An article from Quanta Magazine (below) recaps the history of space-time symmetries in physics and how those symmetries have, in a sense, been simplified:
- Galilean (Newtonian) static, separate space and time.
- Relativistic “flat” space-time – Minkowski / Poincaré / Einstein.
- de Sitter spherical space-time: “… in the same way that the finite speed of light simplifies things, the finite radius makes the de Sitter group simpler and more unified than the Poincaré group.“
Implicit in this article is a distinction between two perspectives. In the first perspective, there’s the mathematical model of the universe which allows us to predict things regardless of where & when we do so. This model is based on symmetries.
In the second perspective, there’s the (real) landscape and what “makes one place different from another.” Homogeneity in substance and form is equated with “perfect” symmetry. The non-uniform (variable) distribution of stuff “broke” symmetry: “Broken symmetries are necessary for existence.” Broke something real or a model? Such reification gives me pause.
• Quanta Magazine > Abstractions Blog > “How (Relatively) Simple Symmetries Underlie Our Expanding Universe” by Natalie Wolchover (July 15, 2019) – Although Einstein’s theory of space-time seems more complicated than Newtonian physics, it greatly simplified the mathematical description of the universe.
… the symmetries of the universe, or all the ways you can shift, rotate and move through it and still measure the same separation between objects or events as before. It is in the language of these symmetries that relativity simplified our mathematical description of the universe.
In fact, the math becomes even nicer when the expansion of space-time is taken into account.
In Newtonian physics, the distance between the start and finish lines and the time a sprinter takes to traverse that distance don’t depend on your point of view. You can carry your clock to a different place or hold the race at a different time, turn the clock upside down, or hop in a car and drive alongside the sprinter, and still you’ll record the same time as before, according to the equations. In other words, there are 10 “symmetries” of absolute space and time: rotations in any of three spatial directions (x, y and z), motion in those directions, and shifts to new positions in x, y, z and time. They’re known as the Galilean transformations.
But those are not the true symmetries of nature.
Instead, as Einstein discovered, space and time are inextricably bound. … And yet, … the “space-time interval” between two events – each person’s combined measurements of the length of the racetrack and the sprinter’s time – always stays the same regardless of one’s point of view.
… the Poincaré symmetries [the 10 ways of changing perspectives on space-time vs. the Galilean symmetries] still assume an infinity by specifying ways of transforming flat space-time, which extends uniformly forever in all directions.
When the radius of the universe is finite — that is, when the space-time fabric looks like the surface of an enormous sphere rather than an infinite sheet of paper — the 10 Poincaré symmetries are replaced by a new group of 10 transformations known as the de Sitter group. … in the same way that the finite speed of light simplifies things, the finite radius makes the de Sitter group simpler and more unified than the Poincaré group.
In a de Sitter universe, the space-time fabric is infused with energy, which not only causes it to curve like a sphere, but also makes it expand over time. … And space-time is indeed infused with energy — the “dark energy” discovered by astronomers in 1998. So do we live in a de Sitter universe, described by the simple de Sitter group of symmetries? The strange answer is: We will eventually.
 There’s a transition in the article from (1) invariances in applying the laws of physics – “all the ways you can shift, rotate and move through it [the universe] and still measure the same separation between objects or events” to (2) variabilities in how the universe looks from separate (perhaps cosmic) vantage points in space-time. Symmetries in the first case are exploited for knowledge. Variabilities in the second case are telltales of something deeper, a metaphysics.
The article concludes with a riff on the fate of the universe due to accelerating expansion, returning eventually to a pure unwrinkled (vacuum) state. (See post “A shelf life for the universe?“)
• Symmetry Magazine > “Nature through the looking glass” by Oscar Miyamoto Gomez (09/22/20) – Handedness – and the related concept of chirality – are double-sided ways of understanding how matter breaks symmetries.
Because our hands are chiral, they do not interact with other objects and space in the exact same way. In nature, you will find this property in things like proteins, spiral galaxies and most elementary particles.
These different-handed object pairs reveal some puzzling asymmetries in the way our universe works. For example, the weak force – the force responsible for nuclear decay – has an effect only on particles that are left-handed. Also, life itself – every plant and creature we know – is built almost exclusively with right-handed sugars and left-handed amino acids.
A chiral twin has been found for every matter and antimatter particle in the Standard Model – with the exception of neutrinos.
The difference between left-handed and right-handed could have influenced another broken symmetry: the current predominance of matter over antimatter in our universe.
According to de Gouvêa [a professor at Northwestern University], the main lesson that chirality teaches scientists is that we should always be prepared to be surprised. “The big question is whether asymmetry is a property of our universe, or a property of the laws of nature,” he says. “We should always be willing to admit that our best ideas are wrong; nature does not do what we think is best.”