Quantum-Mechanics

Video: The race to Absolute Zero

This is the story of Dewar and Kamerlingh Onnes race to liquify gases.  The ultimate challenge was helium.  Dewar gavce up after hydrogen as he found it difficult to get helium and had all along gone light on equipment whilst Onnes used a more industrial approach,.  Onnes received the Nobel prize for doing this. 

The unfortunate thing is that later superconductivity and superfluidity was found by Onnes.  Had Dewar persisted he might have found superconductivity and got the prize anyway!

The ultimate acheivement detailed is the creation of an Bose Einstein condensate in 1995.

If you like science / physics this one is for you!

By Fudgy McFarlen, ago

Derivation of the Normal Gaussian distribution from physical principles – Maximum Entropy

Research Links

 

In many physical systems the question arises what is the probability distribution that describes a system with a given expected energy E  over the interval from -infinity to + infinity?     Again you will use the maximum entropy principle to determine this.

The constraints are as follows:

 

By Fudgy McFarlen, ago

Quantum Mechanics Entanglement and Spooky Action at a distance

Very interesting and experimental approach to entanglement and Bells inequality.
    

Interesting points of note in the video

  • pop bottle bottom glasses on 70's guy!
  • Eigenvalues of a quantum mechanical solution are what you can observe.  You never observe solutions that are combinations of eigenvalues.
  • StarTrek looking test apparatus mock up.  Scotty would have felt at home fixing this bugger!
  • Einstein did not like ghostly action at a distance.  EPR
  • Assume quantum theory is incomplete: Look for a hidden variable. Photon pairs are emitted with a shared equal hidden parameter.
  • Theories using hidden variables have been created that preserve locality and realism
  • Experiments that only test perfect correlations do not force us to choose between quantum explanation and hidden variable method
  • John Bell was the first person to show how to bring the two theories into conflict so they could be tested
  • Testing perfect correlations are tantamount to looking at one sock and seeing it is blue and concluding the sock on the other foot is blue
  • Imperfect correlations: set the target polarizers at unequal angles.
  • Alain Aspect and company tested Bell's Theorem
  • Tunable lasers were required for this test setup

More …….

By Fudgy McFarlen, ago

Use of Maximum Entropy to explain the form of Energy States of an Electron in a Potential Well

The base state of an electron in an infinite potential well has the most "space" for the electron state.  Thus it has the maximum entropy. Take that same state and imagine pinching the electrons existence to nil in the middle of the trough.  Now you have state-2.  The electron now exists in a smaller entropic state and guess what?  It contains exploitable energy now. This is like a spring compressed.  The electron can decompress and exert force / expend energy.  For example in an interaction with another atom possibly a recoil could occur.   In a crystal lattice an electron can transfer its energy to the atom next door and in effect yield conduction.  All these are preliminary suppositions subject to more scrutiny. As mentioned before since the electron exists in this potential well in the form of free fall it can not have any acceleration.  Thus its distribution must thoroughly avoid the edges of the well were it would indeed experience accelerations by bouncing and recoiling off of the walls.

electron-in-infinite-well.bmp

By Fudgy McFarlen, ago