[Insightful Reads] Hyperspace - A Scientific Odyssey through Parallel Universes, Time Wraps and the Tenth Dimension

The title alone throws out a lot of terms taken out of fantasy, but I’ve found that the book is anything but. It attempts to trace through these concepts of dimensional space with the rigor of science and a degree of math still somewhat palatable to most people who have gone through undergrad math (say, linear algebra). Also implicated are major figures in math and physics like Riemann, Einstein and Michael Faraday. There is also a shade of the author, Michio Kaku’s life in there that I found interesting.

Insights

• Beyond Euclidean Geometry: Riemann Geometry, essentially geometry in curved spaces. Zero curvature = a plane, positive curvature = a sphere, negative curvature = a saddle. Also Riemann’s metric tensor is used to express a point in n-dimensional space.
• An imagining of what it looks like to view a lower dimension from a higher dimension, and move through it. Think Flatlanders vs 3d beings. Also, transitioning between multiple spaces with the same dimensions, think Alice In Wonderland.
• Cross-Dimensional Objects : Mobius Strips, Hinton’s Cubes
• Time as the 4th dimension, and how it relates to our 3-dimensional world.
• Collapsing Maxwell’s field equations from 8 into 1 trivial equation when treating time as the 4th dimension - an illustration of ‘beauty’ in physics.
• Einstein rethinking gravitation, how matter and energy correlates to curvature of spacetime. It would be 3 long years before a mathematician friend of his directed him to Riemann’s work from 60 years ago, which allowed Einstein to produce his most celebrated formula/work.
• Kaluza-Klein Theory: Kaluza starts by writing down Einstein’s field equations for gravity in 5 dimensions, unlike the usual 4. He then shows that these 5 dimensional equations not only showcases Einstein’s 4 dimensional theory, but also adds on another piece, which happened to be Maxwell’s theory of light. The implication was the light was a disturbance caused by the rippling of the 5th dimension!
• A conjecture of the Kaluza-Klein Theory is that the 5th dimension had curled up into an extremely tiny ball. It also couldn’t be tested, leaving it untouched for the next 60 years, where the subject of quantum physics took over.
• Quantum theory is a theory of the microcosm, of subatomic particles. In contrast to Einstein’s theory of a force, forces in quantum theory light is chopped up into packets called photons, and when they bump into each other they repel each other and exchange a packet of energy, the photon. Different forces are caused by the exchange of different quanta, and we can never know simultaneously the velocity and position of a subatomic particle (the Heisenberg Uncertainty Principle).
• 3 of the 4 fundamental forces, excluding gravity, can be united by quantum theory, giving us unification without geometry, contradicting the very theme of the book.
• What was annoying was that quantum theory reduces everything to probability waves due to the uncertainty principle. A heresy of sorts.
• The Yang-Mills Field, the Standard Model of Physics. The Standard Model, despite all it’s experimental data, fails in that it is missing a few ‘beauty’ components, one being that it doesn’t have a single symmetry group and does not describe the subatomic world economically.
• Return of the Kaluza-Klein Theory: When the field equations are extended to N dimensions, the physicists found Yang-Mills Field, the key to the Standard Model!
• Supersymmetry, Supergravity theory: Assume each particle has a super-particle version of it, fulfilling certain theories. The field equations can then be extended to 11 dimensions to fit quarks and leptons into it. Unfortunately, superparticles have not been observed in any experiment, and thus the theory began to fall into decline.
• Superstring theory. If a subatomic particle were magnified, we’d see a small vibrating string. Currently the only self-consistent theory of quantum gravity. Clockwise vibrations live in 10 dimensional space, anticlockwise vibrations in 26 dimensions.
• From this point on the book veers more into what’s theoretically possible but not within our current capabilities, or unproven things.
• Exploration of pre-big bang times, including philosophical takes on creation.
• Wormholes, black holes, parallel universes. The Einstein-Rosen bridge that connects 2 universes.
• Time machines, Wave functions of other universes.
• The far future, type 0/1/2/3 civilizations and energy consumption, death of the earth and galaxies.

This insightful book read is one of many book reviews to come, see this post for what I’m trying to do