Steven Weinberg Quotes

In 1999 I finished my three volume book on the quantum theory of fields (..."QTF"), and... set... the task of learning... the theory underlying the great progress in cosmology in the previous two decades. ...Review articles ...gave good summaries of the data, but ...often quoted formulas without ...derivation, and sometimes ...without reference to the original derivation. Occasionally the formulas were wrong, and extremely difficult for me to rederive. ...[O]riginal ...articles sometimes had gaps in their arguments, or relied on hidden assumptions, or used unexplained notation. Often massive computer programs had taken the place of analytic studies. In many cases... it was easiest to work out the relevant theory myself.
This book is the result. Its aim... self-contained explanations of the ideas and formulas... used and tested in modern cosmological observations.

[In] the case of Euclidean space...<math>ds^2 = a^2[d\mathbf{x}^2 + K \frac{(\mathbf{x} \cdot d\mathbf{x}^2)}{1-K\mathbf{x}^2}]</math>...where <math>K =

Either by God you mean something definite or you don't mean something definite. If by God you mean a personality who is concerned about human beings, who did all this out of love for human beings, who watches us and who intervenes, then I would have to say in the first place how do you know, what makes you think so? And in the second place, is that really an explanation? If that's true, what explains that? Why is there such a God? It isn't the end of the chain of whys, it just is another step, and you have to take the step beyond that.

As a special case of Newton's Second Law, a body... when acted on by zero force, will experience zero acceleration—that is, it will move with constant velocity. Newton listed this... as the First Law... The Third Law... action equals reaction: If one body exerts a force on another... the second... exerts an equal force in the opposite direction on the first.

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.

It doesn't work to build half an accelerator. The particles need to go all the way around.

In the case where the universe does not recollapse, the proper distance to the is...<math>d_{MAX}(t) = a(t) \int_{0}^{r_{MAX}(t)} \frac{dr}{\sqrt{1-Kr^2}} = a(t)\int_{0}^{\infty} \frac{dt'}{a(t')}</math>... In the absence of a cosmological constant, <math>a(t)</math> grows like <math>t^{\frac{2}{3}}</math>, and the integral diverges, so there is no event horizon. But with a cosmological constant, <math>a(t)</math> will eventually grow as exp(<math>Ht</math>) with <math>H = H_0 \Omega^{1/2}_\Lambda</math> constant and... an event horizon... approaches... <math>d_{MAX}(\infty) = 1/H</math>. As time passes all sources of light outside our gravitationally bound will move beyond this... and become unobservable. The same is true for the quintessence theory... In that case <math>a(t)</math> eventually grows as exp(const <math>\times\, t^{2/{(2+\frac{\alpha}{2})}}</math>), so for any <math>\alpha \ge 0</math> the integral... [<math>d_{MAX}(t)</math>] converges.

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.

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.

Finally, learn something about the history of science, or at a minimum the history of your own branch of science. The least important reason for this is that the history may actually be of some use to you in your own scientific work.

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.

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.

I hope the readers will let me know of any mistakes... I will post them on... zippy.ph.utexas.edu/~weinberg/corrections.html.

Consider the geometry of a three-dimensional homogeneous and isotropic space. ...[G]eometry is encoded in a metric <math>g_{ij}(\mathbf{x})</math> (with i and j running over the three coordinate directions), or equivalently a line element <math>ds^2 \equiv g_{ij} dx^i dx^j</math>, with summation over repeated indices... <math>ds</math> is the proper distance between <math>\mathbf{x}</math> and <math>\mathbf{x}+\mathbf{dx}</math>, meaning... the distance measured by a surveyor who uses a... Cartesian [coordinate system] in a small neighborhood of... point <math>\mathbf{x}</math>.) One... homogeneous isotropic three-dimensional space with positive definite lengths is flat space, with line element<math>ds^2=d\mathbf{x}^2</math>...The coordinate transformations that leave this invariant are... ordinary three-dimensional rotations and translations. ...Another ...possibility is a four-dimensional with some radius <math>a</math>, with line element<math>ds^2=d \mathbf{x}^2+dz^2,\;\;z^2 + \mathbf{x}^2 = a^2</math>,...Here the transformations that leave the line element invariant are four-dimensional rotations; the direction of <math>\mathbf{x}</math> can be changed to any other direction by a four-dimensional rotation that does not change <math>z</math>. ...[T]he only other possibility (up to a coordinate transformation) is a hyperspherical surface in four-dimensional , with line element<math>ds^2 = d\mathbf{x}^2 - dz^2,\;\;z^2 - \mathbf{x}^2 = a^2</math>,...where <math>a^2</math> is (so far) an arbitrary positive constant. The coordinate transformations that leave this invariant are four-dimensional pseudo-rotations, just like s, but with <math>z</math> instead of time.

A theorist today is hardly considered respectable if he or she has not introduced at least one new particle for which there is no experimental evidence.