Feynman Graphic Novel

A couple weeks back I finished working through Logicomix, a graphic novel of the life of Bertrand Russell. Today I finished another graphic novel on Feynman.

1. Richard Feynman was an incredibly colorful character, a typical genius. Unusually for such geniuses, he was a showman. He had the strange knack of taking things that very few people could understand and boiling them down with incredible clarity and panache.

I've read and blogged about some of his life. For example:

• The Character of Physical Law
• The better part of a biography of him: Quantum Man

I've read the better part of his book, QED, but I don't think I've blogged about it. I have a few more of his books, including the third volume of the lectures he gave at Cal Tech from 1961-63, Surely You're Joking, Mr. Feynman, and Six Not So Easy Pieces.

2. But I would say that if you want somewhere to start, this graphic novel is the place. It has the essential framework... his beginnings that led him to MIT... his early interactions with bedrocks of Twentieth Century physics like Einstein, Niels Bohr, von Neumann, Wheeler, Bethe, etc... how he went to Princeton for grad work and was tapped for the Manhattan Project.

There's the story of his first wife Arlene, who died in the middle of the Manhattan Project. Hints at his womanizing were given. There was the development of his famed Feynman diagrams. He received the Nobel Prize in physics along with two other individuals who helped shape the fundamentals of "quantum electrodynamics" (QED).

In the graphic novel, Feynman reduces the fundamental components of quantum theory to 3. First, you need to know the amplitude of a photon going from one place to another. Then you need to know the amplitude of an electron going from one place to another.  Then you need to know the amplitude of an electron absorbing or emitting an electron.

3. The graphic novel also incorporates the key books and lectures Feynman gave, including the ones I mentioned above. There's the double slit experiment. There's his quirky personality... how he picked safes at Los Alamos... how his friends locked him in a room until he would write up his QED findings... how he took repeated vacations around the world... was offered immense sums of money to be wooed by various institutions but in the end stayed at Cal Tech... how he dramatically showed everyone in a press conference why the Space Shuttle exploded.

I think the most interesting part of this graphic novel to me was the fact that Feynman didn't always understand the equations of others and the various physicists often didn't fully understand each other's work. There was often a period where someone would show that two physicists were really saying the same thing in different ways.

Very well done!

Feynman 7: New Laws of Nature?

And so we reach the end of Richard Feynman's famous lectures, The Character of Physical Law, a series of lectures he gave at Cornell in 1964. The six previous were:

• Gravitation as an example of physical law
• The relation of physics to math
• Great conservation laws
• Symmetry in physical law
• Telling the past from the future
• The quantum mechanical view of nature

1. In the six previous lectures, Feynman had given some descriptions of the principles of nature. But what is nature. What is the something that these are principles of? What is the energy that is conserved? What is the something that has these mechanical laws?

First, that something is matter. Feynman embarks then to give a taste of the panoply of particles that had been discovered by 1964. The "standard model" was then in process of development. In fact, I have another book of Feynman's from the 80s I'd like to blog through sometime called QED, in which he presents some of this material from a vantage point twenty years later.

"All ordinary phenomena can be explained by the actions and the motions of particles" (151). And these particles are present everywhere in the universe. The make-up of matter in far away galaxies is exactly the same as the make-up of matter here.

The many particles that have been discovered--electrons, protons, neutrons, photons, neutrinos, mesons, anti-particles, etc--can be grouped into families. Feynman describes the situation in his time as similar to that of Mendeleev when he was putting together the periodic table and scientists were locating elements on it.

He also mentions a problem that I believe continues even today, which I consider to be Kuhnian "naughty data" just calling for an Einstein or Dirac to solve. Why do so many of the equations of quantum mechanics go to infinity unless you trick them?

2. So how do you find "new laws" of nature? Feynman presents the scientific method. He is worth quoting: "If it disagrees with experiment, it is wrong. In that simple statement is the key to science. It does not make any difference how beautiful your guess is. It does not make any difference how smart you are, who made the guess, or what his name is--if it disagrees with experiment, it is wrong. That is all there is to it" (156).

One interesting feature about the development of twentieth century physics is the fact that studies were sometimes wrong and not immediately recognized to be so. That is encouraging. These individuals who developed relativity and quantum mechanics sometimes presented papers with errors. They weren't like the proofs of geometry. The greatest minds in physics often did not immediately see what was wrong with their experiments or lines of thought. They were, in the end, mere mortals.

Feynman gives a nearly straight line from Karl Popper--"There is always the possibility of proving any definite theory wrong; but notice that we can never prove it right" (157).

3. It is fun to see how Feynman suggests the process begins. First you look in an area where there are problems and unknowns. Then there is a "feeling" around, an intuitive step because you do not know exactly where to look or even perhaps what you are looking for. Let's just say this is not how a lot of people imagine science working.

As the chapter progressed, Feynman makes it clear that he gets regular mail from ignoramic crack pots like me making stupid suggestions in an area about which they are incompetent. Here are some fun quotes from the last part of this chapter:

• "Such remarks are obvious and are perfectly clear to anybody who is working on this problem. It does not do any good to point this out. The problem is not only what might be wrong but what, precisely, might be substituted in place of it" (161).
• "So please do not send me any letters truly to tell me how the thing is going to work. I read them--I always read them to make sure that I have not already thought of what is suggested--but it takes too long to answer them, because they are usually in the class of 'try 10:20:30'" (161-62).
• "The inexperienced, and crackpots, and people like that, make guesses that are simple, but you can immediately see that they are wrong, so that does not count" (171).

He talks about how people tell him to start from first principles. The problem here is that "all the principles that are known are inconsistent with each other" (160-61). It's easy to point out the problems (as I have)--inconsistencies, infinities--but what are you going to substitute in its place? THAT is what is important.

And there are an infinite number of possibilities of these simple types.

4. In the end, Feynman argues, the great discoverers are great guessers. He mentions Newton and Maxwell, the two first greats. Newton's laws were fairly close to the surface. Not so today. Maxwell guessed at the right answers on the basis of a wrong idea. Einstein was driven to resolve paradoxes among existing laws. Quantum mechanics was developed from two completely different starting points.

Here is another key insight of Feynman: "We must keep all the theories in our heads, and every theoretical physicist who is any good knows six or seven different theoretical representations for exactly the same physics. He knows that they are all equivalent, and that nobody is ever going to be able to decide which one is right at that level, but he keeps them in his head, hoping that they will give him different ideas for guessing" (168).

In the end, he does not believe that history repeats itself in physics. The next big discovery will not come in the way it came for Newton or Maxwell or Einstein or Schrödinger. How do you know when it has worked? "Science is only useful if it tells you about some experiment that has not been done" (164). "You can have as much junk in the guess as you like, provided that the consequences can be compared with experiment." "It is not unscientific to make a guess" (165).

When two principles work in a certain area but are inconsistent with each other, how do you find harmony, if you should? "To guess what to keep and what to throw away takes considerable skill. Actually, it is probably merely a matter of luck, but it looks as if it takes considerable skill" (166).

Feynman gives some of his guesses. Here's an interesting one: "I rather suspect that the simple rules of geometry, extended down into infinitely small space, are wrong." In other words, his hunch is that space is not continuous.

5. You can tell that Feynman isn't particularly impressed with a lot of philosophers. However, "the philosophers who are always on the outside making stupid remarks will be able to close in" eventually, as the science gets closer and closer to completeness. Eventually, the unknown of physics will become known, and then the physicists will not be able to "push them away" (173).

The chapter ends with these striking thoughts on the future of physics. "I think it has to end in one way or another" (172). "We are very lucky to live in an age in which we are still making discoveries. It is like the discovery of America--you only discover it once. The age in which we live is the age in which we are discovering the fundamental laws of nature, an that day will never come again."

"There will be a degeneration of ideas, just like the degeneration that great explorers fell is occurring when tourists begin moving in on a territory." "In this age people are experiencing a delight, a tremendous delight that you get when you guess how nature will work in a new situation never seen before." (173).

Why does it work like this? Feynman's feeling is that it is because "nature has a simplicity and therefore a great beauty" (173). Feynman, who of course was a genius the likes of which I have never met, could recognize when he had a breakthrough. "You can recognize truth by its beauty and simplicity. It is always easy when you have made a guess, and done two or three little calculations to make sure that it is not obviously wrong, to know that it is right" (171).

6. The quote at the beginning of the last paragraph is the end of the chapter and the book. Of course, again, these are arguments that have next been extended to God as the great artist and creator, the great designer.

But in my following the flow I have missed what I consider an important point. Many experimental physicists by their very personality as pragmatists may scoff at competing philosophies about what is happening. My post over the previous chapter dipped into some of those debates, which many consider irrelevant.

But Feynman makes it clear that these philosophies can actually be important. These philosophies are "really tricky ways to compute consequences quickly" (169). "A philosophy, which is sometimes called an understanding of the law, is simply a way that a person holds the laws in his mind in order to guess quickly at consequences."

But it may be that one of these approaches to the data gives a slightly better way forward with the unknown. Newton's laws of gravitation worked oh so well except for this tiny discrepancy with Mercury. That gave Einstein a window to completely re-conceptualize the matter. And so, if it were to turn out that pilot waves provided a way forward that indeterminacy does not, even though the results are entirely the same otherwise, that would make it a better theory.

Feynman 6: Quantum Mechanical View of Nature

This is the second to last chapter in Richard Feynman's, The Character of Physical Law, a series of lectures he gave at Cornell in 1964. The five previous were:

• Gravitation as an example of physical law
• The relation of physics to math
• Great conservation laws
• Symmetry in physical law
• Telling the past from the future

1. In this lecture Feynman gives the Bohr interpretation of quantum mechanics, the interpretation of quantum phenomena held by the majority of quantum physicists. Mind you, the majority of quantum physicists are simply followers of a Kuhnian paradigm they learned in school. Much smarter than me, but not the likes of Feynman or Hawking or Kip Thorne. And Hawking is wrong as often as not these days (e.g., on the existence of the Higg's boson).

I suspect most quantum physicists get annoyed at the question of whether the dogma of uncertainty is right. But it smells like classic Kuhn to me. Logical positivism died in philosophy some sixty years ago, but it is still the name of the game among classical physicists. Feynman ends this chapter with a nice touch. It's okay to have biases as long as you're willing to change them given experimental evidence. I'm willing.

But the current situation in physics has Kuhn written all over it. Bohr, it seems to me, was an ideological bully with charisma. When de Broglie proposed that nuclear particles had pilot waves, he was shut down by the Bohr mafia, the clique that ruled the physics roost at that time. John von Neumann claimed in 1932 to have shown that there couldn't be any other hidden variables like de Broglie's pilot waves that go with particles. It's what the Kuhnian dominant group wanted to hear. Case closed.

Except it wasn't. A physicist by the name of Greta Hermann found an error in von Neumann's argument in 1935, a fact ignored till the 1980s. No one wanted to hear.

Similarly, David Bohm in the 1950s was able to solve the problems with de Broglie's original version of pilot wave theory. John Stewart Bell revived Bohm's approach in the 1980s and also clarified why von Neumann's objection didn't work. And now, John W. M. Bush at MIT has shown that analogous phenomenon in fluid mechanics demonstrate the same results as the standard quantum approach. They require more complex explanations, but the results are the same.

2. I checked some of the online physicist response to Bush and it sounds very much like what Kuhn described as the expected reaction of "normal science." "Who cares." "It's just a different interpretation." It yields the same results but the Copenhagen interpretation is simpler. "It's just about what philosophy you feel most comfortable with."

Here I suppose my theology should bias me toward the indeterminant Copenhagen, but my distaste for logical positivism is even greater. Logical positivism basically says that a falling tree doesn't make a noise in the forest unless someone is there to hear it. If you can't observe it, it doesn't exist.

On the other hand, physics has been stuck for a long time. Hawking can talk about a theory of everything but he's got nothin. There hasn't been any real progress made on a unified theory in a half a century. Quantum mechanics and relativity are just as irreconcilable as they were in the 1930s. String theory has produced NOTHING, and Sheldon was smart to give it up (Big Bang Theory).

This situation suggests to me that something needs backed up to first principles, and the Copenhagen bullies seem as good a place to start as any.

3. Of course none of this is what Feynman presents in this chapter. For all Feynman knew in 1964, von Neumann's critique of de Broglie stood. In his words, "That theory cannot be true" (146).

The double slit experiment basically shows a number of seemingly contradictory things (watch the video):

• that electrons go through one of the two slits one at a time (and thus behave like particles)
• that electrons going through two slits produce an interference pattern (an thus behave like waves)

Even if you send the electrons one by one, particle by particle, they will end up producing an interference pattern like a wave. This is a remarkable thing. It's like the electrons know where they need to go to make the interference pattern even though you shoot them one by one.

But if you try to observe which slit each electron goes through, it stops yielding an interference pattern. You can't tell which hole the electron goes through without in effect changing the situation (to detect is to force a different outcome).

4. Feynman again emphasizes that there is nothing that can be understood about this situation. We simply have to accept it. The equations work even though they have no meaning.

"We invent an 'a', which we call a probability amplitude, because we do not know what it means... To get the total probability amplitude to arrive you add the two together and square it" (137).

• Nobody can give you a deeper explanation for this situation. They can only describe it in more detail. So "you can mention that they are complex numbers instead of real numbers" (145). "But the deep mystery is that no one can go any deeper today." 
• Nature herself does not know which slit the electron will go through.

In effect, "the future is unpredictable" (147). "It is impossible to predict in any way, from any information ahead of time, through which hole the thing will go, or which hole it will be seen behind" (146).

4. I am open to the Copenhagen interpretation, mind you. At the beginning of the lecture Feynman warned that intuition and common sense are completely useless in quantum physics because there simply aren't ordinary human world analogies. "I think I can safely say," Feynman said, "that nobody understands quantum mechanics" (129).

Feynman 5: Telling the Past from the Future

This is the fifth of seven chapters in Richard Feynman's, The Character of Physical Law, a series of lectures he gave at Cornell in 1964. The four previous were:

• Gravitation as an example of physical law
• The relation of physics to math
• Great conservation laws
• Symmetry in physical law

Another fascinating lecture. It was a little disappointing at the end because for most of the chapter I might have been listening to an apologist presenting the cosmological argument for the existence of God. He did mention God at the end but did not venture to address ultimate questions. He ended by only saying that those who look at the small workings and those who ask the big metaphysical questions should not look down on each other or on any of those who figure out the stuff in between.

1. Most of the chapter was about the irreversibility of things on a large scale despite the theoretical reversibility of everything on a small scale. So on a small scale, "there does not seem to be any distinction between the past and future" (109). He does mention friction and beta decay as irreversible.

Perhaps the clearest example he gives in the chapter is of mixing together blue and white water. Gradually, they will combine into a whitish blue throughout the whole tank. Nothing in theory would keep it from becoming unmixed again into blue and white corners. We just know it isn't going to happen in a lifetime.

"One of the rules of the world is that the thing goes from an ordered condition to a disordered" (113).

He then hypothesizes an obscure device that might turn because of random air molecules against a vane only allowed to go one way. The illustration didn't work for me but I got the point. Eventually, heat evens out in a system and reaches equilibrium.

2. This sounded exactly like versions of the cosmological argument that I grew up with. He even mentions entropy (121), the famed second law of thermodynamics that Christians often use to argue that the universe had a beginning. Things go from ordered to disordered and the process seems irreversible. That suggests there must have been an orderly beginning.

Feynman doesn't go there. Indeed, like a novel reader, I kept waiting for the denouement. In a universe this vast, it is possible to find a small pocket of random order, but then we would expect complete bluish-white everywhere else. But we don't. So what was the order with which it all began?

3. At another point, Feynman gives us an amazing instance of the anthropic principle of which I had never heard. Apparently, it is easy to suggest how hydrogen atoms might come together to form helium atoms in a primordial soup of hot atoms. But cosmologists hit a snag when it come to the formation of larger atoms like carbon.

Fred Hoyle found a possible way. If one of the electron levels of carbon was at precisely 7.82 million volts, then three helium atoms could stick together just long enough for carbon to form. And so it was. Carbon does have an energy level in its electron orbitals that is 7.82 million volts. If it didn't, there would be no universe other than a random collection of cooling hydrogen and helium atoms (for the most part).

"The most important things in the real world appear to be a kind of complicated accidental result of a lot of laws" (122).

4. He ends the chapter with a concept he calls a "hierarchy of ideas." At the bottom of this hierarchy are the fundamental laws of nature. Then above them are basic principles like heat. Then there are bigger items like surface tension or refractive indices, properties of substances.

Still further up are waves, sun spots, stars. Then things like frogs. Then further up is history, "man," political expediency. Then evil, beauty, hope. It is here that he finally mentions God, although he does not believe that either end is truly closer to God. By implication, both ends point to God.

"The great mass of workers in between, connecting one step to another, are improving all the time our understanding of the world, both from working at the ends and working in the middle, and in that way we are gradually understanding this tremendous world of interconnecting hierarchies" (126).

Feynman 4: Symmetry in Physical Law

This is the fourth of seven chapters in Richard Feynman's, The Character of Physical Law, a series of lectures he gave at Cornell in 1965. The previous three were:

• Gravitation as an example of physical law
• The relation of physics to math
• Great conservation laws

I didn't find this lecture as interesting or as clear. It's curious to me why the idea of symmetry seems at first glance to be rather boring. I suspect it is partly because I don't know much about it. But it is probably also because of some matter of my personality. I remember studying "translation" in high school, mapping one coordinate frame onto another. I remember it seeming very boring.

But the end of the lecture hinted at something interesting about symmetry. Apparently, the laws of conservation in the previous lecture relate in some way to the symmetries in this one.

1. The first part of the chapter explores several different kinds of symmetry in nature. He defines symmetry as being able to change something in some way and it looking exactly as before.

The ones he presents are:

• symmetry of translation (if you move everything over, it operates the same)
• translation of time (if you move stuff forward in time, the laws of nature operate the same)
• rotating things (if you turn everything a certain way, they operate the same)
• motion in a straight line (relative to your frame of reference, everything operates the same)
• atom replacement (you can replace one atom with another same atom and everything works the same)

There are some interesting twists and turns in his presentation of these, although sometimes he gets a little tedious with his "what ifs." Here were the "what ifs" I found most interesting:

• If the universe had a beginning, then the translation of time symmetry wouldn't work for the beginning of time, but usually scientists don't include that part of time in their discussion of such symmetry.
• Einstein's theory of relativity sets the speed of light as an absolute speed limit for the universe, so motion in a straight line only is symmetrical within a frame of reference, not from one frame of reference to another moving relative to it.

2. Then he presents some items of the universe that are not symmetrical.

• Change of scale. If you make something bigger, it does not operate the same way. If you took a matchbox cathedral and increased the scale to the size of an actual cathedral, it would collapse under its own weight. This relates to one of the random discussions on Big Bang Theory on whether a giant rat was possible. 
• Spinning is not symmetrical in the sense that you can tell if you are spinning (e.g., with a gyroscope). By contrast, you cannot tell if you are moving at constant velocity without looking outside your car.
• One of the most interesting apparent non-symmetries is reflection. I did a quick search to see if this non-symmetry still holds. From my brief look, it seems like it does. 

Feynman shows that reflection symmetry holds to a very large extent. There are some interesting twists. For example, apparently living organisms prefer "right-handed" molecules. Bacteria will eat all the sugar that comes from nature. But they will only eat half of the sugar that is artificially produced, even though it has the same chemical formula. (This is an argument, by the way, that all life is derivative on the same basic original life-structure--all life is "right-handed" on the molecular level, so to speak).

But when he gets down to the atomic level, apparently all electrons spin left. You can create a positron (positively charged electron) that spins right, but it isn't (if I understand correctly) an exact mirror. So on the subatomic level, symmetry doesn't hold. You can't create a right-handed electron.

3. So we arrive at the pay off of the chapter, which is a deep connection between symmetry and laws of conservation. He lines them up this way:

• symmetry of translation relates to conservation of momentum
• symmetry in time relations to the conservation of energy
• symmetry in rotation relates to the conservation of angular momentum

Interesting!

Oh Feyn, Man!

When I entered my forties, I went through a kind of nerd mid-life crisis. I began to re-open some of the math and science books I had bought in my teens and early twenties. I hadn't understood them then and I still didn't understand them.

Five years ago I bought some of the latest math and science textbooks, including a university physics book. My goal was only to read a page a day, with the hope I would get through them by the time I turned fifty. That's not going to happen. I'll be lucky to make it by 55.

I'm only a little more than 300 pages into the physics book I bought, but my experience with the Seminary curriculum has already had me thinking a number of things about how one might teach this content in a better way: 

• There's some overlap between physics and chemistry--why separate them so sharply?
• There are a lot of things at the end of the book that could really come earlier. As it is, you hardly get to them, especially if you're only taking two semesters of physics. The stuff I'm most interested in is like 1000 pages in!
• It doesn't really have to be taught in this order, even though it seems like everyone does.

So, lo and behold, I discover that Richard Feynman did much of what I have in mind... in 1963. He touches on relativity and quantum physics really early in the series. He crosses into chemistry type topics. I've been doing video tutorials as I go through the book I have. But a big part of me wishes I had known about these!

What is more, they are all available for free online on the Cal Tech website! What a rush it must have been to be a physics student at Cal Tech when he taught these!

Feynman 3: Great Principles of Conservation

This is the third of seven chapters in Richard Feynman's, The Character of Physical Law, a series of lectures he gave at Cornell in 1965. The previous two were:

• Gravitation as an example of physical law
• The relation of physics to math

In this third lecture, he muses about principles of conservation that seem to apply throughout the universe. I say "muses" because he makes no claims to know why these patterns seem to hold or whether they will continue to hold in the future.

As a sign of his genius, he did not have a prepared manuscript for these lectures, only some notes. They were delivered extempore and then written up from the recordings. For example, in the course of this lecture he constructed a chart on a chalkboard. He is truly unusual among such geniuses to be able to communicate so clearly. Truly amazing.

1. Feynman spent the bulk of the lecture presenting examples of conservation in nature, especially the conservation of energy. But near the end he does begin to reflect on the possible significance of it all.

The main conclusion he reaches is that science is uncertain. It is in its very nature to reach beyond the known to the unknown, and this requires guesswork and the expectation that the laws that already seem to work in one area will also work in another. But he makes it clear that scientists can't assume they will continue to work.

For example, when it was found that a neutron could deteriorate into a proton and an electron, Niels Bohr famously suggested that they had finally found a situation where energy was not conserved. By that time he was so used to time-held notions going out the window that he had a penchant for wanting to overturn time honored scientific notions.

But it turned out he was wrong. There was another tiny particle, an anti-neutrino, that was involved, and energy was conserved.

For Feynman, though, it was important for scientists to be willing to throw out the conservation of energy principle if the evidence seemed to warrant it. And so it is for all true truth-seekers in every area except for the axiomatic.

2. The conservation of energy takes up the most space in the lecture. As usual, Feynman puts it in incredibly clear terms. He uses the analogy of a mother who leaves her child alone in a room with 28 blocks. One way or another, she will always be able to account for 28 blocks when she comes back to the room.

Perhaps the child will throw one block out the window. Perhaps the child has put one in a box--she can weigh the box to find out if she knows how much it weighed before and how much each block weighs. If there is a sink full of water, she can measure how high the water level has risen to account for submerged blocks.

And so he gives the analogy to the conservation of energy. Sometimes the energy hides, but science so far has always been able to account for all the "blocks" before and after some process.

3. Electric charge is always conserved. Feynman gets into a little relativity in his discussion here. Charge is always conserved locally, meaning in a particular frame of motion. Someone in a different frame of motion may not seem to observe conservation of charge.

He notes also that many things that are conserved come in units. Charges come in units. Another thing that comes in units and is conserved are "baryons," a heavier type of atomic particle like a proton or a neutron. The standard model of physics wasn't quite assembled completely when Feynman gave these lectures, but it was well on its way.

Two other conservations he mentions are the conservation of momentum (mass times velocity) and the conservation of angular momentum (the area created by motion over time from a certain reference point, such as the area between the moving planets per given time and the sun).

In all these things, Feynman sees deep yet seemingly inexplicable connections.

The Relationship of Physics to Math (Feynman 2)

Yesterday morning I read the first chapter of Richard Feynman's The Character of Physical Law, a series of lectures he gave at Cornell in 1965, fifty years ago. This morning I read the second chapter, "The Relation of Mathematics to Physics." In this chapter you really catch a glimpse of this man's genius, as well as his uncanny ability to explain things.

This chapter is full of insights that, interestingly enough, I have caught these last twenty years or so at IWU, especially being friends with the likes of Keith Drury and Russ Gunsalus. These are insights that were part of the founding of Wesley Seminary, insights that are hard to catch, hard to communicate, hard to convince. When they train you to be a scholar, they do not teach you to think like Feynman, a physicist. They teach you to think like a mathematician.

1. Feynman of course is not disparaging of mathematicians in the least. Indeed, he ends the chapter by apologizing to the layman for the difficulty of mathematics. "If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in" (58), by which he means math. In the chapter, he references people like me, who read book after book, hoping that the next person will finally be able to explain to me what is going on with quantum physics.

But in the end it is just tough. Either you can hack the stuff or you can't. In the words of Euclid to a king, wanting an easier explanation, "There is no royal road to geometry" (58). In the words of the nineteenth century physicist Jeans, "The Great Architect seems to be a mathematician."

This is a powerful statement: "To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature... [there are] people who have and people who have not had this experience of understanding mathematics well enough to appreciate nature once."

2. Still, Feynman spends most of the chapter indicating that physics is quite distinct from math. He wonders if the mathematicians will prove to be right in the end, that all of nature can be boiled down to certain axioms, certain "building blocks" of knowledge, as it were. He calls this the Greek approach to math, to start with foundational claims and build all other claims from there.

But we are not there yet at all, he indicates. Even in math, he suggests, you can start at different places and get to the same destination. But in physics, things are much more like the Babylonian way of doing math. By his description, the Babylonian way of doing math is that you know a collection of things that are true.

You do not break them down into truth atoms. You see some connections between these various mathematical truths and you intuit when to use one tool and when to use another. There are many analogies in physics, he says, where there are no clear connections between differing rules at all, but they have an uncanny similarity to each other.

3. This is the state of physics right now. It is impossible in physics right now to know what the first principles are--or whether there even are first principles. When Newton was asked what his theory of universal gravitation meant, he indicated that it didn't mean anything. It simply describes how things move.

I have said this many times here and it is in my philosophy book. Science is a collection of very precise myths that express the mystery of the world's operations.

Feynman gave as an illustration three completely independent and apparently unrelated ways to express the phenomenon of movement. The first was Newton's "action at a distance model," where a force is acting on an object at a distance. But there is a second model that looks only on the mass and potential of the object itself. And there is a third model, Euler's principle of least action. This last one was the inspiration for Feynman's claim to fame in quantum physics. Somehow, particles know to take the path of least action.

These three expressions (myths, if you would) are completely unrelated, apparently, but they all explain the motion of a body from one point to another correctly, at least on a macro-scale. "The correct laws of physics seem to be expressible in such a tremendous variety of ways" (55).

4. Practical theology is much more like physics than it is mathematics, in that regard. There are these macro-truths. It isn't always helpful to try to break them down into fundamental truth atoms. As a Biblehead, the game we often play of trying to break down life into Bible atoms (i.e., proof texts) is really embarrassing. It's really just a silly game.

But I digress. There are times when the "physics" of life and morality isn't working right and you need to bring in the "mathematicians." And sometimes the "mathematicians," while exploring the beauty of thought for its own sake, will generate useful tools for life without thinking of its relevance.

Feynman would say that the physicists need the mathematicians at key points, although most of what physicists do, in his own words, is fly by the seat of their pants, to see if something works in the real world. And, of course, Feynman was also very good at math.

Feynman's The Character of Physical Law 1

The second half of June is often the season when administrators take what they can of their remaining vacation days, so I am relaxing a bit these next two weeks (though I am happily and gratefully continuing to work for the Seminary until the end of August).

1. So this morning I picked up an old book of interest to me by Richard Feynman, The Character of Physical Law. I make no promises to finish it, but I read the first chapter this morning.

Feynman was a curious soul. I blogged through the first eight chapters of a biography of him last summer, then stopped when the school year came on heavy. Perhaps I will try to finish working through it. I am cursed with too many interests, too little intellect, and too little time. I wish there was a chamber you could enter where time outside freezes but you can go in and study for a while.

Einstein-Dirac-Feynman-Hawking--that's my current list of the greatest geniuses of twentieth century physics. Feynman gave these lectures in 1965 at Cornell.

2. Chapter 1 is about the law of gravitation, first set down by Newton. I'm not sure what to expect from this book. I'm looking for some insight behind physical law. My hunch is that Feynman will not be able to tell me. My hunch is that he is going to muse about patterns, scientific development, and curious correspondences. But there are no real answers to why the laws of nature work the way they do.

He mentions some of these mysteries in this chapter. So the inverse square of distance seems to have some deep significance, but we don't know what it is (30). It shows up both in the law of universal gravitation and in the formula for electric charge. But the relationship between these two forces is unknown and different on the level of 10 to the 42nd power (a one with 42 zeros after it).

Newton's law of gravitation also had to be modified a little by Einstein, who with the help of David Hilbert set out a general theory of relativity that included gravity. Yet even here, Feynman noted that this theory could not yet account for gravity on the quantum level. This is one of the cutting edges of physics.

Feynman ends this first lecture with three observations.

a. The first is the correspondence between physical reality and mathematics. I've mentioned the inverse square feature.

A fun story in the chapter is when two individuals using only math and the observed movements of Uranus independently asked two different observatories to turn their satellites toward a part of the sky where they expected to find a planet, Neptune. The rationale was the hypothesis that Uranus' orbit was being affected by another large planet.

Feynman's account is different from others. He basically suggests that the British observatory thought it ridiculous that you could find a planet by math, while the German observatory dutifully looked and found. This is probably a better story but perhaps less true.

b. The second observation is that these discoveries are not exact, as in the need for modification by Einstein and still by someone in relation to quantum gravity.

c. The third, though, is the simplicity of Newton's basic equation and fourthly its universal character.

3. In the meantime, the chapter gives a lovely tale of how the law developed from Copernicus to Kepler and Galileo to Newton to Cavendish and several other scientists up till the twentieth century. A reassuring reminder is that it took some four centuries to unfold the content of this chapter and that these scientists worked a lifetime on them. They seem amazingly brilliant after the fact, and no doubt they were.

But they weren't brilliant every day. We tend to miss the trial and error of their probings and the long story of development.

P.S. I forgot to mention the old idea around the time of Galileo that angels pushed the planets around. (Feynman had a flair for the dramatic, so I probably should confirm this) He suggests that this is not entirely wrong, but that they were wrong on the direction in which the angels were pushing. The angels--gravity--were pushing inward toward the sun rather than pushing behind the planet. After all, a body in motion stays in motion all by itself... another mystery whose reasons we know not why.

Feynman 4: Womanizing Genius

On to chapter 8 of Quantum Man, a biography of Richard Feynman. I only was able to slip in one chapter this week.

So far:
Chapters 1-2: High school, MIT, and Princeton
Chapters 3-5: The Path to a Doctorate
Chapters 6-7: Theorizing the Bomb

One of the most disturbing features of Richard Feynman's life was the way he began to use women after his wife died. He became a notorious womanizer. You hear of professors in the late twentieth century who used the charm of their genius to entice grad students. Thankfully, those days are mostly over, I hope. The increased attention to sexual harassment and sexual ethics in the workplace is something to be thankful for. Christians who scoff at this sort of thing with the label, "political correctness," have no idea how unchristian they are being.

There are some more innocuous stories of Feynman's increasing disregard for the rules of society. He seems to have become a real Cynic, in the ancient sense. One I found particularly entertaining is how he would sometimes sneak into Los Alamos--the high security place where they were building the first atomic bomb. Then he would leave by the front gate with no record of him ever coming in.

He was flamboyant. He loved the Feynman legends that arose about him. He was a showman. Another stunt was when he intentionally convinced several military psychologists that he was mentally unfit.

The physics of this chapter deals with the some eighteen years between Dirac's breakthrough in which he formulated a relativistic version of Schrodinger's wave equation and a conference on Shelter Island off of Long Island, New York in June of 1947. I. I. Rabi described these years as "the most sterile of the century" (119).

The antiparticle version of the electron--the positron, effectively an electron with a positive charge--was predicted by Dirac's equation and found in 1932. But it gave rise to an even greater pool of infinite occurrences, for there was the possibility in QED, Quantum Electrodynamics, that a photon would momentarily split into an electron-positron pair, only to return to a photon. These sorts of possibilities, occurring seemingly randomly, were part of the new quantum reality.

Most of the calculations of the atom in this period seemed to give nonsensical answers that went to infinity. What the theoreticians seemed to need at this time was some hint from experimental data. Krauss notes that Willis Lamb stepped into this void, "one of the last of a breed of physicists who were equally adept in the laboratory and performing calculations" (119).

In 1946 Lamb found a way to measure the spectrum of the hydrogen atom more finely than had ever been done before. These results were concrete, not some theoretical infinite. He presented them on Shelter Island at a conference called, "Conference on the Foundations of Quantum Theory," a conference Feynman would call the most important one he ever attended. Wheeler, Oppenheimer, Bethe, another young physicist superstar named Julian Schwinger--they were all there.

Lamb presented his results. Bethe was so excited he fixed some of the existing equations on the train on his way to his mother's in upstate New york after the conference. He called Feynman immediately. The race was now on to move forward with quantum theory.

Feynman's look at total paths of particles would play a key role. Relativistic problem enter in when you get to talking about the specific time of different particles, since different objects in motion potentially have different time frames. By looking at the overall energy sums and paths, Feynman had a potential way around the problem.

Let me close with a theological aside. One of the reasons there are so many different interpretations of the Bible and so many different theologies is that there isn't always "experimental data" to ground it. Much of individual theologizing and interpretation is, extensively, unbridled speculation. Indirectly, of course, we as interpreters and theorizers of religion are grounded by our concrete circumstances and the cultures in which we are embedded.

Most of us don't realize that these are as powerful drivers of our interpretations and thoughts as the Bible or God--I would say far more influential, actually. We like to think we are speaking for God or proclaiming the Word of God, but much of it is just self-therapy, giving expression to our inner desires and conflicts.

This is why I long to know the original meaning of the Bible, the real meaning it had in its original times and places. History is cold and uncaring. It is a more or less scientific inquiry. It is the most likely meaning we can suggest given the known literary and historical context.

It is not always certain. In fact it is far less certain than many of us Bible scholars like to think. But, at the same time, it at least eliminates quickly a great mass of things thought and said about the Bible within Christendom. It is a kind of experimental grounding to interpretation and thus gives a tangible grounding to theology.

Feynman 3: The Bomb and then Depression

This is my third installment reviewing a biography about Richard Feynman called Quantum Man, one of the greatest physicists of all time.

So far:
Chapters 1-2: High school, MIT, and Princeton
Chapters 3-5: The Path to a Doctorate

Now chapters 6-7.

Chapter 6: Loss of Innocence
Finishing his PhD degree at Princeton was a condition for Richard and his fiancee Arline to get married. And so, even though she was deathly ill with tuberculous--and generating significant friction between Feynman and his mother--they got married. She would die two months before the bomb dropped on Hiroshima.

If you remember from last week, Feynman had helped work on the question of separating Uranium 235 from 238. He had worked with Robert Wilson's team on this, and it had been accomplished. Then next step was to build a nuclear reactor to do the separation, and this was taking place in Chicago with Enrico Fermi and John Archibald Wheeler, Feynman's doctoral mentor.

So Feynman went to Chicago. Soon after he arrived, he blew away the "theory group" by performing a calculation that had eluded them for months (78). Robert Oppenheimer picked Los Alamos as the place where the Manhattan Project would play out, and he picked Feynman to come with the first wave of scientists in 1943.

Oppenheimer was an unusual scientist because, as Feynman himself put it, he "was extremely human" (79). He not only understood the science. He had organizational skills and cared about people. He would notoriously regret the role he played in the creation of the atomic bomb. His words at the first successful testing were from the Bhagavad Gita: "Now I am become Death, the destroyer of worlds." Feynman merely grinned as he contemplated the physical causes of the mushroom cloud and sonic boom.

Feynman, once again working best in conversation, ended up almost by accident in a conversation in Los Alamos with a seasoned theoretician named Hans Bethe. Bethe would bounce ideas off of Feynman, who being very loud could be heard to cry out, "No, no! That's crazy." From Feynman's recollection, Bethe always proved to be right. From Bethe's recollection, Feynman was probably the most ingenious person in the whole division.

Bethe was the scientist who discovered that fusion fueled the sun. Bethe said of Feynman that "he could do anything, anything at all" (87). He was put in charge of the computing division. You have to wonder whether the Manhattan Project would have ended before the war if Feynman hadn't have been there.

For example, Feynman developed a mathematical method for integrating third-order differential equations that was more accurate than what they were doing with second-order differential equations. When several boxes full of the parts of an IBM computer arrived, Feynman and another person managed to put them together before the professionals from IBM arrived. It had never been done before.

Oppenheimer would say of Feynman that "He is by all odds the most brilliant young physicist here" (92).

Chapter 7: Paths to Greatness
As an academic Dean, I think I am somewhat unusual. I absolutely love knowledge for its own sake. My boss often quotes me as saying, "No one loves the irrelevant more than I do." But I am a pragmatist and a realist. In most cases, it doesn't matter how brilliant a teacher is if he or she can't teach. And in most cases, it doesn't matter how excellent your program is if no one is buying.

Of course there are top flight research institutions that are so heavily endowed that their professors can push the bounds of knowledge without a care and survive off of some small number of purely genius students. Feel free to hire me to teach there. But that is just not where the majority of academic institutions are. And, for all your pretense to greatness, most purists seem to have a penchant for self-destruction (and an overestimation of how great they are).

So I won't tell you what I wrote in the margins of this biography on reading about how the chair of Berkeley delayed making an offer to Feynman on Oppenheimer's recommendation. When he finally did, he had the gall to tell Feynman that no one had ever refused an offer from Berkeley's graduate department of physics.

Feynman did. He went to Cornell, who had the smarts to hire him two years earlier and give him a leave of absence while he was at Los Alamos. Stupid Berkeley.

But Feynman himself was pessimistic and depressed. What future was there, now that there was such a bomb. "What one fool can do, another can," he said (93). Indeed, it is amazing seventy years later that the bomb has not been used again.

It was natural that Feynman would feel like he had wasted three prime years of his intellect--the greatest discoveries of a physicist are usually made in one's twenties. His father had died of a stroke a year after his wife Arline. Teaching takes a whole lot more work than most imagine and back then there was no training in how to teach.

Feynman was being showered with praise from all corners, but he felt like his best years were behind him. Others thought he was incredible. He felt stupid. "They were absolutely crazy" (96), he thought of offers from Princeton and the Institute for Advanced Study.

Bethe, upon hearing of Feynman's depression, remarked that, "Feynman depressed is just a little more cheerful than any other person... exhuberant" (97).

There is a great story about how hard it was for Feynman to finally write up his dissertation for publication. Apparently, two of his friends forced him to write it up while he was visiting them in the summer of 1947. They practically locked him up in a room. It was easy for him to express his ideas in conversational form. But to write them down in a beginning to end argument in detail, with everything exactly write. That he found a hard time doing.

[I know a couple people I'd frankly like to lock in a room to crank some of their gems out. On the other hand, one might argue that I would have written more scholarly pieces these last ten years if I hadn't started blogging.]

However, writing it up seemed to get him over a hump. Quantum mechanics began to be more visual for him. For the first time, he began to describe quantum mechanics in the language of sums over paths, with each path having an amplitude. It was a fundamental reformulation of quantum mechanics on which all the quantum mechanics since is based. His next task was to relativize it, to incorporate Einstein's relativity into his new version of the older model.

The rest of the chapter mostly flashes back to Dirac's relativizing of the original quantum mechanical equation of Schrodinger. We hear about the spin of particles called fermions, after Enrico Fermi. We hear about boson particles that don't spin. We hear of Wolfgang Pauli's exclusion principle and Dirac's theoretical discovery of antiparticles.

Meanwhile, Feynman was trying to find a way to picture the overall paths of these particles in a way that incorporated relativity the way Dirac had for a single particle at particular time and momentum...

Feynman 2: The Path to a Doctorate

A couple weeks ago, I started reviewing a biography about Richard Feynman called Quantum Man, one of the smartest physics geniuses of all time. It is incredibly humbling to read about him, a genius among geniuses. Sometimes we college professors slip into thinking we have something upstairs--we need a Feynman occasionally to knock the wind out of our presumptuous sails.

Chapters 1-2: High school, MIT, and Princeton

Chapter 3: A New Way of Thinking
We left off with Feynman at Princeton with John Archibald Wheeler, the one who coined the phrase "black hole." One of the things that struck me in the chapters today is the extent to which Feynman thrived in his early years by having someone to spar with intellectually. There's a certain kind of synergy that great designers or artists or thinkers can experience when they're bouncing ideas back and forth with others who are on the same wavelength. The whole becomes even greater than the sum of its parts. Wheeler was one such partner for Feynman.

Wheeler and Feynman had some crazy ideas together that did not end up in their first form, but turned out to be headed in promising directions. I mentioned in the last post the idea that certain photons might move back in time (he would later argue this of antiparticles). Another idea was that all elements were made up of electrons (quarks came closer later).

In 1941, Feynman the gifted grad student presented to the Princeton physics department professors (rather than to fellow students), with Albert Einstein, Wolfgang Pauli, John von Neumann, and other physics titans present.

We also meet the love of Feynman's life in this chapter, Arline. She would suffer and eventually die of tuberculosis, just as Feynman was reaching the end of the Manhattan Project.

While the theory Wheeler and Feynman cooked up about particles moving backward in time would not pan out eventually, it led Feynman to invent a new chapter in calculus. In the theory they were cooking up, "the path of a particle at a given time is affected by the path of another at a different time" (48). It was here that Feynman turned to Lagrange's principle of least action, mentioned in the previous post: "an object will take that path where the total sum of the difference between its kinetic energy at each point and its potential energy at each point is lowest."

So rather than think of events at specific times that cause events at a subsequent time, Feynman would focus on an overall space-time path.

Chapter 4: Alice in Quantumland
In this chapter, biographer Krauss spends a little time over-viewing some of the basics of quantum mechanics as they had developed in the two decades previous to Feynman's time at Princeton. He starts with Erwin Schrödinger's wave equation. His equation opened the door to the probability of finding a particle at any given place in space at a specific time. Strangely, it is not the equation itself but the square of the equation that gives this probability.

The equation by itself sometimes involves the square root of negative 1, which isn't a real number (literally ;-). It's called an "imaginary" number. But √-1 is all over quantum mechanics.

Because quantum mechanics works with probabilities, there is a sense in which a particle can take all the different possible paths from a to b. Feynman's idea was to look at the paths associated with the probabilities in Schrödinger's equation rather than the probabilities of where a particle is at any moment.

Chapter 5: Endings and Beginnings
At a beer party at a tavern in Princeton, Feynman ran into a European physicist named Herbert Jehle who happened to be in town. They got to talking and Feynman mentioned that he was trying to explore the path of particles using Lagrange's least action principle.  Jehle mentioned a paper that Paul Dirac had written on the subject in 1932.

According to Jehle, next day in the library, on the spot, working the math more quickly than he could follow, Feynman took Dirac's paper to the next level. Feynman would meet Dirac in 1946 and mention it to him. The almost entirely uncommunicative Dirac was said to say, "Oh, that's interesting." A story about another conversation between the two is that Dirac asked Feynman, "I have an equation, do you?"

I suspect that this was a conversation between the two greatest minds in physics in the twentieth century.

It was the moment that birthed what would become Feynman's thesis and his greatest contribution to quantum physics. He would develop a system of drawing probable paths of particles. He would show that his new approach to paths both reduced to Schrödinger's equation over short paths and to Newtonian ones on a large scale.

Meanwhile, World War 2 had started. In 1942, Feynman was tapped to work on the Manhattan Project. Robert Wilson, an instructor at Princeton in experimental physics, showed up at Feynman's office one day and asked if he was interested in helping him develop a method for separating Uranium 235 from Uranium 238. These are two isotopes of uranium--same type of atom but with different numbers of neutrons. U238 is stable (although it can become unstable plutonium). U235 is prone to deteroriate into Barium and Krypton, while releasing free neutrons that can then impact the nuclei of other U235 nuclei, setting off a chain reaction.

At first Feynman wasn't interested, but in the end couldn't turn down the opportunity. Wheeler thought he was close enough to finish his doctoral thesis in 1942 and urged him to turn it in. Feynman "had re-derived quantum mechanics in terms of an action principle involving a sum" (an integral). He had been able to apply Schrödinger's equation to situations where the standard equation didn't work. He had not yet incorporated relativity. That was what was needed for a full blown theory of quantum electrodynamics (QED).

Almost all of the most important theoretical advances in fundamental physics in the late twentieth century were made possible by Feynman's reformulation because it made it possible to bracket out Heisenberg's uncertainty principle here and there. Measurement of a quantum system by a physicist causes "the collapse of the wave function." The observer inevitably eliminates the possibility of other measurements by making one measurement. Feynman figured out a way to look at the whole picture in a way that did not engage individual moments of a particle's position and thus didn't collapse the function, if I understand correctly.

Greatest Physics Genius of the 1900s

Last week I finished blogging through Thirty Years That Shook Physics, a great book by George Gamow on the first thirty some years of the 1900s, when the groundwork of modern physics was laid.

If I were to pick, I would pick Einstein as the dominant figure of the first twenty years of the twentieth century. Max Planck may have suggested the quantum, but Einstein ran with it and, in the meantime, established both special (1905) and general (1915) relativity.

For the next twenty some years, 1920-40, I pick Paul Dirac as the greatest mind in physics. There are lots of candidates. I pick Niels Bohr as the most influential figure, but I don't think the greatest mind. Heisenburg, Schrodinger came up with the most central concepts of quantum mechanics, but at times it seems like they just were the ones who did what someone else would have done anyway. It was Dirac who combined Schrodinger's famous wave equation with relativity, the last time that longed for synthesis was successfully accomplished.

But I'm not sure that any of those I've mentioned were as genius as Richard Feynman. I don't feel like I know enough to have a firm opinion yet, but Feynman may have been the most brilliant physicist of the modern era. The book I'm reading for the next few weeks for my Science Fridays is Lawrence Krauss' biography of Feynman, Quantum Man.

Introduction
Krauss begins with some fun memories of his own personal engagement with Feynman. A book given to him in high school about Feynman's notion that antiparticles were particles moving back in time (it was originally John Archibald Wheeler's idea). In college he had Feynman's lectures on hand. And of course he mentioned Feynman's moment in the spotlight, when he showed everyone why the Challenger blew up.  (He dropped an O ring into ice water on television)

1. Feynman in High School
Feynman was born in 1918. He was obviously a genius. Unlike Dirac, from whom you could hardly extract a word, Feynman was flamboyant and was loud. But he could also tunnel into a problem for long periods of time. He kept notebooks with multiple solutions to the same problems. he was methodical. He taught himself subjects years before he got to them in school.

He was incredibly gifted at math--not all physicists are, Einstein for instance. Of course you have to remember that when I say, "not gifted at math," I mean that Einstein didn't invent a new branch of math. Heisenburg reinvented matrix mechanics on his own. Dirac made major contributions to linear algebra for his relativistic quantum mechanics. So Feynman would invent path integrals. Meanwhile, Einstein couldn't have worked out general relativity without the help of David Hilbert.

One principle Feynman learned in high school that he didn't like but that would be key to his later fame was Fermat's principle of least time: light takes the path through various media that gets it most quickly to its ultimate destination. It is a weird concept because it seems to imply planning on the part of light, as if it knows where it wants to go and plans accordingly.

Apparently, another way to state this principle is this: an object will take that path where the total sum of the difference between its kinetic energy at each point and its potential energy at each point is lowest. This sum is called the "Lagrangian" and the "action" of an object.

2. Feynman at MIT and Princeton
Feynman declared as a physics major at the end of his first year at MIT. It was just right for him between the non-concrete pure math and the all concrete engineering. He and a student named Ted Welton started taking advanced graduate physics courses their sophomore year. One of those professors met with the two of them their junior year to teach them quantum mechanics. This was about 1938.

Then he turned down Harvard to go study at Princeton, which at that time had Einstein and John Archibald Wheeler. Feynman was Jewish, and his parents worried both about whether he could make a go at physics and whether he would be accepted as a Jew there. He and Wheeler (the guy that coined the phrase, "black hole") worked well together.

It was during this period that Wheeler suggested some particles might move back in time. The specific problem they tackled was the self-energy of an electron. They unsuccessfully tried to eliminate that factor from the energy equation because it went to infinity according to calculations at that time. Their suggestion was to try to eliminate the idea of a electromagnetic field. The idea was that interactions would only take place by the direct interaction of charged particles, by the exchange of photons. The prevailing wisdom was that forces interact by "action at a distance," which is what fields allegedly do.

Wheeler and Feynman were apparently wrong, but it was exactly the kind of interaction that fed Feynman's growing sense of possibilities.

Krauss takes a couple pages in this chapter to give a quick two points on the nature of quantum mechanics. The first point is that, in QM, objects can be in different places doing different things simultaneously. The second is the Heisenberg uncertainty principle. There are certain pairs of qualities (position and momentum, energy and time) where the more we know one, the less we know the other. The product of our uncertainty in knowing one and the uncertainty of knowing the other will never be smaller than Planck's constant.

That's probably enough for one day...