Time is either +1 or -1 Searching the web 21 results The phrase "time is either +1 or -1" is a concise (and somewhat poetic) way to capture a key feature in modern physics: the signature of spacetime in relativity and beyond.In the mathematical description of our universe (Minkowski spacetime from special relativity, extended to general relativity), we combine 3 spatial dimensions with 1 time dimension into a 4D manifold. But time isn't "just another dimension" like the spatial ones—the way distances (or intervals) are measured treats time differently.The metric signature (the pattern of + and - signs in the line element ds²) encodes this:The most common convention in particle physics and much of modern theoretical work is (+,-,-,-) — time gets the +1, and the three space dimensions get -1 each. The older/more common convention in many general relativity textbooks is (-,+,+,+) — time gets the -1, and space gets +1 each. So literally: time is assigned either +1 or -1 in the signature, depending on which convention the physicist chooses. (Both describe the exact same physics; it's just a relabeling of signs, like flipping overall minus signs in equations.)Why This Matters (and Ties to "Illusion" of Time)This difference in sign is what makes spacetime pseudo-Riemannian rather than fully Euclidean. It enforces:The light cone structure → causality (events can influence only inside/outside the cone). Hyperbolic geometry for time → the "arrow" feeling, time dilation, the impossibility of faster-than-light travel. The distinction between timelike, spacelike, and lightlike intervals. If time had the same sign as space (all ++++ or all ----), the universe would behave like ordinary 4D Euclidean space—no causality, no proper notion of "before/after," no light cones, no hyperbolic motion. Physics as we know it collapses.In theories where time is emergent or illusory (as we discussed earlier—Rovelli, Page-Wootters, block universe, etc.):At the fundamental level (e.g., Wheeler-DeWitt equation in quantum gravity), time often "disappears" entirely—no parameter t left in the equations. The +1 vs -1 distinction (the Lorentzian signature) is something that emerges along with classical spacetime from a more timeless, quantum, or entropic substrate. Some approaches (e.g., certain causal set theories, or ideas in emergent gravity) speculate that the signature itself isn't fundamental but arises statistically or from deeper degrees of freedom—making even the +1/-1 choice a kind of "effective" illusion from our coarse-grained perspective. In short: Yes, in the math that best describes reality, time literally gets labeled either +1 or -1 in the metric—unlike the uniform treatment of space. This single sign flip is responsible for almost everything weird and wonderful about time: its one-way street, relativity of simultaneity, the block-universe timelessness at deep levels, and why the flowing, directional time we experience feels so real yet so fragile/illusory when probed fundamentally.

No comments:

Post a Comment