Wednesday, August 30, 2023

What the Hell is a Particle when we are talking about Quantum Mechanics? Two Positions in Configuration Space! Hiley

 https://www.youtube.com/watch?v=xT6KVnRhQNc&t=0s

44 minutes into this Wigner Institute talk...(see below)

at 9 minutes:

"since a point in phase space has no physical meaning" - Hiley disagrees with George Mackey and his "doctrine of the primacy of configuration space"....

 a "representation" in P or X is the "doctrine of configuration space" that never looks at phase space!

Forget about the uncertainty principle... 

then translate the X space and P space...

We don't worry about the wave function. We go to the algebra into terms of the density matrix...

We were talking with Herbert Frohlich... very interested in superconductivity and superfluids...and I want to make it a function of two points in configuration space. In other words this is not a local theory....

 In quantum field theory they look at "global" momentum.... and global properties because they are concerned that energy will not be conserved...

"I'm dealing with a single particle but I'm describing it with two positions in configuration space....What the hell is a particle when we're talking about quantum mechanics...?"

 44 minutes.

you can squeeze y and x but you can NOT squeeze x and P (momentum) as the complementary variables....  "the symplectic camel" The head stuck and the rest does not follow through the eye of a needle.. NOn-Squeezing Theorem - that's classical physics... quantum physics adds that there is a minimal cell structure of h-bar...

For a single particle to have two points associated with it simultaneous
"because we have noncommutativity, order of operations is very important...."

What the Hell does that mean?

 write the wave function in terms of its real and imaginary parts....

go for the limit at h-bar squared.....

"For me the real structure is in this noncommutative algebra"
He saw the impossible done - John Bell on Bohmian phase space being nonlocal ...

There's nothing here at all. Why are Beables, if they are beables, electrons, why are they moving like that? Well, what we've got to do is look at the quantum potential! And then you find that here is the two slits in the background. If the trajectory, I'll call it a trajectory, along the plateau there it's a straight line. But as soon as it hits a potential that suddenly dips and comes back up again at the rate of potential which is a force.... and so you get...that's across like that...We used the Bohm theory that you could replace all the mysteries .... the whole lot can be fitted into this particular story....

If you take the Moyal Bracket and you go to the order of H-Bar Squared you find you get the Poisson Bracket...

31 minutes....

At the Baker Bracket - everything becomes commutative provided you're not looking at the order greater than H-bar squared...Because of noncommutativity - when you add and subtract - you get The Moyal Bracket "in the limit of order H-bar squared."

The Baker Bracket (Jordan) - 

"it has a minus sign" - it's not a derivation - what the! I mustn't swear when I'm on camera...What the Hell does that mean!

 Go to the limit as H-Bar squared - and you find the Hamilton-Jacobi equation and that's where Schroedinger started...

Schroedinger would have had to know all about this noncommutative structure to deduce his equation.




 


 


 

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