Richard Feynman

"Every instrument that has been designed to be sensitive enough to detect weak light has always ended up discovering that the same thing: light is made of particles."

"I'll never make that mistake again, reading the experts' opinions. Of course, you only live one life, and you make all your mistakes, and learn what not to do, and that's the end of you."

"What I would like to do now... is to... try to tell you what actually what physicists do when they make calculations, so they can predict... correctly the probabilities of events for all the experiments, at least in a certain range where they know some things about electrons and photons... and light and matter and chemistry and ordinary phenomena not involving gravitation in detail or nuclear phenomena in d... Well, actually today... nuclear phenomena are now probably under control too."

"Light is something like raindrops — each little lump of light is called a photon — and if the light is all one color, all the "raindrops" are the same."

"I returned to civilization shortly after that and went to Cornell to teach, and my first impression was a very strange one. I can't understand it any more, but I felt very strongly then. I sat in a restaurant in New York, for example, and I looked out at the buildings and I began to think, you know, about how much the radius of the Hiroshima bomb damage was and so forth... How far from here was 34th street?... All those buildings, all smashed — and so on. And I would go along and I would see people building a bridge, or they'd be making a new road, and I thought, they're crazy, they just don't understand, they don't understand. Why are they making new things? It's so useless. But, fortunately, it's been useless for almost forty years now, hasn't it? So I've been wrong about it being useless making bridges and I'm glad those other people had the sense to go ahead."

"Since then I never pay attention to anything by "experts". I calculate everything myself."

"That's called monochromatic light, light of one color. ...I'm going to discuss all my phenomena for a while with light of one color, because it's simpler"

"The idea of quantum mechanics that I want to describe now is a positive thing. It's a way that we actually use to make calculations and understand nature. Excuse me, to make calculations! We really don't understand it very well... Understanding real nature, we are unable to do."

"So there are two aspects of an amplitude. An amplitude is a sort of two dimensional thing and therefor you can represent it... on a plane as an arrow. So an amplitude is a physical thing, which also is identical, we... make it very equal by using three lines [ ≡ ] instead of two [ = ], the same as these arrows that I've been talking about on a plane, and that's, by the way, for those that know mathematics, that can be equivalent to representing everything by s. You can do it algebraically, in other words, not just by drawing the arrows.AMPLITUDE ≡ ARROW ( ≡ COMPLEX NUMBERS)"

"The scale of light can be described by numbers — called the frequency — and as the numbers get higher, the light goes from red to blue to ultraviolet. We can't see ultraviolet light, but it can affect photographic plates. It's still light — only the number is different."

"There were certain things I didn't like, such as tipping. I thought we should be paid more, and not have to have any tips. But when I proposed that to the boss, I got nothing but laughter. She told everybody, "Richard doesn't want his tips, hee, hee, hee; he doesn't want his tips, ha, ha, ha." The world is full of this kind of dumb smart-alec who doesn't understand anything."

"[John] von Neumann gave me an interesting idea: that you don't have to be responsible for the world that you're in. So I have developed a very powerful sense of social irresponsibility as a result of von Neumann's advice. It's made me a very happy man ever since. But it was von Neumann who put the seed in that grew into my active irresponsibility!"

"One time I was in the men's room of the bar and there was a guy at the urinal. He was kind of drunk, and said to me in a mean-sounding voice, "I don't like your face. I think I'll push it in."I was scared green. I replied in an equally mean voice, "Get out of my way, or I'll pee right through ya!""

"While in Kyoto I tried to learn Japanese with a vengeance. I worked much harder at it, and got to a point where I could go around in taxis and do things. I took lessons from a Japanese man every day for an hour. One day he was teaching me the word for "see." "All right," he said. "You want to say, 'May I see your garden?' What do you say?" I made up a sentence with the word that I had just learned. "No, no!" he said. "When you say to someone, 'Would you like to see my garden?' you use the first 'see.' But when you want to see someone else's garden, you must use another 'see,' which is more polite." "Would you like to glance at my lousy garden?" is essentially what you're saying in the first case, but when you want to look at the other fella's garden, you have to say something like, "May I observe your gorgeous garden?" So there's two different words you have to use. Then he gave me another one: "You go to a temple, and you want to look at the gardens..." I made up a sentence, this time with the polite "see." "No, no!" he said. "In the temple, the gardens are much more elegant. So you have to say something that would be equivalent to 'May I hang my eyes on your most exquisite gardens?" Three or four different words for one idea, because when I'm doing it, it's miserable; when you're doing it, it's elegant. I was learning Japanese mainly for technical things, so I decided to check if this same problem existed among the scientists. At the institute the next day, I said to the guys in the office, "How would I say in Japanese, 'I solve the Dirac Equation'?" They said such-and-so. "OK. Now I want to say, 'Would you solve the Dirac Equation?' — how do I say that?" "Well, you have to use a different word for 'solve,' " they say. "Why?" I protested. "When I solve it, I do the same damn thing as when you solve it!" "Well, yes, but it's a different word — it's more polite." I gave up. I decided that wasn't the language for me, and stopped learning Japanese."

"[T]he Mayan[s]... had a scheme for predicting... when Venus was a morning... or . ...[T]hey had a rule for... making corrections and... had a very good way of predicting when Venus was coming up. ...Suppose that the professors (the priests in those days) ...were giving a lecture ...to explain ... these wonderful predictions ...He would say, "What we're doing is counting the days, just like you're putting nuts in a pod." ...[The students] did not know a quick and tricky way to add 365 x 8. ...These students were learning ...the laws of arithmetic. Something... to us now, because we have public, free, general education, almost everybody has to... learn... by a tricky scheme... The waitress, just an ordinary person, in two minutes does that. How..? ...She's ...counting ...415 pennies ...then ...287 more ...and telling you how many pennies you would have got if you counted ...beginning to the end. But it's highly educated and very trained to... do that... quickly. ...In the 14th century [it was] mathematicians... who could do that."

"I don't know about philosophy of Mayans. We have very little information due to the efficiency of the Spanish es and... mostly their priests, who burned all the books... hundreds of thousands of books, and there's three left... [O]ne of them has this Venus calculation... Just imagine our civilization reduced to three books... left by accident."

"For each reflection you make an arrow. This arrow... for the reflection from front surface, and this arrow... from the back surface... and... you tie the arrows together this way... [Y]ou put the tail of the other one on the head of that one... and you put these two arrows together by this rule, and you look at the vector sum,] how far off you've come from the end... You count the number of beans you put in the barrel, I mean you make these pictures. ...[T]hen you ask, "How big is this circle [whose radius is the vector sum of the front and back arrows] in area?" And that area represents the probability... If the circle area is big, then you get a high probability, if... small, you get a small probability."

"[T]his rule explains several of the ordinary phenomena... such as angle of incidence equals angle of reflection, and , that light bends... from air to water, and travels in straight lines... It's all hidden in that one rule."

"If we try to say how big a photon is, or how it's spread out, or what it looks like, we're going to get into some difficulty with some experiment. It isn't going to behave that way you'd expect. ...[I]t's going to be impossible for me to tell you how big a photon is, where it is... Nevertheless... I'll tell you a series of crazy rules by which you can tell exactly what will happen in any experiment with photons... without ever being able to say what a photon looks like... in the sense of some sort of model of waves in space. ...And so to make a complete theory, we cannot do it with a model. We can only make an incomplete theory and what my purpose is today is to tell you the complete theory, not the incomplete approximations..."

"Finally, I must tell you what the arrow is for the net result. When a thing can happen in alternative ways you do what we call "add the arrows"... I know how to add numbers. How do you add arrows? The rule is... you simply put one arrow head on the tail of the other... I just draw the second arrow off from the first one... exactly parallel... it's drawn the same, but it's centered, it's moved... it's tied one onto the other, head to tail, and the result, it's supposed to be the sum. The adding is this net arrow that you would get, from where you started [from the beginning of the first arrow] to where you ended [at the end of the second arrow]. The way of thinking of it, that is rather nice, is to think of each arrow as indicating the direction of a step to be taken. If we take a step, on this plane, this way [the distance and direction of arrow #1] and then take a step that way [the distance and direction of arrow #2] and we say, where did we actually move? We could have done it all in one step, this one [from the beginning of arrow #1 to the end of arrow #2]. So this is the one step which is the equivalent of the succession of the other steps. Adding means putting together steps... The square of the [summation] arrow determines the probability of the reflection."

"People are always asking for the latest developments in the unification of this theory with that theory, and they don't give us a chance to tell them anything about what we know pretty well. They always want to know the things we don't know."

"The theory of quantum electrodynamics describes Nature as absurd from the point of view of common sense. And it agrees fully with experiment. So I hope you accept Nature as She is — absurd."

"It is to be emphasized that no matter how many [amplitude] arrows we draw, add, or multiply, our objective is to calculate a single final arrow for the event. Mistakes are often made by physics students at first because they do not keep this important point in mind. They work for so long analyzing events involving a single photon that they begin to think that the arrow is somehow associated with the photon [rather than with the event]."

"Why are the theories of physics so similar in their structure? There are a number of possibilities. The first is the limited imagination of physicists: when we see a new phenomenon, we try to fit it into the framework we already have—until we have made enough experiments, we don't know that it doesn't work. So when some fool physicist gives a lecture at UCLA in 1983 and says, “This is the way it works, and look how wonderfully similar the theories are,” it's not because Nature is really similar; it's because the physicists have only been able to think of the same damn thing, over and over again. Another possibility is that it is the same damn thing over and over again—that Nature has only one way of doing things, and She repeats her story from time to time. A third possibility is that things look similar because they are aspects of the same thing—some larger picture underneath, from which things can be broken into parts that look different, like fingers on the same hand. Many physicists are working very hard trying to put together a grand picture that unifies everything into one super-duper model. It's a delightful game, but at present time none of the speculators agree with any of the other speculators as to what the grand picture is."

"I don't know what's the matter with people: they don't learn by understanding; they learn by some other way — by rote or something. Their knowledge is so fragile!"

"The electron is a theory we use; it is so useful in understanding the way nature works that we can almost call it real."

"And this is medicine?"

"And then I thought to myself, "You know, what they think of you is so fantastic, it's impossible to live up to it. You have no responsibility to live up to it!"It was a brilliant idea: You have no responsibility to live up to what other people think you ought to accomplish. I have no responsibility to be like they expect me to be. It's their mistake, not my failing."

"Finally, I said that I couldn’t see how anyone could be educated by this self-propagating system in which people pass exams, and teach others to pass exams, but nobody knows anything."

"I have to understand the world, you see."

"One of the most important things in this 'guess — compute consequences — compare with experiment' business is to know when you are right. It is possible to know when you are right way ahead of checking all the consequences. 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. When you get it right, it is obvious that it is right — at least if you have any experience — because usually what happens is that more comes out than goes in. Your guess is, in fact, that something is very simple. If you cannot see immediately that it is wrong, and it is simpler than it was before, then it is right. The inexperienced, the crackpots, and people like that, make guesses that are simple, but you can immediately see that they are wrong, so that does not count. Others, the inexperienced students, make guesses that are very complicated, and it sort of looks as if it is all right, but I know it is not true because the truth always turns out to be simpler than you thought."

"That was the beginning and the idea seemed so obvious to me that I fell deeply in love with it. And, like falling in love with a woman, it is only possible if you don't know too much about her, so you cannot see her faults. The faults will become apparent later, but after the love is strong enough to hold you to her. So, I was held to this theory, in spite of all the difficulties, by my youthful enthusiasm."

"What the students are taught ...now ...about physics ...The numbers are much bigger... so enormous you can't count them directly, and so we've invented a fantastic array of tricks and gimmicks for putting together the numbers... without actually doing it. ...We don't actually ...draw 7,000 arrows and find... the end point... just like we don't actually count 415 pennies... We do it by... the tricks of mathematics, and that's all. So... we're not going to worry about that. ...[Y]ou don't have to know about mathematics. All you have to know is what it is... tricky ways of doing something which would be laborious otherwise."

"[I]n the years we have developed enormous abilities in mathematics and it takes a long time to train the students, and so they're very highly educated in that, but if you ask them why. Now we go back to the Mayans... [W]hy the rule? ...They don't know. They don't understand... The more accurately they can do it... adds nothing to their understanding... The student who is able to make these calculations of Venus... Mars, the Sun, the eclipses and everything else is a super priest, doesn't know why, any better. And if you were to explain that it was nothing but counting days, you would be reduced to the truth... and to an honest statement that he doesn't understand it."

"If we make an instrument that can detect light, that's as sensitive as it can possibly be made. ...This ...is called a photomultiplier."

"Amplify. ...[W]hen we have a device like this and we put it in the dark... it goes click, click... Every once in a while a light particle comes in: a photon. This is a particle in every sense. ...[I]f you have a very weak light... and... you put two cells out, and there's just a few... [photons] coming, then it goes on one or the other... the particle is either here or there. ...It is particles, in every way, whenever you can detect it. ...If we were ten times more sensitive to light, then in the dark, we would see... little flashes, little tiny... dots of light, the nerves would go off just like the photomultiplier, in spots. But the human eye is not quite that sensitive, and it takes 5 or 6 ...photons ...to make one nerve fiber go off. ...So we cannot detect, with the eye, light quite low enough to notice the fact that it comes in the form of rain drops."

"[T]he size of the arrow depends upon the... materials... [Y]ou make an arrow, and depending upon the time it takes for the light to get from the source to... where you... count it, you turn that arrow like a clock... round, round, depending on how much time it takes... every second it goes around... 1 followed by 15 zeros [10^{15}] times... It doesn't take light very long to get from the source... but it still turns a lot of times... It's like the roulette wheel and just the moment it hits the counter, it happens to be setting at some angle... It can look like a small angle when you're done, but you had to turn... like a clock hand after 25 years... it can start at 2:00 and end up at 2:15. ...That's ...the arrow for the first surface. Now the arrow for the second surface. Rule: same as the arrow for the first surface... [rotated] in the... opposite direction... When you go from air to glass it's one way... glass to air you change it around. ...You start this way for the second surface, and you turn this [arrow]... for the time, and when you get finished with this roulette wheel in the second one it comes out so. And now you add them together... and that's the laws of... light, and that will tell you whether it reflects or doesn't reflect."

"The probability of an event is always... the square of an amplitude... the size [area] of a circle corresponding to an arrow. An arrow is called an amplitude. For every event you calculate an amplitude (which is an arrow on a plane). The probability is the area corresponding to that arrow."

"I start with the simplest phenomena... the first... is the phenomena of light. Early on, when light was being investigated by Newton, he thought that the light that came into the eye was like a rain of particles, like rain drops... [M]ore light meant more particles... and one kind of color light would one kind of rain drop and another... would be a different kind of rain drop... over the whole spectrum... and if we would some day have sufficiently delicate instruments, we would presumably discover that it was like a pattering... [I]t would go click, click, click when the particles came raining down. ...He also discovered ...the light from the soap bubbles or light from thin films... The brightness of reflection... depends on how thick the film is. As the film gets thicker and thinner, it gets brighter and darker. That was hard for him to understand from the point of view of particles. Finally a theory of waves was invented which explained that very easily... until we measured light very precisely... and lo and behold, to our horror, it behaved like particles."

"The different colored light... correspond to particles of different energy, that is energy comes in lumps and these lumps have different sizes for the different colored light. [I]t was hard... virtually impossible to understand... that the reflection of light... from layers of different thicknesses varies by using particles... [T]hat makes a problem which I want to describe..."

"[T]o make it easy... we'll suppose that all the light... is exactly one color... At night... they have these yellow street lights... that's a sodium light... and that emits light all of one color... Then take the soap bubble and blow it at night.. and then you'll see the bands... [You] can take... very thin glass... you can see very thin bands, even in a reasonable size thickness... [S]uppose then that we do have light like from sodium-vapor so that all the light... is always photons of exactly the same energy. We call it monochromatic, one color light."

"There has never been a satisfactory model of the very simple process of reflection of light from thin surfaces or... for any other phenomenon. Satisfactory in the old fashioned classical view. A logical hocus-pocus has to be done quantum mechanically in order in order to describe these things... This is another example of the type of difficulty when you try to reason in a straight forward... in a classical way about a simple phenomenon."

"I want you to think of an arrow in another way... Here is an arrow... Now if we multiply, you have to think in a different way than for adding. There's an arrow... and imagine there's a [different] standard arrow... always horizontal and has unit length, that's the standard unit arrow. Now suppose I have a second arrow and I want to multiply them... [W]hat do I mean by multiplying? ...Let me first describe this [first] arrow [number 1] ...compare it to the standard arrow and ask for the relation... You can turn... and shrink it. So an arrow describes... how much I have to shrink the standard, and how much I have to rotate it to get the arrow I want. Now multiplication of arrows means that you do these rotations and shrinkings in succession. ...Now if I take this arrow [#2] ...this red [arrow #3] is the product [of arrow #1 and arrow #2].... It bears the same geometric relationship to the purple arrow [#2] as the blue one [arrow number 1] bears to the black one [standard arrow]. In other words it's supposed to be turned the same degree and shrunk the same degree as the blue one [arrow #2] is to the black [standard] one. In other words this [arrow #1] is to that [standard arrow], as this [arrow #3] arrow is to that [arrow #2]."

"That's the way multiplication works you know, with numbers it's the same. ...That's why we call it multiplication. ...Suppose you wanted to say that 6 = 3 x 2, which is true. But let me look at it a different way... This is the analog [to arrow multiplication]... The 2 bears a relation, 2 is not a number from this point of view. It's a relationship. It bears a relation to 1. It's an expansion of 1. How much do you have to expand 1? ...Yeah, double. ...That's what you do to 3 to get 6. That's why... it's called multiplication, because we do to this arrow [#2], what we had to do to the original one [standard arrow] to get the blue one [arrow #1]."

"Will you understand what I'm going to tell you? ... No, you're not going to be able to understand it. ... That is because I don't understand it. Nobody does."

"While I am describing to you how Nature works, you won't understand why Nature works that way. But you see, nobody understands that."

"When a photon comes down, it interacts with electrons throughout the glass, not just on the surface. The photon and electrons do some kind of dance, the net result of which is the same as if the photon hit only on the surface."

"You will have to brace yourselves for this — not because it is difficult to understand, but because it is absolutely ridiculous: All we do is draw little arrows on a piece of paper — that's all!"

"Immediately you would like to know where this number for a coupling comes from: is it related to pi, or perhaps to the base of natural logarithms? Nobody knows. It's one of the greatest damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the "hand of God" wrote that number, and "we don't know how He pushed His pencil." We know what kind of a dance to do experimentally to measure this number very accurately, but we don't know what kind of dance to do on the computer to make this number come out — without putting it in secretly!"

"I wanted very much to learn to draw, for a reason that I kept to myself: I wanted to convey an emotion I have about the beauty of the world. It's difficult to describe because it's an emotion. It's analogous to the feeling one has in religion that has to do with a god that controls everything in the whole universe: there's a generality aspect that you feel when you think about how things that appear so different and behave so differently are all run "behind the scenes" by the same organization, the same physical laws. It's an appreciation of the mathematical beauty of nature, of how she works inside; a realization that the phenomena we see result from the complexity of the inner workings between atoms; a feeling of how dramatic and wonderful it is. It's a feeling of awe — of scientific awe — which I felt could be communicated through a drawing to someone who had also had this emotion. It could remind him, for a moment, of this feeling about the glories of the universe."