The Feynman Lectures on Physics, Vol. I: The New Millennium Edition: Mainly Mechanics, Radiation, and Heat (Volume 1)

by Richard P. Feynman

Color Vision

The human eye

There are many interesting phenomena associated with vision which involve a mixture of physical phenomena and physiological processes, and the full appreciation of natural phenomena, as we see them, must go beyond physics in the usual sense. We make no apologies for making these excursions into other fields, because the separation of fields, as we have emphasized, is merely a human convenience, and an unnatural thing. Nature is not interested in our separations, and many of the interesting phenomena bridge the gaps between fields.

There are several kinds of cells: there are cells that carry the information toward the optic nerve, but there are others that are mainly interconnected “horizontally.” There are essentially four kinds of cells, but we shall not go into these details now. The main thing we emphasize is that the light signal is already being “thought about.” That is to say, the information from the various cells does not immediately go to the brain, spot for spot, but in the retina a certain amount of the information has already been digested, by a combining of the information from several visual receptors. It is important to understand that some brain-function phenomena occur in the eye itself.

Color depends on intensity

Among the interesting consequences of this shift is, first, that there is no color, and second, that there is a difference in the relative brightness of differently colored objects. It turns out that the rods see better toward the blue than the cones do, and the cones can see, for example, deep red light, while the rods find that absolutely impossible to see. So red light is black so far as the rods are concerned.

The phenomenon is called the Purkinje effect.

We see that the peak sensitivity of the rods is in the green region and that of the cones is more in the yellow region. If there is a red-colored page (red is about m) we can see it if it is brightly lighted, but in the dark it is almost invisible.

A faint star or nebula can sometimes be seen better by looking a little to one side than directly at it, because we do not have sensitive rods in the middle of the fovea.

Measuring the color sensation

Is there more than one spectral distribution which produces the same apparent visual effect? The answer is, definitely yes.

The second principle of color mixing of lights is this: any color at all can be made from three different colors, in our case, red, green, and blue lights.

Any three differently colored lights whatsoever2 can always be mixed in the correct proportion to produce any color whatsoever.

The chromaticity diagram

Inside the boundary are colors that can be made with lights, and outside it are colors that cannot be made with lights, and nobody has ever seen them (except, possibly, in after-images!).

The mechanism of color vision

Physiochemistry of color vision

Color is not a question of the physics of the light itself. Color is a sensation, and the sensation for different colors is different in different circumstances.

It is very important to appreciate that a retina is already “thinking” about the light; it is comparing what it sees in one region with what it sees in another, although not consciously.

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Mechanisms of Seeing

The sensation of color

The physiology of the eye

(It would be nice if we could make optical glass in which we could adjust the index throughout, for then we would not have to curve it as much as we do when we have a uniform index.)

Been there. Done that. Have the T-shirt.

We have already emphasized another strange thing about the eye, that the light-sensitive cells are on the wrong side, so that the light has to go through several layers of other cells before it gets to the receptors—it is built inside out! So some of the features are wonderful and some are apparently stupid.

The rod cells

The compound (insect) eye

Our eye works from angstroms to angstroms, from red to violet, but the bee’s can see down to angstroms into the ultraviolet!

Other eyes

Neurology of vision

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Quantum Behavior

Atomic mechanics

“Quantum mechanics” is the description of the behavior of matter in all its details and, in particular, of the happenings on an atomic scale. Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen.

Because atomic behavior is so unlike ordinary experience, it is very difficult to get used to and it appears peculiar and mysterious to everyone, both to the novice and to the experienced physicist. Even the experts do not understand it the way they would like to, and it is perfectly reasonable that they should not, because all of direct, human experience and of human intuition applies to large objects. We know how large objects will act, but things on a small scale just do not act that way. So we have to learn about them in a sort of abstract or imaginative fashion and not by connection with our direct experience.

An experiment with bullets

An experiment with waves

An experiment with electrons

The interference of electron waves

We conclude the following: The electrons arrive in lumps, like particles, and the probability of arrival of these lumps is distributed like the distribution of intensity of a wave. It is in this sense that an electron behaves “sometimes like a particle and sometimes like a wave.”

Watching the electrons

It is true, or is it not true, that the electron either goes through hole 1 or it goes through hole 2?” The only answer that can be given is that we have found from experiment that there is a certain special way that we have to think in order that we do not get into inconsistencies. What we must say (to avoid making wrong predictions) is the following. If one looks at the holes or, more accurately, if one has a piece of apparatus which is capable of determining whether the electrons go through hole 1 or hole 2, then one can say that it goes either through hole 1 or hole 2. But, when one does not try to tell which way the electron goes, when there is nothing in the experiment to disturb the electrons, then one may not say that an electron goes either through hole 1 or hole 2. If one does say that, and starts to make any deductions from the statement, he will make errors in the analysis. This is the logical tightrope on which we must walk if we wish to describe nature successfully.

First principles of quantum mechanics

Summary

We have no ideas about a more basic mechanism from which these results can be deduced.

Yes! physics has given up. We do not know how to predict what would happen in a given circumstance, and we believe now that it is impossible, that the only thing that can be predicted is the probability of different events. It must be recognized that this is a retrenchment in our earlier ideal of understanding nature. It may be a backward step, but no one has seen a way to avoid it.

The uncertainty principle

The uncertainties in the position and momentum at any instant must have their product greater than or equal to half the reduced Planck constant.

The uncertainty principle “protects” quantum mechanics. Heisenberg recognized that if it were possible to measure the momentum and the position simultaneously with a greater accuracy, the quantum mechanics would collapse. So he proposed that it must be impossible. Then people sat down and tried to figure out ways of doing it, and nobody could figure out a way to measure the position and the momentum of anything—a screen, an electron, a billiard ball, anything—with any greater accuracy. Quantum mechanics maintains its perilous but accurate existence.

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