually tried to read one of the winning essays.

It's a PDF. That's bad enough, but it's a PDF of badly scanned document.

This is pure madness. The FQXi is a sad waste.

Bayes and the infinite universe

I used to teach Bayesian reasoning to informatics students. I couldn't justify to them why such simple math felt both spooky and profound. I still can't, but this story fits.

Cosmologists tell us that, comparing a subset of models to available data using Bayesian methods, the 14 billion year old universe is somewhere between 3,500,000,000,000 and an infinite number of light years across (emphases mine) ....

Cosmos At Least 250x Bigger Than Visible Universe - Technology Review

... the photons in the cosmic microwave background have travelled ... 45 billion light years to get here. That makes the visible universe some 90 billion light years across.

... one line of thinking is that if the universe expanded at the speed of light during inflation, then it ought to be 10^23 times bigger than the visible universe... .... Other estimates depend on a number factors and in particular on the curvature of the Universe: whether it is closed, like a sphere, flat or open. In the latter two cases, the Universe must be infinite.

... in recent years, astronomers have various ingenious ways of measuring the curvature of the Universe. One is to search for a distant object of known size and measure how big it looks. If it's bigger than it ought to be, the Universe is closed; if it's the right size, the universe is flat and if it's smaller, the Universe is open.

Astronomers know of one type of object that fits the bill: waves in the early universe that became frozen in the cosmic microwave background. They can measure the size of these waves, called baryonic acoustic oscillations, using space observatories such as WMAP.

There are also other indicators, such as the luminosity of type 1A supernovas in distant galaxies.

But when cosmologists examine all this data, different models of the Universe give different answers to the question of its curvature and size. Which to choose?

The breakthrough that Vardanyan and pals have made is to find a way to average the results of all the data in the simplest possible way. The technique they use is called Bayesian model averaging ...

... Instead of asking how well the model fits the data, its asks a different question: given the data, how likely is the model to be correct. This approach is automatically biased against complex models--it's a kind of statistical Occam's razor.

In applying it to various cosmological models of the universe, Vardanyan and co are able to place important constraints on the curvature and size of the Universe. In fact, it turns out that their constraints are much stricter than is possible with other approaches.

They say that the curvature of the Universe is tightly constrained around 0. In other words, the most likely model is that the Universe is flat. A flat Universe would also be infinite and their calculations are consistent with this too. These show that the Universe is at least 250 times bigger than the Hubble volume. (The Hubble volume is similar to the size of the observable universe.) ...

This is Occam's razor statistics - "... we should tend towards simpler theories .... until we can trade some simplicity for increased explanatory power".

Given the available information, the universe is most likely infinite, but it could be as "small" as 3,500,000,000,000 light years across. Big enough for one human like civilization for every human that has ever lived.

Probably though, much bigger than that.

It is a bit much. Surely, there is a simpler, less extravagant explanation. I'd like to see the authors rerun their analysis with a broader range of explanatory models. I think I know what the answer would be [1] ...

See also (Gordon's Notes unless otherwise noted)

• Earth: the measure of all things (3/2007): Back then we thought the universe might be "only" 140 light years across. So Earth was midway between the Planck length (quantum foam scale) and the universe.
• Bayes theorem: binding reasoning to the physical universe (5/2007)
• Boltzmann's brain hits the big Times (1/2008): We are the dreams of a desperate god in a terrible universe. It is the simplest explanation ...
• Reality, perception, Hume, the red pill - and John Tierney (8/2007): If you're going to be crazy like me, it helps to have David Humen for company.
• CV is hurting my head again: The anthropic principle and our peculiar relation to the arrow of time ... (8/2007): Too many coincidences
• The Algebraist and the religion of the eternal simulation (1/2008): Iain Banks is a fabulous writer.
• Ten cosmologies and Theory 10 (8/2006): The original page is gone. You can guess what theory 10 is.
• SETI, the Fermi Paradox and The Singularity: Why our search for extraterrestial intelligence has failed (footnote 9) (@2003) Before I did blogging, I stuck these things in web pages. "... Vernor Vinge wrote a very short story for one of the millenial year issues of either Nature or Science where he explores exactly this premise ... It's interesting to think about how one would "detect" a simulation ... Vinge explored this in a 2004? short story about a woman who realizes she's been trapped in a simulation ... the simulation would be imperfect, that it would generate "artifacts" in the same sense that JPEG lossy compression of a stripped image will product artifacts. One might, for example, look for physical phenomena consistent with techniques that would reduce the computational demands of the simulation. Or one might attempt to expose flaws (bugs) in the simulation -- or even "crash" it (risky!) ... identify physical phenomena that are inexplicable except in the context of a "simulation" (such as "connectedness" in theoretically disconnected parts of the universe).
• Gordon's Notes: Are You Living in a Computer Simulation? (11/04 - one of my earliest posts in this particular thread)

- fn --

[1] An omniscient universe-creating deity is equivalent to the "Boltzmann's Brain" explanation, so creationists are in good company. Alas, this "deity" is not the one they're looking for.

Warp drives and extracting energy from information

I'm behind the curve on metamaterials (emphasis mine) ...

Technology Review: Blogs: arXiv blog: How to Build a Warp Drive Using Metamaterials

...Metamaterials are substances in which their ability to support electric and magnetic fields can be changed. Fiddle with these properties in just the right way and you can steer electromagnetic waves in all kinds of strange and exotic ways.

The highest profile use of this idea is to build invisibility cloaks but there's another more fascinating application. It turns out there is a formal mathematical analogy between the way metamaterials bend light and the way gravity does it. Inside metamaterials, electromagnetic space becomes distorted in exactly the same way as spacetime in general relatively.

That means physicists can use metamaterials to simulate the universe itself and all the weird phenomenon of general relativity. We've looked at various attempts to recreate black holes, the Big Bang and even multiverses...

I liked the May 2010 multiverse link ...

Today, Igor Smolyaninov at the University of Maryland in College Park... says it is possible to create metamaterials that are analogous to various kinds of spaces dreamt up by cosmologists to explain aspects of the Universe.

In these theories, space can have different numbers of dimensions that become compactified early in the Universe's history, leaving the three dimensions of space and one of time (3+1) that we see today. In symmetries of these spaces depend on the dimensions and the way they are compactified and this in turn determines the laws of physics in these regions.

It turns out, says Smolyaninov, that it is possible to create metamaterials with electromagnetic spaces in which some dimensions are compactified. He says it is even possible to create substances in which the spaces vary from region to region, so a space with 2 ordinary and 2 compactified dimensions, could be adjacent to a space with just 2 ordinary dimensions and also connected to a 2d space with 1 compactified dimension and so on.

The wormholes that make transitions between these regions would be especially interesting. It ought to be possible to observe the birth of photons in these regions and there is even a sense in which the transition could represent the birth of a new universe."A similar topological transition may have given birth to our own Universe," says Smolyaninov.

He goes on to show that these materials can be used to create a multiverse in which different universes have different properties. In fact it ought to be possible create universes in which different laws of physics arise.

That opens up a new area for optical devices. Smolyaninov gives the example of electromagnetic universes in which photons behave as if they are massive, massless or charged depending on the topology of space and the laws of physics this gives rise to...

In more recent related news Hawking radiation has also been detected in a non-metamaterial optical experiment that created a physical system with the mathematical properties of black hole.

Talk about the unreasonable effectiveness of mathematics. The universe is feeling awfully recursive; maybe Wolfram was on to something. If you're going to run a simulated universe, it's good to make it highly recursive.

Meanwhile another group of physicists have implemented Maxwell's demon, and have allegedly demonstrated the extraction of energy from information. Soon they'll extract so much information they'll create  a black hole (sorry, I'm feeling a bit giddy).

Oh, I almost forgot. You can't make an FTL warp drive, but maybe you can make a 1/3 c warp drive. I wonder if the warped space time would make gravitational wakes ...

Update 10/4/10: More on information physics. How long before someone announces that they've discovered how to reboot the universe?

Archives of In Our Time: Smolin, Gribbin and Greene

Every physics hobbyist should be familiar with the names of Smolin, Gribbin and Greene. All are literate physicists who've written excellent books and essays on tough topics, while still doing exciting research. If you're in this club, you'll love these superb In Our Time programs from the archives.

• Grand Unified Theory - 2000 - Brian Greene and Martin Rees
• Time - 1999 - Lee Smolin and Neill Johnson
• Quantum Gravity - 2001 - John Gribbin, Lee Smolin and Janna Levin

I'm a fan of Gribbin and Greene in particular. I tagged several Gribbin posts back when I was catching up with modern interpretations of Quantum Mechanics - before we started doing entanglement experiments with grossly macroscopic entities. Greene wrote the best modern physics book of the past decade (the non-string bits are the best), I'm way late to give it a review.

These gentleman turn out to be verbal gymnasts as well as physicists and writers. Really, it's not fair - but at least they share.

See also:

• Putting 'In Our Time' on your iPod (2006) - turn Real Audio stream into MP3
• In Our Time archives - EVERY EPISODE from Oct 15 1998 onwards
• Our Time: Symmetry, Moonshine, String Theory and E8
• Gordon's Notes: In Our Time (tag)

One of these things is not like the other: Gravity

In this popular account from 1860 [1]) the observation that "electricity" traveled through a medium implied that "other" fundamental forces such as light and gravity must also travel through a medium (emphases mine) ...

April 1860 -Scientific American - Electrical Theory

... The results of the experiments instituted by Sir William Grove are exceedingly curious, and must be regarded as all but proving the truth of the modern theory, which assumes that electricity is not, in any sense, a material substance but only an affection (state) or motion of the particles of ordinary matter.

If electricity is unable to pass over or through a vacuum, it is probable that all the other so-called imponderable forces—light, heat, magnetism, and possibly attraction—obey the same law, and as these agencies freely travel the interplanetary spaces, the supposition of Newton that such spaces may be filled with an ethereal form of matter receives an indirect but powerful support....

There is no ethereal form of matter in the 19th century sense however. Electricity has a relationship to fundamental electromagnetic forces, but it is not the same sort of thing. Once electricity was divided from "light" it was possible to find common models for light and magnetism.

In 2010 some people are trying to deal with the unquantifiability of gravity through a similar approach ...

arXiv blog: Gravity Emerges from Quantum Information, Say Physicists..

One of the hottest new ideas in physics is that gravity is an emergent phenomena; that it somehow arises from the complex interaction of simpler things.

A few month's ago, Erik Verlinde at the the University of Amsterdam put forward one such idea which has taken the world of physics by storm. Verlinde suggested that gravity is merely a manifestation of entropy in the Universe. His idea is based on the second law of thermodynamics, that entropy always increases over time. It suggests that differences in entropy between parts of the Universe generates a force that redistributes matter in a way that maximises entropy. This is the force we call gravity.

What's exciting about the approach is that it dramatically simplifies the theoretical scaffolding that supports modern physics. And while it has its limitations--for example, it generates Newton's laws of gravity rather than Einstein's--it has some advantages too, such as the ability to account for the magnitude of dark energy which conventional theories of gravity struggle with.

But perhaps the most powerful idea to emerge from Verlinde's approach is that gravity is essentially a phenomenon of information.

Today, this idea gets a useful boost from Jae-Weon Lee at Jungwon University in South Korea and a couple of buddies. They use the idea of quantum information to derive a theory of gravity and they do it taking a slightly different tack to Verlinde.

At the heart of their idea is the tricky question of what happens to information when it enters a black hole. Physicists have puzzled over this for decades with little consensus. But one thing they agree on is Landauer's principle: that erasing a bit of quantum information always increases the entropy of the Universe by a certain small amount and requires a specific amount of energy.

Jae-Weon and co assume that this erasure process must occur at the black hole horizon. And if so, spacetime must organise itself in a way that maximises entropy at these horizons. In other words, it generates a gravity-like force.

That's intriguing for several reasons. First, Jae-Weon and co assume the existence of spacetime and its geometry and simply ask what form it must take if information is being erased at horizons in this way.

It also relates gravity to quantum information for the first time. Over recent years many results in quantum mechanics have pointed to the increasingly important role that information appears to play in the Universe.

Some physicists are convinced that the properties of information do not come from the behaviour of information carriers such as photons and electrons but the other way round. They think that information itself is the ghostly bedrock on which our universe is built.

Gravity has always been a fly in this ointment. But the growing realisation that information plays a fundamental role here too, could open the way to the kind of unification between the quantum mechanics and relativity that physicists have dreamed of..

In short, one way to deal with the gravity problem is to make gravity go away. It's merely a confusing epiphenomena.

Hey, it worked for electricity ...

[1] Just prior to the American civil war. In a few years the SciAm "150 year back" article excerpts will be all about military science relevant to the most bloody battles of the 19th century. That should be interesting.

Galaxies like stars in the sky

There's an antidote to reading about the Cheney torture program and the GOP's insurance-company funded attack on health insurance reform.

Download the images linked here, and open them in a robust image viewer. Browse at will. Visit galaxies as they were billions of years ago. Squint very hard, and image you're seeing something squinting up from one of the billions of worlds in the billions of stars ...

ESO - ESO 39/08 - A Pool of Galaxies - Associated Image

... The new image released by ESO combines data obtained with the VIMOS instrument in the U- and R-bands, as well as data obtained in the B-band with the Wide-Field Imager (WFI) attached to the 2.2 m MPG/ESO telescope at La Silla, in the framework of the GABODS survey.

The newly released U-band image – the result of 40 hours of staring at the same region of the sky and just made ready by the GOODS team – is the deepest image ever taken from the ground in this wavelength domain. At these depths, the sky is almost completely covered by galaxies, each one, like our own galaxy, the Milky Way, home of hundreds of billions of stars.

Galaxies were detected that are a billion times fainter than the unaided eye can see and over a range of colours not directly observable by the eye. This deep image has been essential to the discovery of a large number of new galaxies that are so far away that they are seen as they were when the Universe was only 2 billion years old....

Be sure to try the zoom tool.

Subversive theophysics - Greg Egan

I've been composing a post about Greg Egan's Permutation City for a while. I'm afraid I'll never get to the whole thing, so I'm going to toss off the short version. (Warning, contains spoilers)

Greg Egan is usually said to write "hard" science fiction. That's inadequate. He writes neutronium grade science fiction. His mathematical physics bent has become so extreme that his latest book is a thin layer of fiction around a core of speculative physics (Amazon promises me a copy in 3-4 weeks, apparently they have to retype it. Egan has put a prequel to the story on his web site).

Permutation City is one of his best works. Despite the math science bent several of the characters have stuck with me.

The best part though, is the fusion between theology and physics -- theophysics. In Permutation City reality is fundamentally mathematical, much as imagined by Stephen Wolfram and many more conventional physicists. A group of experimental modelers creates an artificial world with a different sort of mathematical reality.

No wait, hang in here for a minute. I'm really going somewhere.

The creatures of this new world are fantastically alien, but like us they're compelled to understand their world. Problem is, their world is fundamentally incomprehensible. It was created by omniscient and omnipotent Creators. Gods.

So the alien critter(s) is(are) "anguished". They are compelled to understand, but they cannot understand. The human Creators are sympathetic, and decide to manifest themselves in the alien world. The Truth shall be known, and the aliens will understand.

Except, the aliens come up with their own Theory of Everything; their equivalent of quantum gravity. It looks crazy and absurd, but it's internally consistent. It explains everything but the appearance of the Creators, and that detail can be quickly forgotten.

The Creators suddenly find themselves written out of the script, but that's a different story. I'm telling the story of the subversive aspects of Egan's fiction.

Obviously, the invented aliens of Permutation City aren't alone. We too are compelled to comprehend, and modern physics is getting pretty damned absurd...

Relativity as a consequence of quantum entanglement

Useful at parties ...

Relativity as a Consequence of Quantum Entanglement: A Quantum Logic Gate Space Model for the Universe

Everything in the Universe is assumed to be compromised of pure reversible quantum Toffoli gates, including empty space itself...

The nature of time - essential reading for reality hobbyists

Are you an amateur epistemontologist? Curious about the nature of reality? Not willing to accept the illusions of the senses?

Then you've got reading ...

The Envelope Please… | Cosmic Variance | Discover Magazine

The results are in for the Foundational Questions Institute essay competition on “The Nature of Time,” which we discussed here. And the winners are:

... Julian Barbour on “The Nature of Time”

... Claus Kiefer on “Does Time Exist in Quantum Gravity?”

... Sean Carroll on “What if Time Really Exists?”...

Love it.

A quantum state eternally evolving in an infinite-dimensional Hilbert space

It's time for your morning exercise ...

FQXi Community: Articles, Forums, Blogs, News

.... The arrow of time finds a plausible explanation in a 'Heraclitean universe,' described by a quantum state eternally evolving in an infinite-dimensional Hilbert space....

Sean Carroll of Cosmic Variance fame has entered an essay contest on the nature of time.

I've asked Sean to tell us what the other good ones are.

The wikiepdia entry on Heraclitus might be of assistance.

Dark flow - false alarm, right?

I've grown somewhat accustomed to the idea that our universe is far weirder than my brain can comprehend. Even so, this "dark flow" idea is pushing the envelope. For context, the In Our Time Multiverse program spent quite a bit of time talking about how no-one can imagine a way to test the nature of the universe beyond our event horizon.

I'm looking forward to commentary from my favorite physics bloggers. I assume it's a false alarm of some sort ...

SPACE.com -- Mysterious New 'Dark Flow' Discovered in Space

... Patches of matter in the universe seem to be moving at very high speeds and in a uniform direction that can't be explained by any of the known gravitational forces in the observable universe. Astronomers are calling the phenomenon "dark flow."

The stuff that's pulling this matter must be outside the observable universe, researchers conclude...

...Scientists discovered the flow by studying some of the largest structures in the cosmos: giant clusters of galaxies ... observing the interaction of the X-rays with the cosmic microwave background (CMB), which is leftover radiation from the Big Bang, scientists can study the movement of clusters.

The X-rays scatter photons in the CMB, shifting its temperature in an effect known as the kinematic Sunyaev-Zel'dovich (SZ) effect. This effect had not been observed as a result of galaxy clusters before, but a team of researchers led by Alexander Kashlinsky, an astrophysicist at NASA's Goddard Space Flight Center in Greenbelt, Md., found it when they studied a huge catalogue of 700 clusters, reaching out up to 6 billion light-years, or half the universe away. They compared this catalogue to the map of the CMB taken by NASA's Wilkinson Microwave Anisotropy Probe (WMAP) satellite.

They discovered that the clusters were moving nearly 2 million mph (3.2 million kph) toward a region in the sky between the constellations of Centaurus and Vela. This motion is different from the outward expansion of the universe (which is accelerated by the force called dark energy).

"We found a very significant velocity, and furthermore, this velocity does not decrease with distance, as far as we can measure," Kashlinsky told SPACE.com. "The matter in the observable universe just cannot produce the flow we measure."

The scientists deduced that whatever is driving the movements of the clusters must lie beyond the known universe.

A theory called inflation posits that the universe we see is just a small bubble of space-time that got rapidly expanded after the Big Bang. There could be other parts of the cosmos beyond this bubble that we cannot see.

In these regions, space-time might be very different, and likely doesn't contain stars and galaxies (which only formed because of the particular density pattern of mass in our bubble). It could include giant, massive structures much larger than anything in our own observable universe. These structures are what researchers suspect are tugging on the galaxy clusters, causing the dark flow.

"The structures responsible for this motion have been pushed so far away by inflation, I would guesstimate they may be hundreds of billions of light years away, that we cannot see even with the deepest telescopes because the light emitted there could not have reached us in the age of the universe," Kashlinsky said in a telephone interview. "Most likely to create such a coherent flow they would have to be some very strange structures, maybe some warped space time. But this is just pure speculation...

I suspect thse guys are jumping the gun by a fair bit, but looking forward to more commentary.

Cosmology and Complexity - almost understandable

This Aaronson lecture is surprisingly readable. Thank you scribe!

PHYS771 Lecture 20: Cosmology and Complexity

...But that's only one thing that's wrong with the simple "spherical/flat/hyperbolic" trichotomy. Another thing wrong with it is that the geometry of the universe and its topology are two separate questions. Just assuming the universe is flat doesn't imply that it's infinite. If the universe had a constant positive curvature, that would imply it was finite. Picture the Earth; on learning that it has a constant positive curvature, you would conclude it's round. I mean, yes, it could curve off to infinity where you can't see it, but assuming it's homogenous in curvature, mathematically it has to curve around in either a sphere or some other more complicated finite shape. If space is flat, however, that doesn't tell you whether it's is finite or infinite. It could be like one of the video games where when you go off one end of the screen, you reappear on the other end. That's perfectly compatible with geometric flatness, but would correspond to a closed topology. The answer, then, to whether the universe is finite or infinite, is unfortunately that we don't know....

Very fun topic. I finally have a personal story for the limits of information -- when bits become a black hole.

Curious relationship between computation and the cosmological constant.

Three Shtetl-Optimized posts for livening the mind

I really need to study, so I'm noting these for future reading.

These are a set of Aaronson posts, found by tracing back from the latests, that taken together are very good reading in physics and philosophy:

• The relativity of originality
• His review of Wolfram (pdf)
• Newcomb's problem
• PHYS771 Free will

All the essays touch, more or less directly, on the question of whether "free will" (as Scott rigorously defines it) is possible. Note this is distinct from the concept of responsibility -- every reasonable thinker over the past few centuries has understood that "responsibility" is a social construction with no intellectual integrity.

By way of background scientists philosophers have gone back and forth on this since science was more or less born with Francis Bacon. Things looked particularly bad in the 20th century; in the absence of quantum mechanics general relativity seemed to predict a universe frozen in space-time, in which every moment occurred at once and invariably. Maybe this is where Vonnegut's Tralfamadorean determinism came from.

QM seemed to restore free will, but it introduced some disturbing predictions of its own. Physicists attempted to restore the concept of an observer-independent reality through the transactional interpretation, but that did in free will

More recently reality (or realism) seems to be out favor, so maybe free will is back.

Now you're prepped to read Aaronson.

PS. See also - Sean Carroll's favorite posts.