Endnotes
Note 3: Why light travels below c inside materials
- Quote: When traveling through a material, such as water or glass, even objects with zero rest mass must move slower than c.
- Endnote: The slower speeds result from complex interactions between the swift objects and the materials they’re passing through.
- Discussion (coming soon) [see also my article on the Cerenkov radiation that results when electrically charged objects move slower than c but faster than light’s speed in that material, and also one of its applications in particle physics.]
Note 4: Gravitational lensing
- Quote: The gravity of a big black hole, or indeed of any object with large gravitational mass, causes light from the objects behind it to be deflected inward. This distorts our view of these distant objects in much the way that objects’ images can be distorted by a lens made of curved glass.
- Endnote: Indeed, this effect is called gravitational lensing.
- Discussion
Note 5: Rest mass vs. gravitational mass
- Quote: For an observer who sees an object as stationary, the object’s rest mass and gravitational mass are the same. But otherwise its gravitational mass, which is relative, can be larger than its rest mass. Photons are always in motion, so it is perfectly acceptable for them to have both nonzero gravitational mass and zero rest mass.
- Endnote: A photon’s gravitational mass depends on its frequency, which we’ll discuss in later chapters. That frequency is perspective-dependent; it rises if you are moving toward the source of the light and falls if you are moving away.
- Discussion: I was a little cavalier in the book in speaking of “gravitational mass”, since experts disagree as to whether and how to define it. But here’s an unambiguous fact.
If two pulses or beams of light pass each other, going in different directions, they will attract each other gravitationally. The degree of attraction depends on the total energies of the two beams.
But total energy is relative — as noted in chapter 8. For example, in the language of chapter 16: if you are moving relative to me and toward a pulse of light that we are both observing, we will agree on the number of photons in the pulse, but we will disagree about the photons’ frequency — you will see it “blue-shifted” to a higher frequency. Therefore, by the quantum formula that relates the frequency of a photon to its energy, you will see the pulse as having more energy than I do. Consequently, you’ll see its gravitational effects as larger than I do.
For those with the math background, some interesting details are captured in sections 2-4 of this paper.
Note 8: Elegance and Einstein’s gravity
- Quote: As you will see later in this book, the Higgs field exhibits the most inelegant of the known laws governing fields and particles. There’s an amusing tendency for those who tout beauty to ignore this, as though it were an inconvenient family member, and to focus instead on Einstein’s elegant theory of gravity. Yet even that theory has its issues
- Endnote: Einstein’s theory of gravity is amazingly elegant as long as one ignores the puzzle of “dark energy,” which would have been easier to do had it been exactly zero, and as long as gravity is a very weak force, as its weakness leads to extremely simple equations. In string theory, Einstein’s equations become much more complex, and the elegant simplicity of the math shifts to the level of the strings themselves . . . perhaps.
- Discussion
