Potpourri: Quantum Mechanics

1. Potpourri: Quantum Mechanics by  Robert Nemiroff Michigan Technological University

2. Physics X: About This Course • Officially "Extraordinary Concepts in Physics" • Being taught for credit at Michigan Tech • Light on math, heavy on concepts • Anyone anywhere is welcome • No textbook required • Wikipedia, web links, and lectures only • Find all the lectures with Google at: • "Starship Asterisk" then "Physics X"  • http://bb.nightskylive.net/asterisk/viewforum.php?f=39

3. Symmetry and Conservation: Noether's Theorem Symmetries underlie conservation laws (assumes principle of least action) Symmetry               Conservation law Rotation                  Angular momentum Translation             Linear momentum Time                       Energy Many others involving more complex symmetries.

4. Acceleration, Jerk, and Snap:The Movement Paradox To move from rest, and object must have change its position  over time, which means it must attain a velocity v.   To attain velocity v from rest, the object must accelerate, a. But how does an object attain acceleration from rest? Higher order motion: jerk = da/dt, snap = d(jerk)/dt . Snap is also called "jounce".  All orders are needed for motion from rest, but these are the only ones with names.

5. Charge versus Mass Although both electric charge and gravitational mass appear in similar inverse square laws, there are differences.

6. Experimental Relativity E = m c2 is a theorist's equation E = α mβ c2γ + ζ is more experimental where α, β, and γ are near 1, and ζ is near 0. I don't know what the current experimental limits on these "free parameters" are.  This might make an interesting research project.

7. Quantum Effects: As plain as the nose on your face? Quantum effects have been observable since humans began, just not understood.  Using one eye, one can align a point source (say a star) just over the nose on your face and see diffraction rings.  Try it! 

8. Quantum Effects: Visible with imperfect lens and blurry vision? To see quantum effects, you don't even have to have a nose!  Assuming your eye's lens is imperfect and your vision is even a little bit blurry, look closely at a distant point light source.  You will notice several "speckels" that are caused by the fluid in your eye.   But notice that each of these speckels have a diffraction pattern around them.  Try it! 

9. P versus NP Problem Technically the premiere problem in computer science but might be relevant to physics one day. Can answers be generated as quickly as they can be verified? In particular, if answers can be verified in polynomial time on a computer, can the answers be generated in polynomial time as well? (Seems like "no" to me: one can open a lock quickly, given a key, but one can't generate a key as quickly.) Related to the arrow of time?  Wave function collapse?

10. Holographic Principle A conjecture that states that a volume of space has all its information encoded on the area that bounds it.   Originally used to describe the entropy of black holes -- the entropy inside a black hole can be computed from its bounding event horizon. Extended to string theory and the universe in general.   Might be applicable to cosmology.

11. Unruh Effect Accelerating observers measure different blackbody radiation than non-accelerating observers Accelerated observers see a different type of underlying background vacuum than non-accelerating observers. Say a thermometer at rest in a vacuum reads zero temperature.  If that same thermometer is waved about in the vacuum, it will read a finite temperature. 

12. Unruh Effect Unruh temperature: What temperature will the thermometer read? where  • h is reduced Planck's constant • a is acceleration • c is the speed of light • k is Boltzmann's constant

13. Higgs Mechanism A leading mechanism for how (some) particles have inertial mass. Space is filled with a virtual sea of Higgs bosons (among other things).  Fundamental particles perturb this sea so that a crowd of virtual Higgs particles surrounds it.  Slogging through this field creates inertial mass. For protons and neutrons, inertial mass is thought to be mostly provided by the exchange of virtual color gluons.

14. Strangelets Strangelets are a form of matter not seen on Earth consisting of equal numbers of up, down, and strange quarks.  Standard nucleons don't contain strange quarks. Strangelets • are more compact than nuclear matter • may grow to arbitrary size • involves runaway reaction • might make massive "strange stars" • might convert any nucleon to a strangelet upon contact

15. Large Hadron Collider • Currently largest collider, started in 2009 • Frequently known by abbreviation LHC • Located in Switzerland Purposes: • Find or rule out predicted Higgs boson • Bolster the Higgs mechanism • Search for supersymmetric particle partners • Search for extra space dimension • Search for dark matter particles

16. Large Hadron Collider: Black Hole Controversy Black Holes • LHC will create micro black holes that will devour the Earth • Such mBHs should have been created already in cosmic rays, but the Earth remains.

17. Large Hadron Collider: Strangelet Controversy Strangelets formed in the LHC could change the Earth into one big strange particle • Stranglets might not be found in cosmic rays since they would have decayed before striking the Earth • But still some of them should survive, as does the Earth -- so little danger • Strangelets are more likely to have been created in other colliders, but have never been found