Hot answers tagged emergent-properties
8
There are thousands of such examples, it is basically all situations in condensed matter physics. You see a lot of regularities that have no explanation.
Here's one of the most annoying ones for me: Moseley's law--- you can knock out one of the two electrons most tightly bound to a heavy atom (in the K-shell). This leaves a hole orbiting the nucleus. The ...
5
This is an example from hydrodynamics. When the effects of viscosity can
be ignored (inviscid flow), a uniform incident flow can exert on immersed
bodies only lift forces perpendicular to the asymptotic flow velocity.
However, there exist an infinite number of solutions of the flow
equations of motion satisfying the asymptotic conditions at infinity and
the ...
4
Your second sentence is not correct in our current understanding of physics. Photons are not an "emergent property of space-time" - photons appear even when we take space-time to be a fixed object. Photons are "not due to electrons... jumping around" - they can be created by the motion of charges but they are independent objects. Photons are just as real as ...
3
A key difference between spontaneously broken symmetries and "emergent symmetries" is that emergent symmetries are never exact while spontaneously broken symmetries are backed by exact maths although the ground state isn't invariant. In most cases, the "emergent symmetries" only emerge if some parameters are fine-tuned, and even if it is so, they are only ...
2
The simplest model is the spin-1/2 chain with Majumdar–Ghosh interaction:
$$H=\sum_i P_{3/2}(i-1,i,i+1),$$
where $P_{3/2}(i,j,k)$ is the projection operator that projects a state onto the subspace with total spin-3/2 on sites $i,j,k$. The ground states are two dimer states (see the figure on wikipedia Majumdar–Ghosh model):
...
2
As Ron noted, there are many, many examples within condensed matter; they often share a very similar story where the microscopic laws are known well (exactly, for the case of simulations), but the macroscopic laws are derived by symmetry concerns.
Take for example, liquid crystals. We could simulate a collection of hard rods or ellipsoids - this is our ...
1
Any problem that requires solving of non-trivial Schroedinger equations. For example, protein folding problem. It is known what equations the system should satisfy and those equations can be written down. Yet they cannot be solved with modern computers which would take millions of years tor that.
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