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.

It is... convenient to state Coulomb's law in modern terms, first used... by James Clerk Maxwell. The electric force... is always proportional to the electric charge... We call the factor of proportionality the electric field so...Electric force... = Electric charge... x Electric field

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.

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.

If there is no point in the universe that we discover by the methods of science, there is a point that we can give the universe by the way we live, by loving each other, by discovering things about nature, by creating works of art. And that—in a way, although we are not the stars in a cosmic drama, if the only drama we're starring in is one that we are making up as we go along, it is not entirely ignoble that faced with this unloving, impersonal universe we make a little island of warmth and love and science and art for ourselves. That's not an entirely despicable role for us to play.

Symmetry is not enough by itself. In electromagnetism, for example, if you write down all the symmetries we know, such as Lorentz invariance and gauge invariance, you don’t get a unique theory that predicts the magnetic moment of the electron. The only way to do that is to add the principle of renormalisability – which dictates a high degree of simplicity in the theory and excludes these additional terms that would have changed the magnetic moment of the electron from the value Schwinger calculated in 1948.

[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 =

... I found that I was unable to explain the foundations of quantum mechanics in a way that I found entirely satisfactory.

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.

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.

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?

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.

Acceleration is the rate of change of . ...The units are ...velocity per unit time, or distance-per-time per time. ...[F]alling bodies ...near ...earth fall with an acceleration or 9.8 meters-per-second per second ...after the first second ...falling at speed ...9.8 meters per second, after two seconds... 19.6 ...and so on. [T]he units of velocity are length/time... and units of acceleration... (distance/time)/time, or equivalently distance/time<sup>2</sup> ...[T]he acceleration near... Earth would be written 9.8 m/sec<sup>2</sup> for short.

I have a friend — or had a friend, now dead — Abdus Salam, a very devout Muslim, who was trying to bring science into the universities in the Gulf states and he told me that he had a terrible time because, although they were very receptive to technology, they felt that science would be a corrosive to religious belief, and they were worried about it... and damn it, I think they were right. It is corrosive of religious belief, and it's a good thing too.