If you’d like to hear about any topic in math or physics, request it in the comments here, or shoot me an email at questions.thephysicsmill@gmail.com.
If you’d like to hear about any topic in math or physics, request it in the comments here, or shoot me an email at questions.thephysicsmill@gmail.com.
I have been asked to explain the levels of infinity. This will be one of my first posts.
If you had to come up with the most probable form of faster than light travel, what would it be, and how exactly would it circumvent the universal speed limit? What about FTL communications?
Thanks, Kosh. A three part seeriesw on faster than light travel is up now. The parts are:
http://www.thephysicsmill.com/2012/11/19/the-speed-of-light-is-constan/
http://www.thephysicsmill.com/2012/11/25/the-universal-speed-limit/
http://www.thephysicsmill.com/2012/12/02/ftl-part-3-general-relativity-shortcuts/
I really enjoyed your first article on levels of infinity. You mentioned a point about the completeness axiom at the end of the post. I would be interested in its implications with respect to topology, which I know is a topic of great interest to many casual mathematics students.
Can you write about a small toy version of physics where the points of the universe form the surface of a doughnut and the group of Lorenz transformations is replaced by some little finite group? I would like to know what particles would exist in this universe.
Where did Einstein start to derive E = mc2? Could you also comment briefly on the interpretation of and provability of the Equivalence Principal.
Namely if Inertial mass is the mass that appears in Newton’s Second Law, and
Gravitational mass is the mass that appears in Newton’s Law of Gravity.
Then Einstein’s Equivalence Principle requires that inertial mass and gravitational mass be the same.
Audiophile friends tell me that vinyl records have a much richer sound than MP3 files. Is that really the case, and if so, why?
Thanks, sunstreetreviews, I’ve answered your question here:
http://www.thephysicsmill.com/2013/01/06/sound-vinyl-records-vs-digital-files/
Re:refraction: Feynman’s “Red Books” had a section, IIRC, on reflection and refraction using waves and interference to derive certain properties. This avoids the infinitesimal, perfect boundary, and employs the least time principal, which to me is much more intuitive. (I don’t have mine handy, or I’d look up the volume and pages.)
It didn’t go into the more complicated derivation of refraction indices by material. (BTW, can we do that yet?)
Thanks for catching that, QM! I would be very presumptuous to say that I could explain things better than Feynman! I’ve added this reference to the post. I just checked, and he discusses the principle of least time in volume 1, section 26-2. He discusses the index of refraction in volume 1, section 31-1.
In many special cases, we can derive the index of refraction. However, not always. The story is, as always, much more complicated than classical physics would lead one to believe. The refractive index doesn’t just depend on how tightly bound electrons are to their atoms, it also depends on how the atoms bond to form a material. For instance, in the crystalline materials, it depends strongly on the crystal structure. We can take advantage of this to make so-called “metamaterials,” where we design the crystal structure of the material to engineer the optical properties. Using this, we can make materials with NEGATIVE indexes of refraction, which is very weird.
http://en.wikipedia.org/wiki/Metamaterials