First posted 31 Oct 2003 - Another wrinkle to follow, if you're interested. Be-ables and Change-ables.
At the end of If you think you understand this, then you don't, I mention Bell's Inequality. Experimental tests of the theorem show that no hidden variable theory can be consistent with quantum mechanics' well documented and highly accurate predictions. Or do they?
Reading the article below in Nature Science Update, I learned that a new theory may show how a deterministic universe is consistent with QM's mathematical formalism and its experimental findings.
Einstein may be smiling in his grave. Having made one of the breakthroughs that led to the quantum revolution, he expressed great dissatisfaction with QM's indeterminacy. He believed that it was simply incomplete, and that a more comprehensive theory would show the indeterminacy to have been simply a result of our earlier ignorance. This looked impossible until recently.
Physicist proposes deeper layer of reality. Nobel winner Gerard 't Hooft says that QM's apparent indeterminacy is due to information loss as we zoom outward from the Planck scale, where deterministic physical laws rule. Although the article says he is not attempting to resurrect hidden variables, he is quoted as saying:
"Contrary to common belief," he says, "it is not difficult to construct deterministic models where quantum mechanics correctly describes stochastic behaviour, in precise accordance with the Copenhagen doctrine."
Where the Copenhagen doctrine is the most widely accepted interpretation of QM, stating that the world really is probabilistic at quantum levels - that there are some things we simply cannot know, some things that we cannot even say exist independent of observation.
't Hooft splits measurable properties into two classes - Be-ables which maintain their precision as one moves from Planck scales to laboratory scales, and Change-ables, which don't. Change-ables really aren't observable properties but rather ways of describing how a system behaves when it is perturbed. The trick is that we can't know in advance whether a property is a Be-able or a Changeable.
No, I don't understand all of this, but it is good to see that the deterministic debate is still alive and well in science as well as philosophy.
Originally posted 5 May 2005.
My first proper military assignment began in West Germany in March 1991, a year and a half after the fall of the Berlin wall and only months before the full collapse of the Soviet Union. Yet the unit I joined maintained its Cold War mission at least until I left in the Spring of 1993, and probably significantly longer.
The Allied Command Europe (ACE) Mobile Force (Land Component) was much bigger as a unit title than it was as a unit. This brigade-sized, seven-nation unit was largely a diplomatic tool, whose usefulness mainly depended on the blood spot it would leave behind when it was over-run by Soviet tanks. Let me explain.
The job of the AMF(L), as it was more conveniently known, was to deploy rapidly to the flanks of NATO's heavily guarded central European defences if the enemy hordes tried to do an end run. This meant that the unit had to be ready to fly to Denmark, Norway, Greece or Turkey at the drop of a hat. As such, it was one of the few light units in Germany. (Most were full of tanks and armoured personnel carriers).
Now, being light was good news for being able to deploy quickly, but it wasn't necessarily great when looking down the barrels of 200 thundering T-55 tanks. So in all probability, had the balloon ever really gone up, the AMF(L) would have deployed with its soldiers wearing their seven different national uniforms; these brave soldiers would have locked arms and fought bravely in the name of international solidarity (for about 35 seconds); and they would have been annihilated. Their deaths in unified endeavour would have helped to cement the resolves of their respective domestic publics and thereby their home governments to commit (as each had promised to do by treaty) to the mutual protection of Western Europe. So, as I said before, the squidgy AMF(L) blood spot that remained once the communist hordes had rolled through would be our true contribution to freedom and democracy.
As a pretty selfless guy who was up for a challenge and happy to do his part, I didn't mind all of this very much at all. I didn't, however, go out of my way to spell it out for the 40 men whose lives I was responsible for. I suspect they may have had concerns with a couple of the finer points. Still, the risk had become a purely theoretical one by the time that I arrived at the U.S. headquarters company of the brigade - HQ CO AMF(L), (are you getting this abbreviation stuff)? - to take charge of my infantry platoon.
As it turned out, it was a lot of fun. We didn't waste loads of time maintaining tanks and personnel carriers - because we didn't have any. We got lots of cool training time around Germany. And we got super cool training deployments to Denmark, Turkey, Italy and the UK.
What's more, we worked closely with, and thereby learned to disrespect, distrust and generally look down upon, soldiers from many other countries - almost as much as we looked down upon our countrymen in competing armed services (Navy, Air Force). I joke. We developed real respect for our Nato brethren forces and enjoyed working with them - especially the Brits and Germans.
I swear I had a conversation with a Turkish officer who told me, when I asked why he carried a pistol loaded with LIVE ammunition at all times, that he needed it to protect himself from his troops. He went on to say that he could kill nine of his soldiers per year without having to fill out any paperwork. Once he hit double figures, he needed to complete some forms. Maybe he was just pulling my leg.
Our deployment to Italy was unique for two reasons: first, we could not take any weapons or gas masks, because the Austrians would not allow us to travel through their country by train with these things; second, our company commander didn't go, so I was in charge of things. It was winter / mountain survival training in the Alps north of Venice, and it was great. Without the weapons, it felt like a boy scout jamboree - cross-country skiing, downhill skiing, snowshoeing, sleeping in snow caves - fantastic!
I remember another such outing - without weapons but with our commander - to Bavaria for mountaineering training. This training wasn't especially military, as it was run as part of the U.S. military's recreational facilities at Garmisch - the sight of the Winter Olympics many moons ago. Our hiking guide during one phase of the training carried a guitar with him, and we sang for much of the night once we reached our hut on a ridge overlooking Austria. It was like The Sound of Music all over again - but with a country & western twang and no lederhosen.
Don't get me wrong. There was plenty of 'proper' military training as well, even if the unit's raison d'etre had recently dissolved.
First posted 21 Sep 2004. Reading back through it now, this seems a descent summary of about as far as I got to in understanding the debates on the interpretation of quantum mechanics. I'm not at all sure things have progressed in the last 13 years. I know that my understanding hasn't!
I find it hard to ascertain exactly what the current status of the quantum mechanics (QM) interpretation debate is.
I know that Einstein believed that QM was incomplete as a theory because it suggested an irreducibly random atomic world with 'spooky action at a distance'. He believed that God would do better by us than that, that the world must be causally deterministic and local. The seeming randomness behind QM, according to him, really came down to our lack of understanding. Future theoretical and experimental work would discover currently hidden variables that would put QM back onto causal, ontological grounds.
Niels Bohr won the day, though, with his interpretation, rooted in logical positivism. QM, he said, does not describe a quantum world but rather only our observations and measurements of subatomic activity. We cannot know and should not be concerned with what, if any, metaphysical entities underlie those observations. In bolder moments, he seemed to suggest the stronger claim that no such entities did exist independent of observation.
J.S. Bell, hoping to swing the argument back in the direction of Einstein's thinking, developed a test for whether any hidden variables approach might conform with experimental results. Alain Aspect devised the actual experiment to carry these tests out, and the resulting data supported Bohr's view, which has since come to be called the Copenhagen Interpretation (CI). Many tests, some similar and others quite different, have confirmed those initial findings.
But let's look more closely at just what those findings were. Bell's theoretical test and the experiments based on it were meant to decide whether any LOCAL and DETERMINISTIC hidden variables theory could fit our observations. David Bohm came up with a wholly deterministic, ontological interpretation of QM that passes Bell's test. Bohm's theory did not wholly satisfy Einstein, though, because it was still non-local (allowed action at a distance) - intentionally and explicitly so.
[Non-locality is demonstrated by the entanglement of particles that have interacted with one another, where the choice of measurement on one impacts the other (via conservation laws) instantaneously, even at a great distance. I need to understand this better, as it seems to me that the measurement of the one particle only affects WHAT WE CAN KNOW about the second particle, which is very different from having a causal impact on the particle itself. Anyway, many people say that such instantaneous 'action' is not a problem, as long as it doesn't involve the transmission of information at above light speed (which it doesn't)].
The scientific community has never liked Bohm's approach. As far as I can tell, this is for two reasons. First, it gives a privileged place to position vis-a-vis momentum, two characteristics of any particle that the CI gives equal weight. This asymmetry lacks elegance. Second, it imparts a physical reality to the 'wave function,' which in CI is simply a mathematical tool for describing the evolution of an unobserved system. CI itself is unable to explain the collapse of this wave function at the time of measurement, but Bohm's theory runs afoul of Ockham's Razor, which says that we should not call into existence any more entities than absolutely necessary in explaining a phenomenon. Still, Bohm's interpretation is perfectly consistent with the mathematical formalism of QM and with observed behaviour of sub-atomic systems.
In 1995, Tim Palmer pointed out that, strictly speaking, J.S. Bell's test and the results to date do NOT preclude there being a local, deterministic hidden variables theory behind QM. Chaos theory has introduced new and powerful concepts to the stage. There exist wholly deterministic non-linear dynamic systems that are non-computable - that is, there is no algorithmic way to 'solve' for their results. These systems have interlaced riddled basins (a basin is the 'region' of initial conditions that 'flows' to a given attractor). Palmer showed that just such a system could fit perfectly with the seemingly random elements of QM and the 'collapse' to concrete states upon measurement. Palmer updated and amended his approach in a later paper, but with the same conclusion - that a local deterministic interpretation of QM is NOT impossible.
Of course, neither does that mean that QM necessarily IS local or deterministic. It just means we cannot, as so many orthodox QM theorists have wanted to, close the door on the possibility. I have so far not found any responses to Palmer's papers, so I don't know whether the 'community' sees the debate as an open one or not.
Anton Zeilinger noted in his survey of the interpretations of QM that it did indeed seem to be lacking some fundamental, unifying principle. He went on to nominate just such a principle, that 'An elementary system carries one bit of information.' Here, an elementary system is a fundamental building block of the material world - like the spin of an electron. What does this principle do? Well, it explains why our experience of the microscopic world is quantised - because information, the only access we have to that world, is itself quantised. We interrogate the sub-atomic world with yes-no questions, and the answers cannot be broken down into anything simpler (e.g. smoother) than the 0s and 1s that our computers use. Zeilinger's principle also provides a more intuitive explanation of the uncertainty principle and entanglement. Zeilinger himself subscribes to Bohr's CI and believes that his information-based view gives additional support to that interpretation.
Of course I realise that I understand very little of the guts of information theory and quantum theory. I still can't help pointing out that the implications drawn from Zeilinger's principle concern what we can know about the world rather than what the world is actually like. It is epistemological rather than ontological in nature. This may be entirely appropriate, since what is beyond our knowing is beyond our knowing - full stop. Yet I still feel that we should make some commitment to what our best inference therefore points to as regards what the world IS like. David Bohm took such an ontological approach. He also died believing that information stood alongside matter and energy as a fundamental component of nature. I am anxious to reconcile (at my surface level of understanding) his views with the emerging insights from Zeilinger's work.
While I was a light infantry platoon leader in Germany with the US Army, I got a chance to take a US platoon (30-40 men) through a 3-week course at the Centre d'Entrainement Commando on the French - German border. Although the main camp was located on the German side of the border, on the edge of the Black Forest, the training (as the name suggests) was run by the French. My platoon was attached to a French combat engineer company that was rotating through the course as part of its annual training calendar.
The US platoon I led was a composite one - half picked from across my own company and half from a US combat engineer unit from the same NATO brigade. The senior NCO was from neither of these units, as his main job was translating within the Protocol Office of the international headquarters in Heidelberg. He was there to help us communicate with our French comrades, in case my 6 years of French classes let me down. If this all sounds a bit complex, then you are getting the picture.
The idea of the course was to put small units and their individual members through stressful physical and psychological tests to help them bond and work better in the future. This objective was only partly applicable to us, because my bastard platoon would disband, with members heading back to their respective permanent units, as soon as the course finished. For us, it was more a chance to do some tough training and improve cross-national relations and understanding at a grass-roots level. The real pressure was to make sure that we did well in the course so as not to let our country down!
The first task was a timed five-mile road march, which the entire unit had to complete within a given time period. Failure meant being sent home from the course in ignominy. About half-way through, it became obvious that one of the NCOs from the engineer unit was having a very difficult time. He began lagging the rest of the unit. Coaxing, cheering, shouting and threatening all failed to get him to pick up the pace. His body was simply not up to it. In a rare moment of Rambo machismo, I took the pack from his back and strapped it onto my chest. I had been training a lot, so carrying two didn't kill me (although it did take the starch out of me!). He was able to catch up during the final mile, and the unit made it into the course - but not by much. We had to plan carefully how to help that guy through each of the tough events that remained before us. (He worked hard and did fine!)
I remember that much of the training had to do with conquering fear of heights or enclosed spaces (e.g. tunnels). Several of my men had these fears in spades, so it took a fair bit of psychology to figure out which buttons to push to get them through some things. The good thing was that it didn't leave time for me to worry much about the heights and tunnels, which might well have frightened me considerably if I'd had more time to take notice of them.
The hardest bit came when a severe claustrophobic had to crawl through a long sewer-like tunnel to gain access for the rest of the group into a depot we were meant to be raiding. He was a squad leader - in charge of 9 men. He was facing his worst nightmare, but he couldn't back down. If he did, all of his men would see it. That would spell the end to his days as a leader in that unit. We had a five minute heart-to-heart at the mouth of that tunnel, and he did it. He came out the other end crying and trembling, but no one cared about that. He had faced his fear, so he maintained (and amplified) the right to demand that his men do the same if and when the time came. I've rarely been more proud of anyone than I was of him that night.
The officers and NCOs had meals in a special mess. The breakfasts introduced me to a great French military tradition. When a person entered the mess, he shook the hand of each person already eating and said good morning. Each incumbent rose to shake the newcomer's hand as he approached. What a friendly way to start the day.
I became quite good mates with the second-in-charge of the French engineer company. My halting French combined with his decent English meant that we could communicate just about anything we wanted to one another. He was from Alsace, the French region just a few miles away, so he spoke good German as well. He admitted that he had not been impressed by our US unit in the early days, but that he was amazed how quickly we came together as a unit and managed to get through everything even though we had weaknesses as individuals.
One of my soldiers put his boots by the fire after we reached a rest camp on part of a long mission. We all grabbed a few hours sleep before moving on at sunlight. Unfortunately, the poor guy's boots had melted by the time he went to put them back on. Luckily, he had a second pair.
Each day we also had training in hand-to-hand combat. The (very tough) instructor latched onto one of our guys as his guinea pig for demonstrating submission holds. He stated proudly that one could make someone do almost anything by applying the right sort of pressure to a painful area. Upon wrenching my guy's wrist in an ugly way, he demanded the poor soldier take a bite of grass. I was on the verge of an international incident, as I felt I might have to intervene on this guy's behalf. The instructor gave me a look as if to say, 'Trust me on this one.' My soldier held tough for one excruciating minute then gave in. The instructor immediately let him up, offered him hearty congratulations for holding out so long, said he'd been made to do the same thing in earlier days and invited him to dine in the instructor's mess. Wheeow, glad that one ended okay.
Another of the instructors was new to the course and pretty junior as a soldier, but he was of southeast asian heritage and obviously extremely well schooled in the martial arts. I, for my sins, was asked to hold a small twig between my teeth while he did a reeling 360 degree flying kick. He flicked it from my mouth without leaving a scratch. We found out two weeks after returning to our base that the course had been hit by a bout of bacterial meningitis and that he had died from it. We must have made it out just in time.
The final exercise involved a long covert, foot movement through the Black Forest, with a raid at the end. These French engineers specialised in path-finding - laying out a route for others to follow, so they took the lead through most of it. Eventually, time came for us to forge the path. A number of my soldiers were pretty bushed by then, so we had to devise a strategy on the fly to split my unit into two parts. I would take the 'fast' group and mark the trail for the rest, while the rest of the unit moved at a more even pace.
My 'leadership' worked fine in getting the fast group through, but then it gave way somewhat to my more powerful 'sleepiness'. Despite trying to stay up and make sure that my second echelon made it in safely, I drifted off into un-leader-like sleep. My excellent second-in-command brought in the trailing group good as gold. The watch woke me, and we all celebrated completing the course successfully (and getting some really cool badges for our uniforms).
Still, drifting off seemed one of those things that MacArthur or Eisenhower (or my own best squad leaders) would not have done. It's one of the many small examples in which my weakness broke the surface into the light of day. I didn't have the resoluteness, the physical selflessness, to be a real leader in the Army. I've nothing but respect for those who do.
First posted 29 March 2005 - Bohm's eastern influence was primarily Indian / Hindu, but I see strong parallels now with Taoism as well. An amazing man trying to unite worlds that we too easily assume are distinct, incommensurate and irreconcilable.
At the end of my post on Tim Palmer, I related his model to that of David Bohm. There's a lot more to say about Bohm, and this post will be my attempt to pull it together.
David Bohm's name is associated with many things these days - his communist ideology (which cost him his academic post and nearly his freedom during the McCarthy witch hunts), his turn to Indian mysticism and close relationship with an Indian guru, his development of a new technique of dialogue for reaching more creative group solutions to problems and his call for a new scientific order. He did ground-breaking work in plasma physics and made important contributions to quantum theory (proposing the first EPR experiment, for instance), yet most of his work in quantum physics is viewed as outside the canon, ignored or embarrassingly dismissed by the physics community.
Bohm always wanted to understand EVERYTHING, and not just in its details but also in its WHOLENESS. His scientific, mystic and social views were inextricably linked.
The most useful metaphor for his model of the universe is that of the hologram. A hologram is sort of like a photograph, in that it is a visual representation of reality. But while a photograph captures only two dimensions, a hologram captures all three. When light is shone through a holographic plate, a three dimensional image is projected into the space before it. As you move around the image, you capture it from a different perspective, just as if it were the original object it represents. If the holographic image is of a person, you stand in front of it to see the face and chest; from the side you get a profile view; from the rear you see the back.
Yet there is something I think is even more interesting: if you drop the holographic plate and break it, EACH resulting piece of the former plate still can serve to project the entire image. Shine light through a small piece, and you'll still get the full three-dimensional image, just at a lower resolution. The smaller the piece of plate, the less well-defined the projected image. Contrast this with what happens when you rip a photograph in half: each half only shows you half of the image.
So, each piece of a holographic plate contains information about the ENTIRE three-dimensional image. How does this relate to the universe as a whole? Bohm believed that each particle in the universe contained information about the universe as a whole. I've put this sloppily, so let's look in greater detail at what he said.
One of the greatest (perhaps the greatest) mystery in science is demonstrated by the double slit experiment. I've explained the experiment elsewhere, so I won't go further into it here. Suffice it to say that the experiment suggests that particles fired individually through the test apparatus 'know' how they would have interacted (interfered) with one another had they been sent through together.
Physics has twisted itself into some amusing contortions (including the well-known ostrich head-in-the-sand trick) to account for this. Bohm believed that the particles themselves only 'knew' this because they were guided by a new field that he introduced, called the quantum potential. This quantum potential was holographic in its effects in that at any point in the universe, it contained information about the entire universe. Unlike other forces and fields in physics, its effects did not diminish with distance, so even very remote particles were in a sense linked by it. (Those steeped in quantum theory will recognise the link to the phenomenon of entanglement.) This potential was essentially a source of active information, intricately and infinitely enfolded (per chaotic non-linear dynamic systems) into scales below our ability to detect it.
This enfolded order that lay under the seemingly random behaviour of sub-atomic particles, Bohm called the implicate order, which he differentiated from our observable universe, the explicate order. The implicate order was deeper and more fundamental than the explicate one, but only bits of it could ever be unfolded at one time (hence Heisenberg's Uncertainty Principle).
In a later, quantum field theoretical version of the same basic thinking, Bohm added another, yet deeper order, the super implicate order. In this model, the particle was replaced by the quantum potential as the fundamental building block of nature. Particles were just focused knots within the quantum potential itself, and the evolution of the quantum potential over time was guided by the super-quantum potential. In fact, Bohm reckoned there could be (and probably were) an infinite number of these levels. Since the super-quantum potential was sensitive to pseudo-particle-level phenomena, a feedback loop arose, and this calls for another metaphor.
If you think of a video game, the screen images themselves are the explicate order (the particles, etc that we see in our world), the computer programme that dictates how the screen image alters as the game is played is the implicate order (the quantum potential) and the person playing the game and sending signals to the computer programme is the super-implicate order (the super-quantum potential). The loop is completed as the player adjusts his actions based on his perceptions on the screen. This super-implicate order is now the home of active information (but please don't see it, because of its analogy with the human player above, as an actual conscious thing).
Bohm was able to express all of this mathematically and to relate it to the more conventional mathematical formulae of quantum mechanics. His theory predicts observed behaviour just as well as the conventional methods. Yet it never caught on.
There are aesthetic grounds for this rejection, in that Bohm's interpretation gave a certain prominence to a particle's position (as opposed to its momentum). Penrose has said that Bohm's model essentially assumes that every measurement is a measurement of position. But the simplest explanation is that since the conventional view was already operationalised in the scientific community, and since Bohm's model made no different predictions than the conventional view, they should just stick with what they had. More cynically, you could say that physicists no longer cared about the ontological implications of the theories that provided their predictions.
One thing that strikes me as odd is that Bohm himself did NOT view his system as mechanical (deterministic). He felt that the feedback loops (per the video game metaphor) opened room for contingency. I just cannot square this. Feedback loop or not, the dynamics are deterministic, even if non-computable. Palmer's approach, which arrives at much the same place (active, holograph-like information enfolded minutely and hidden from view) albeit with a bit less metaphysical baggage, does not shirk from this.
What IS attractive about both - and let's remember that they are entirely consistent with experimental results - is the holism they bring to the universe. This holism brings nearly common-sensical answers to most of quantum theory's mysteries, and it does so in a way that does not violate the spirit of Einstein's relativity.
Everything is connected, not in some new-age way but ACTUALLY inter-related. Doesn't this just seem to FIT well with the notion of everything having started with the Big Bang? If the entire universe started in a quivering instability the size of a dime, it would be hard to imagine bits that were NOT related to the rest. We are all connected - to one another, to all living things, to everything that exists. A universe undivided.
I am fundamentally weak, in both physical strength and emotional resolve, so it's quite odd that I ended up as an Infantry officer in the U.S. Army. Just goes to show what a series of ill-considered decisions by an individual, coupled with low-quality screening on the part of large public bodies, can accomplish. It didn't take long for me to realise that I was more likely to follow in the footsteps of Gomer Pyle (okay, he was a Marine) than those of Patton and Bradley.
I showed up at my first unit - one of the few light infantry units in Germany, where tanks dominate the terrain - when my company was on a field exercise. The lieutenant whose platoon I was taking over (as he moved to another role in the company) let me borrow his equipment so I could get straight out to lead the next mock operation. I literally didn't even drop off my bags back at the garrison.
My platoon had three squads of about ten men each, plus a communications specialist, a medic and an NBC (nuclear, biological and chemical) specialist. They had been 'in the field' for a number of days before I arrived and were already pretty tired. They were, though, understandably excited to see their new platoon leader. I had the tough-man's short haircut and the badges to show that I was parachute and Ranger qualified. Surely this let them know I was a leader worthy of their respect???
We were to conduct what is called a 'movement to contact' in the wee hours between midnight and sunrise. A force embarks on this type of mission when they have a rough idea but no specific intelligence of where the enemy is. Essentially, it involves moving in a formation that lends itself to rapid deployment from traveling to fighting posture, so that when you encounter the enemy you can quickly transition to the attack.
My platoon sergeant, the oldest and most experienced member of the unit, was injured, so one of the squad leaders was acting in his place. Our plan was based on a standard template of such operations. I would travel behind the lead squad, with him just ahead of the trail one. The radio man was with me, the medic and most of the heavier weapons (machine guns) with him. When we met the enemy, his contingent would quickly pull up beside mine to gain and maintain a superior base of fire on the enemy forces. Then I would peel off with an assault force to swing around the flank while the platoon sergeant and half of the platoon continued to lay down covering fire.
I carefully mapped out our route and distributed the relevant compass azimuths and distances of each leg of the mission to the squads. After a thorough briefing, careful equipment preparation and detailed rehearsals of the scenario described above, we set out on the mission.
The movement was going well, but in the relatively featureless terrain I had a hard time (which I never admitted, of course) verifying our position on the ground relative to the map used in the planning and in guiding our movements. By the time that we had covered more than the planned distance to the enemy without any sight of them, and as the scheduled hour of the confrontation came and went, I had to stop the formation and convene a leaders' meeting to double-check our position relative to the map.
We (myself and these over-tired squad leaders and stand-in platoon sergeant) decided that we were actually very near where the enemy must be. I took an executive decision to quietly move the platoon sergeant and his contingent into a perfect position to lay down fire on the identified terrain. Then I set out with my assault team to sneak up on the enemy from the flank. When I gave the signal, we would spring a perfect surprise attack on the opposing force, none of whom had yet realised we were on their doorstep.
It was all coming together. In addition to demonstrating textbook planning and preparation and executing a good (if somewhat uncertain) tactical movement, I was exhibiting the sort of flexibility that came with real tactical genius. I was on a buzz; my men had shrugged off their sleepiness and looked sharp and poised. We stealthily swept around in an arc, knowing we were moments from dealing death to the baddies.
A shot rang out just ahead. One of the enemy must have spotted us. I ordered my assault team to return fire and launched a green flare - the signal to the platoon sergeant and his fire support team to start shooting as well - into the air. All hell broke lose. The rattle and cough of automatic weapons echoed in the pre-dawn darkness. The smell of cordite filled the air.
I moved my assault team forward in bounding rushes. First one half, then the other. Everyone moving in short bursts - three steps then hit the ground, three steps then hit the ground. We closed in for the final assault. Time to signal to the platoon sergeant to lift his fire, as we were about to sweep across the enemy position and didn't want to get shot by our own men - the ultimate tragedy.
Before I had time to launch the appropriate flare for that signal, I caught sight of several faces of the enemy, only to realise that they were not the enemy at all! My sweeping arc had had a rather grander swing to it than I thought. I had circled round completely. Both my assault team and the platoon sergeant's support team had inflicted heavy casualties, but unfortunately we had inflicted them on one another! In a spectacular display of tactical ineptitude, I had completely destroyed my own unit.
The actual opposing force was sitting a half mile away, it's men getting bored, waiting eagerly for sunrise and breakfast and wondering what all the fighting was off to the southeast.
My company commander, who always had a soft spot for me and luckily subscribed to the school of learning through mistakes, assured me that my unit and I had done many things well. My men were also strangely forgiving of the fact that I'd led them to slaughter themselves. Over not too great a time I was able to (re?) gain their respect and enjoy a great year, including many more field exercises.
My commander was right - we learn from our mistakes. Despite having bucket loads of fun with a quality bunch of guys, I left the infantry when I got the chance and left the military once I had completed my obligatory service. I'll leave the fighting to those better suited to it.
Originally posted 15 Mar 2005 - Phew, I can't believe I got that much to grips with the technical discussion back when I was more 'into it'. As I've mentioned in previous posts (I recommend you read If You Think You Understand This, Then You Don't and Bell's Inequality and Bell Revisited before reading this post), I'm not so exercised now about whether the world is deterministic and local. It seems quite likely that it is at least non-local, which fits with my best intuition at this point anyway.
Beginning with his 1995 paper, Tim Palmer, from the European Centre for Medium-Range Weather Forecasting, questioned the binding force of Bell's Inequality and demonstrated that wholly deterministic (although non-computably chaotic) non-linear dynamical systems could produce the apparent randomness of quantum state measurement while keeping our understanding of the universe on a local and real footing. He has refined his thinking and presented it in further papers in 2004 and 2005. I think that he is onto something real and big.
Through the happy chance of working with someone whose partner works with Tim at ECMWF, I got the opportunity to meet him and talk a bit about his thinking. Keep in mind that Tim's day job is in meteorological research, so his physics work is in his spare time. Although I clearly lack schooling in the range of mathematical tools necessary to follow all of the technical details, through reading his papers and talking for that hour or so, I've got a pretty good idea what he's up to.
The core points
There are two common and related themes to his physics work:
Although the evolution of the state vector through time is a deterministic one, the reduction of the system to an observable state appears to be random. Conventional QM takes this indeterminacy as given. Palmer thinks that the apparent randomness hides a chaotic dynamic that is simply too messy to untangle, which makes his approach what is known as a 'hidden variables' one.
Chaos theory uses the concepts of attractors and basins when speaking of how different initial conditions migrate via iterations of some non-linear operation toward some resting place. A resting place is called an attractor, and the collection of initial states that migrates to that attractor is called its basin.
What I have just said is, of course, a gross over-simplification. Not all non-linear systems converge to an attractor at all. Some just explode towards infinity.
Nor does an attractor necessarily constitute a single number at which the system settles forever. An attractor may be a cyclical one, whose cycle may involve simply flipping regularly between two numbers or may involve cycling through a sequence of numbers so long that it would not repeat in the history of the universe to date.
Also, not all basins are defined by smooth outlines. An attractor's basin may be very messy indeed, with any point within the basin having other points arbitrarily close to it that DO NOT belong to the basin. Such basins are said to be riddled.
Now imagine a system with two attractors: whose basins collectively cover the entire possible set of initial conditions; whose basins are of equal area (or volume, if the space is three dimensional) to one another; and whose basins are jointly riddled (that is to say, intertwined) as above.
It is possible to construct such a system that is so riddled that (given truncation errors) it is impossible to compute algorithmically which basin a given set of initial conditions belongs to. Given the equal size of the basins, there is a 50% chance that any set of initial conditions belongs to either basin. It is also possible to construct this system in such a way that it is consistent with other aspects of the formalism of QM for the measurement of bivalent properties like spin, and Palmer shows this.
There may be more work to do, but the point is that Palmer has shown that a deterministic system may exist that is consistent with QM.
What about locality?
But isn't such a system bounded by Bell's inequality, which is known to be violated by both QM prediction and experimental evidence? No, says Palmer, because Bell's proof makes an implicit assumption about certain counterfactual propositions having definite (yes or no) truth values.
Where does this notion of counterfactual reasoning enter Bell's proof? Let's remember the experiment that tests it. Zero angular momentum electron pairs (Right and Left) are emitted from a special source. One device measures the spin of each Right electron along some axis in the plane that is orthogonal (perpendicular) to the electrons' path. Another device measures the spin of each Left electron along one of two axes, each of which constitutes a different rotation (say x for one and z for the other) from the axis of the Right device. Bell's inequality is then a relationship among the measurements taken at these three (R, Lx, Ly) orientations.
The important thing to remember, though, is that for any given pair of electrons, only TWO of these measurements can be taken (R & Lx, or R & Ly). The theorem makes the assumption that the measurements among many pairs of electrons can be lumped together and then relates correlations within the large set. So, in fact, the relationship observed for any GIVEN pair of electrons is one of two:
The elements in italics are the counterfactual ones. In reality, ONLY x OR z can be chosen as the orientation for the Left member of any given pair. The assumed measure of what it would have been were the other angle chosen is taken from the statistical behaviour of the pairs whose Left element was measured at the other angle.
Determinism, Free Will, and the observer as part of the system
What is the upshot of all of this? I want to (try to) go into a bit more of the technical detail in a minute, but it is possible to think about this initially at a philosophical level. IF the universe is deterministic in the philosophical sense, then everything that happens (everything that has ever happened and will ever happen) happens NECESSARILY. It COULD NOT have happened any other way. Palmer shows with his demonstration of a particular chaotic system that determinism is consistent with QM observations.
So, in effect, we're saying that the observer only measured, say, R and Lx for a particular electron pair. And we're saying that the universe has evolved in such a way that - however free the observer felt himself to be in his choice of the L measurement orientation - he COULD NOT have chosen it to be y. So introducing a counterfactual proposition about what MIGHT have happened HAD he chosen y is meaningless. Even though it feels like a small hypothetical change in the context of a large universe, it is simply not within the set of possible states of the world.
As uncomfortable as many feel with determinism, because of its implications for our pure notion of free will, this is hard to get around. Neither the electron pair nor the observer can be taken outside the universe itself. And if the evolution of that universe is deterministic (as it is if it can be modeled by a non-linear dynamical system) then not only the spin measurements but also the orientations at which they are made follow necessarily from the initial conditions of the universe and the laws that govern is evolution.
Over our heads
Now, Tim Palmer expresses all of this in a much more disciplined way. He gives an example of a universe defined by a famous attractor, known as the Lorenz Attractor (named after the father of non-linear dynamics, who discovered it). This attractor is defined by three differential equations on three variables. If the initial conditions of the universe sit on the attractor, and if these differential equations govern the universe's evolution, then the smallest of perturbations to one of the variables will move the system off of the attractor (given the attractor's fractal nature), thereby violating the laws of the universe.
But Palmer needs to bridge a gap here. The wave function of quantum mechanics (defined by Schrodinger's equation) uses complex (i.e., using 'i', the square root of -1) linear dynamics. Palmer is talking about real (i.e. no square root of -1) NON-linear dynamics. How can his system do the work of Schrodinger's?
At this point, it gets pretty hairy for us non-mathematicians. Palmer introduces a new definition of i as an operator on a sequence of real numbers. Quantum states can be defined by sets of these sequences, and Palmer shows how his i operator performs in a way analogous to the maths of the upward cascade of fluctuations in a turbulent flow (something from his meteorological world).
The effect of these steps is to present a way of describing the state function in granular (like the quantum world itself) terms rather than in the continuous terms of the Hilbert space that is used in conventional QM. Applying this to the test of Bell's inequality, this means that we can't pick any angle in a continuum but are instead confined to a finite (but as large as we wish) set of angles. Palmer proves that there is no way that measurements for both the Lx and Ly angular differences from the R orientation can be simultaneously defined. All of this amounts to the more rigorous and mathematical proof of the point I made philosophically and sloppily in the section above. The bottom line is that any real physical state must be associated with a computable real number (even if the only way to compute it is to let nature 'integrate' it through a physical experiment!).
Where does this take us? If we re-interpret the wave function as a set of binary sequences as described above, we can think of the elements of those sequences as 'real' bits of quantum reality, which means that even in the absence of a measurement, we take the quantum state to have definite values rather than a superposition of possible values.
Also, a sequence itself encodes information not just about the system it describes but also about that system's relationship to the whole. Palmer uses an analogy with the DNA in our bodies' cells. This hearkens back to the explicate and implicate order in David Bohm's interpretation of quantum theory. Look for more on Bohm in an upcoming post.
First posted 5 May 2005. These days... actions, words, beliefs are all equally 'parts' of what happens. What a person says and does is what the person is. The speaking of the words is just a subset of the actions. The actions owe no consistency to one another, but rather each renders consistency with the moment in which it happens, of which it is a part.
Are a person's actions the true expression of their beliefs? Part of me thinks so. I think the existentialists have a point when they say the real votes are the ones that we make with our feet. If you say you value integrity but routinely tell white lies, then you really don't value integrity (at least as it applies to you). Our actions define us.
Yet I have a couple of doubts. The first one, you might call Catholic. The Catholics (among others) recognise our fundamental human frailty and might say that the white lies in the example above do not speak against the person's values themselves, but rather against the person's discipline and strength in attempting to live by those values. I have a little time for this angle, but not much.
The more significant doubt is based on the unconscious activities of our brains, and it really comes down to the definition of belief. If we define a belief as a wholly conscious mental product, and if we admit that many of the drivers of our actions are sub- or unconscious ones, then we would have to disagree with the existentialists. We believe one thing as conscious beings, but we are not ONLY conscious beings. It is unsurprising that our actions, which have sources outside the conscious realm, do not speak with the same voice as the conscious mind.
On the other hand, if a belief is a mental entity that includes not just conscious components but unconscious ones as well, then I guess we would say that the conscious mental formulation or utterance that we imprecisely call a belief is actually something thinner and less complete than the real belief - just a shadow of a belief. This, I guess, paves the way back to the existentialist conclusion that only the 'whole package' (both conscious and unconscious) as demonstrated through action constitutes the real belief.
In the summer of 1987, I reported back to the U.S. Air Force Academy, where I'd spent a semester on exchange from West Point the previous year. This time, it was for a three week training programme in Survival, Evasion, Resistance and Escape - a course designed for current and future pilots, in case they get shot down behind enemy lines.
If I remember correctly, the first couple of weeks were very soft, unlike Army courses, where there tended to be hazing for hazing's sake, this one was very civilised until the time came to impose a hostile scenario to consolidate the learning. The survival phase was mainly classroom work, other than a 'survival meal' in which we (in small groups) had to kill and eat a rabbit and a chicken. I'd had to do that in previous courses I'd done anyway. Things got interesting when we launched into the evasion phase. Three man teams were designated to navigate from a place where they were notionally shot down, via partisan camps and avoiding enemy patrols, to a point of safe passage to friendly territory.
Another Army guy was in my small team. Our Air Force counterpart badly sprained his ankle relatively early on the first day, when we had three days walking and many wooded miles to cover. I have to say, he was incredibly stoic and brave, but still he had to lean on one or both of us. Of course, we had only minimal equipment and next to no food. We purified water from mountain streams or lakes with iodine tablets so as not to fall prey to dehydration.
We managed to avoid the enemy patrols, who concentrated disproportionately on obvious points like open space and road crossings, where lazy teams would wander to minimise the distance they had to travel. The smart money was on putting in the extra distance in order to avoid those traps, but that meant that the pressure was always on to ensure we didn't miss the time windows for presenting ourselves at the partisan camps, where we could get stew or other sustenance.
The resistance phase was 24 hours in a simulated POW camp. We were blindfolded and placed in solitary confinement - including little cramped boxes one could barely fit into by sitting and hunching over in a ball. This didn't bother me particularly, as I quite like spending time on my own and don't mind close spaces. I do remember, though, as I do from most of my military training courses, just being terribly impatient with the fact that my freedom was so restricted.
I was a bad student in that I never immersed myself in the scenario to get the most from it. I always satisficed AS A STUDENT rather than stepping fully into the role AS A PRISONER or whatever other role I was cast in. This is not to say that I never played the game. During interrogation, I gave no useful information and even managed to stick to a consistent story of misinformation. But how hard was that? They couldn't exactly chop my fingers off, kick me in the nuts or threaten to kill my family. They could only put me into some temporarily uncomfortable 'stress' positions that I knew caused no lasting damage.
As with most of my military training, I learned at least as much about myself as I did about the specific content of the course.
'A cadet will not lie, cheat or steal, nor tolerate those who do.'
Thus spake the Honor Code at West Point. Anyone deemed to be in violation of it had to appear before an 'Honor Board' in which the alleged facts of the case and any defense were presented to a 'jury' of peers, who would decide whether the charged cadet was 'found' (guilty) or 'not found.' A cadet found on an honor violation was punished severely, most often by expulsion from the academy.
The rationale for the weight placed on the honor code lay in the absolute trust that one officer must have in another in the profession of arms. As an officer of the state's armed forces, one's character and actions had to be beyond reproach. We all took it very seriously.
The first three elements of the code were relatively simple:
Don't lie - period. Not about your age when trying to buy alcohol, not about where you were when a surprise inspection the night before had detected you were not in your own room.
Don't cheat - period. Not on your homework. Not in an exam. Not when doing your push-ups for the physical fitness test.
Don't steal - period. This one, unlike the two above, hardly ever tripped anyone up.
The fourth element of the code - called the non-toleration clause - was more personally demanding, as it required that you report any known cadet infringements of the code. It didn't matter whether the culprit was someone you didn't know or your best friend, a rival or someone you owed a favour to. If you were found to have known of a violation and to have failed to report it, then you were in violation yourself.
My sense was always that cadets accepted the first three elements without question, but that some harbored doubt about the non-toleration clause. The trouble lay in the clause's perceived undermining of the value of camaraderie - another essential glue among military professionals. You had to know that your buddy would be there for you, no matter what. You were a team, in it together. Yet the non-toleration clause could be seen as flying in the face of that tightness.
In the end, I subordinated camaraderie as a stand-alone value to the principle of non-toleration. This was, of course, in keeping with what the academy wanted us to do, and I bought the official reasoning: camaraderie, team spirit, is not commendable when it serves an ignoble end (e.g. lying, cheating, stealing). Were we to elevate camaraderie above our ethical principles, we might find ourselves supporting cover-ups of looting, massacres, rapes or genocide during war, in the interest of 'protecting buddies'. I certainly didn't think that would be right. I do think that most at the academy bought into the non-toleration clause as I did, but it wouldn't shock me to learn that a (quiet) minority prioritised camaraderie instead.
I graduated from West Point in 1988. In 2002, I received a message from another academy grad, asking me to get in touch. I must have copied the phone number incorrectly, because I was unable to reach him. He left a further message and expressed a certain urgency to speak with me. Although we knew one another pretty well as cadets, we had never been especially close friends. Without other clear ideas for why he might be phoning, I suspected he might be looking for a job with my current employer and hoping for some help.
When we finally caught up with one another by phone, we engaged in the usual talk-once-a-decade chit chat about where our lives had got to, etc. He then adopted a very sober tone and said that something had been digging at his conscience for years and that he needed to make a confession to me.
He went on to remind me (I had no recollection) that he had been charged with an honor violation during my final year at the Academy and that he had called me as a character witness. I 'testified' as to my views of his character at the time, and in the end - on the basis of all the assembled evidence - he was not found. His confession to me in this phone call, you will have guessed, was that he had committed the offence, the details of which I can't remember.
It had obviously taken some real courage for him to come out with that, and I told him that I appreciated his call and admired him for undertaking to set the record straight with me. He did the same with every person who was involved in the case, and indeed with the Academy itself. For me, that is sufficient to expunge the stains from that period of weakness at West Point, but I'm not sure what the Academy's official view is.
Can honor, once lost, be recovered? I would like to think so.
I'm curious. I like looking beneath and behind the obvious, also looking for what is between me and the obvious, obscuring or distorting my view.