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The laws of physics are only symmetric under euclidean rotations in the three dimensions of space. When mixing time and space, you have to use a hyperbolic rota

The laws of physics are only symmetric under euclidean rotations in the three dimensions of space. When mixing time and space, you have to use a hyperbolic rotation, and there is no hyperbolic rotation that turns time into space.

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 ago
  I'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.

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 ago
I'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.