1. Symmetry Operations    
2. Translation in space
3. Translation in time
4. Rotation through a fixed angle    
5. Uniform velocity in a straight line (Lorentz transformation):
6. Reversal of time: if we could see the individual molecules, we would not be able to discern whether the machinery was working forwards or backwards.
7. Reflection of space
8. Interchange of identical atoms or identical particles: all electrons are the same; all protons are the same; all positive pions are the same; and so on.
9. Quantum-mechanical phase
10. Matter-antimatter (charge conjugation)  

• Dirac predicted that in addition to electrons there must be another particle, called the positron (discovered at Caltech by Anderson), that is necessarily related to the electron.
• All the properties of these two particles obey certain rules of correspondence: the energies are equal; the masses are equal; the charges are reversed; but, more important than anything, the two of them, when they come together, can annihilate each other and liberate their entire mass in the form of energy, say γ-rays.
• The positron is an antiparticle to the electron.

• The rule of the “anti” is not just that it has the opposite charge, it has a certain set of properties, the whole lot of which are opposite.
• The antineutron is distinguished from the neutron in this way: if we bring two neutrons together, they just stay as two neutrons, but if we bring a neutron and an antineutron together, they annihilate each other with a great explosion of energy being liberated, with various π-mesons, γ-rays, and whatnot.

• Light always travels at 186,000 mi/sec in all systems, even when they are in relative motion.
• In other words, when the outsider sees the man in the spaceship lighting a cigar, all the actions appear to be slower than normal, while to the man inside, everything moves at a normal rate. So not only must the lengths shorten, but also the time-measuring instruments (“clocks”) must apparently slow down.
• So the Lorentz transformation is analogous to a rotation, only it is a “rotation” in space and time,

• Imagine, Peter and Paul, who are twins, born at the same time. Paul flies away at very high speed. Because Peter, who is left on the ground, sees Paul going so fast, all of Paul’s clocks appear to go slower, his heartbeats go slower, his thoughts go slower, everything goes slower, from Peter’s point of view.
• Of course, Paul notices nothing unusual, but if he travels around and about for a while and then comes back, he will be younger than Peter, the man on the ground!
• That is actually right; it is one of the consequences of the theory of relativity which has been clearly demonstrated.

• Einstein had a different interpretation of the law of gravitation. According to him, space and time—which must be put together as space-time—are curved near heavy masses.
• And it is the attempt of things to go along “straight lines” in this curved space-time which makes them move the way they do.
• The particles always take the longest proper time—in space-time a quantity analogous to the “shortest distance.” That’s the law of motion in a gravitational field.

1. Time and distance rates depend on the place in space you measure them and on the time. This is equivalent to the statement that space-time is curved. From the measured area of a sphere we can define a predicted radius, And the curvature must be the same no matter who is looking at the matter or how it is moving.
2. Particles move on “straight lines” (trajectories of maximum proper time) in this curved space-time.

E = (M-m)c^2. This equation was used to estimate how much energy would be liberated under fission in the atomic bomb, for example. The mass of the uranium atom was known—it had been measured ahead of time—and the atoms into which it split, iodine, xenon, and so on, all were of known mass. In other words, both M and m0 are known. So by subtracting the two numbers one can calculate how much energy will be released if M can be made to split in “half.”

For this reason poor old Einstein was called the “father” of the atomic bomb in all the newspapers.