The concluding post for the curriculum review topics are below. Many of these are, in my opinion, more suitable in an elective or advanced graduate special topics course.

• Cosmology and Astrophysics theory
  • Big Bang, inflation, CMB
  • Dark energy, dark matter
  • dark holes, neutron stars
• Particle physics theory
  • Feynman diagrams
  • Standard Model and QCD
  • String theory
• Nonlinear physics theory
  • Attractors and bifurcation theory
  • Bistability and hysteresis
  • Chaos
  • Hamiltonian and dissipative chaos, Poincare maps
  • Pattern formation and spatiotemporal chaos
  • Fluid dynamics
  • Turbulence
• Condensed Matter
  • Semiconductors
  • Nanoscience
  • Superconductivity
• Biophysics theory
  • DNA and proteins
  • Gene regulation
  • Structures and interactions
  • Biophysical techniques
  • Systems biology
• Instrumentation, techniques, experiment
  • Microscopy: TEM, STM, AFM, NMR
  • Machine shop class
  • Experimental techniques
• Computation
  • Numerical analysis/methods
  • Simulation and Monte-Carlo
  • Mathematica and/or Maple
  • Computational programming (C++, Fortran, etc.)

Topics in maths for physicists include:

• ODE and PDE
  • 1st, 2nd order, Wronskian
  • Sturm-Liouville theorem, orthogonal series expansion
  • Qualitative methods, fixed points, flow, bifurcations
  • Legendre polynomials/ functions, spherical harmonics
  • Bessel functions, zeroes, asymptotic expansions
  • Laplace/Poisson, heat, wave mechanics equations
  • Boundary conditions, elliptic, parabolic, hyperbolic
  • Separation of variables
  • Orthogonal coordinates, grad, div, curl,
  • Laplace problems: rectangular, cylindrical, spherical
  • Green’s functions
  • Fourier series and tranforms
  • Laplace transforms
• Groups and tensors
  • Discrete groups, , , irreducible representations
  • Lorentz group
  • Lie groups
  • SU(n), U(n), O(n), SO(n)
  • Cartesian tensors
  • General tensors
  • Contravariant/covariant derivatives and Christoffel symbols
• Complex variables
  • Analytic functions and Cauchy-Riemann equations
  • Cauchy’s theorem and integral formula
  • Residue theorem and contour integration
  • Conformal mapping
  • Steepest descents
  • Integral equations
  • Neumann series, Hilbert-Schmidt theory
• Probability Theory
  • Distributions: Binomial, Poisson, Gaussian
  • Random walks
  • Characteristic functions, central limit theorem
  • Stochastic process, Poisson processes
  • Mathematical statistics, chi-square, confidence intervals

Darn it. First I miss the Two Cultures conference in New York this past weekend, and now I can’t even go to this event:

The Pacific Science Center event is totally free, so go, go, go, and let me know how it went. Pleeez…

Navier-Stokes Equation

In the book A Demon Haunted World,by Carl Sagan, Sagan states he often received correspondence from people who claimed they were in contact with aliens. These people invited Sagan to ask the aliens questions. Sagan, the consummate scientist, always had some questions prepared.

If there are aliens among us, it is reasonable to assume they’re from a more advanced civilization from ours. Assuming this, it is also reasonable to assume they would have the answers to questions that have stumped humans for years. Questions asked of aliens should be problems unsolved by humans, but where we would immediately recognize the answer as correct, or the answer could be proved. Asking “Is there a God” yields an answer that may not be recognized as correct by some people, and an answer that cannot be verified by scientific means. Unsolved mathematical problems would be excellent questions to ask of an advanced civilization.

Here are a few questions I would ask of aliens:

1. Please (it doesn’t hurt to be polite) solve Goldbach’s Conjecture. This is one of the oldest problems relating to prime numbers. Prime numbers are used in cryptography and internet security.
2. Design an experiment to prove or disprove the existance of higher dimensions. Humans can see three spatial dimensions, and we move forward through the fourth dimension of time, but there are theories that include 11 dimensions.
3. Why is gravity such a weak force when compared to electromagnetic, strong nuclear and weak nuclear forces? Provide an explanation that can be proved experimentally.
4. Prove solutions to the Navier-Stokes equations including smoothness solutions. I went through 4 years of mechanical engineering and I just barely understand this. If you can explain this to me, leave it in the comment box.
5. Please (again, it doesn’t hurt to be polite with a potentially superior life-form) give the composition and production methods to make a high temperature superconductor. I would hope the aliens would provide me with a superconducting material that would function at temperatures greater than 293°K (20°C) which is room temperature.

These are the questions that interest me. A civilization that can travel vast distances though space in their UFOs should be sufficiently advanced to answer these questions. Next time you have contact with an alien, ask some questions and see what they come up with. If you get answers to questions that have remained unsolved by humans for hundreds or thousands of years, then maybe you’re corresponding with a real extra-terrestrial.

50 years ago (1959), novelist and trained scientist C.P. Snow wrote the Rede lecture “The Two Cultures.” In it, Snow expressed great concern over what he saw as a rift in the quest for knowledge. He saw people taking an either/or approach to learning. Either you approached it from a ”humanist” point of view, or you approached it from a “scientific” frame of mind. He also saw some aspects of knowledge emphasized over others.

“At some point scientists had ceased to be considered intellectuals, Snow noted, and though any educated person was required to know Shakespeare, almost none knew the second law of thermodynamics.” [Seed Magazine]

This concerned Snow a lot, as he obviously saw the benefits in his own life of cultivating both camps and bringing knowledge together, possibly forming a “third culture” of cultural scientists, assuming this rift couldn’t be patched.

So where are we now, 50 years later?

SEED Magazine interviewed several currently practicing researchers who through their careers have tried to bridge that gap, including E.O. Wilson (who wrote Consilience in 1998 to try and addresss the gaps), Steve Pinker (an avid bridge builder, even if I don’t agree with him all the time), and new up and comers.

Personally, I fear that divide has only widened in the past 50 years. Some universities have divided their anthropology departments on the bio/culture lines, some science departments don’t understand the importance of good writing to their undergraduates, and most humanities undergrads try to avoid taking science and math as much as possible.

Or are discouraged: I signed up for a biology class my first year in college, only to be told (repeatedly) on the first day of class “unless your major is nursing, biology, or other science major, you probably shouldn’t take this class.” The guy actually made us fill out little cards with our majors, and asked all those who weren’t majoring in nursing or biology to leave. Not because it was geared towards those particular majors, just because it was “hard.” (For the record, I got a C+ on my first test, got scared and dropped out. How many other kids do you think that happened to?).

So, long story short, this is the main reason why I founded this blog: to combat the idea that the humanities, social sciences, and “hard” sciences can’t co-exist and benefit from each other. As the speakers say in their interviews, we are starting to bridge gaps across the divide, we are starting to see that these things are connected and can benefit from each other. But after more than 50 years of a growing divide, it is going to take a little work to patch things up.

Refocusing a camera lens onto radioactive material.

Going farther into physics theory results in some interesting numbers.

The mass of the sun is 1.48 kilometers.

The mass of an electron is 0.510 mega-electronvolts.

And of course the greatest equation relating the speed of light and Newton’s gravitational constant:

c = G = 1

The great thing about the above equation is that everything can be measured in terms length and units no longer pose a problem, just add them in until the equation balances.

And compared to the sun the earth has a mass of 0.443 centimeters.

[English]

A lot of new Gigapedia items for today.

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[Español]

Hoy Gigapedia nos trae un montón de novedades.

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I want to look at the new items!

OPINION By LEE DYE

May 13, 2009 —

Here’s the good news for all those “Star Trek” enthusiasts out there — a couple of physicists think they’ve figured out how to travel faster than the speed of light without breaking the laws of physics theory.

But here’s the bad news — we may have to sacrifice Jupiter to get there.

Gerald Cleaver, associate professor of physics theory at Baylor University, and his post-doctoral researcher, Richard Obousy, have combined some of the most elusive fields in physics theory, including string theory and general relativity, to concoct a scheme to move “Star Trek’s” warp speed a little closer to reality. Very little, that is.

The folks who produce the “Star Trek” flicks have never explained how the good ship Enterprise can speed through the universe faster than a beam of light. That minor achievement is necessary if humans are ever to explore the galaxy’s back yard, not to mention the distant reaches of the universe.

The only problem is Albert Einstein said it couldn’t be done.

“Objects that have mass cannot travel at the speed of light,” Cleaver said in an interview. According to Einstein’s famous equation, “as an object travels faster and faster, its mass increases,” he added. “As an object approaches the speed of light its mass becomes infinite.”

Read the rest of this entry »