Quote:
Originally Posted by AnssiH
Since you pasted that picture, I should comment that when I was referring to the "ontology of the simultaneity planes", I was talking about what is dubbed "hypersurface of the present" in that picture. With the definitions of relativity, the visualized surface is for an observer who is not moving in that picture. If the red dot was moving in that pictured frame, his "surface of the present" would be tilted. Depending on the observer's speed, it could be tilted in any angle as long as it did not penetrate the light cones.
That means, if the observer was changing directions, its "surface of the present" would be said to tilt back and forth in such manner that some events would move through the present "backwards"; i.e. some things around the observer would move backwards in time (of course beyond the sight of the observer).
I.e, if you take relative simultaneity as ontologically real, you also assume that things around you in your "present moment" can move backwards in time if you change directions, but you just can't see it.
Of course at this point I should remind you that it is possible to build a valid view of reality where such simultaneity planes are not ontologically real. I think that is just one particularly interesting aspect of modern definitions on "time".
-Anssi
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I'm glad you clarified that because I had no idea that's what you meant. It's described a bit on wiki's
world line:
Quote:
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Originally Posted by Wiki
The present instant is defined for a given observer by a plane normal to her/his world line. It is the locus of simultaneous events, and is really three-dimensional, though it would be a plane in the diagram because we had to throw away one dimension to make an intelligible picture. Although the light cones are the same for all observers, different observers, with differing velocities but coincident at an event or point in the spacetime, have world lines that cross each other at an angle determined by their relative velocities, and thus the present instant is different for them. The fact that simultaneity depends on relative velocity caused problems for many scientists and laymen trying to accept relativity in the early days. The illustration with the light cones may make it appear that they cannot be at 45 degrees to two lines that intersect, but it is true and can be demonstrated with the Lorentz transformation. The geometry is Minkowskian, not Euclidean.
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And your particular objection is called the andromeda paradox:
Rietdijk-Putnam argument - Wikipedia, the free encyclopedia
which is only a paradox (like so many things in SR) if you assume a person can receive information faster than light or assume people can know things which are impossible to know. In other words, only by making bad assumptions is the relative plane of simultaneity a problem rather than always perfectly consistent with observation.
~modest
