Favourites - The Feynman Lectures on Physics

Rereading some of my favourite sections and thought i'd share what lessons I think professor Feynman was trying to convey. Enjoy.

Each piece, or part, of the whole nature is always an approximation to the complete truth, or the complete truth so far as we know it. In fact, everything we know is only some kind of approximation, because we know that we do not know all the laws as yet. Therefore, things must be learned only to be unlearned again or, more likely, to be corrected.......The test of all knowledge is experiment. Experiment is the sole judge of scientific “truth”.
~Volume I, 1-1, Introduction

A poet once said, "The whole universe is in a glass of wine." We will probably never know in what sense he meant that, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe. There are the things of physics: the twisting liquid which evaporates depending on the wind and weather, the reflections in the glass, and our imagination adds the atoms. The glass is a distillation of the Earth's rocks, and in its composition we see the secrets of the universe's age, and the evolution of stars. What strange arrays of chemicals are in the wine? How did they come to be? There are the ferments, the enzymes, the substrates, and the products. There in wine is found the great generalization: all life is fermentation. Nobody can discover the chemistry of wine without discovering, as did Louis Pasteur, the cause of much disease. How vivid is the claret, pressing its existence into the consciousness that watches it! If our small minds, for some convenience, divide this glass of wine, this universe, into parts — physics, biology, geology, astronomy, psychology, and so on — remember that Nature does not know it! So let us put it all back together, not forgetting ultimately what it is for. Let it give us one more final pleasure: drink it and forget it all!
~Volume I, 3-10, The relation of Physics to other sciences

It is important to realize that in physics today, we have no knowledge what energy is. We do not have a picture that energy comes in little blobs of a definite amount.
~Volume I, 4-1

We can't define anything precisely. If we attempt to, we get into that paralysis of thought that comes to philosophers… one saying to the other: "you don't know what you are talking about!". The second one says: "what do you mean by talking? What do you mean by you? What do you mean by know?"
~Volume I, 8-2

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.
~Volume II, 1-6 end

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.
~"The Laws of Thermodynamics"

If, in some cataclysm, all scientific knowledge were to be destroyed, and only one sentence passed on to the next generation of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or atomic fact, or whatever you wish to call it) that all things are made of atoms — little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence you will see an enormous amount of information about the world, if just a little imagination and thinking are applied.

Poets say science takes away from the beauty of the stars — mere globs of gas atoms. Nothing is "mere". I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination — stuck on this carousel my little eye can catch one-million-year-old light. A vast pattern — of which I am a part... What is the pattern or the meaning or the why? It does not do harm to the mystery to know a little more about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?
~Footnote

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.

...the "paradox" is only a conflict between reality and your feeling of what reality "ought to be."
~Volume III, p. 18-9

...and you will find someday that, after all, it isn’t as horrible as it looks.
~Volume III, Epilogue

~"Physics is like sex. Sure, it may give some practical results, but that's not why we do it."

Back to the future

Groing up, I have always pondered on what the future holds. What will the future bring? If the inflationary model is correct, all of us live on a planet that is lost in the multiverse. Almost nowhere, are the physical conditions like those we observe. And our rare pocket of the universe is running out of time. Dark energy has already overtaken all other forms of matter and radiation, and has taken command of the expansion of the universe.

In a trillion years, our home will be well on its way toward a vacuous oblivion. Virtually all the galaxies we see today will still exist, but the stars will be gradually burning out. There will in all likelihood still be stars, planets, and life. But the accelerated expansion due to dark energy will have spread out the galaxies so much that nothing beyond the Andromeda Galaxy be visible to us.

The surviving civilizations in the Milky Way will know from the historical record that the universe was once filled with billions of galaxies, which emerged from tiny fluctuations in a hot plasma uniformly spread over space. But all the observational clues available today will be long gone by then. It is hard to imagine that a newly emerging civilization could piece together cosmic history on its own. In the inflationary model, therefore, the present is a unique epoch in the evolution of the universe where we can see both substantial amounts of the matter and radiation that dominated our past and the dark energy that will dominate our future. At other epochs, only one or the other would be detectable.

The same trillion-year prospectus applies if the Cyclic model is correct, but it holds nearly everywhere in space, not just in isolated pockets. After a trillion years, however, the story changes dramatically. The branes begin to approach each other, the dark energy decreases, and expansion slowly grinds to a halt. There will be no galaxies or other distant sources that future observers can use to detect the expansion rate, unless the future civilizations send regular test probes beyond the Milky Way. Yet there will be some novel physical effects to indicate that the end of the cycle is near. First, many fundamental physical constants of nature, like the strength of gravity and the strong, weak, and electromagnetic forces, will begin to change noticeably because their values depend on the separation between the branes. They don’t change during earlier stages, like today, because the brane separation is frozen. That is why they are interpreted as constants of nature. However, once the branes start to rush toward each other, all the physical constants will start to change in concert. A number of sensitive experiments exist today that monitor these constants and search for time variation. So far, no conclusive evidence for change has been found. According to the cyclic model, physicists performing those same experiments during the last 10 billion years before the next brane collision would detect a large variation of the constants, whose rate would increase as the branes speed up. In the final moments before the crunch, the rapid changes would become dramatic: particles would lose their mass and the laws of nature would be restored to a much simpler and more symmetrical form.

In reality, what is happening is that something enormous is approaching fast along a dimension we cannot see. The realization will come in a flash when, suddenly, everywhere in space lights up with new matter and radiation from the collision. The temperature soars to 10^15 times the surface temperature of the sun, evaporating any remnant structures from the previous cycle. The quarks and gluons of which we all are made join the flood of new quarks and gluons created at the bang, and the cycle of the cosmos is renewed.

One Hundred Years

The cosmological debate between the inflationary and the cyclic models is only just beginning to simmer in the scientific community. Many cosmologists have not yet given the issue much consideration because they see no reason for thinking about an alternative until some observation or experiment contradicts the inflationary picture. Others are reluctant to consider a model so deeply rooted in concepts like extra dimensions or branes because they regard these ideas as too far-fetched, even though string theorists are finding these concepts to be essential for unifying our understanding of the fundamental forces. In fact, contemporary versions of the inflationary model are now using the same stringy building blocks.

The reluctance of some to introduce so many new elements into cosmology is understandable. Science usually advances through small variations on an established idea. Radically new directions are not considered unless the scientific case is compelling. For that to happen, the problems with the conventional picture (which might be swept under the rug if there were no competing idea) have to become recognized, and the novel components underlying the new approach have to become familiar. Historically, this conservative approach has served science well, enabling it to make steady progress without getting diverted. In cosmology, for example, the main elements of the current inflationary model – the big bang picture, inflationary expansion, dark matter, and dark energy – were all subject to the same resistance when they were first introduced, and it took many years for them to be accepted.

The cyclic model, if it is worthy, will require similar patience. As discussions and investigations of the cyclic picture continue over the next few years and some of the weaknesses of the inflationary model become more exposed, interest will grow. The fact that two such dissimilar models can predict such similar results is too intriguing to ignore. Creative experiments will feel compelled to mount the decisive test between the two views of cosmic history because the issues at stake are too captivating to be ignored.

In settling the debate, cosmologists will have come to grips with the most fundamental questions about space and our place in the cosmos; about time and our moment in cosmic history; and about nature and our ultimate ability to figure out its laws. The answers will be our legacy to future generations. One hundred years from now, they will be taught to every schoolchild. They will permeate human discourse and inform our philosophical and religious views. And they will motivate many of the scientific advances of the twenty-second century.

Every elementary science textbook will include the WMAP snapshot or some improved image of the cosmic background radiation across the sky. The authors of the textbook will point to it as one of the great achievements of the twenty-first century. What will they claim about its significance?

If the inflationary model is proven correct, they will write that the image shows primordial wrinkles created at the end of inflation, about 10^-35 seconds after the big bang, when the temperature of the universe was about 10^27 degrees. The universe had a beginning of some sort, perhaps the big bang, but the period of rapid expansion diluted all information about what happened before inflation. Because human-made particle accelerators cannot possibly reach the energies needed to probe conditions before inflation, there is a limit to how much we can learn through observations or experiments about the fundamental laws of the universe. If the inflationary landscape picture survives, it may be impossible to discover the secrets of the universe because everything we see, no matter how far we look, has little in common with the rest of the cosmos, which consists of a combination of inflating regions and pocket universes with different physical properties. As for our own island, the likely outcome is that we are approaching a vacuous, uninhabitable state that will last forever. Perhaps we live in a misanthropic universe.

If the cyclic model proves to be correct, the textbook authors will write that the image shows the splatter of matter and radiation created at the big bang itself. The big bang was not the beginning but the moment separating our current period of expansion and cooling from a previous one. They will explain that the universe has an extra dimension, that the extra dimension is bounded by branes, and that the branes collided with each other to create the bang. They will show how the image can be used to determine the collision speed of the branes and to check that all the matter and radiation we see was created by the collision.

They will write that the WMAP image is also a window on the previous cycle. The small wrinkles in distribution of matter and energy were created billions of years before by random quantum waves that spontaneously appeared on the surfaces of the branes. A similar effect is beginning now that will eventually give birth to new galaxies and new stars in the next cycle. Because conditions everywhere in the universe are similar to what we observe here and because we can collect observable and measureable traces from an entire cycle, the whole cosmos can be comprehended from our single vantage point.

In 2010, it is too early to say which, if any, of these models will appear in the textbooks of the next century. But all of us can watch as a new theory blossoms into maturity and a mature theory is reinvigorated by the challenge. We can have the fun of debating the two visions of the universe and weighing in with our personal convictions while the matter remains in doubt. And we can do all this secure in the knowledge that the debate will not be endless.

Quantum Philosophy

Quantum Mechanics
Let us consider briefly the two aspects of this problem. As always, one is the philosophical implication for physics, and the other is the extrapolation of philosophical matters to other fields. When philosophical ideas associated with science in general, are dragged into another field, they are usually completely distorted. Therefore we shall confine our remarks as much as possible to physics itself.

First of all, the most interesting aspect is the idea of the uncertainty principle; making an observation affects a phenomenon. It has always been known that making observations affects a phenomenon, but the point is that the effect cannot be disregarded or minimized or decreased arbitrarily by rearranging the apparatus. When we look for a certain phenomenon we cannot help but disturb it in a certain minimum way, and the disturbance is necessary for the consistency of the viewpoint. The observer was sometimes important in prequantum physics, but only in a trivial sense. However, there is no doubt that a problem has been raised: if a tree falls in forest and there is nobody there to hear it, does it make a noise? A real tree falling in a real forest makes a sound, of course, even if nobody is there. Even if nobody is present to hear it, there are other traces left. The sound will shake some leaves, and if we were careful enough we might find somewhere that some thorn had rubbed against a leaf and made a tiny scratch that could not be explained unless we assumed the leaf were vibrating. So in a certain sense I guess, we would have to admit that there is a sound made. We might ask some question like: was there a sensation of sound? No, sensations have to do, presumably, with consciousness. And whether ants are conscious and whether there were ants in the forest, or whether the tree was conscious, we do not know. Let us just leave that problem in that form.

Another thing that people have emphasized since quantum mechanics was developed is the idea that we should not speak about those things which we cannot measure. Unless a thing can be defined by measurement, it has no place in a theory - simple as that. And since an accurate value of the momentum of a localized particle cannot be defined by measurement, it therefore has no place in the theory. The idea that what was the matter with classical theory is a false position. It is careless analysis of the situation. Just because we cannot measure position and momentum precisely does not a priori mean that we cannot talk about them. It only means that we need not to talk about them. The situation in the sciences is this: A concept or an idea which cannot be measured or cannot be referred directly to experiment may or may not be useful. It need not exist in theory. In other words, suppose we compare the classical theory of the world with the quantum theory of the world, and suppose that it is true experimentally that we can measure position and momentum only imprecisely. The question is whether the ideas of the exact position of a particle and the exact momentum of a particle are valid or not. The classical theory admits the idea, and hence, the quantum theory does not. This does not mean that classical physics is wrong. When the new quantum mechanics was discovered, the classical people - which by the way included everyone except Heisenberg, Schrödinger, and Born - said something like, "Look, your theory is not any good because you cannot answer certain questions like: what is the exact position of a particle? Which slit does it go through?" etc … and Heisenberg's answer would've been something like, "I do not need to answer such questions because you cannot ask such a question experimentally" It is that we do not have to. Consider two theories a and b. a contains an idea that cannot be checked directly but which is used in the analysis, and the other, b, does not contain the idea. If they disagree in their preconditions, one could not claim that b is false because it cannot explain this idea that is in a because that idea is one of the things that cannot be checked directly. It is always good to know (in my opinion) which ideas cannot be checked directly, but it is not necessary to remove them all. It is not true that we can pursue science completely by using only those concepts which are directly subject to experiment.

In quantum mechanics itself there is a probability amplitude, there is a potential, and there are many constructs that we cannot measure directly. The basis of science is its ability to predict. To predict means to tell what will happen in an experiment that has never been done. How can we do that? By assuming that we know what is there, independent of the experiment. We must extrapolate the experiments to a region where they have not yet been checked. If we do not do that, we have no prediction. So it was perfectly sensible for the classical physicists to go happily along and suppose that the position - which lets say obviously meant something for a baseball - meant something for an electron. It was a sensible procedure. Today we say that the law of relativity is supposed to be true at all energies, but someday somebody may come along and say how stupid we were. We do not know where we are "stupid" until we "stick our neck out" and so the whole idea is to put our neck out. And the only way to find out that we are wrong is to find out what our predictions are. It is absolutely necessary to make constructs.

We have already made a few remarks about the indeterminacy of quantum mechanics. That is, that we are unable now to predict what will happen in physics in a given physical circumstance which is arranged as carefully as possible. If we have an atom that is in an excited state and so is going to emit a photon, we cannot say when it will emit the photon. It has a certain amplitude to emit the photon at any time, and we can predict only a probability for emission: we cannot predict the future exactly. This is given rise to all kinds of nonsense and questions on the meaning of freedom of will, and of the idea that the world is uncertain.

Of course we must emphasize that classical physics is also indeterminate, in a sense. It’s usually thought that this indeterminacy, that we cannot predict the future, is an important quantum mechanical thing, and this is said to explain the behavior of the mind, feelings of free will etc ... But if the world were classical - if the laws of mechanics were classical - it is not quite obvious that the mind would not feel more or less the same. It is true classically that if we knew the position and the velocity of every particle in the world, or in a box of gas, we could predict exactly what would happen. Therefore the classical world is deterministic. Suppose, however, that we have a finite accuracy and do not know exactly where just one atom is, say to one part in a billion. Then as it goes along it hits another atom, and because we did not know the position better then to one part in a billion, we find an even larger error in the position after the collision. If we start with only a tiny error it rapidly magnifies to a very great uncertainty. For me to give an example, lets say, if water falls over a dam, it splashes obviously. If we stand nearby, every now and then a drop will land on our nose. This appears to be completely random, yet such a behavior would be predicted by purely classical laws! The exact position of all drops depends upon the precise wigglings of the water before it goes over the dam. Maybe you’re asking yourself now, how? Well, the tinniest irregularities are magnified in falling, so that we get complete randomness. Obviously, we cannot really predict the position of the drops unless we know the motion of the water absolutely, exactly.

Given an arbitrary accuracy, no matter how precise, one can find a time long enough that we cannot make predictions valid for that long a time. Now the point is that this length of time is not very large. It is not that the time is millions of years if the accuracy is one part in a billion. The time goes, in fact, only logarithmically with the error, and it turns out that in only a very, very tiny time we lose all our information. If the accuracy is taken to be one part in billions and billions - no matter how many billions we wish, provided we do stop somewhere - then we can find a time less than the time it took to state the accuracy - after which we can no longer predict what is going to happen! It is therefore not fair to say that from the apparent freedom and indeterminacy of the human mind, we should have realized that classical "deterministic" physics could not ever hope to understand it, and to welcome quantum mechanics as a release from a completely mechanistic universe. For already in classical mechanics there was indeterminability from a practical point of view.

~ Food for thought