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Minkowski concluded that time and space should be treated equally, and so arose his concept of events taking place in a unified four-dimensional spacetime conti
by potiuper 5y ago
Minkowski concluded that time and space should be treated equally, and so arose his concept of events taking place in a unified four-dimensional spacetime continuum. Even though Minkowski space treats time differently than space unlike 4D Euclidean space that does not mean that a transformation can not exist that preserves the Minkowski space(time) interval between two events, which is the defining property of a Lorentz transformation. The action of a hyperbolic versor (https://en.wikipedia.org/wiki/Versor#Hyperbolic_versor https://en.wikipedia.org/wiki/Versor#Hyperbolic_versor) with the further development of special relativity came to be called a Lorentz boost (https://en.wikipedia.org/wiki/Lorentz_transformation#boost https://en.wikipedia.org/wiki/Lorentz_transformation#boost). Boosts are a rotation-free Lorentz transformation; should not be conflated with mere displacements in Minkowski space(time). They describe only the transformations in which the spacetime event at the origin is left fixed; can be considered as a hyperbolic rotation of Minkowski space(time).
Unfortunately, as Einstein was already aware, a quasi-Euclidean four-space that includes time is not valid, because it excludes the phenomenon of gravitation. In the presence of gravity, spacetime is described by a curved 4-dimensional manifold for which the tangent space to any point is a 4-dimensional Minkowski space. Further, the article takeaway describes a different bound on the applicability of Minkowski (physical) space: "the discovery that, in the case of time, only discrete time-translation symmetry may be broken by time crystals puts a new angle on the distinction between time and space."
- whatshisface 5y agoI'm not sure what you're getting at - it's still impossible to have a rotation that transforms a spatial basis vector into a time basis vector.