Spacetime and Euclidean geometry

  title={Spacetime and Euclidean geometry},
  author={Dieter R. Brill and Ted Jacobson},
  journal={General Relativity and Gravitation},
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the spacetime Pythagoras theorem. 

From Einstein's 1905 postulates to the geometry of flat space‐time

Minkowski diagrams in 1+1 dimensional flat space‐time are given a strictly geometric derivation, directly from two gedanken experiments incorporating the principle of the constancy of the velocity of

Relativity on Rotated Graph Paper

It is shown that many quantitative results can be read off a spacetime diagram by counting boxes, using a minimal amount of algebra, in the spirit of the Bondi k-calculus.

Alice and Bob and Hendrik

This paper offers an alternative approach to discussing both the principle of relativity and the derivation of the Lorentz transformations. This approach uses the idea that there may not be a

Physics and the Pythagorean Theorem

Pythagoras' theorem lies at the heart of physics as well as mathematics, yet its historical origins are obscure. We highlight a purely pictorial, gestalt-like proof that may have originated during

Plane Geometry in Spacetime

Minkowski’s spacetime diagrams are extracted directly from Einstein’s 1905 postulates, using only some very elementary plane geometry. I have spent a significant part of my career looking at familiar

Theory of Relativity – Biggest Mistake of the 20th Century?

  • W. Nawrot
  • Physics
    International Journal of Theoretical and Mathematical Physics
  • 2021
According to the thesis presented here, the correct model of reality should be based on two major discoveries of the 20th century: Einstein's discovery that reality is four-dimensional (1905) and de

The cissoid of Diocles in the Lorentz–Minkowski plane

This article presents the cissoid of Diocles and the cissoid of two circles with respect to origin in the Lorentz-Minkowski plane.



Black Holes and Wormholes in 2+1 Dimensions

Vacuum Einstein theory in three spacetime dimensions is locally trivial, but admits many solutions that are globally different, particularly if there is a negative cosmological constant. The

Space–time intervals as light rectangles

Two inertial observers in relative motion must each see the other’s clock running at the same rate. The representation of this symmetry of the Doppler effect in a two-dimensional space–time diagram

Relativity and Common Sense: A New Approach to Einstein


A Theory of Time and Space

THE appearance of Dr. Robb's treatise, if such a word can be applied to a volume which opens out a new field of philosophical inquiry on the basis of modern physical science, is a very welcome event,

El l i s and R . M . W i l l i am s, Fl at and C urved Spacetim es

  • 2000

part by the NSF under grants PHY-9800967 and PHY-0300710 at the University of Maryland, and by the CNRS at the Institut d

  • part by the NSF under grants PHY-9800967 and PHY-0300710 at the University of Maryland, and by the CNRS at the Institut d