scientists understand what kinds of symmetries
can appear in such a unified theory.
One candidate relies on a proposed connection
between two types of complementary theories: A
quantum theory of particles on a t wo-dimensional
surface without gravity can act as a hologram for
a three-dimensional theory of quantum gravity
in curved spacetime. That means the information
contained in the 3-D universe can be imprinted on
a surrounding 2-D surface (SN: 10/17/15, p. 28).
Picture a soda can with a label that describes
the size and location of each bubble inside. The
label catalogs how those bubbles merge and pop.
A curious researcher could use the behavior of the
can’s surface to understand goings-on inside the
can, for example, calculating what might happen
upon shaking it. For physicists, understanding a
simpler, 2-D theory can help them comprehend a
more complicated mess — namely, quantum gravity— going on inside. (The theory of quantum
gravity for which this holographic principle holds
is string theory, in which particles are described
by wiggling strings.)
“Noether’s theorem is a very important part
of that story,” says theoretical physicist Daniel
Harlow of MIT. Symmetries in the 2-D quantum
theory show up in the 3-D quantum gravity theory in a different context. In a satisfying twist,
Noether’s first and second theorems become
linked: Noether’s first theorem in the 2-D picture
makes the same statement as Noether’s second
theorem in 3-D. It’s like taking two sentences,
one in Japanese and one in English, and realizing upon translating them that both say the same
thing in different ways.
Everyday physics relies on Noether’s theorem
as well. The conservation laws it implies help to
explain waves on the surface of the ocean and air
flowing over an airplane wing.
Simulating such systems helps scientists make
predictions — about weather patterns, vibrations of
bridges or the effects of a nuclear blast, for example. Noether’s theorem doesn’t automatically apply
in computer simulations, which simplify the world
by slicing it up into small chunks of space and time.
So programmers have to manually add in conservation laws for energy and momentum.
“They throw away all of the physics, and then
they have to try and force it all back in somehow,”
says mathematician Elizabeth Mansfield of the
University of Kent in England. But Mansfield
has found new ways to make Noether’s theorem apply in simulations. She and colleagues
have simulated a person beating a drum inside a
simplified Stonehenge, determining how sound
waves would wrap around the stone — while automatically conserving energy. Mansfield says her
method, which she will present in September in
London at a Noether celebration, could eventually be used to create simulations that behave
more like the real world.
In addition to Noether’s importance in physics,
in mathematics her ideas are so prominent that
her name has become an adjective. References to
Noetherian rings, Noetherian groups and Noetherian modules are sprinkled throughout current
Noether’s work “should have been a wake-up
call to society that women could do mathematics,” Gregory says. Eventually, society did awaken.
In a 2015 lecture she gave about Noether at the
Perimeter Institute for Theoretical Physics in
Waterloo, Canada, Gregory showed a slide of herself with five female colleagues, then at the center
for particle theory at Durham University. While
women in science still face challenges, no one in the
group had to struggle to get paid for her work. “That
is Noether’s legacy, and I honestly think she would
have been really jazzed,” Gregory says. “I think this
would have been her real ... vindication.” s
s Perimeter Institute for Theoretical Physics.
Convergence public lecture. “Emmy Noether:
Her life, work and influence.” June 21, 2015.
s Auguste Dick. Emmy Noether 1882–1935.
Scratch the surface A theory of how particles act
in two dimensions can serve as a hologram for quantum
gravity in three dimensions. It’s like being able to study the
bubbles inside a soda can just by reading its label.