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Measuring/Geometry/Feynman: there are properties that are independent of the particular type of measurement. For example, the distance between two points in a rotated coordinate system when one of the two points is in the origin.
The square of the distance is x² + y² + z².
What about space-time?
Space-Time/Geometry/Feynman: it is easy to show that there is also an invariance here:
The combination c²t² x² y² z² is the same before and after the transformation:
c²t' ² x' ² y' ² z' ² = c²t² x² y² z².
Ontology/Feynman: this quantity is something that like distance is "real" in a sense. It is called the Def "interval" between two space-time points._____________Explanation of symbols: Roman numerals indicate the source, arabic numerals indicate the page number. The corresponding books are indicated on the right hand side. ((s)…): Comment by the sender of the contribution.
Vom Wesen physikalischer Gesetze München 1993
Vorlesungen über Physik I München 2001