x.com/MasterTimBlais/status/2113737350358704365
1 correction found
the "tachyons only" universe is indistinguishable from ours.
That overstates the symmetry. In the cited dimensionality analyses, a 1+3 “tachyons only” world is only mathematically related to ours; it is described as having distinct predictability/stability problems, not as physically indistinguishable.
Full reasoning
Max Tegmark’s papers on this exact spacetime-dimension graph do not treat the 1+3 / “tachyons only” case as observationally identical to our 3+1 universe.
- In "On the dimensionality of spacetime" (1997), Tegmark says the
(1,3) case is mathematically equivalent to (3,1) with tachyons, but immediately adds that in this case an observer would be unable to make predictions, because well-posed problems require data outside the lightcones. - In the later, more detailed "Is 'the theory of everything' merely the ultimate ensemble theory?" (1998), Tegmark again says a 1+3-dimensional world would be "just like ours except that all particles would be tachyons", but then explicitly says it is premature to conclude such a world could support the needed stability and predictability. He lists concrete differences: arbitrary-energy photons could decay into tachyon–antitachyon pairs, and long-wavelength tachyon-field fluctuations would grow exponentially. The figure caption itself says a 1+3-dimensional spacetime "may fail on the stability requirement."
So there is a limited mathematical symmetry here, but calling the tachyon-only universe "indistinguishable from ours" is too strong: the literature the graph comes from describes physically important differences and possible instabilities, not a fully indistinguishable twin universe.
2 sources
- On the dimensionality of spacetime
"Since a mere minus sign distinguishes space from time, the remaining case (n,m)=(1,3) is mathematically equivalent to the case where (n,m)=(3,1) and all particles are tachyons... Also in this case, an observer would be unable to make any predictions, since ... well-posed problems require data to be specified in the non-local region outside the lightcones."
- Is "the theory of everything" merely the ultimate ensemble theory?
"A 1+3-dimensional spacetime is equivalent to a 3+1-dimensional one with tachyons only, and may fail on the stability requirement." Later: "a 1+3-dimensional world would be just like ours except that all particles would be tachyons ... but new instabilities appear. A photon of arbitrary energy could decay into a tachyon-antitachyon pair ... fluctuations in the Tachyon field ... would be unstable and grow exponentially."