Physicists From The United States

"[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."

"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."

"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."

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

"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"

"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."

"[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."

"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."

"[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."

"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."

"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."

"We are at the very beginning of time for the human race. It is not unreasonable that we grapple with problems. But there are tens of thousands of years in the future. Our responsibility is to do what we can, learn what we can, improve the solutions, and pass them on. ...It is our responsibility to leave the people of the future a free hand. In the impetuous youth of humanity, we can make grave errors that can stunt our growth for a long time. This we will do if we say we have the answers now, so young and ignorant as we are. If we suppress all discussion, all criticism, proclaiming "This is the answer, my friends; man is saved!" we will doom humanity for a long time to the chains of authority, confined to the limits of our present imagination. It has been done so many times before. ...It is our responsibility as scientists, knowing the great progress which comes from a satisfactory philosophy of ignorance, the great progress which is the fruit of freedom of thought, to proclaim the value of this freedom; to teach how doubt is not to be feared but welcomed and discussed; and to demand this freedom as our duty to all coming generations."

"Therefore psychologically 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."

"It is not unscientific to make a guess, although many people who are not in science think it is. Some years ago I had a conversation with a layman about flying saucers — because I am scientific I know all about flying saucers! I said “I don’t think there are flying saucers”. So my antagonist said, “Is it impossible that there are flying saucers? Can you prove that it’s impossible?” “No”, I said, “I can’t prove it’s impossible. It’s just very unlikely”. At that he said, “You are very unscientific. If you can’t prove it impossible then how can you say that it’s unlikely?” But that is the way that is scientific. It is scientific only to say what is more likely and what less likely, and not to be proving all the time the possible and impossible. To define what I mean, I might have said to him, "Listen, I mean that from my knowledge of the world that I see around me, I think that it is much more likely that the reports of flying saucers are the results of the known irrational characteristics of terrestrial intelligence than of the unknown rational efforts of extra-terrestrial intelligence." It is just more likely. That is all."

"Nature's imagination far surpasses our own."

"In general, we look for a new law by the following process: First we guess it. Then we – now don't laugh, that's really true. Then we compute the consequences of the guess to see what, if this is right, if this law that we guessed is right, to see what it would imply. And then we compare the computation results to nature, or we say compare to experiment or experience, compare it directly with observations to see if it works. If it disagrees with experiment, it's wrong. In that simple statement is the key to science. It doesn't make any difference how beautiful your guess is, it doesn't make any difference how smart you are, who made the guess, or what his name is. If it disagrees with experiment, it's wrong. That's all there is to it."

"In general we look for a new law by the following process. First we guess it. Then we compute the consequences of the guess to see what would be implied if this law that we guessed is right. Then we compare the result of the computation to nature, with experiment or experience, compare it directly with observation, to see if it works. 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."

"Do not keep saying to yourself, if you can possibly avoid it, "But how can it be like that?" because you will get "down the drain", into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that."

"I think I can safely say that nobody understands quantum mechanics."

"Our imagination is stretched to the utmost, not, as in fiction, to imagine things which are not really there, but just to comprehend those things which are there."

"For those who want some proof that physicists are human, the proof is in the idiocy of all the different units which they use for measuring energy."

"So in order to understand the physics one must always have a neat balance and contain in his head all of the various propositions and their interelationships because the laws often extend beyond the range of their deductions. This will only have no importance when all the laws are known."

"So we have these wide principles which sweep across all the different laws, and if one takes too seriously its derivations, and feels that this is only valid because this [assumed more fundamental principle] is valid, you cannot understand the interconnections of the different branches of physics. Some day, when physics is complete, then maybe with this kind of argument we'll know all the laws, then we can start with some axioms (and no doubt somebody will figure out a particular way of doing it) and then all the deductions will be made. But while we don't know all the laws, we can use some to make guesses at theorems which extend beyond the proof."

"Now we have a problem. We can deduce, often, from one part of physics like the law of gravitation, a principle which turns out to be much more valid than the derivation. This doesn't happen in mathematics, that the theorems come out in places where they're not supposed to be!"

"Mathematics is not just a language. Mathematics is a language plus reasoning. It's like a language plus logic. Mathematics is a tool for reasoning. It's, in fact, a big collection of the results of some person's careful thought and reasoning. By mathematics, it is possible to connect one statement to another."

"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. ... If you want to learn about nature, to appreciate nature, it is necessary to understand the language that she speaks in."

"chapter 2, “The Relation of Mathematics to Physics,” p. 58; video"

"...Dirac discovered the correct laws for relativity quantum mechanics simply by guessing the equation. The method of guessing the equation seems to be a pretty effective way of guessing new laws. This shows again that mathematics is a deep way of expressing nature, and any attempt to express nature in philosophical principles, or in seat-of-the-pants mechanical feelings, is not an efficient way. ...It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypotheses that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities."

"[T]he total amount that a physicist knows is very little. He has only to remember the rules to get him from one place to another..."

"Nature uses only the longest threads to weave her patterns, so each small piece of her fabric reveals the organization of the entire tapestry."

"It is impossible, by the way, when picking one example of anything, to avoid picking one which is atypical in some sense."

"If we have confidence in a law, then if something appears to be wrong it can suggest to us another phenomenon."

"The next question was — what makes planets go around the sun? At the time of Kepler some people answered this problem by saying that there were angels behind them beating their wings and pushing the planets around an orbit. As you will see, the answer is not very far from the truth. The only difference is that the angels sit in a different direction and their wings push inward."

"This is the key of modern science and is the beginning of the true understanding of nature. This idea. That to look at the things, to record the details, and to hope that in the information thus obtained, may lie a clue to one or another of a possible theoretical interpretation."

"A person talks in such generalities that everyone can understand him and it's considered to be some deep philosophy. However, I would like to be very rather more special and I would like to be understood in an honest way, rather than in a vague way."

"On the infrequent occasions when I have been called upon in a formal place to play the bongo drums, the introducer never seems to find it necessary to mention that I also do theoretical physics."

"Perhaps you will not only have some appreciation of this culture; it is even possible that you may want to join in the greatest adventure that the human mind has ever begun."

"I hope ... that you will find someday that, after all, it isn't as horrible as it looks."

"The "paradox" is only a conflict between reality and your feeling of what reality "ought to be.""

"There are those who are going to be disappointed when no life is found on other planets. Not I — I want to be reminded and delighted and surprised once again, through interplanetary exploration, with the infinite variety and novelty of phenomena that can be generated from such simple principles. The test of science is its ability to predict. Had you never visited the earth, could you predict the thunderstorms, the volcanoes, the ocean waves, the auroras, and the colorful sunset? A salutary lesson it will be when we learn of all that goes on on each of those dead planets — those eight or ten balls, each agglomerated from the same dust cloud and each obeying exactly the same laws of physics."

"Whenever you see a sweeping statement that a tremendous amount can come from a very small number of assumptions, you always find that it is false. There are usually a large number of implied assumptions that are far from obvious if you think about them sufficiently carefully."

"It requires a much higher degree of imagination to understand the electromagnetic field than to understand invisible angels. ... I speak of the E and B fields and wave my arms and you may imagine that I can see them ... [but] I cannot really make a picture that is even nearly like the true waves."

"The same equations have the same solutions"

"The physicist needs a facility in looking at problems from several points of view. The exact analysis of real physical problems is usually quite complicated, and any particular physical situation may be too complicated to analyze directly by solving the differential equation. But one can still get a very good idea of the behavior of a system if one has some feel for the character of the solution in different circumstances. Ideas such as the field lines, capacitance, resistance, and inductance are, for such purposes, very useful. ... On the other hand, none of the heuristic models, such as field lines, is really adequate and accurate for all situations. There is only one precise way of presenting the laws, and that is by means of differential equations. They have the advantage of being fundamental and, so far as we know, precise. If you have learned the differential equations you can always go back to them. There is nothing to unlearn."

"From a long view of the history of mankind — seen from, say, ten thousand years from now — there can be little doubt that the most significant event of the 19th century will be judged as Maxwell's discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade."

"So far as we know, all the fundamental laws of physics, like Newton's equations, are reversible."

"In fact, the science of thermodynamics began with an analysis, by the great engineer Sadi Carnot, of the problem of how to build the best and most efficient engine, and this constitutes one of the few famous cases in which engineering has contributed to fundamental physical theory. Another example that comes to mind is the more recent analysis of information theory by Claude Shannon. These two analyses, incidentally, turn out to be closely related."

"There are many interesting phenomena ... 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."

"Finally, we make some remarks on why linear systems are so important. The answer is simple: because we can solve them! So most of the time we solve linear problems. Second (and most important), it turns out that the fundamental laws of physics are often linear. The Maxwell equations for the laws of electricity are linear, for example. The great laws of quantum mechanics turn out, so far as we know, to be linear equations. That is why we spend so much time on linear equations: because if we understand linear equations, we are ready, in principle, to understand a lot of things."

"So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentalization is really artificial, and we should take our intellectual pleasures where we find them."