Saturday, 8 August 2015

Quantum and Symmetry Mechanics

Often we discover that topics in theoretical mathematics, and real world phenomena, wind up having unforeseen connections. One example of this is the relationship between group theory - the study of proportion - and quantum mechanics.




Quantum mechanics analyzes the habits of subatomic particles. Electrons, and other subatomic particles, do not behave in fairly the same way as items in our typical daily world.

For example, in the real life, if a person spins around one time, they will certainly return to their original state. You can try this out - if you stand up from your computer, and in fact physically spin yourself around one time, you'll be back in your original position, though maybe slightly dizzy.

In Automobiles

Similarly with automobiles - if a car drives around in a circle, and returns to the spot where it started, it will certainly be the same vehicle - perhaps with a little less gas, however the same.

Electrons are not like this, however. If an electron spins around one time, it alters its electromagnetic structure. This is something like if the Earth's north and south poles switched each time the Earth spins around: the Earth would then need to spin two times for its north and south poles to wind up in the same position.

  • In the same way, an electron needs to spin around 2 times - really, 2.002 times, to be more accurate - to show up back in its original state.
  • And it ends up that group theory - the language of permutations - offers a natural method of explaining how the electron behaves in this way. 
  • Group theory provides a method to model the electron's "double spin" habits in such a way that can not be done using more easy mathematics.
  •  Another way to consider this is: the way electrons behave is more like the method cards behave when they are mixed, than the way billiard balls act on the pool table.




The information are on the level of graduate mathematics, but the takeaway point is that a branch of mathematics, established nearly 300 years earlier, ends up being the perfect language for describing elements of nature we have actually just recently found.There are many Museums for Arts that are mainly involved physics.




LaGrange and Gauss definitely had no chance of visualizing this - to them, the universe was seen as a gigantic billiard table, like a machine in system javascripts. It ends up that, at the subatomic level, the truth is far more complex, however mathematics provides us a natural language to understand how it runs.