Steven Weinberg Quotes

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.

Almost all of modern cosmology is based on this Robert-Walker metric, at least as a first approximation.

One of the things that excited me so much about quantum chromodynamics after the work of Gross and Wilczek and Politzer was that it seemed to provide a rational explanation for what had always been mysterious to me — the fact that there were symmetries, like parity conservation, charge conjugation invariance, and strangeness conservation, that were very good symmetries of the strong and electromagnetic interactions — as far as we knew exact — and yet were not respected by the weak interactions. Why should nature have ... symmetries that are symmetries of part of nature but not other parts of nature?

When the velocity and the acceleration are changing, we can define the instantaneous velocity or acceleration at any moment as the average values... over a vanishingly small time interval centered on that moment. Newton's Law actually relates the force to the instantaneous acceleration.

Considering the pervasive importance of quantum mechanics in modern physics, it is odd how rarely one hears of efforts to test quantum mechanics experimentally with high precision.…The trouble is that it is very difficult to find any logically consistent generalization of quantum mechanics. One obvious target for generalization is the linearity of quantum mechanics, but if we arbitrarily add nonlinear terms to the Schrodinger equation, how do we know that the theory we obtain will have a sensible physical interpretation? At least in part, it is the dearth of generalized versions of quantum mechanics that has made it so hard to plan experimental tests of quantum mechanics.

I decided to exclude material that was highly speculative... cosmological theory in higher dimensions... anthropic reasoning... holographic cosmology... conjectures about the details of inflation, or many other new ideas. ...The present book is largely concerned with ...mainstream cosmology: ...inflation driven by one or more scalar fields ...followed by a big bang dominated by radiation, , baryonic matter, and .

As everyone today knows, in specifying the value of a gauge coupling constant it is necessary to say not only what its value is but where — that is at what normalization scale — it has that value.

The more the universe seems comprehensible, the more it also seems pointless.

(...Newton's theory... is now known only to be an approximation... for particles... not moving too fast and gravitational forces... not too strong. ...It is one of the consequences of General Relativity that gravitation is produced by and acts on energy as well as mass, so that it even affects particles of zero mass, like the photon.

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

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.

In fact, there is something puzzling about the Higgs mass we now do observe. It is generally known as the “hierarchy problem.” Since it is the Higgs mass that sets the scale for the masses of all other known elementary particles, one might guess that it should be similar to another mass that plays a fundamental role in physics, the so-called Planck mass, which is the fundamental unit of mass in the theory of gravitation. (It is the mass of hypothetical particles whose gravitational attraction for one another would be as strong as the electric force between two electrons separated by the same distance.) But the Planck mass is about a hundred thousand trillion times larger than the Higgs mass. So, although the Higgs particle is so heavy that a giant particle collider was needed to create it, we still have to ask, why is the Higgs mass so small?

The laws of motion... were set out by... Newton at the beginning of... the Principia. ...[T]he key principle is ...in the Second Law... paraphrased as... the force to give an object a certain acceleration is proportional to the product of the and the .

In 1858 Johann Heinrich Geissler... invented a pump that used columns of mercury as pistons and consequently needed no gaskets. ...Geissler's pump was used... by ... [M]etal plates inside a glass tube were connected to a powerful source of electricity. ...[W]hen almost all of the air was evacuated ...the light disappeared through most of the tube, but a greenish glow appeared ...near the cathode. ...A few years later, ... introduced a name... s.
We know now that these rays are streams of electrons. ...But this was far from obvious to nineteenth century physicists. ...Plücker ...observed that the position of the glow on the walls of the tube could be moved by ...a magnet ...

Elementary particles are terribly boring, which is one reason why we're so interested in them.