The concept of antimatter being related to negative time, or time running backward, originates from Richard Feynman's interpretation of antimatter as matter traveling backwards in time, an idea that is mathematically equivalent to Dirac's theory.
In a 1964 science fair project, I postulated a "dual" (matter-antimatter) universe equally divided between separate matter and anti-matter aggregates. While not knowing anything of Feynman's concept, I intuitively took the antimatter counterpart to our matter universe to be governed by negative time in terms of its particles and interactions. I explained it thus:
"The invariant space-time interval is inextricably associated with both matter and anti-matter. Thus, neither matter nor anti-matter can attain a state whereby it exists as an extended sequence of time loci when isolated from its respective region. In effect, time proceeds backwards in the anti-matter universe relative to ours, i.e.
Thus, we can never see anti-matter stars or galaxies in our universe, just as the anti-matter, negative curvature universe can never have matter stars or galaxies."
In line with this I also posited that the differing universes had to assume different non-Euclidean shapes, with the matter universe Riemannian or spherical, and the anti-matter universe Lobachevskian or like a horse saddle shape. It was the differing times that dictated the geometry - the latter being a kind of inverse sphere ("pseudo-sphere") to the spherical Riemannian matter universe. The proper terms for the respective spaces are: elliptic (for Riemannian or + curved), and hyperbolic (for Lobachevskian or (-)-curved.
If you look closely at the photo shown above, from a March 31, 1964 Miami Herald piece, you can see on the right the 2 universes integrated into a model- with the negative time Lobachevskian embedded into the spherical Riemannian. A better view of the negative time geometry is shown below:
A more comprehensive analytic approach is possible, wherein I associated lines and points with a particular geometry and particle paths. A
simplified form for this may be expressed using the matrix formulation in
4(a).
Where the left side denotes a line [u1, u2, u3]. If one finds that the point specified by (x1, x2, x3) is the same as for another point specified (y1,y2, y3) such that the matrix relation in 4(b) is true then we can say that the correlation constitutes a polarity. It is possible that a suitable choice of polarity can be found for any combination of points for a line [u1, u2, u3] such that: u1 = x1, u2 = x2 and u3 = cx3. In this case, if c = +1 (positive time) the geometry is elliptic (e.g. Riemannian), and if c =-1 (negative time) it is hyperbolic.
Recently, a groundbreaking experiment challenged conventional wisdom by introducing the concept of "negative time." This idea arose from observations made during photon interactions within certain transparent materials. The study showed photons being absorbed and re-emitted in such short durations that researchers measured them as less than zero—hence "negative time."
The study,
led by Professor Aephraim Steinberg at the University of Toronto, ignited considerable debate. Although the
findings await peer review, Steinberg emphasizes their importance. He describes
the work as essential to unraveling the strange behaviors within quantum
systems, despite its controversial reception.
Schematic of the experimental setup is shown below. Left (a) is the Atomic level scheme. Right we see (b) Conceptual diagram of the experimental apparatus. Here a resonant pulsed beam (signal) and off-resonant continuous-wave beam (probe) counter-propagate through a cloud of cold 85Rb atoms, detected at opposite sides of the apparatus.
In traditional theories, photons have always been assumed to follow a straightforward timeline of absorption and re-emission. But Steinberg's team discovered these events could seemingly occur backward, disrupting established ideas about time in quantum mechanics.
Previously, scientists dismissed such strange timing as mere measurement errors. However, Steinberg and his colleagues have argued these results reflect genuine quantum phenomena. They suggest these odd timings arise naturally within the probabilistic world of quantum mechanics.
Steinberg's approach, as readers can see, is more prosaic compared to mine. Based on laboratory experiments using actual detectors and measuring devices, rather then deductions from the fundamental geometry of the universe. But both his and mine are similar in postulating the potential for time to run forwards or backwards: mine based on the ground form geometry of whether the particle is in a positively or negatively curved universe (matter or antimatter) and Steinberg's in terms of whether short durations of absorption and re-emission constitute negative time.
See Also:
Time Loops Are "Real" - At Least In Some Theoretical Universes (And Maybe In Ours)
