Category Archives: Quantum Mechanics

Book Review — The Universe Speaks in Numbers

Let’s say that back in the day, as a budding grad student in chemistry you had to take quantum mechanics to see where those atomic orbitals came from.   Say further, that as the years passed you knew enough to read News and Views in Nature and Perspectives in Science concerning physics as they appeared. So you’ve heard various terms like J/Psi, Virasoro algebra, Yang Mills gauge symmetry, Twisters, gluons, the Standard Model, instantons, string theory, the Atiyah Singer theorem etc. etc.  But you have no coherent framework in which to place them.

Then “The Universe Speaks in Numbers” by Graham Farmelo is the book for you.  It will provide a clear and chronological narrative of fundamental physics up to the present.  That isn’t the main point of the book, which is an argument about the role of beauty and mathematics in physics, something quite contentious presently.  Farmelo writes well and has a PhD in particle physics (1977) giving him a ringside seat for the twists and turns of  the physics he describes.  People disagree with his thesis (http://www.math.columbia.edu/~woit/wordpress/?p=11012) , but nowhere have I seen anyone infer that any of Farmelo’s treatment of the physics described in the book is incorrect.

40 years ago, something called the Standard Model of Particle physics was developed.  Physicists don’t like it because it seems like a kludge with 19 arbitrary fixed parameters.  But it works, and no experiment and no accelerator of any size has found anything inconsistent with it.  Even the recent discovery of the Higgs, was just part of the model.

You won’t find much of the debate about what physics should go from here in the book.  Farmelo says just study more math.  Others strongly disagree — Google Peter Woit, Sabine Hossenfelder.

The phenomena String theory predicts would require an accelerator the size of the Milky Way or larger to produce particles energetic enough to probe it.  So it’s theory divorced from any experiment possible today, and some claim that String Theory has become another form of theology.

It’s sad to see this.  The smartest people I know are physicists.  Contrast the life sciences, where experiments are easily done, and new data to explain arrives weekly.

 

 

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Good to see Charlie’s still at it

Good to see Charlie Perrin is still pumping out papers, and interesting ones to boot.  I knew him in grad school.  He’s got to be over 80.

This one —J. Am. Chem. Soc. 141, 4103 (2019) –is about something that any undergraduate organic chemist can understand (if not the techniques he used) — keto/enol tautomerism, in which the hydrogen bounces between two oxygens, so that, given N molecules in solution, N/2  have the hydrogen bound to one oxygen and N/2 have it bound to the other.

No so in what Charlie found — a compound where the hydrogen is smack dab in the middle.  Some fancy NMR techniques were used to show this.

Hydrogen bonds are extremely subtle (which is why we don’t understand water as well as we might).  Due to the small mass of the proton it isn’t appropriate to treat the proton in hydrogen bonded systems as a classical particle.  When quantum mechanics enters, aspects such as zero point motion, quantum delocalization and tunneling come into play.  These are called quantum nuclear effects (aka Ubbelohde effects).

Book recommendation

“It’s complicated”.  No this isn’t about the movie with Meryl Streep but the response I got from several Harvard PhD physicists five years ago at Graduate Alumni Day in April 2014.  A month earlier the BICEP2 experiment claimed to have seen B-mode polarization in the cosmic background radiation, which would have been observational proof of cosmic inflation.  Nobel prize material for sure.  Unfortunately the signal turned out to be from dust in our galaxy, the milky way

You can read all about it in “Losing the Nobel Prize” by Brian Keating, who developed the instrumentation for BICEP2.  I recommend the book for several reasons.  The main reason is the discussion of cosmology and its various theories starting with Galileo (p. 28) getting up to  the B-Modes that BICEPs thought it saw by p. 138.  The discussion is incredibly clear, with discussions (to name a few) of how Galileo knew Ptolemy was wrong (the way the moons of Jupiter moved around it in time), refracting vs.reflecting telescopes, Hubble and cepheid variables, Vera Rubin and why she didn’t get a Nobel — she died too soon, how polaroid glasses work, and why bouncing of water is enough to polarize unpolarized light.  Want more? Fred Hoyle and steady state cosmology, the problems with the big bang (smoothness problem, horizon problem, flatness problem) solved by Alan Guth and inflation, false vacuum, and finally what B-modes actually are.

If you’ve a typical reader of blogs scientific but not a pro in physics, astronomy, cosmology, you’ve probably heard all these terms. Keating explains them clearly.

Even better, he writes well and is funny.  Here is the opening paragraph of the book.

“Each year, on December tenth, thousands of worshippers convene in Scandinavia to commemorate the passing of an arms dealer known as the merchant of death.  The eschatological ritual features all the rites and incantations befitting a pharaoh’s funeral.  Haunting dirges play as the worshippers, bedecked in mandatory regalia, mourn the merchant.  He is eerily present; his visage looms over the congregants as they feast on exotic game, surrounded by fresh-cut flowers imported from the merchant’s mausoleum.  The event culminates with the presentation of gilded, graven images bearing his likeness.”

Anything dealing with the creation of the universe has theological overtones, and we can regard the book as a history of various scientific creation myths, the difference being that they are abandoned when evidence is found which contradicts them.  Georges’ Lemaitre, a catholic priest and relativist puts in more than an appearance (p. 56) as he predicted what is probably the first big bang theory — the primeval atom with its subsequent expansion.

The book isn’t all science, and the author whose Jewish father abandoned them was raised by a catholic step-father describes being an altar boy for a time.   Then there are adventure stories of journeys to the south pole for the BICEP experiment.

There’s a lot more in the book, which is definitely worth a read.

Finally a few personal notes.  The man who brought BICEP2 down to earth David Spergel appears.  He’s a good guy.  At my 50th reunion there my wife and I  were standing in our reunion suits outside our hotel across route 1 waiting for a bus to take us across.  Some guy (Spergel) sees us an offers a ride to campus. On the ride over I asked what he did, and he says astronomy and physics.  So I asked how come the universe is said to be homogenous when all we see is clumpy galaxies and stars — you asked the right guy saith Spergel, and he launches into an explanation (which I’ve forgotten).  I mention that Jim Hartle is a class member.  “He’s very smart” saith David.  Later I tell Hartle the same story.  “He’s very smart” saith Jim.

Another good person is Meryl Streep.  A cousin is in movies both acting in the past and now directing and knows her.  Her father was a great admirer, so Meryl took the trouble to hike over to New Jersey and say hello.  She didn’t have to do that.  Unfortunately in the movie mentioned first, Meryl had to play a porn star with her aged scrawny body (probably Harvey Weinstein put her up to it).  I couldn’t stand it and walked out at that point.

Book recommendation

“Losing the Nobel Prize”  by Brian Keating is a book you should read if you have any interest in l. physics. 2. astronomy 3. cosmology 4. the sociology of the scientific enterprise (physics division) 5. The Nobel prize 6. The BICEPs and BICEP2 experiments.

It contains extremely clear explanations of the following

l. The spiderweb bolometer detector used to measure the curvature of the universe

2. How Galileo’s telescope works and what he saw

3. How refracting and reflecting telescopes work

4. The Hubble expansion of the universe and the problems it caused

5. The history of the big bang, its inherent problems, how Guth solved some of them but created more

6. How bouncing off water (or dust) polarizes light

7. The smoothness problem, the flatness problem and the horizon problem.

8. The difference between B modes and E modes and why one would be evidence of gravitational waves which would be evidence for inflation.

9. Cosmic background radiation

The list could be much longer.  The writing style is clear and very informal.   Example: he calls the dust found all over the universe — cosmic schmutz.   Then there are the stories about explorers trying to reach the south pole, and what it’s like getting there (and existing there).

As you probably know BICEP2 found galactic dust and not the polarization pattern produced by gravitational waves.  The initial results were announced 17 March 2014 to much excitement.  It was the subject of a talk given the following month at Harvard Graduate Alumni Day, an always interesting set of talks.  I didn’t go to the talk but there were plenty of physicists around to ask about the results (which were nowhere nearly as clearly explained as this book).  All of them responded to my questions the same way — “It’s complicated.”

The author Brian Keating has a lot to say about Nobels and their pursuit and how distorting it is, but that’s the subject of another post, as purely through chance I’ve known 9 Nobelists before they received their prize.

It will also lead to another post about the general unhappiness of a group of physicists.

Buy and read the book

Off to band camp for adults 2018

No posts for a while, as I’ll be at a chamber music camp for adult amateurs (or what a friend’s granddaughter calls — band camp for adults).  In a week or two if you see a beat up old Honda Pilot heading west on the north shore of Lake Superior, honk and wave.

I expect the usual denizens to be there — mathematicians, physicists, computer programmers, MDs, touchy-feely types who are afraid of chemicals etc. etc. We all get along but occasionally the two cultures do clash, and a polymer chemist friend is driven to distraction by a gentle soul who is quite certain that “chemicals” are a very bad thing. For the most part, everyone gets along. Despite the very different mindsets, all of us became very interested in music early on, long before any academic or life choices were made.

So, are the analytic types soulless automatons producing mechanically perfect music which is emotionally dead? Are the touchy-feely types sloppy technically and histrionic musically? A double-blind study would be possible, but I think both groups play pretty much the same (less well than we’d all like, but with the same spirit and love of music).

A few years ago I had the pleasure of playing Beethoven with Heisenberg —   along with an excellent violinist I’ve played with for years, the three of us read Beethoven’s second piano trio (Opus 1, #2) with Heisenberg’s son Jochem (who, interestingly enough, is a retired physics professor).  He is an excellent cellist who knows the literature cold.  The violinist and I later agreed that we have rarely played worse.  Oh well. Heisenberg, of course, was a gentleman throughout.

Later that evening, several of us had the pleasure of discussing quantum mechanics with him. He didn’t disagree with my idea that the node in the 2S orbital (where no electron is ever found) despite finding the electron on either side of the node, forces us to give up the idea of electron trajectory (aromatic ring currents be damned).   He pretty much seemed to agree with the Copenhagen interpretation — macroscopic concepts just don’t apply to the quantum world, and language trips us up.

One rather dark point about the Heisenberg came up in an excellent book about the various interpretations of what Quantum Mechanics actually means: “What Is Real?” by Adam Becker.  I have no idea if the following summary is actually true, but here it is.   Heisenberg was head of the German nuclear program to develop an atomic bomb.  Nuclear fission was well known in Germany, having been discovered there.  An old girl friend wrote a book about Lise Meitner, one of the discoverers and how she didn’t get the credit she was due.

At the end of the war there was an entire operation to capture German physicists who had worked on nuclear development (operation Alsos).  Those captured (Heisenberg, Hahn, von Laue and others) were taken to Farm Hall, an English manor house which had been converted into a military intelligence center.  It was supplied with chalkboards, sporting equipment, a radio, good food and secretly bugged to high heaven.  The physicists were told that they were being held “at His Majesty’s pleasure.”.  Later they told the American’s had dropped the atomic bomb.  They didn’t believe it as their own work during the war led them to think it was impossible.

All their discussions were recorded, unknown to Heisenberg.  It was clear that the Germans had no idea how to build a bomb even though they tried.  However  Heisenberg  and von Weizsacker constructed a totally false narrative, that they had never tried to build a bomb, but rather a nuclear reactor.  According to Becker, Heisenberg was never caught out on this because the Farm Hall transcripts were classified.  It isn’t clear to me from reading Becker’s book, when they were UNclassified, but apparently Heisenberg got away with it until his death in 1978.

Amazing stuff if true

 

A creation myth

Sigmund Freud may have been wrong about penis envy, but most lower forms of scientific life (chemists, biologists) do have physics envy — myself included.  Most graduate chemists have taken a quantum mechanics course, if only to see where atomic and molecular orbitals come from.  Anyone doing physical chemistry has likely studied statistical mechanics. I was fortunate enough to audit one such course given by E. Bright Wilson (of Pauling and Wilson).

Although we no longer study physics per se, most of us read books about physics.  Two excellent such books have come out in the past year.  One is “What is Real?” — https://www.basicbooks.com/titles/adam-becker/what-is-real/9780465096053/, the other is “Lost in Math” by Sabine Hossenfelder whose blog on physics is always worth reading, both for herself and the heavies who comment on what she writes — http://backreaction.blogspot.com

Both books deserve a long discursive review here. But that’s for another time.  Briefly, Hossenfelder thinks that physics for the past 30 years has become so fascinated with elegant mathematical descriptions of nature, that theories are judged by their mathematical elegance and beauty, rather than agreement with experiment.  She acknowledges that the experiments are both difficult and expensive, and notes that it took a century for one such prediction (gravitational waves) to be confirmed.

The mathematics of physics can certainly be seductive, and even a lowly chemist such as myself has been bowled over by it.  Here is how it hit me

Budding chemists start out by learning that electrons like to be in filled shells. The first shell has 2 elements, the next 2 + 6 elements etc. etc. It allows the neophyte to make some sense of the periodic table (as long as they deal with low atomic numbers — why the 4s electrons are of lower energy than the 3d electons still seems quite ad hoc to me). Later on we were told that this is because of quantum numbers n, l, m and s. Then we learn that atomic orbitals have shapes, in some wierd way determined by the quantum numbers, etc. etc.

Recursion relations are no stranger to the differential equations course, where you learn to (tediously) find them for a polynomial series solution for the differential equation at hand. I never really understood them, but I could use them (like far too much math that I took back in college).

So it wasn’t a shock when the QM instructor back in 1961 got to them in the course of solving the Schrodinger equation for the hydrogen atom (with it’s radially symmetric potential). First the equation had to be expressed in spherical coordinates (r, theta and phi) which made the Laplacian look rather fierce. Then the equation was split into 3 variables, each involving one of r, theta or phi. The easiest to solve was the one involving phi which involved only a complex exponential. But periodic nature of the solution made the magnetic quantum number fall out. Pretty good, but nothing earthshaking.

Recursion relations made their appearance with the solution of the radial and the theta equations. So it was plug and chug time with series solutions and recursion relations so things wouldn’t blow up (or as Dr. Gouterman, the instructor, put it: the electron has to be somewhere, so the wavefunction must be zero at infinity). MEGO (My Eyes Glazed Over) until all of a sudden there were the main quantum number (n) and the azimuthal quantum number (l) coming directly out of the recursion relations.

When I first realized what was going on, it really hit me. I can still see the room and the people in it (just as people can remember exactly where they were and what they were doing when they heard about 9/11 or (for the oldsters among you) when Kennedy was shot — I was cutting a physiology class in med school). The realization that what I had considered mathematical diddle, in some way was giving us the quantum numbers and the periodic table, and the shape of orbitals, was a glimpse of incredible and unseen power. For me it was like seeing the face of God.

But what interested me the most about “Lost in Math” was Hossenfelder’s discussion of the different physical laws appearing at different physical scales (e.g. effective laws), emergent properties and reductionism (pp. 44 –> ).  Although things at larger scales (atoms) can be understood in terms of the physics of smaller scales (protons, neutrons, electrons), the details of elementary particle interactions (quarks, gluons, leptons etc.) don’t matter much to the chemist.  The orbits of planets don’t depend on planetary structure, etc. etc.  She notes that reduction of events at one scale to those at a smaller one is not an optional philosophical position to hold, it’s just the way nature is as revealed by experiment.  She notes that you could ‘in principle, derive the theory for large scales from the theory for small scales’ (although I’ve never seen it done) and then she moves on

But the different structures and different laws at different scales is what has always fascinated me about the world in which we exist.  Do we have a model for a world structured this way?

Of course we do.  It’s the computer.

 

Neurologists have always been interested in computers, and computer people have always been interested in the brain — von Neumann wrote “The Computer and the Brain” shortly before his death in 1958.

Back in med school in the 60s people were just figuring out how neurons talked to each other where they met at the synapse.  It was with a certain degree of excitement that we found that information appeared to flow just one way across the synapse (from the PREsynaptic neuron to the POST synaptic neuron).  E.g. just like the vacuum tubes of the earliest computers.  Current (and information) could flow just one way.

The microprocessors based on transistors that a normal person could play with came out in the 70s.  I was naturally interested, as having taken QM I thought I could understand how transistors work.  I knew about energy gaps in atomic spectra, but how in the world a crystal with zillions of atoms and electrons floating around could produce one seemed like a mystery to me, and still does.  It’s an example of ’emergence’ about which more later.

But forgetting all that, it’s fairly easy to see how electrons could flow from a semiconductor with an abundance of them (due to doping) to a semiconductor with a deficit — and have a hard time flowing back.  Again a one way valve, just like our concept of the synapses.

Now of course, we know information can flow the other way in the synapse from POST synaptic to PREsynaptic neuron, some of the main carriers of which are the endogenous marihuana-like substances in your brain — anandamide etc. etc.  — the endocannabinoids.

In 1968 my wife learned how to do assembly language coding with punch cards ones and zeros, the whole bit.  Why?  Because I was scheduled for two years of active duty as an Army doc, a time in which we had half a million men in Vietnam.  She was preparing to be a widow with 2 infants, as the Army sent me a form asking for my preferences in assignment, a form so out of date, that it offered the option of taking my family with me to Vietnam if I’d extend my tour over there to 4 years.  So I sat around drinking Scotch and reading Faulkner waiting to go in.

So when computers became something the general populace could have, I tried to build a mental one using and or and not logical gates and 1s and 0s for high and low voltages. Since I could see how to build the three using transistors (reductionism), I just went one plane higher.  Note, although the gates can be easily reduced to transistors, and transistors to p and n type semiconductors, there is nothing in the laws of semiconductor physics that implies putting them together to form logic gates.  So the higher plane of logic gates is essentially an act of creation.  They do not necessarily arise from transistors.

What I was really interested in was hooking the gates together to form an ALU (arithmetic and logic unit).  I eventually did it, but doing so showed me the necessity of other components of the chip (the clock and in particular the microcode which lies below assembly language instructions).

The next level up, is what my wife was doing — sending assembly language instructions of 1’s and 0’s to the computer, and watching how gates were opened and shut, registers filled and emptied, transforming the 1’s and 0’s in the process.  Again note that there is nothing necessary in the way the gates are hooked together to make them do anything.  The program is at yet another higher level.

Above that are the higher level programs, Basic, C and on up.  Above that hooking computers together to form networks and then the internet with TCP/IP  etc.

While they all can be reduced, there is nothing inherent in the things that they are reduced to which implies their existence.  Their existence was essentially created by humanity’s collective mind.

Could something be going on in the levels of the world seen in physics.  Here’s what Nobel laureate Robert Laughlin (he of the fractional quantum Hall effect) has to say about it — http://www.pnas.org/content/97/1/28.  Note that this was written before people began taking quantum computers seriously.

“However, it is obvious glancing through this list that the Theory of Everything is not even remotely a theory of every thing (2). We know this equation is correct because it has been solved accurately for small numbers of particles (isolated atoms and small molecules) and found to agree in minute detail with experiment (35). However, it cannot be solved accurately when the number of particles exceeds about 10. No computer existing, or that will ever exist, can break this barrier because it is a catastrophe of dimension. If the amount of computer memory required to represent the quantum wavefunction of one particle is Nthen the amount required to represent the wavefunction of k particles is Nk. It is possible to perform approximate calculations for larger systems, and it is through such calculations that we have learned why atoms have the size they do, why chemical bonds have the length and strength they do, why solid matter has the elastic properties it does, why some things are transparent while others reflect or absorb light (6). With a little more experimental input for guidance it is even possible to predict atomic conformations of small molecules, simple chemical reaction rates, structural phase transitions, ferromagnetism, and sometimes even superconducting transition temperatures (7). But the schemes for approximating are not first-principles deductions but are rather art keyed to experiment, and thus tend to be the least reliable precisely when reliability is most needed, i.e., when experimental information is scarce, the physical behavior has no precedent, and the key questions have not yet been identified. There are many notorious failures of alleged ab initio computation methods, including the phase diagram of liquid 3He and the entire phenomenonology of high-temperature superconductors (810). Predicting protein functionality or the behavior of the human brain from these equations is patently absurd. So the triumph of the reductionism of the Greeks is a pyrrhic victory: We have succeeded in reducing all of ordinary physical behavior to a simple, correct Theory of Everything only to discover that it has revealed exactly nothing about many things of great importance.”

So reductionism doesn’t explain the laws we have at various levels.  They are regularities to be sure, and they describe what is happening, but a description is NOT an explanation, in the same way that Newton’s gravitational law predicts zillions of observations about the real world.     But even  Newton famously said Hypotheses non fingo (Latin for “I feign no hypotheses”) when discussing the action at a distance which his theory of gravity entailed. Actually he thought the idea was crazy. “That Gravity should be innate, inherent and essential to Matter, so that one body may act upon another at a distance thro’ a Vacuum, without the Mediation of any thing else, by and through which their Action and Force may be conveyed from one to another, is to me so great an Absurdity that I believe no Man who has in philosophical Matters a competent Faculty of thinking can ever fall into it”

So are the various physical laws things that are imposed from without, by God only knows what?  The computer with its various levels of phenomena certainly was consciously constructed.

Is what I’ve just written a creation myth or is there something to it?

Relativity becomes less comprehensible

“To get Hawking radiation we have to give up on the idea that spacetime always had 3 space dimensions and one time dimension to get a quantum theory of the big bang.”  I’ve been studying relativity for some years now in the hopes of saying something intelligent to the author (Jim Hartle), if we’re both lucky enough to make it to our 60th college reunion in 2 years.  Hartle majored in physics under John Wheeler who essentially revived relativity from obscurity during the years when quantum mechanics was all the rage. Jim worked with Hawking for years, spoke at his funeral and wrote this in an appreciation of Hawking’s work [ Proc.Natl. Acad. Sci. vol. 115 pp. 5309 – 5310 ’18 ].

I find the above incomprehensible.  Could anyone out there enlighten me?  Just write a comment.  I’m not going to bother Hartle

Addendum 25 May

From a retired math professor friend —

I’ve never studied this stuff, but here is one way to get more actual dimensions without increasing the number of apparent dimensions:
Start with a 1-dimensional line, R^1 and now consider a 2-dimensional cylinder S^1 x R^1.  (S^1 is the circle, of course.)  If the radius of the circle is small, then the cylinder looks like a narrow tube.  Make the radius even smaller–lsay, ess than the radius of an atomic nucleus.  Then the actual 2-dimensional cylinder appears to be a 1-dimensional line.
The next step is to rethink S^1 as a line interval with ends identified (but not actually glued together.  Then S^1 x R^1 looks like a long ribbon with its two edges identified.  If the width of the ribbon–the length of the line interval–is less, say, than the radius of an atom, the actual 2-dimensional “ribbon with edges identified” appears to be just a 1-dimensional line.
Okay, now we can carry all these notions to R^2.  Take S^1 X R^2, and treat S^1 as a line interval with ends identified.  Then S^1 x R^2 looks like a (3-dimensional) stack of planes with the top plane identified, point by point, with the bottom plane.  (This is the analog of the ribbon.)  If the length of the line interval is less, say, than the radius of an atom, then the actual 3-dimensional s! x R^2 appears to be a 2-dimensional plane.
That’s it.  In general, the actual n+1-dimensional S^1 x R^n appears to be just n-space R^n when the radius of S^1 is sufficiently small.
All this can be done with a sphere S^2, S^3, … of any dimension, so that the actual k+n-dimensional manifold S^k x R^n appears to be just the n-space R^n when the radius of S^k is sufficiently small.  Moreover, if M^k is any compact manifold whose physical size is sufficiently small, then the actual k+n-dimensional manifold M^k x R^n appears to be just the n-plane R^n.
That’s one way to get “hidden” dimensions, I think. “

Nicastrin the gatekeeper of gamma secretase

Once a year some hapless trucker from out of town gets stuck trying to drive under a nearby railroad bridge with a low clearance. This is exactly the function of nicastrin in the gamma secretase complex which produces the main component of the senile plaque, the aBeta peptide.

Gamma secretase is a 4 protein complex which functions as an enzyme which can cut the transmembrane segment of proteins embedded in the cell membrane. This was not understood for years, as cutting a protein here means hydrolyzing the amide bond of the protein, (e.g. adding water) and there is precious little water in the cell membrane which is nearly all lipid.

Big pharma has been attacking gamma secretase for years, as inhibiting it should stop production of the Abeta peptide and (hopefully) help Alzheimer’s disease. However the paper to be discussed [ Proc. Natl. Acad. Sci. vol. 113 p.n E509 – E518 ’16 ] notes that gamma secretase processes ‘scores’ of cell membrane proteins, so blanket inhibition might be dangerous.

The idea that Nicastrin is the gatekeeper for gamma secretase is at least a decade old [ Cell vol. 122 pp. 318 – 320 ’05 ], but back then people were looking for specific binding of nicastrin to gamma secretase targets.

The new paper provides a much simpler explanation. It won’t let any transmembrane segment of a protein near the active site of gamma secretase unless the extracellular part is lopped off. The answer is simple mechanics. Nicastrin is large (709 amino acids) but with just one transmembrane domain. Most of it is extracellular forming a blob extending out 25 Angstroms from the membrane, directly over the substrate binding pocket of gamma secretase. Only substrates with small portions outside the membrane (ectodomains) can pass through it. It’s the railroad bridge mentioned above. Take a look at the picture — https://en.wikipedia.org/wiki/Nicastrin

This is why a preliminary cleavage of the Amyloid Precursor Peptide (APP) is required for gamma secretase to work.

So all you had to do was write down the wavefunction for Nicastrin (all 709 amino acids) and solve it (assuming you even write it down) and you’d have the same answer — NOT. Only the totally macroscopic world explanation (railroad bridge) is of any use. What keeps proteins from moving through each other? Van der Waals forces. What help explain them. The Pauli exclusion principle, as pure quantum mechanics as it gets.

A book recommendation, not a review

My first encounter with a topology textbook was not a happy one. I was in grad school knowing I’d leave in a few months to start med school and with plenty of time on my hands and enough money to do what I wanted. I’d always liked math and had taken calculus, including advanced and differential equations in college. Grad school and quantum mechanics meant more differential equations, series solutions of same, matrices, eigenvectors and eigenvalues, etc. etc. I liked the stuff. So I’d heard topology was cool — Mobius strips, Klein bottles, wormholes (from John Wheeler) etc. etc.

So I opened a topology book to find on page 1

A topology is a set with certain selected subsets called open sets satisfying two conditions
l. The union of any number of open sets is an open set
2. The intersection of a finite number of open sets is an open set

Say what?

In an effort to help, on page two the book provided another definition

A topology is a set with certain selected subsets called closed sets satisfying two conditions
l. The union of a finite number number of closed sets is a closed set
2. The intersection of any number of closed sets is a closed set

Ghastly. No motivation. No idea where the definitions came from or how they could be applied.

Which brings me to ‘An Introduction to Algebraic Topology” by Andrew H. Wallace. I recommend it highly, even though algebraic topology is just a branch of topology and fairly specialized at that.

Why?

Because in a wonderful, leisurely and discursive fashion, he starts out with the intuitive concept of nearness, applying it to to classic analytic geometry of the plane. He then moves on to continuous functions from one plane to another explaining why they must preserve nearness. Then he abstracts what nearness must mean in terms of the classic pythagorean distance function. Topological spaces are first defined in terms of nearness and neighborhoods, and only after 18 pages does he define open sets in terms of neighborhoods. It’s a wonderful exposition, explaining why open sets must have the properties they have. He doesn’t even get to algebraic topology until p. 62, explaining point set topological notions such as connectedness, compactness, homeomorphisms etc. etc. along the way.

This is a recommendation not a review because, I’ve not read the whole thing. But it’s a great explanation for why the definitions in topology must be the way they are.

It won’t set you back much — I paid. $12.95 for the Dover edition (not sure when).

More Quantum Weirdness

If you put 3 pigeons in two pigeonholes, two pigeons must be in one of them. Not so says quantum mechanics in a new paper [ Proc. Natl. Acad. Sci. vol. 113 pp. 532 – 535 ’16 ]. I can’t claim to understand the paper, despite auditing a course in QM in the past decade, but at least I do understand the terms they are throwing about. I plan to print it out and really give it a workout

The paper does involve something called a beam splitter, which splits photon waves into two parts. I’ve never understood how this works on a mechanistic level. Perhaps no such understanding is possible. Another thing I don’t understand is what happens when a photon wave (or particle) is reflected from a mirror. Perhaps no such understanding is possible. Another thing I don’t understand is how a photon is diffracted when it passes through a slit. It must in some way sense the edge of the slit. I’ve certainly watched waves being diffracted by a breakwater — just go up to the bar at the top of the Sears Tower in Chicago, get an estimate on a beer and look out at lake Michigan.

Can anyone out there help?