Steven Weinberg Quotes

Thomson used Newton's Second Law to obtain a general formula... to interpret measurements of the cathode-ray deflection... produced by... electric or magnetic forces... In his cathode ray tube, the ray particles pass through... the deflection region... subjected to electric and magnetic forces... at right angles to their original direction... then through a much longer force-free... drift region... in which they drift freely until they hit the end of the tube... [a] glowing spot... The forces exerted on the cathode ray particles give them an acceleration at right angles to the axis of the tube, so... the particles have a small component of velocity at right angles to their original motion... equal to the product of the acceleration and the time... in the [very short] deflection region... [T]he downward displacement of the ray when it hits the end of the tube is the downward velocity produced in the deflection region times the length of time... in the drift region... [T]he electric force... on a particle is proportional to the [particle's] electric charge... [U]nlike the electric force, the magnetic force... on a particle is proportional to the particle's velocity as well as its charge. By measuring... deflections due to... [both] forces, Thomson... could determine both the ray-particle velocities and the ratio of their charge and mass.

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.

A superconductor of any kind is nothing more or less than a material in which a particular symmetry of the laws of nature, electromagnetic gauge invariance, is spontaneously broken. ... These rotations act on a two-dimensional vector, whose two components are the real and imaginary parts of the electron field, the quantum mechanical operator that in quantum field theories of matter destroys electrons. The rotation angle of the broken symmetry group can vary with location in the superconductor, and then the symmetry transformations also affect the electromagnetic potentials ... The symmetry breaking in a superconductor leaves unbroken a rotation by 180°, which simply changes the sign of the electron field. In consequence of this spontaneous symmetry breaking, products of any even number of electron fields have non-vanishing expectation values in a superconductor, though a single electron field does not. All of the dramatic exact properties of superconductors – zero electrical resistance, the expelling of magnetic fields from superconductors known as the Meissner effect, the quantization of magnetic flux through a thick superconducting ring, and the Josephson formula for the frequency of the AC current at a junction between two superconductors with different voltages – follow from the assumption that electromagnetic gauge invariance is broken in this way, with no need to inquire into the mechanism by which the symmetry is broken.

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.

Perrin... showed in 1895 that the rays deposit negative electrical charge on a charge collector... inside... the tube.

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.

In this derivation Bohr had relied on the old idea of classical radiation theory, that the frequencies of spectral lines should agree with the frequency of the electron’s orbital motion, but he had assumed this only for the largest orbits, with large n. The light frequencies he calculated for transitions between lower states, such as n=2 → n=1, did not at all agree with the orbital frequency of the initial or final state. So Bohr’s work represented another large step away from classical physics.

The s and s in nuclei, like the electrons surrounding the nuclei, can be excited to states of higher energy or... fall back to a state of lower energy, but the energies... are typically a million times those need to excite the electrons...

The last thirty years of Einstein's life were largely devoted to a search for a so-called unified field theory that would unify James Clerk Maxwell's theory of electromagnetism with the general theory of relativity, Einstein's theory of gravitation. Einstein's attempt was not successful, and with hindsight we can now see that it was misconceived. Not only did Einstein reject quantum mechanics; the scope of his effort was too narrow. ... Nevertheless Einstein's struggle is our struggle today. It is the search for a final theory.

The principles of quantum mechanics are so contrary to ordinary intuition that they can best be motivated by taking a look at their prehistory.

Perhaps the most important immediate consequence of Planck’s work was to provide long-sought values for atomic constants.

When several forces act... the total force is the sum... each component of the total force is the sum of the corresponding components of the individual forces.

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.

Heisenberg’s starting point was the philosophical judgment, that a physical theory should not concern itself with things like electron orbits in atoms that can never be observed. This is a risky assumption, but in this case it served Heisenberg well.

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.