More on this book
Kindle Notes & Highlights
Read between
November 15, 2015 - February 4, 2021
E-book ISBN: 978-0-465-04085-8
I think, however, that there isn’t any solution to this problem of education other than to realize that the best teaching can be done only when there is a direct individual relationship between a student and a good teacher—a situation in which the student discusses the ideas, thinks about the things, and talks about the things.
Each piece, or part, of the whole of nature is always merely an approximation to the complete truth, or the complete truth so far as we know it.
The test of all knowledge is experiment.
if an apple is magnified to the size of the earth, then the atoms in the apple are approximately the size of the original apple.
there is nothing that living things do that cannot be understood from the point of view that they are made of atoms acting according to the laws of physics.
When we say we are a pile of atoms, we do not mean we are merely a pile of atoms, because a pile of atoms which is not repeated from one to the other might well have the possibilities which you see before you in the mirror.
The “stage” on which the universe goes is the three-dimensional space of geometry, as described by Euclid, and things change in a medium called time. The elements on the stage are particles, for example the atoms, which have some properties.
That is what makes physics difficult—and very interesting. It is hard because the way things behave on a small scale is so “unnatural”; we have no direct experience with it. Here things behave like nothing we know of, so that it is impossible to describe this behavior in any other than analytic ways. It is difficult, and takes a lot of imagination.
We seem gradually to be groping toward an understanding of the world of subatomic particles, but we really do not know how far we have yet to go in this task.
(Mathematics is not a science from our point of view, in the sense that it is not a natural science. The test of its validity is not experiment.)
Certainly no subject or field is making more progress on so many fronts at the present moment, than biology, and if we were to name the most powerful assumption of all, which leads one on and on in an attempt to understand life, it is that all things are made of atoms, and that everything that living things do can be understood in terms of the jigglings and wigglings of atoms.
Well, it is sad to be alone, but that is the way it is in this world.
The stuff of which we are made, was “cooked” once, in a star, and spit out.
Next, we consider the science of psychology. Incidentally, psychoanalysis is not a science: it is at best a medical process, and perhaps even more like witch-doctoring.
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.
It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined!
What men are poets who can speak of Jupiter if he were like a man, but if he is an immense spinning sphere of methane and ammonia must be silent?
Conservation of Energy
It states that there is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes.
That is a most abstract idea, because it is a mathematical principle; it says that there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is just a strange fact that we can calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same.
In order to verify the conservation of energy, we must be careful that we have not put any in or taken any out. Second, the energy has a large number of different forms, and there is a formula for each one. These are: gravitational energy, kinetic energy, heat energy, elastic energy, electrical energy, chemical energy, radiant energy, nuclear energy, mass energy. If we total up the formulas for each of these contributions, it will not change except for energy going in and out. It is important to realize that in physics today, we have no knowledge of what energy is.
It is an abstract thing in that it does not tell us the mechanism or the reasons for the various formulas.
The general name of energy which has to do with location relative to something else is called potential energy.
In the last analysis, we do not understand the conservation laws deeply. We do not understand the conservation of energy. We do not understand energy as a certain number of little blobs.
So we do not understand this energy as counting something at the moment, but just as a mathematical quantity, which is an abstract and rather peculiar circumstance.
As independence in space has to do with the conservation of momentum, independence of time has to do with the conservation of energy, and finally, if we turn our apparatus, this too makes no difference, and so the invariance of the world to angular orientation is related to the conservation of angular momentum.
Time and Distance
Only with quantitative observations can one arrive at quantitative relationships, which are the heart of physics.
What really matters anyway is not how we define time, but how we measure it.
Measurements of distance and of time give results which depend on the observer. Two observers moving with respect to each other will not measure the same distances and times when measuring what appear to be the same things. Distances and time intervals have different magnitudes, depending on the coordinate system (or “frame of reference”) used for making the measurements.
Perfectly precise measurements of distances or times are not permitted by the laws of nature.
Probability
By the “probability” of a particular outcome of an observation we mean our estimate for the most likely fraction of a number of repeated observations that will yield that particular outcome.
Every different observation must at least be at a different time or place. All we can say is that the “repeated” observations should, for our intended purposes, appear to be equivalent. We should assume, at least, that each observation was made from an equivalently prepared situation, and especially with the same degree of ignorance at the start.
The probability density function we have been describing is one that is encountered most commonly. It is known as the normal or gaussian probability density.
The uncertainty principle describes an inherent fuzziness that must exist in any attempt to describe nature. Our most precise description of nature must be in terms of probabilities.
In its efforts to learn as much as possible about nature, modern physics has found that certain things can never be “known” with certainty. Much of our knowledge must always remain uncertain. The most we can know is in terms of probabilities.
The Theory of Gravitation
What is this law of gravitation? It is that every object in the universe attracts every other object with a force which for any two bodies is proportional to the mass of each and varies inversely as the square of the distance between them.
This was a tremendous idea—that to find something out, it is better to perform some careful experiments than to carry on deep philosophical arguments.
First of all, Kepler found that each planet goes around the sun in a curve called an ellipse, with the sun at a focus of the ellipse.
Thus Kepler’s three laws are: Each planet moves around the sun in an ellipse, with the sun at one focus. The radius vector from the sun to the planet sweeps out equal areas in equal intervals of time. The squares of the periods of any two planets are proportional to the cubes of the semimajor axes of their respective orbits: .
(In those days, one of the theories proposed was that the planets went around because behind them were invisible angels, beating their wings and driving the planets forward. You will see that this theory is now modified! It turns out that in order to keep the planets going around, the invisible angels must fly in a different direction and they have no wings. Otherwise, it is a somewhat similar theory!)
Any great discovery of a new law is useful only if we can take more out than we put in.
If a law does not work even in one place where it ought to, it is just wrong.
If one cannot see gravitation acting here, he has no soul. This figure shows one of the most beautiful things in the sky—a globular star cluster.
Why can we use mathematics to describe nature without a mechanism behind it? No one knows. We have to keep going because we find out more that way.
No machinery has ever been invented that “explains” gravity without also predicting some other phenomenon that does not exist.
Motion
