A translator gets distracted by every rustle in the hall, and a one-hour meeting stretches into two. That's roughly how ordinary quantum mechanics works: a particle evolves in time, while space serves as the stage. But what if we swapped their roles? Then the particle 'moves' through space, and time becomes a static backdrop. That's exactly how TSI quantum mechanics is set up, and in it, as the authors discovered, an unexpected symmetry is hiding.
The foundation is an operator called the 'momentumian'—from the word momentum. It resembles the square root of an energy difference, and it can be factored, just as the number 9 factors into 3 × 3. From this factorization, as if from a box with a false bottom, paired equations and supercharges emerge — mathematical twins that link different states of a particle. This structure is known as supersymmetry, but here it isn't imposed from outside; it's born on its own.
The most intriguing part is the memory effect. The equations feature fractional time derivatives (for instance, half-order rather than integer), and the wave function begins to 'remember' its history. This is like the wake trailing behind a boat: it affects the current motion even though the source is far behind. Such memory is woven into the very fabric of the theory, not added by hand.
A fractional derivative of 1/2 is like measuring speed not per second but per 'half a second squared,' and the result would depend on the entire path, not just the current moment.
In Kurt Vonnegut's novel Slaughterhouse-Five, the aliens from Tralfamadore see time all at once, like a mountain range. TSI quantum mechanics offers a similar view, where space and time are on equal footing, and the past doesn't vanish.