# Pedagogy

An amusing XKCD.

That was the question I always had when people explained how wings worked and the Bernoulli Effect. The answer, of course, is that there are lots of ways to get lift, but that this is the most efficient one with the least drag. You can get lift from a barn door. Stick your hand out the window in a fast car, and you can get lift by just increasing the angle of attack, but the L/D is terrible. So when aerobatic planes are upside down, they have to keep nose up (down, from the pilot’s perspective) and up the thrust quite a bit to maintain altitude.

## 50 thoughts on “Pedagogy”

1. There is also the fact that the geometry is not fixed assuming you have flaps. Some combination of engine thrust and flaps may only allow you to fly until that sudden stop.

2. not spam says:

The best explanation for aerodynamic lift is momentum exchange.

Air is accelerated downward, so according to F = dp / dt there is an upwards force created.

Simple physics (E=1/2 m v^2) then leads you to the conclusion that you need to work with as much air as possible but deflect it only by a small amount in order to have good L/D. Hence the high aspect ratio wings of sailplanes.

3. Jane Bernstein Rosen says:

I have a friend who explains it as “Air Go Down, Wing Go Up.” Anything that deflects air downwards, efficiently or otherwise, is going to suffer a reaction force that causes lift.

4. Actually, the physics of it has always seemed pretty simple to me:

1) Disturb the airflow as little as possible
2) Use the Pythagorean theorem as applied to forces

So you take an airflow and very slightly deflect it down. Because the change in “forward” air velocity is far lower than the change in “vertical” air velocity (due to the sum of squares law), the vertical force greatly exceeds the horizontal force. The lower the angle of attack, the higher the ratio of the forces.

The standard airfoil just is a low drag airfoil with a built-in angle of attack. Aerobatic planes often don’t have an angle of attack built in, and fly just as well upside down as right side up. As long as you are not stalling, the same is true of other standard airfoils – the airfoils are just designed to stall earlier upside down than right side up, since planes don’t normally fly upside down.

So your last statement is not necessarily true – you can often maintain the exact same throttle level in inverted flight, as long as you don’t push the envelope for your airfoil.

5. Bruce Hoult says:

That there is lift at all in this diagram is only an artifact of “Angle of Attack” being defined as relative to the longest line segment that can be draw with its endpoints within the airfoil. With this definition a non-symmetrical shape will generally have non-zero lift at an angle of attack of zero.

It might make more sense to define angle of attack such that an AoA of zero is the orientation that gives zero lift. Unfortunately this can in general only be determined by experiment (or CFD these days), not on the drawing board.

No doubt it’s too late to change the definition now.

6. cthulhu says:

Well, Jane’s friend is closest here to the true effect – the wing does indeed push the air down which leads to a force that causes lift. But the most important effect is the circulation that develops around the airfoil – this circulation is necessary to enforce the Kutta-Zhoukouski condition, which causes the trailing edge of the airfoil to be a streamline of the flow. A sharp trailing edge is necessary for this to happen. One of the best layman’s explanations of this I’ve seen is on the site http://www.av8n.com along with a bunch of other useful flight material (and physics stuff too).

David’s Newtonian approach to lift is only valid at low angle-of-attack at hypersonic speeds, as it completely neglects the circulation effect. I also disagree somewhat with the “built-in angle of attack” concept. Most main wing airfoils are cambered – when looking at a cross section of the airfoil, the mean thickness line (the camber line) is displaced vertically from the line connecting the leading edge and the trailing edge of the airfoil (the chord line). This is similar to but not the same as installed wing incidence, which is the angle the wing chord line makes with the centerline of the aircraft, and is truly a “built in angle of attack”. Nonzero camber makes the wing less symmetrical and therefore makes the positive and negative stall angle-of-attack different; more importantly for most aircraft designers, it changes the drag characteristics of the airfoil at a given lift, so that you can optimize the wing camber for the typical cruise lift needed to minimize the drag. Not as big an effect for aerobatic aircraft, but still a consideration. Camber also changes the moment characteristics of the airfoil, which has stability and control implications.

Thus endeth the lesson… 🙂

7. not spam says:

cthulhu: All these high level explanations like the Kutta-Zhoukouski condition are just explanations on _how_ the wing accelerates air downward. And they are immensely useful when trying to build an efficient wing.

But there has to be downward acceleration of air, otherwise there is no lift. Lift certainly is not caused by electromagnetic interaction, gravity, weak or strong force. So the only thing that remains is momentum exchange.

8. What’s crazy is that the most efficient airfoil design has been improved on very little since the Wright Brothers. Most gliders before their time used wings that were modeled after a bird’s wing. However, when the Wright’s built a glider using the most advanced understanding of the wing design at the time they realized that they were not getting anywhere the amount of lift that was needed. So, they threw out all the texts written by the so called “experts” and decided to do their own research. They quickly realized that building multiple full size gliders of various wing designs was going to be time consuming and expensive. So, their novel approach was to build the world’s first wind tunnel and test wing sections of various shapes until they found the optimal one. Despite all the advanced knowledge and sophisticated computers of our time we’ve only been able to increase their wing’s lifting efficiency by a few percent.

9. Cthulhu,

I had thought that the circulation effect could just be considered as “Disturb the airflow as little as possible”. I realize the using Newtonian physics (specifically, newtonian deflection of the air) only works at hypersonic speeds, but isn’t it still true that L/D being larger than 1 is caused by the squares law, applied to net air movement?

I find that to be a useful analogy – you can do the same thing with a rocket engine, for example: take a 10 G force engine, point it at 6 degrees from horizontal. You get 1 G of vertical acceleration, plus 9.95 G of horizontal acceleration. So you can get almost “free” lift.

10. not spam says:

Newtonian physics works for all speeds. Not the naive notion of air molecules as billard balls. But the fact that if you look at a volume of air at rest before the passage of the plane, it will move downward after the passage, regardless of how the wing is formed. The interaction of the air with the wing close to the wing might be arbitrarily complex, but whatever the interaction is, after the wing has passed the air is moving downward.

An efficient plane will interact with a very large volume of air, so the downward movement will be very small. But it must be there, otherwise there can not be any lift.

There are only a few fundamental ways to generate a force: gravity, electromagnetic interaction, strong and weak nuclear force, and accelerating reaction mass. Strong and weak nuclear force are out because they don’t work over long distances. Gravity is what makes you need lift in the first place. Electromagnetic interaction is also out, so all that remains is accelerating reaction mass.

11. AstroMathman says:

“there has to be downward acceleration of air, otherwise there is no lift” — fails to explain why hot air balloons or helium balloons fly.
Downward acceleration is one method. Buoyancy is another. Decreasing the air pressure above a surface will result in a upwards differential pressure, creating lift. I once saw a guy ‘fly’ a screwdriver by blasting a stream of compressed air across the end of the handle. The speed of the air across the handle was so fast that there was essentially no downward air pressure, leaving a net upwards air pressure that lifted the screwdriver.

12. Frank says:

I’d opine that REAL aerobatic aircraft designed for inverted flight (for the sake of arguement say it’s inverted half the time during a performance) will have a wings with symmetrical top and bottom cambers. So except for things like fuel flow and oil recovery while inverted, the plane could care less whether it was inverted or not.

13. Doug says:

Here is someone who thinks differently about the whole concept!

http://www.seykota.com/rm/

Thinks Bernoulli is full of it.

14. larry j says:

High performance aerobatic planes like the Extra 300 or even the more more modest Decathlon have symmetrical airfoils. The curvature for these wing sections is equal on the top and bottom. They depend on angle of attack to generate lift regardless of whether they’re rightside up or upside down. This makes for better aerobatic performance.

A plane with a non-symmetrical airfoil needs to maintain a more pronounced angle of attack to fly upside down than rightside up. It’s readily apparent if you watch a video of an old design like the Stearman or a Waco biplane doing an airshow act.

15. Toes192 says:

As a professional (now retired) pilot …
(USMC… Continental… Saudi Arabian Airlines) for 38 years with …
Maybe 25,000+ hours flying in real airplanes… let me make it clear for you geniuses…
.
Push the yoke… Airplane goes down…
.
Pull … It goes up…
.
Got it …?

16. Michael Antoniewicz II says:

Well, if they could get the ‘Hopeless Diamond’ to fly, then I can see getting a barn door too also.

Although, iirc, the aerodynamicists at the Skunk Works came at it backwards (they could get a bard door to fly so they’ll get the ‘Hopeless Diamond’ in the air and controllable to boot!). 😉

17. MPM says:

According to the Wikipedia page on lift and the sources quoted in it the cartoon illustrates the “Equal Transit-Time Fallacy”. Yes, the air on top goes faster, but it doesn’t meet up with the air at the bottom.

18. Bart says:

not spam Says:
October 12th, 2010 at 8:29 am

“There are only a few fundamental ways to generate a force: gravity, electromagnetic interaction, strong and weak nuclear force, and accelerating reaction mass.”

There are FOUR fundamental ways, and “accelerating reaction mass” is not one of them. They are: Gravity, Electromagnetic, Weak, and Strong. “Accelerating reaction mass” always comes about because of one of these four. Most everyday reactions with which we are familiar are either gravitational or electromagnetic. When you push an object to skate across the floor, that is electromagnetic, reactions on a micro- scale involving repulsion between the atoms in your fingertips and the atoms locked in the object’s embrace.

cthulhu and AstroMathman are essentially correct. The key to flight is pressure differential.

19. Pete says:

While the circulation theory of lift is obviously correct in an all roads lead to Rome kind of way, in the simple case it is somewhat akin to going to Rome via the South Pole.

Basic momentum theory seems to serve as a far more useful general theory and one that most people eventually arrive at (pedants excepted), even if they were originally taught otherwise.

20. I checked the code in the matrix. There is no lift and you need no wings.

Oh… and there is no spoon either.

21. Toes192 says:

I pushed the “submit” button …
.
Is posting here more complicated than that …?
.
btw…I forgot to mention…
.
Swivel the yoke clockwise and the airplane turns right…
.
Swivel the yoke counter-clockwise and the airplane turns left …
.
I think that completes your lesson on flying for now …
.
Oops… the rudders… I never was quite sure what one used them for …

22. Leland says:

Toes,

I thought when you pushed the yoke, the trees get bigger. When you pull back, the trees get smaller.

23. Attempting to refute the Bernoulli principle explanation for providing lift has been a cottage industry in the scientific fringe community for decades. The Newtonian laws of motion explanation has been proven for decades as well. The two are not in conflict, they provide two explanations for the distribution of forces.

My theory is that people don’t like the Bernoulli principle explanation because it doesn’t approach the problem from a typical physics perspective. In fact I believe it was originally derived empirically, and the mathematical derivation was produced after the principle was well established. Also the pure application of Bernoulli’s principle requires an incompressible fluid, and air is highly compressible, which makes it seem like a bit of convenient hand-waving (“Oh, we’ll just assume that the air is incompressible, it still works!”).

Regardless of which way you examine the lift effect, both Newton’s Laws and Bernoulli’s principle eventually boil down to “air goes down, wing goes up”.

It will probably eventually require a quantum mechanical explanation to truly explain how lift is produced by a wing in a fluid medium. In the end I suspect it’s all about proton’s surfing the quantum foam.

24. jack bunce says:

Yoke? Real airplanes don’t have yokes… they have sticks… and rudders, too. The latter are useful for picking up wings when flying very slowly, canceling out p-forces on takeoff, and mitigating adverse yaw in aircraft with ailerons.

Toes 192 the stuff you flew went way too fast!

25. not spam has it right.

I once saw the effect of the air being moved down by the airplane. The Royal Australian Air Force wanted to do position error measurements on the Pilatus PC-9 (T-6 in the USA)as they had conflicting information from the manufacturer. As this was just before GPS was available the plan was to fly the aircraft at 100 feet over a point on the ground while tracking with a kinetheodolite as various airspeeds. I had built them a pair of very stable high resolution pressure altimeters(one foot resolution), one of which was installed in the back seat of the airplane and the other on the ground under the flight path. Knowing the pressure and temperature on the ground and the geometric height of the airplane above the ground point from the kinethedolite film, from the real static pressure at the airplane and that observed on the hi res altimeters the position error could be derived.

As the aircraft flew overhead the altimeter on the ground showed a decrease in altitude(increase in pressure) of one to two feet. Quite repeatable and consistent.

26. gebrauchshund says:

Balloons don’t fly, they float.

27. betheweb says:

While pushing the stick forward will make the trees get bigger and pulling it back will make them get smaller, continuing to pull back on the stick will eventually make the trees get larger.

28. Carl Pham says:

Here’s a fun demonstration of a peculiar way of generating lift.

Also, just to keep the chaff blowing, this is not correct, Bart:

When you push an object to skate across the floor, that is electromagnetic, reactions on a micro- scale involving repulsion between the atoms in your fingertips and the atoms locked in the object’s embrace.

The repulsions between atoms responsible for the solidity of matter are not actually classically electromagnetic in origin. These “excluded volume” forces are strictly a quantum mechanical effect, founded on the fact that fermions (electrons) cannot occupy the same state, and hence cannot be in the same location and have roughly the same energy at the same time. Hence, if you want to push electrons into the same physical space, you must boost most of them to very high energy states, which would require enormous forces.

These forces would operate even if electrons were uncharged (but still fermions), and in fact the uncharged example is the excluded volume forces that prevent neutron stars from collapsing under their own weight.

So, really, it’s fair to speak of five forces of nature: the strong and weak nuclear forces, electromagnetism, gravity, and quantum exchange-correlation forces. I think the only reason physicists don’t is because the quantum forces are strictly many-body effects: they are not associated with a quantum field or force carrying particle.

29. Shawn Coyle says:

Check out ‘See How it Flies’ for a complete understanding of lift.

30. It might make more sense to define angle of attack such that an AoA of zero is the orientation that gives zero lift. Unfortunately this can in general only be determined by experiment (or CFD these days), not on the drawing board.

Wouldn’t that make the definition of angle of attack (a) dependent on Mach number, and (b) pretty hard to compute and to send to the instrument panel?

31. AstroMathman says:

Downward acceleration is one method. Buoyancy is another. Decreasing the air pressure above a surface will result in a upwards differential pressure, creating lift.

I think you are confusing different things here. “Buoyancy” refers to the net pressure force that arises from the gravitatational field gradient. Every extended object in a fluid under gravity experiences a buoyant force. Depending on the object’s mass and the other forces involved, buoyancy may or may not be negligible. It’s negligible when designing a fighter airplane, but not when you’re designing a zeppelin.

When you start talking about airfoils in a flowfield, yes, there is a pressure difference between the upper and lower surface, but that force is not “buoyancy”. Only a tiny, negligible part of the pressure difference is due to gravity.

32. Bart says:

cthulhu and AstroMathman are essentially correct. The key to flight is pressure differential.

Yes, but the question is: what causes the pressure differential? The Bernoulli “explanation” is fundamentally incorrect.

33. CosmicConservative says:

My theory is that people don’t like the Bernoulli principle explanation because it doesn’t approach the problem from a typical physics perspective.

About 15 years ago we batted this question around in the SCIMATH forum on CompuServe. When I came into the discussion I held generally the view you’re espousing, that the “Newtonian” and “Bernoulli” views were just different ways of expressing the same end result. In the course of the discussion, though, I came up with a number of reasons I didn’t like the Bernoulli explanation, and found no fundamental problems with the Newtonian approach.

The real problem with the Bernoulli approach is that it depends on a simplified (an incorrect) notion of what the flowfield over the airfoil is doing. Specifically, it assumes that the air above and the air below the foil must travel the chord in the same time, and that if the airfoil is drawn with a flat bottom and a curved top, the air above must be traveling faster.

There are some problems with this picture. Problem #1 is that even flat airfoils (“barn doors”) have lift if you put them at an angle of attack. Problem #2 is that if you have a curved uniformly thin foil, even at zero angle of attack it will have lift, but the flow above and below travel exactly the same distance, so Bernoulli would predict zero lift. Problem #3 is that real airfoils have boundary layers, so the flow velocity at the airfoil surface is exactly ZERO and again Bernoulli would predict zero lift. Problem #4 is that a symmetrical diamond airfoil placed at an angle of attack in a supersonic flowfield has a pressure distribution that is more or less exactly determined by oblique shock and expansion fan theory — and shocks create entropy, and thus you can’t apply Bernoulli’s equation to this airfoil. Problem #5 is that airfoils are often equipped with ailerons, and the aileron effectiveness is not computed correctly by the Bernoulli paradigm. I had more reasons, but hopefully you get the picture.

The thing is, if you want to express the lift in terms of the pressure distribution on the wing surfaces (which you can, obviously — it’s just that you can’t compute the pressure correctly using Bernoulli’s equation), it’s probably more correct to integrate the pressure perpendicular to the streamlines than along the streamlines. Bernoulli’s equation is what you get when you integrate the equations of motion along a streamline. However, if you integrate the momentum equation in streamline coordinates, you find that the centripetal acceleration due to streamline curvature gives rise to a pressure gradient. What does this mean? It means that for the flow moving on an upper cambered surface, curving away from the distant uniform flow, the pressure at the surface is lower than ambient. And for the flow moving on a lower cambered surface, curving towards the distant uniform flow, the pressure at the lower surface is higher than ambient. And this observation applies even if the upper and lower flows have the same speed, and even if the velocity goes to zero at the surface due to boundary layer effects.

34. Carl Pham says:

he centripetal acceleration due to streamline curvature gives rise to a pressure gradient

That is the single most interesting comment on airfoils I have ever heard.

35. R Anderson says:

Problem #3 is that real airfoils have boundary layers, so the flow velocity at the airfoil surface is exactly ZERO and again Bernoulli would predict zero lift.

Disregarding the lift/no-lift aspect of that problem, the boundary layer only serves to “thicken” the wing, as the free-stream encounters it. The same effect is seen in Rayleigh flows, where a tube of sufficient length will naturally accelerate whatever flow (subsonic; for supersonic flows the effect is reversed) passes through it, until a natural limit (and converging; the supersonic flows experience this limit as well) of Mach 1.0 is reached. This is also part of why efforts to reduce boundary layer effects have such a positive impact on drag reduction – without reducing metal, you’ve still reduced the effects of its presence in the flowfield.

On the other hand, there’s always the Michael Bay Principle of Aerodynamics: Any shape you can imagine will fly – if there’s sufficient thrust available…

36. Carl:

In streamline coordinates, the component of the pressure gradient in the “normal” direction (perpendicular to the streamline, in the osculating plane) is equal to rho*V^2/R, where R is the radius of curvature, rho is the density, and V is the flow speed. This statement is for steady flows without gravity. If you want to include gravity you have to modify “P” to be P*=P+rho*g*z. Unsteady flows require terms arising from the partial derivative of the velocity with respect to time.

37. R Anderson says:

The same effect is seen in Rayleigh flows, where a tube of sufficient length will naturally accelerate whatever flow (subsonic; for supersonic flows the effect is reversed) passes through it, until a natural limit (and converging; the supersonic flows experience this limit as well) of Mach 1.0 is reached.

Do you mean “Fanno line” flows, i.e. flows with friction? The Rayleigh line is for heat addition. Neither of these, BTW, has anything to do with boundary layers per se, although real flows with boundary layers can mimic them.

38. P Agle says:

In fluid dynamics, Bernoulli’s principle states that for an inviscid flow, an increase in the speed of the fluid occurs simultaneously with a decrease in pressure or a decrease in the fluid’s potential energy.
1. Yes, Bernoulli’s principle does work and can be demonstrated with a manometer.
2. Air is thin enough for the inviscid flow assumption to be valid.
3. The wings are shaped with a longer top path and a shorter (straight) bottom path so there will be a Bernoulli effect.
4. From observation wings do seem to have an upward turn so there is a Newtonian effect.

Bottom line – I’m not sure what the discussion is about. Both effects are in play and the Bernoulli effect is going to make a low drag contribution to lift. If you put pressure sensors on the top and bottom of the wing the ratio of Bernoulli to Newtonian lift could be computed.

39. Bart says:

Carl Pham Says:
October 12th, 2010 at 3:09 pm

‘These “excluded volume” forces are strictly a quantum mechanical effect, founded on the fact that fermions (electrons) cannot occupy the same state, and hence cannot be in the same location and have roughly the same energy at the same time.’

There has to be more to it than that. At what distance does this “fifth force” become significant? Is it inverse r^2 or some other relationship? Wouldn’t there have to be a force carrier exchange?

I’ve browsed a few web sites. It appears this is an open question in physics. here is an interesting recent paper.

40. Carl Pham says:

Well, it depends on what you mean by “more.” Excluded volume force doesn’t have a range per se, because it’s not associated with a field, and there is no force carrier particle. You’re thinking of it as a direct interaction between particles, which it is not, any more than the “force” that prevents particles from exceeding the speed of light is the result of an interaction with other particles. It’s rather a strictly many-body effect, as I said. It doesn’t exist in any one-particle (e.g. mean field) theory, although of course people hack up effective mean fields that capture some of the effects.

People sometimes speak of exchange-correlation forces having an exponential fall-off with distance, because if you think of the many-body wavefunction as built up out of single-particle orbitals, the exchange-correlation energy is proportional to various overlap integrals of the single-particle wavefunctions, and these tend to fall off exponentially with separation between important centers, e.g. the distance between atoms in two objects. simply because single-particle orbitals for spherically-symmetric potentials fall off exponentially.

I’m not sure what you mean by an “open” question, either. Certainly no one doubts the nature and importance of excluded volume forces. Indeed, they dominate the physical behaviour of nearly all condensed phases (liquids and solids). The underlying origin, that fermions will not occupy the same quantum state, stems directly from the assumption that particles are strictly indistinguishable and that all observables are represented by Hermitian operators on the wavefunction, both core axioms of quantum mechanis.

The fact that all fundamental particles, electrons in particular, are fermions — they could be bosons, or some other weird mixed-symmetry thing — has no explanation of which I’m aware. It’s just one of those True Facts about our world.

41. Bart says:

“Certainly no one doubts the nature and importance of excluded volume forces.”

Yes but, this is like saying nobody doubts the nature and importance of gravity. It does not convey any information about the actual mechanism.

The journal article I linked to is from “Progress in Physics”, which Wikipedia describes as an “alternative American scientific journal,” which does not sound very authoritative, so I guess the author’s suggestion that the force is mediated by “magnetons” is at least as likely not as so.

But, somehow, information must be exchanged to tell the electrons “don’t go there”. There has to be a deeper explanation. As I cannot find one which appears well accepted, I must presume the subject lies on the periphery of the unknown.

One other thought occurs to me: what of composite bosons? If I slam one of them into the other, what happens?

42. Bart says:

But, somehow, information must be exchanged to tell the electrons “don’t go there”.

Well, yes and no, mostly no.

Consider a simpler system: the hydrogen atom. You are perhaps familiar with the way hydrogenic electron orbitals are enumerated: 1s2, 2s2, 2p6, etc… A single neutral hydrogen atom has one electron, which can occupy the 1s1 ground state or any excited state; transitions between states give rise to the famous Lyman, Balmer, Paschen, etc., series of spectral lines. What you may not be familiar with is that these orbitals are solutions of an eigenvalue equation, the Schrodinger equation for the Coulomb attraction between a point nucleus and a point electron. So the starting point is the description of the force between the nucleus and the electron, which is the classical Coulomb inverse-square force — expressed in terms of a Hamiltonian or energy functional H(p,q) where p is momentum and q is displacement; the Coulomb potential energy of course goes as 1/r.

Now, what happens when we add electrons to the system? e.g. suppose we try to model a helium atom with Z=2 electrons. You have to add the Coulomb repulsion between the electrons to the Hamiltonian but otherwise the situation is very similar. In fact you get a very similar eigenvalue structure, 1s2, 2s2, etc. except the actual energies are a little different.

The fun really begins when you add a third electron, e.g. lithium (Z=3). It turns out that the ground state is not 1s3 — there is no 1s3 orbital! And the reason is a little subtle. It turns out that for spin 1/2 particles like electrons, the multi-particle wave function changes sign when you interchange two identical particles (this is a result of the “spin statistics theorem”). And it also turns out that spin 1/2 particles can only have two independent spin states, spin up and spin down (aka m=+1/2 and m=-1/2). So when you have three or more spin 1/2 particles, at least two must be in the same spin state. If it were possible for the electrons to have the same spatial eigenstate as well as the same spin state, the wave function would not only change sign, but would be invariant under interchange. That in turn is only possible if the wave function is identically zero (what is the solution of x = -x?), i.e. the electrons are nowhere…. That’s a long-winded way of explaining the Pauli exclusion principle!

The really important part of this is that Pauli exclusion is not the result of any term in the Hamiltonian — it’s not the result of a “force”. Yes, there are Coulomb repulsion terms, but they have essentially nothing to do with quantum mechanical exclusion. Pauli exclusion is really the result of the symmetries of the wave function for fermions (half-integer spin particles). And there is a deeper reason for that, but it’s buried in the spin-statistics theorem….

Do you want to know more?

43. Carl Pham says:

But, somehow, information must be exchanged to tell the electrons “don’t go there”.

Ah, ok, I see where you’re going. Well…these are indeed deep waters. What you’re asking about, in a sense, can be roughly equated to asking how an electron at A “knows” that the nearby amplitude of the wavefunction of an electron currently still at B (but approaching A) has become nontrivial. That’s actually a pretty corrupt way of phrasing the question, because it’s a mishmash of classical and quantum thinking, and one-body versus true many-body thinking, but I think it gets close to what you’re asking.

The problem is: no one knows. We have no theory for how information about a wavefunction propogates, or if it even makes sense to think about it doing so. You can find much more discussion under the google heading of “quantum teleportation” where people think about these things. And there is, by definition, no way to directly measure the amplitude of a wavefunction — indeed, we do not know if it makes sense to attribute any degree of physical reality to the beast, or whether it might just be a weird convenient mathematical trick that rationalizes some deeper model of how reality works. Alas. No progress on this problem has been made in 90 years.

The best answer I could give you is this: you have to think about how you prepare a many body system in the first place. Do you put all the electrons in some place, let things settle down (“equilibrate”), then start moving A towards B? Well, in that case B already “knows” about A, because it’s had plenty of time to learn — or more precisely, your act of setting up the system and saying where A is and where B is is what conveyed the “information” to both parties. Whatever forces you used did the trick, and they’re now fully informed of each other’s nature and presence, and their paths will be circumscribed by that fact.

Another way to think of it is that when you ask “how” electron A is “prevented” from occupying the space of B, you are presupposing a possibility which does not, in fact, exist. It’s like asking “how” I avoid being in two places at the same time, or “how” the forces of natural law would “prevent” my killing my own grandfather if I traveled back in time. Well, I don’t need to “avoid” being in two places at the same time, nor must there be an electromagnetic force to prevent me from firing a pistol at my poor Grandpop when I emerge from the Time Machine — because these situations are simply logically incoherent, impossible, inconsistent.

I am fooled into thinking they might exist be because I can construct a grammatical English sentence which seems to describe these situations. I’m fooled by the fact that English is a sufficiently fuzzily-defined formal system that I can make statements that seem to make sense, even though, on rigorously logical examination, they would not, just as the practise of representing 3D objects on a 2D surface is sufficiently ambiguous that it’s possible to draw an “impossible” Escher-like painting that seems to be a representation of a 3D object, but which really isn’t.

From this point of view, an electron A isn’t “prevented” from occupying the space of electron B — it’s simply a logically incoherent situation, like having A simultaneous exist and not exist. Why does it seem so psychologically compellingly real that A could be in the same place as B? Presumably because our intuition is formed at the macroscopic level, where particles and trajectories are always distinguishable. We have no good intutiion about the nature of behaviour of truly indistinguishable particles. Indeed, if you think about it a bit, I promise you that you will begin to get more and more puzzled about what, exactly, are “indistinguishable” particles? What does that mean? How could you tell two particles are indistinguishable, and in what sense, even, can you say there are “two” of them?

The only true fundamental bosons are force-carriers, e.g. photons and so forth. Presumably it doesn’t bother you so much that photons could smash all on top of each other. Composite particles, e.g. an H atom in its ground state, a boson, are only bosons at low energy, where you do not probe the structure inside the composite particle. As soon as you start to proble that internal structure, it stops being a boson and starts being a many-body system made up two fermions with total spin 0,

44. Bart says:

I regret that I have to be somewhere tomorrow and will not be able to rejoin this conversation before it has gone stale and you two never look back. I do want to know more and your answers could easily spawn dozens more questions. But, thanks for the insights.

45. It’s like asking “how” I avoid being in two places at the same time

If you accept the multiverse concept, you don’t. 😉

I am fooled into thinking they might exist be because I can construct a grammatical English sentence which seems to describe these situations.

Are you trying to undermine TV SF?

But seriously, you really don’t have to travel far to get from the familiar world to one you can’t understand at all (a presumption being if we had a better understanding we could manipulate it in ways that would seem magical.)

Yet, we live with the magical (the physics that make electronics possible, etc.) and consider it mundane.

I wish I understood more of it. It’s fascinating.

46. Carl Pham says:

Eh, for the most part, ken, the problems of fundamental physics these days are weird formal and/or aesthetic, not so much a lack of understanding. That is, there are (with a few very interesting exceptions) almost no experimental data that can’t be rationalized and explained by theory. We’re not in the situation of Michelson trying to figure out why there’s no damn ether drift, or Curie watching this radium that glows apparently forever and thinking WTF? Conservation of Energy, hello?

The key problems in physics are kind of “why” problems: why do particles have spin, and hence act like fermions or bosons, and why the division between them? Why four forces, or three, or at least two? No one thinks there will be experiments probing the Planck length or energy anytime soon, so quantum gravity remains entirely without consequence — but people still feel there ought to be a quantum gravity. Why are the fundamental constants the way they are? Why is the expansion of the universe accelerating? These are the kinds of questions that folks want to answer.

(There are a few experimental results that are mystifying, still, like the nature or even existence of dark energy and dark matter, or where cosmic rays above the GKZ limit come from.)

The key problem with physics, however, is that the bulk of modern theory is done with strings, and it seems like string theory is absurdly overcomplete, meaning not just this universe, but an unimaginably larger variety of other universes are all quite consistent with it, so that we are left with a theory that can make no testable predictions at all: any conceivable experimental result is, at present, consistent with strings, the buggers. This is a very deplorable state of affairs. You might as well theorize God the Father made it all out of ylem and apple cores. The physicist Lee Smolin wrote a very interesting book about this problem (The Trouble With Physics) in which he more or less argues that fundamental physics came to a sterile standstill 20 years ago, and has made no significant advances since.

47. I know I’ve read some Smolin, although at the moment nothing comes to mind. I’m not sure you can say that understanding a formalism is any kind of real understanding. It seems to me, when you understand something you aught to be able to use that understanding in useful ways (of course we are, but it seems so arbitrarily limited.)

Then again, I always seem to be disappointed with the rate of progress we make in most areas. I see inefficiencies everywhere.

48. Carl Pham says:

Well, but if you saw efficiencies everywhere, ken, that would imply that you were stupid. Which would you rather be, smarter than average or pleased with the cleverness of the average man? It’s one or the other.