The best military historians in fact do recognize the difficulty in stating rules of generalship. They do not speak of a science of war, but rather of a pattern of military behavior that cannot be taught or stated precisely but that somehow or other sometimes helps in winning battles. This is called the art of war. In the same spirit I think that one should not hope for a science of science, the formulation of any definite rules about how scientists do or ought to behave, but only aim at a description of the sort of behavior that historically has led to scientific progress—an art of science.
American theoretical physicist (1933-2021)
Steven Weinberg (born 3 May 1933 – 23 July 2021) was an American physicist. He was awarded the 1979 Nobel Prize in Physics (with colleagues Abdus Salam and Sheldon Glashow) for combining electromagnetism and the weak force into the electroweak force.
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Dreams of a Final Theory (1992; 2nd edition 1994)
The development of quantum mechanics in the 1920s was the greatest advance in physical science since the work of Isaac Newton. It was not easy; the ideas of quantum mechanics present a profound departure from ordinary human intuition. Quantum mechanics has won acceptance through its success. It is essential to modern atomic, molecular, nuclear, and elementary particle physics, and to a great deal of chemistry and condensed matter physics as well.
Consider... [the formula given by special relativity for the magnitude of the ]<math>P \equiv m_0 \sqrt{g_{ij}\frac{dx^i}{d\tau}\frac{dx^j}{d\tau}}</math>...where <math>d\tau^2 = dt^2 - g_{ij} dx^i dx^j</math>. [This holds because in] a locally inertial Cartesian coordinate system, for which <math>g_{ij} = \delta_{ij}</math>, we have <math>d\tau = dt\sqrt{1 - \mathbf {v}^2}</math> where <math>v^i = \frac{dx^i}{dt}</math>... [The <math>P</math>] is evidently invariant under arbitrary changes in the spatial coordinates, so we can evaluate it... in Robertson-Walker coordinates. ...[T]o save work ...adopt a spatial coordinate system in which the particle position is near the origin <math>x^i = 0</math>, where <math>\tilde{g}_{ij} = \delta_{ij} + \mathit0(\mathbf{x})</math>, and we can therefore ignore the purely spatial components of <math>\Gamma_{jk}^i</math> of the . General relativity gives [the momentum]... with a metric <math>g_{ij} = a^2(t)\delta_{ij}</math>...<math>P(t) \propto 1/a(t)</math>... for any non-zero mass, however small... Hence, although for photons both <math>m_0</math> and <math>d\tau</math> vanish... [the momentum relation] is still valid.
Many people do simply awful things out of sincere religious belief, not using religion as a cover the way that Saddam Hussein may have done, but really because they believe that this is what God wants them to do, going all the way back to Abraham being willing to sacrifice Isaac because God told him to do that. Putting God ahead of humanity is a terrible thing.
This book is written for readers who may not be familiar with classical physics, but who are willing to pick up enough... to be able to understand the rich tangle of ideas and experiments that make up the history of twentieth century physics. This background is provided in a number of "flashback"sections on the nature of electricity, Newton's laws of motion, electric and magnetic forces, conservation of energy, atomic weights and so on... inserted wherever... needed to allow the reader to understand the next point in the history. ...Generally ...the student or reader is ...is offered only one path ...ideal for ...physicists, but for many ...an impassable desert ...I invite the reader to plunge immediately into... key topics ...using each ...as an entreé into just those concepts and methods ...needed to understand that topic. ...Most of what I know about physics and mathematics I have learned only when there was no alternative ...in order to get on with my work. ...So the plan of this book may be closer to the actual education of working scientists than many ...My hope ...that this book may contribute to a radical revision in the way ...science is brought to the nonscientists. ...This book is intended to be comprehensible to readers who have no prior background in science, and no familiarity with mathematics beyond arithmetic. ...Appendices present some of the calculations that underlie the reasoning in the main text. ...The great scientific achievements described here form the a large part of the soil from which our... recent harvest of discoveries have sprung. ...I hope that scientists find some ...enlightening.
I also hope that this book will be enjoyed by students and practitioners of the history of science.
[T]o extend this to the geometry of spacetime... include a term... in the spacetime line element, with <math>a</math> now an arbitrary function of time (known as the Robertson-Walker scale factor):<math>d\tau^2 \equiv -g_{\mu\nu}(x) dx^\mu dx^\nu = dt^2-a^2(t)[d\mathbf{x}^2 + K \frac{(\mathbf{x} \cdot d\mathbf{x}^2)}{1-K\mathbf{x}^2}]</math>
[I]n 1897 Thomson... detected a deflection... by electric forces between the rays and the electrified metal plates. ...due largely to the use of better vacuum pumps ...to where the effects of residual gas ...became negligible. (Some evidence for... deflection was [also] found... by Goldstein.) [D]eflection was toward the positively charged plate... away from the negatively charged one, confirming Perrin... that the rays carry negative electric charge.
Planck’s quantization assumption applied to the matter that emits and absorbs radiation, not to radiation itself. As George Gamow later remarked, Planck thought that radiation was like butter; butter itself comes in any quantity, but it can be bought and sold only in multiples of one quarter pound. It was Albert Einstein (1879–1955) who in 1905 proposed that the energy of radiation of frequency ν was itself an integer multiple of hν.
It seems to me that we are in the position of a company of players who have by chance found their way into a great theater. Outside, the city streets are dark and lifeless, but in the theater the lights are on, the air is warm, and the walls are wonderfully decorated. However, no scripts are found, so the players begin to improvise—a little psychological drama, a little poetry, whatever comes to mind. Some even set themselves to explain the stage machinery. The players do not forget that they are just amusing themselves, and that they will have to return to the darkness outside the theater, but while on the stage they do their best to give a good performance. I suppose that this is a rather melancholy view of human life, but melancholy is one of the distinctive creations of our species, and not without its own consolations.
There’s something I’ve been working on for more than a year — maybe it’s just an old man’s obsession, but I’m trying to find an approach to quantum mechanics that makes more sense than existing approaches. I’ve just finished editing the second edition of my book, Lectures on Quantum Mechanics, in which I think I strengthen the argument that none of the existing interpretations of quantum mechanics are entirely satisfactory.
Velocity, acceleration, and force are vectors... they have direction as well as magnitude. It is often convenient to describe... [vectors] in terms of their components along specified directions. ...Components of vectors can be negative as well as positive ...Newton's Second Law applies separately to each component... it says... the component of force in any direction is equal to the mass times the corresponding component of acceleration.
To start, we will consider a single particle moving in three space dimensions under the influence of a general central potential. Later we will specialize to the case of a Coulomb potential, and work out the spectrum of hydrogen. One other classic problem, the harmonic oscillator, will be treated at the end of this chapter.