Richard Feynman Quotes

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.

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

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.

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.

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].

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].

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)

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.

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.

[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.

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...

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...

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.

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.

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.