"To say that the four-dimensional continuum "exists now" implies that all cross sections "exist now" or, in other words, that the cross section t = t0 is identical with the cross-section t = t1. Otherwise, it could not exist "now." If we allow for this confusing way of thinking, the assertion that the "four-dimensional space-time continuum" has always existed and we are merely traveling through it asserts no more than the statement that the three-dimensional space continuum changes in time. ...if we call the ...space-time continuum a "reality," we are encouraged to adopt Lagrange's assertion that mechanics is a four-dimensional geometry, and to say that the four-dimensional continuum "exists now," and that therefore all future events exist now, and the "future" consists in our moving through the... continuum. But exactly as before Minkowski's formulation... we must also admit that the use of the word "now" in the formulation is rather misleading. By "now" we mean the cross section of the four-dimensional space-time continuum that is defined by t = t0. Therefore it is self-contradictory that any future instant of time t > t0 can exist "now." Use has often been made of this four-dimensional space-time continuum to "prove" that the future is "predetermined." ... The four-dimensional formulation is a useful instrument for the presentation of physical events, but it cannot be interpreted in our everyday language by simply speaking about the... space-time continuum as we have been accustomed to speak about our ordinary three-dimensional space."
Spacetime

January 1, 1970

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Original Language: English