Tuesday, February 24, 2015

Malodorous, hmm ...

From the Wikipedia article: today we are talking about the gene ABCC11 and its alleles, which have the following unfortunate consequences.
"The product of this gene participates in physiological processes involving bile acids, conjugated steroids, and cyclic nucleotides. In addition, an SNP in this gene is responsible for determination of human earwax type and presence of underarm odour."
My earwax type, like most Europeans, is 'wet earwax'. To be honest I could be happy with no earwax at all - lose the regular eardrops and self-syringing! Here are the alleles of the ABCC11 gene as segregating at SNP locus rs17822931 according to SNPedia.
(C;C)
Wet earwax. Normal body odour. 
(C;T)
Wet earwax. Slightly better body odour.
(T;T)
Dry earwax. No body odour. Likely Asian ancestry. 
They're very polite over at SNPedia. Here's what Razib Khan noted in this post.
"The subjects were a few hundred Filipins. This is a population where the allele of interest segregates in intermediate frequencies. So there are many individuals with dry earwax as well as wet earwax, and all the associated traits.

Here are some tables I extracted*:

Mean malodour scores
5 hours24 hours
TT2.592.6
CT3.263.4
CC3.213.5
Genotype
TTCTCC
Uses deodorant0.50.860.97
Does not use0.50.140.03

"I have no idea how subjective malodour scales work, but the moral is pretty straightforward. Those with the TT genotype saturate at a much lower point. This manifests in daily behavior. There is a fair amount of Japanese data that people who go to the doctor for body odor issues are much more likely to have wet earwax. This data from the Philippines illustrates that individuals with the derived genotype, TT, must be conscious enough of their lack of body odor to forgo deodorant purchases, even though I assume it is normative in the American influenced culture of the Philippines."
My own 23andMe data returns this:

My 23andMe data for the ABCC11 gene


Keep those showers coming and don't forget the Sure is, I think, the message here.

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The real puzzle is how the relatively recent (c. 50,000 years ago) T mutation swept to near fixation in the Han Chinese and neighbouring populations. What on earth was the selective advantage? *

From the comment by Greg Cochran at Razib's post:

"It’s essentially impossible for selection to favor a pure recessive trait. You’re never going to see it. Therefore, we can conclude that some effect of this mutation shows up in heterozygotes and is favored by natural selection – but nobody seems to know what it is."

Why is it "essentially impossible for selection to favor a pure recessive trait"? The recessive mutation is initially rare in the population and the offspring of the carrier will almost certainly be heterozygous. This hides the selective advantage of the recessive allele so it doesn't get to spread in the population. Most likely it will simply die out.

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* Update: it could be sexual selection for smelling better: CT beats CC leading to heterozygote advantage, then TT wins out.

"The Egg" by Andy Weir

Just finished reading that superlative hymn to engineering can-do, The Martian, by Andy Weir. The man is a compelling writer as this story below illustrates (h/t my sister again).

More short stories from Andy Weir.

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The Egg

By: Andy Weir

You were on your way home when you died.
It was a car accident. Nothing particularly remarkable, but fatal nonetheless. You left behind a wife and two children. It was a painless death. The EMTs tried their best to save you, but to no avail. Your body was so utterly shattered you were better off, trust me.
And that’s when you met me.
“What… what happened?” You asked. “Where am I?”
“You died,” I said, matter-of-factly. No point in mincing words.
“There was a… a truck and it was skidding…”
“Yup,” I said.
“I… I died?”
“Yup. But don’t feel bad about it. Everyone dies,” I said.
You looked around. There was nothingness. Just you and me. “What is this place?” You asked. “Is this the afterlife?”
“More or less,” I said.
“Are you god?” You asked.
“Yup,” I replied. “I’m God.”
“My kids… my wife,” you said.
“What about them?”
“Will they be all right?”
“That’s what I like to see,” I said. “You just died and your main concern is for your family. That’s good stuff right there.”
You looked at me with fascination. To you, I didn’t look like God. I just looked like some man. Or possibly a woman. Some vague authority figure, maybe. More of a grammar school teacher than the almighty.
“Don’t worry,” I said. “They’ll be fine. Your kids will remember you as perfect in every way. They didn’t have time to grow contempt for you. Your wife will cry on the outside, but will be secretly relieved. To be fair, your marriage was falling apart. If it’s any consolation, she’ll feel very guilty for feeling relieved.”
“Oh,” you said. “So what happens now? Do I go to heaven or hell or something?”
“Neither,” I said. “You’ll be reincarnated.”
“Ah,” you said. “So the Hindus were right,”
“All religions are right in their own way,” I said. “Walk with me.”
You followed along as we strode through the void. “Where are we going?”
“Nowhere in particular,” I said. “It’s just nice to walk while we talk.”
“So what’s the point, then?” You asked. “When I get reborn, I’ll just be a blank slate, right? A baby. So all my experiences and everything I did in this life won’t matter.”
“Not so!” I said. “You have within you all the knowledge and experiences of all your past lives. You just don’t remember them right now.”
I stopped walking and took you by the shoulders. “Your soul is more magnificent, beautiful, and gigantic than you can possibly imagine. A human mind can only contain a tiny fraction of what you are. It’s like sticking your finger in a glass of water to see if it’s hot or cold. You put a tiny part of yourself into the vessel, and when you bring it back out, you’ve gained all the experiences it had.
“You’ve been in a human for the last 48 years, so you haven’t stretched out yet and felt the rest of your immense consciousness. If we hung out here for long enough, you’d start remembering everything. But there’s no point to doing that between each life.”
“How many times have I been reincarnated, then?”
“Oh lots. Lots and lots. An in to lots of different lives.” I said. “This time around, you’ll be a Chinese peasant girl in 540 AD.”
“Wait, what?” You stammered. “You’re sending me back in time?”
“Well, I guess technically. Time, as you know it, only exists in your universe. Things are different where I come from.”
“Where you come from?” You said.
“Oh sure,” I explained “I come from somewhere. Somewhere else. And there are others like me. I know you’ll want to know what it’s like there, but honestly you wouldn’t understand.”
“Oh,” you said, a little let down. “But wait. If I get reincarnated to other places in time, I could have interacted with myself at some point.”
“Sure. Happens all the time. And with both lives only aware of their own lifespan you don’t even know it’s happening.”
“So what’s the point of it all?”
“Seriously?” I asked. “Seriously? You’re asking me for the meaning of life? Isn’t that a little stereotypical?”
“Well it’s a reasonable question,” you persisted.
I looked you in the eye. “The meaning of life, the reason I made this whole universe, is for you to mature.”
“You mean mankind? You want us to mature?”
“No, just you. I made this whole universe for you. With each new life you grow and mature and become a larger and greater intellect.”
“Just me? What about everyone else?”
“There is no one else,” I said. “In this universe, there’s just you and me.”
You stared blankly at me. “But all the people on earth…”
“All you. Different incarnations of you.”
“Wait. I’m everyone!?”
“Now you’re getting it,” I said, with a congratulatory slap on the back.
“I’m every human being who ever lived?”
“Or who will ever live, yes.”
“I’m Abraham Lincoln?”
“And you’re John Wilkes Booth, too,” I added.
“I’m Hitler?” You said, appalled.
“And you’re the millions he killed.”
“I’m Jesus?”
“And you’re everyone who followed him.”
You fell silent.
“Every time you victimized someone,” I said, “you were victimizing yourself. Every act of kindness you’ve done, you’ve done to yourself. Every happy and sad moment ever experienced by any human was, or will be, experienced by you.”
You thought for a long time.
“Why?” You asked me. “Why do all this?”
“Because someday, you will become like me. Because that’s what you are. You’re one of my kind. You’re my child.”
“Whoa,” you said, incredulous. “You mean I’m a god?”
“No. Not yet. You’re a fetus. You’re still growing. Once you’ve lived every human life throughout all time, you will have grown enough to be born.”
“So the whole universe,” you said, “it’s just…”
“An egg.” I answered. “Now it’s time for you to move on to your next life.”
And I sent you on your way.

Since this whole conversation takes place 'out of time' perhaps our careless driver is in fact God as well, but God doesn't know it?

Monday, February 23, 2015

A strange attractor in the car park at Wells

Greg Egan has a short story in Axiomatic, "Unstable Orbits in the Space of Lies", where humanity has had some kind of mass sea change in which prevailing belief systems manifest as psychic forces that compel all within their range to believe, and the city of the story is divided into zones of belief that vie and shift, with the protagonist one of a minority who seem to have kept free by constantly keeping between the zones, never being overwhelmed by any one belief system.

The protagonist finally realises that his nomadic journeying around the city is not free at all: he is confined within the physical limits of the strange attractor which corresponds to his own libertarian beliefs.

I thought of this as we walked across the car park in town towards the library this morning. Clare kept pulling off to the right. Eventually, as I gazed at her oddly, she became self-aware and advanced an explanation: "I'm being pulled towards Whiting's."

This being the hardware emporium  which could keep a body entertained for a week.



Sunday, February 22, 2015

What every schoolkid kinda knows ...

XKCD: Fundamental Forces

And here's the (mouse-over) punchline:
"Of these four forces, there's one we don't really understand."

"Is it the weak force or the strong?"

"It's gravity."

Yes folks, it's true.

Mars One

Just started "The Martian" by Andy Weir, passed to me by my sister.
"In Andy Weir’s novel, The Martian, an American astronaut named Mark Watney is stranded on Mars after a vicious sandstorm cuts him off from his fellow crew members. They assume, with good reason, that he has been killed in the storm; their only recourse is to save themselves by aborting the mission and returning to Hermes, the mother ship.

Watney’s situation then is the most dire that can be imagined. He has no means of communication with Hermes or Earth; as far as the known universe is concerned, he is dead and therefore no rescue operations are contemplated.
...
Watney is heir to the labours of countless other individuals — he has at his disposal numerous gadgets left behind by his fellow astronauts, ranging from a hammer and screwdriver to a plutonium-fuelled generator called a radioisotope thermoelectric generator. (Such a device does exist by the way — Weir’s future fiction is pretty much set in the present.)

It is through these devices — mainly an atmospheric regulator, oxygenator and a water reclaimer — that Watney is able to keep breathing and moving around and even to start planting and harvesting a potato crop on the soil of Mars."
The ludicrous "Mars One" project is doomed in a variety of ways, but the most telling fact is that the kind of guys you need on a no-return, ramshackle Mars base are plumbers, electricians, botanists and electronic engineers: people with mechanical aptitude and green fingers. The people who've signed up all seem to be folk with doctorates in black hole physics. As I said, doomed.

---

In "Wolf Hall" last week, Thomas Cromwell advises his son, who is about to joust with King Henry 8th for the first time. Cromwell explains that he once met a superb jouster in Turkey who explained the key to success: relax in the saddle, hold the lance as if it were light as air, and lose all care as to whether you will survive or not.

This is a very familiar trope. I recall some years ago watching a very bad film about King Arthur. I dimly recall someone like Danny Kaye playing the knight Lancelot, who at this point is wandering around incognito as the sword-fighting equivalent of a prize fighter, taking on all comers. A young man asks him the secret of his success. Kaye/Lancelot replies with the usual - do this with the sword, watch your opponent like that .. and then his final advice, and don't care whether you live or die.

Do you recognise this as another example of 'hawk vs. dove' or the game of chicken? A superlative dogfighting tactic was simply to fly head-on at your opponent, firing all the time. Both aircraft are small targets, but the first one to break away exposes itself completely to its opponent's fire and will be shot down. The pilots who 'didn't care whether they lived or died' were the ones who lived.

I think this advice comes down to: we can't all be psychopaths but sometimes it pays to emulate one.

---

I am a really slow learner. For years I tolerated being thirteen and a half stone, with a spherical abdomen and a vast, forty inch plus waistline. Six months of the 5:2 diet a couple of years ago lost me two and a half stone and for ages I was stable at just over 11 stone (70 kg). Recently I realised that I was still tolerating a layer of flab under the rib cage and a residual layer of abdominal fat. Why?

I guess I just hadn't engaged. I have now decided to forget BMIs and target weights, I just don't need to carry this extra stuff around. I was 10 stone 12 (69 kg) this morning and the loss of a kilogram is already noticeable at the gym (more power!). I have in the past been briefly 10 stone 9 lb and it's looking like ten and a half stone might be a healthier weight to be at. We shall see.

I recall Matthew Parris's famous remark on dieting. 'If you're a bit overweight, skip breakfast; if the problem is a little more serious, skip lunch too. The problem will soon be resolved.'

I agree.

Monday, February 16, 2015

Two unenviable choices


More quirky writing from Dr Michelsen, describing the two main options for understanding what quantum mechanics really means. This surely answers the question; "How would Jesus have explained it?"
"Dr. Xavier E. Rox believes in predictability. There can be no collapse, no random events. Physics is deterministic, just like the old classical physicist, Dr. Diehard, says. Dr. Rox observes, “Diehard’s only problem is that his math is wrong. Physics follows the Schrödinger equation.”

Of course, to be consistent with experiment, Dr. Rox must assume that at every instant, the quantum state of the entire universe, including himself(!), splits into a new superposition of all possible results. “Better complexity and confusion than uncertainty,” he declares, much to the dismay of Werner Heisenberg.

On Sunday, Dr. Rox goes to the Church of Duplicity, and worships a rapidly growing list of very similar gods.

***

Dr. Ophelia C. Cam retorts, “Stuff and nonsense! I can only ever perceive one world, so it is unscientific to talk about others. They are, by definition, outside the possibility of observation, and therefore, also by definition, outside the realm of science.” She believes that each observer, with each observation, collapses her own wave-function of the universe. That is, to be consistent with experiment, she must assume that each observer has her own wave-function for the universe, which collapses only when its owner makes an observation. This means the quantum state of the universe is different for different observers.

How can a wave-function collapse? How can a wave-function be subjective, and not absolute? “I don’t know, and I don’t care,” says Dr. Cam. “Like it or not, it is what it is. The measured results provide a single reality for all observers, so there is no physical consequence of personalized wavefunctions.”

On Wednesdays, Dr. Cam goes to the Church of One Mind, where she prays to a very lonely God.

Who is right, then, Dr. Rox or Dr. Cam? This is not a scientific question, since both professors make the same experimental predictions. Whom you believe depends on which church you attend."
You see what he did there? With the names?

Satire aside, it's interesting that this is the best that the greatest minds on the planet have been able to come up with, in a century of trying. We're missing something important.

"Tweets"

Dilbert
---

Public culture has a cutesy understanding of Evolution: how it brings about perfect little creatures - how nice! I was watching the sparrows on the earth in the garden, pecking at the seeds we had scattered like benign Gods. Actually, I could hardly see them, they were so well camo'ed. Around each sparrow I 'see' a dozen virtual ones - all those tiny, vulnerable sparrow-brethren who were not so beautifully drab .. and who were picked off by predators, to die in horrible ways so that evolution could do its cutesy work.

Someone should surely tell the children.

---

Why aren't sheep green? We are tall creatures and often view sheep from a distance. Their fleeces stand out against the green backcloth of the grassy meadow. But their predators are low and close. Their view of sheep-background comprises tree-trunks and the branches of bushes. That's why sheep are brown ... *

* (To be fair, most terrestrial, herbivorous, temperate ungulates are .. as were sheep before domestication.)

---

Today I got a letter from the NHS advising me that it was time again for my colon-cancer-preventative faecal occult blood (FOB) test. Important but unaesthetic. But I had a colonoscopy two months ago (q.v.). I phoned - and I'm let off for two years.

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I think it was Marx who said that all capitalists would like the workers to be paid more ... by their competitors! Naturally the effect would be to increase demand for their own products while saddling their rivals with increased costs.

The Government asked businesses (in the run-up to the election) to pay their workers more. How d'you reckon that's working out, Karl?

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"No-one ever went to their death-bed wishing they had spent more time at the office."

Apparently. So say those advocates for 'work-life balance' and time made for family and friends.

But what about wishing they had spent more time studying quantum mechanics? Or differential geometry?

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It's hard to see how you're going to explain R3 x R as emergent on the basis of quantum theory, when space-time is assumed a priori in the development of quantum theory. Or is it me?

[A physicist writes; "Yes, it is you."]

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I don't have a Twitter account so I save my more banal thoughts for here ...

Saturday, February 14, 2015

New phone (and Flipper)

Goes with the Flipper ...
The Flipper wasn't so hard to install and has been a great success (so far!). Alex and myself spent some time today putting the phone above into shape. The fast dial buttons are for my sister and myself.

Wednesday, February 11, 2015

Many Worlds: the "loss of coherence" and decoherence

What problem does the "many worlds interpretation" try to solve? The core idea is captured by the infamous Schrödinger's cat thought-experiment. The cat ends up in a superposition:

α |cat-alive> + β |cat-dead>           (where α, β are complex amplitudes)

but in reality we never observe such a superposition. What we see is either that the Geiger counter has triggered, releasing the poison and the cat is dead or there was no particle-emission and the cat remains alive. Making the act of measurement explicit, the observer becomes entangled with the cat-box on observation and joins the superposition thus (with updated amplitudes α' and β') :

α'∣Live cat> ⊗ ∣Observer sees live cat> + β'∣Dead cat>  ⊗ ∣Observer sees dead cat>.

The overall situation is still a superposition, but an Everettian would say that since the observer has 'split',  each 'copy' doesn't see a superposition but just one outcome. If world-splitting is not your thing, then you have to postulate (as an extra axiom) that 'measurement' somehow causes the superposition to collapse to one or the other outcome according to the probabilities |α'|2 and |β'|2.

We now focus more precisely on how the process of 'measurement' destroys superpositions - a topic called 'decoherence'. The formal treatment of decoherence involves graduate-level concepts and is formidably inaccessible, while analogies such as 'phase information leaking into the environment' are unhelpful at best. I will say more about a 'simplest possible model' another day.

However, something can be said even at undergraduate level, and for this we are indebted to non-Everettian Eric L. Michelsen and his excellent "Quirky Quantum Concepts: Physical, Conceptual, Geometric, and Pictorial Physics that Didn't Fit in Your Textbook (Undergraduate Lecture Notes in Physics)". This is available as a PDF but in a fit of guilt I bought it. An extract, [somewhat annotated] follows.

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"In theoretical QM, we usually focus on perfect systems, and pure states. We frequently say that a measurement “collapses” the quantum state vector to one agreeing with the measurement, and this is often a useful simplification of the measurement process. However, in practice, the measurement process is more complicated than that, because most measuring equipment, and all observers, are macroscopic. The “decohered” state is the norm; you must work hard to achieve even an approximately pure entangled state.

We show here that elementary QM can explain some of the features of real measurements, however, the full explanation of decoherence is beyond our scope. (The term “decoherence” has a specific meaning: the process of a system becoming entangled with its environment in irreversible ways, resulting in the loss of a consistent phase relationship between components of the system state. We therefore use the more general term “loss of coherence” for both decoherence and other processes.)

Most macroscopic measurements do not show quantum interference [as in the two-slit experiment]. Why not? One reason is that macroscopic bodies suffer unknowable, and unrepeatable energy interactions, i.e. they gain or lose an unknowable amount of energy due to uncontrollable interactions with their environments. In other words, they are subject to simple “noise.” This results in the loss of a consistent phase relationship between components of a superposition state. We discuss below how such a loss of consistent phase leads to classical probabilities.

Let us walk through a plausible measurement, and consider the elementary quantum mechanics involved. [The system pictured below shows the famous Stern-Gerlach experiment, which first demonstrated the quantization of angular momentum.]



Suppose we start with a particle which can be in either of two states, |s1> or |s2>, such as polarization (horizontal or vertical), or spin (up or down). A general particle state is then:

|ψ> = a|s1> + b|s2>     where a,b are complex coefficients and |s1>,  |s2>  are basis states.


This is called a coherent superposition, because a and b have definite phases. (This is in contrast to a mixed state or incoherent mixture, where a and b have unknown phases.) All that is required for loss of coherence is for the relative phases of a and b to become unknown. For simplicity, we take |s1> and |s2> to be energy eigenstates, and the particle is spread throughout our measurement system [i.e. it is in a spatial superposition].

According to the Schrödinger equation, every state time-evolves with a complex phase determined by its energy, then our 2-state system time evolves according to:

|ψ(t)> = ae-iE1t/|s1> + be-iE2t/|s2>.

Since the energies E1 and E2 are quantized, the complex phases multiplying |s1> and |s2> maintain a precise (aka coherent) relationship, though the relative phase varies with time.

When we measure the particle state, the state of the measuring device becomes entangled with the measured particle. Let |M1> and |M2> be states of the whole measuring system in which either detector 1 detected the particle, or detector 2. If we look directly at the indicator lights, we will observe only state 1 or state 2, but never both. This means |M1> and |M2> are orthogonal. As the measuring system first detects the particle, the combined state of the particle/measuring-device starts out as a coherent superposition: [this is the same as the Schrödinger's cat case above]

|Ψ> = c|M1>|s1> + d|M2>|s2>       where c, d are complex coefficients.

The combined system time evolves according to its new energies:

|Ψ(t)> = ce-i(E1 + EM1)t/|M1>|s1> + de-i(E2 + EM2)t/|M2>|s2>

If the energies of the two measuring device states fluctuate even a tiny bit, the two components of the superposition will rapidly wander into an unknown phase relation. They will lose coherence.

Every macroscopic system suffers unrepeatable and unknowable energy fluctuations due to its environment.

We estimate a typical coherence loss rate shortly.

[So what does this loss of phase coherence mean in practice?]. Let us examine the effects of various kinds of energy transfers between a system and its environment. In our two-path experiment, [I think he means that this is a variant experiment where we don't 'look at' (i.e. measure) the indicator lights 1 and 2 so allowing the interference pattern to emerge on the screen in the figure to the right] the interference pattern is built up over many trials, by recording detections on film. Now suppose one path suffers an energy transfer to/from its environment before recombining and interfering. There are four possibilities:

  1. The energy transfer is knowable and repeatable. Then one can predict and see an interference pattern in the usual way.
  2. The energy transfer is unknowable, but repeatable. Then we can record an interference pattern, and from it, determine the relative phases of the two paths (mod 2π), and therefore the relative energies (mod 2πħ/t) from (ΔE/)t.
  3. The energy transfer is knowable for each trial, but not repeatable. Essentially, each trial has its own position for the interference pattern. One can then divide the detection region into intervals of probability calculated for each trial, and then show consistency with QM predictions, but contrary to classical probability.
  4. The energy transfer is unknowable and unrepeatable. Then there will be no interference pattern, and repeated trials do not allow us to measure any quantum effects, since the phase is unknown on each trial. Therefore, the measurements are equivalent to classical probabilities: it is as if a single path was chosen randomly, and we simply don’t know which path it was.

This fourth condition, of unknowable and unrepeatable energy transfer, causes loss of coherence, the randomization of phase of components of a superposition. Loss of coherence makes measurements look like the system behaves according to classical probabilities, with no “wave” effects. Loss of coherence destroys the interference pattern when we try to measure through “which slit” a particle passes. Full loss of coherence leads to classical probabilities.

Our example process leading to loss of coherence follows directly from the Schrödinger equation and unknown energy transfers. There is no need to invoke any “spooky” quantum effects.

Note that even accounting for loss of coherence, quantum theory still requires the axiom of collapse of the wave-function upon observation. When a particle’s wave splits, then passes through both detector 1 and detector 2, and then loses coherence because of entanglement with a macroscopic measuring device, the system is still left in a superposition of both slits:

|Ψ(tafter)> = f|M1>|s1> + g|M2>|s2>

we just don’t know f or g. We can’t generate an interference pattern from multiple trials, because each trial has a different phase relation between f and g, putting the peaks and valleys of any hoped-for interference pattern in a random place on each trial. These shifts average over many trials to a uniform distribution. Nonetheless, each trial evolves in time by the Schrödinger equation, which still leaves the system in a superposition. Once we “see” the result, however, the unobserved component of the wave-function disappears, i.e. the wave-function collapses.

Collapse of the wave-function is outside the scope of the Schrödinger equation, but within the scope of QM, because collapse is a part of QM theory. It is one of our axioms. Some references confuse this issue: they try to avoid assuming such a collapse as an axiom, but cannot derive it from other axioms. From this, they conclude that QM is “incomplete.” In fact, what they have shown is that the axiom of collapse completes QM.

Note that once the measuring system fully loses coherence, we could just as well say that the wavefunction has then collapsed, because from then on the system follows classical probabilities (equivalent to a collapsed, but unknown, wave-function). However, we now show that a binary model of “collapse or not” cannot explain partial coherence.

Partial coherence: What if we start with a microscopic system but replace our microscopic atoms with mesoscopic things: bigger than microscopic, but smaller than macroscopic? Mesoscopic things might be a few hundred atoms. These are big enough to lose coherence much faster than single atoms, but still slowly enough that some amount of interference is observed. However, the interference pattern is weaker: the troughs are not as low, and the peaks are not as high. A superposition leading to a weak interference pattern is called partially coherent. We describe partial coherence in more detail in section 8.4. The simple model that the wave-function either collapsed or didn’t cannot describe the phenomenon of partial coherence.

The larger the mesoscopic system, the more uncontrollable interactions it has with its environment, the faster it loses coherence, and the less visible is any resulting interference pattern. We can estimate the time-scale of coherence loss from our example energy fluctuations as follows: a single 10 μm infrared photon is often radiated at room temperature. It has an energy of ~0.1 eV = 1.6 x 10–20 J. This corresponds to ω = E/ħ ~ 2 x 1014 rad/s. When the phase of the resulting system has shifted by an unknowable amount > ~2π, we can say the system has completely lost coherence. At this ω, that takes ~ 4 x 10–14 s. In other words, thermal radiation of a single IR photon causes complete loss of coherence in about 40 femtoseconds. In practice, other effects cause macroscopic systems to lose coherence in dramatically shorter times.

Summary: A measurement entangles a measuring device with the measured system. The entangled state of device and system time-evolves according to the Schrödinger equation. Macroscopic devices lose coherence, due to interactions with the environment. Lack of coherence prevents any interference pattern within the system. Therefore, measurement by a macroscopic device produces subsequent results that are classical, as if the system collapsed into a definite state upon measurement, but observers only “see” which state when they look at the measuring device. Any observation by a person is necessarily macroscopic, because people are big. Such an observation collapses the (incoherent) device/system/world state to that observed. Quantum interference can only be seen if it occurs before any entanglement with a macroscopic system (and therefore before any loss of coherence in the system).

The model of “collapse of the wave-function” is a binary concept: either the wave-function collapses or it doesn't. Such a model cannot account for the phenomenon of partial coherence. Loss of coherence is a continuous process, taking a fully coherent state through less and less partially coherent states and eventually to incoherent (aka “mixed”) states. Continuous loss of coherence fully explains partial coherence and the varying visibility of interference patterns.

Some quantum effects, such as the spectrum of atoms, do not rely on interference, and are therefore macroscopically observable. In fact, measurement of such effects led to the development of QM."

Tuesday, February 10, 2015

Using may be hard but configuration is rubbish!

This is for my convenience later this week ...



Product page here. Elaine & Mike did the ordering for my mother - I'm phone tech-support for the current (Sky) remote! Looking at it though, we could all benefit from this simplified device 90% of the time.

Monday, February 09, 2015

And all shall be well

After recent posts of MWI exotica, I think it's time to come down to mundane reality as informed by Julian of Norwich:

And all shall be well and
All manner of thing shall be well

We took the car to the car wash this morning, and as the mud and salt came off, further dents and rust marks were revealed at the back of the vehicle. The eye of suspicion was directed at your humble correspondent but as the weather improves from a chilly four degrees my accuser will be the one with the paintbrush in hand (you go, girl!).

My mother's TV has again mysteriously gone 'on the blink' but hopefully this can be fixed shortly.

Both Clare's and my weight had been creeping slowly upward - so much so that Clare wrote plaintively in her diary "I have let myself go!" Yesterday we took ourselves in hand and this morning we had both lost two pounds! (We are not so naive as to think 7,000 Calories of fat can be burned off in a day: in the short run, scales measure your food and fluid intake).

The Malvern Hills
We have family visiting this weekend-coming and a holiday booked in the Malvern Hills for next month: this brings my catalogue of modestly-upbeat news to an end.

Many Worlds: whence and what?

Where does the idea of the "Many Worlds Interpretation of Quantum Mechanics" actually come from? Everettians claim that it's simply a matter of taking the formalism seriously, in its own terms, as David Wallace explains from his paper: "A prolegomenon to the ontology of the Everett interpretation".
"To see how that works, let’s suppose we have a measurement device represented by a pointer, that can be in three states: pointing left, pointing right, and pointing nowhere. And suppose the measurement is set up so that if the electron is measured in position x the pointer moves so that it points left, and if it is measured in position y, it moves so that it points right. We can certainly find a state space suitable for such a pointer, and indeed can find wave-packet states φL (for the pointer pointing left), φR (for it pointing right), and φ0 (for it pointing nowhere). The idea of these states, as with the electron, is that φL (say) is a state such that, if we measure where the pointer is — with the naked eye, or otherwise — we’re pretty much guaranteed to get the result that it’s in the pointing-left position.

Given state spaces for the electron and for the pointer, quantum theory gives us a recipe to construct a state space (the so-called “tensor product space”) for the combined system of electron-plus-pointer. If φ is any state for the electron alone, and ψ any state of the pointer alone, there is then a combined state φ ⊗ ψ of both together, which gives the same experimental predictions as φ for measurements of the electron and the same experimental predictions as ψ for measurements of the pointer.

If the measurement device works as intended, the dynamics of measurement must look something like this:

ψx ⊗ φ =>  ψx ⊗ φL

ψy ⊗ φ0  =>  ψx ⊗ φR

In other words, if the electron starts off in a state such that its position is always found to be x, the pointer must reliably end up in a state such that its position is always found to be on the left (and similarly for y). But now, the linearity of the dynamics causes trouble: what if we measure the electron’s position when it is in the mysterious state αψx + βψy? The dynamics in this case have to give

( αψx + βψy) ⊗ φ0  =>   αψx ⊗ φL + βψy ⊗ φR

So now there seems to be a contradiction between our measurement algorithm and the actual physical process of measurement. The algorithm tells us that the measurement should give x a fraction |α |2 of the time and y the rest of the time, and hence that the pointer should point left a fraction |α |2 of the time and right the rest of the time. But the actual physical process never gives ‘left’ or ‘right’ as pointer states at all, and is not indeterministic at all: instead, it deterministically gives the strange, indefinite state

αψx ⊗ φL + βψy ⊗ φR,

in which the pointer seems to be pointing left and pointing right at the same time.

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The immediate question one asks about the Everett interpretation — why do we only see one pointer, if actually there are two? — can be resolved by remembering that you too, dear reader, are a physical system, and if χ L and χ R are, respectively, states in your state space representing you seeing a pointer pointing left and you seeing it pointing right, then the same linearity argument used above predicts that the state of (you-plus-pointer-plus-electron), once you look at the pointer, will be

αψx ⊗ φL ⊗ χL + βψy ⊗ φR⊗ χR


In other words, you will be in a state of seeing left and seeing right at the same time, and this state (according to the Everett interpretation) should also be understood as telling us that there are two yous, one seeing the pointer pointing left and one seeing it pointing right.

Notice — crucially — that although the state above is the sum of two macroscopically very different state, in each term in the sum the results of the two measurements are correlated (in each term the electron has a particular position, the pointer records it as having that position, and you observe the pointer as so recording it.)

Once a system gets above a certain size, it cannot help being measured constantly — by chance collisions with the atmosphere and with sunlight, if by nothing else. In doing so, the multiplicity spreads to more and more systems, while the correlations in each term in the state remain. In due course, the state (schematically) evolves into something like

α (Whole planet is as if electron was found in position x) + β (Whole planet is as if electron was found in position y).

When this, too, is understood as representing both states of affairs simultaneously, the “many-worlds” label for the Everett interpretation starts to sound apposite."
Notice that we are doing nothing more here than taking the superposition seriously. But what kinds of mathematical (and physical) entities correspond to taking all the elements of the superposition as being concurrently 'present'? This is not at all obvious, and as I read Wallace's book and many papers, it seems that the Everettian community finds this stuff pretty opaque too. Sometimes, as above, each superposition branch is claimed to look like the 3 + 1 dimensional space-time which we appear to inhabit; other times the micro-physics underlying the world of appearances seems decidedly weird! Crudely: the quantum state lives in high-dimensional Hilbert space - and the world we inhabit doesn't.

And don't mention the g-word!

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Gravity. A workable theory of quantum gravity might be strange in the micro-physics (i.e. at extremely small length scales - or in areas of extreme field strength) so that our placid large-scale experience of reality is once again emergent.

Saturday, February 07, 2015

Interim report

Obligatory cat picture
A note from Dee Ann a couple of days ago. She and her husband, Craig, were colleagues in the States when we were employed at Cable & Wireless in Reston, Va.  They were working in the HR/psychometrics area and moved to Singapore after the demise of C&W Worldwide. They're delighted to be back in Carolina. It was good to hear from them.

I read "J" by Howard Jacobson which was short-listed for the 2014 Man Booker Prize. Jacobson does a fine job enmeshing the reader in the existential fragility of the Jewish experience: the suitcase pre-packed in the wardrobe, always just a few days from the need to flee. The suffocation of the relentlessly-nice, repressively-tolerant and chillingly-threatening post-atrocity state is particularly salient (when is it not?). Don't want to say more as Clare is currently reading it. But it's really good - what happens when an author cares about what they're writing.

"The Emergent Multiverse: Quantum Theory according to the Everett Interpretation" by David Wallace. Working my way through this and lost in jaw-dropping admiration for the erudition of Oxford Philosopher of Science David Wallace. Subject to my caveats below, the Multi-World Interpretation (MWI) of QM (Quantum Mechanics) is quite well explained in the Wikipedia article.

I'm not going to say much here: it needs an essay, not just a few trite remarks. Just this: it's an illusion that you can access even the concept of the MWI of QM (no matter how many science-fiction books you've read or SF films/TV episodes you've watched) without completing a university-level course on QM. The MWI tries to solve a problem (what does QM actually mean?) which can't even be understood without familiarity with the theory itself.

Furthermore, the MWI needs some extra concepts, beyond the scope of a first (undergraduate) QM course: in particular creative use of the density matrix and in particular its application to decoherence. Sorry, without the maths you can't engage .. and without engaging you can't have a view as to the truth or utility of Hugh Everett's intellectual creation.

I'm still working through it and I would class myself as an MWI-agnostic, akin to those people who consider themselves agnostic supporters of the Church of England or the Catholic Church. Perhaps I will eventually be converted when I understand more!

There you are, Dee Ann. I said I would write about it - and that no-one would read it!

Monday, February 02, 2015

Menagerie à trois

En route to Bristol today - with Joni Mitchell warbling 'California' in the background. I turn from the steering wheel to ask, "Did anyone ever suggest that Joni should've taken up engineering instead?"

Clare was loyal: "Joni is so smart, she would have made a success of anything."

A few miles later it's John Lennon belting out "When I get home to you, you know the things that you do ..." . I say, "Apart from 'Maxwell's Silver Hammer', did the Beatles ever release any tracks on STEM subjects?"

And they wonder why the UK has a shortfall of 50,000 engineers. Finally, here's some of what transpired after we all got back from Costa at Next.


When the district nurse comes round, legend has it that they all hide ...