Monday, November 14, 2016

Why are the macroscopic and microscopic related?

Through a nice blog post by Anshul Kogar,
I became aware of a beautiful Physics Today Reference Frame (just 2 pages!) from 1998 by Frank Wilczek
Why are there Analogies between Condensed Matter and Particle Theory?

It is worth reading in full and slowly. But here a few of the profound ideas that I found new and stimulating.

A central result of Newton's Principia was
"to prove the theorem that the gravitational force exerted by a spherically symmetric body is the same as that due to an ideal point of equal total mass at the body's center. This theorem provides quite a rigorous and precise example of how macroscopic bodies can be replaced by microscopic ones, without altering the consequent behavior. " 
More generally, we find that nowhere in the equations of classical mechanics [or electromagnetism] is there any quantity that fixes a definite scale of distance.
Only with quantum mechanics do fundamental length scales appear: the Planck length, Compton wavelength, and Bohr radius.

Planck's treatment of blackbody radiation [macroscopic phenomena] linked it to microscopic energy levels.

Einstein then performed a similar link between the specific heat of a crystal and the existence of phonons: the first example of a quasi-particle.

Aside: I need to think of how these two examples do or do not fit into the arguments and examples I give in my emergent quantum matter talk.

Wilczek says
it is certainly not logically necessary for there to be any deep resemblance between the laws of a macroworld and those of the microworld that produces it  
an important clue is that the laws  must be" upwardly heritable" 
[This is Wilczek's own phrase which does not seem to have been picked up by anyone later, including himself.]
the most basic conceptual principles governing physics as we know it - the principle of locality and the principle of symmetry  .... - are upwardly inheritable.
He then adds the "quasi material nature of apparently empty space."

Overall, I think my take might be a little different. I think the reason for the analogies in the title are that there are certain organising principles for emergence [renormalisation, quasi-particles, effective Hamiltonians, spontaneous symmetry breaking] that transcend energy and length scales. The latter are just parameters in the theory. Depending on the system they can vary over twenty orders of orders of magnitude (e.g., from cold atoms to quark-gluon plasmas).

But, perhaps Wilczek would say that once you have symmetry and locality you get quantum field theory and the rest follows....

What do you think?

1 comment:

  1. Very nice points indeed. Two remarks.

    1. Although this is rather trivial, it is seldom pointed out that it is the fact that the commutation (or anticommutation) relations are local that allows them to be satisfied also for the center of mass and total momentum of a large particle. This reinforces the point about locality.

    2. Although the Bohr radius and other small lengths come in when one includes electromagnetism, mass etc, the absolute scale for "smallness" is the quantum of action given by Planck's constant. This (along with broken symmetry) is what allows macroscopic superconducting qubits, for example, to let the laws of quantum mechanics be manifest despite the large size of these objects.