If we use 4D space in the wave function for free particle,
Ψ = A exp( i(p•X– Et )) omit “h-” and vector marks for convenience of observation.
Then,｜A｜² is a constant. It means the probability of appearance of the particle in any point of 4D space is the same. In turn, it means the probability of the X4 state the free particle be in is the same. The situation is the same in any position x in the 3D space.
Because it’s a free particle, no interaction is concerned, the above analysis reflects the property of the particle itself regardless it is moving or not.
When X4 = 1, X = x, the 4D space is equivalent to the 3D space.
The macroscopic “glass” in the topic of this thread is made up of microscopic particles. So the same principle is applicable.
In traditional QM, value area for 3D space x is (-∞, +∞). In X4 Theory, it’s a bit different, positive values of X4 represent “not anti” while negative values of X4 represent “anti”. So, 4D space has something to do with matter state. The value area can be either positive or negative. Put it aside temporarily.
The purpose of this step is to use a special (space) dimension to accommodate the uncertainty.
(4D space definition see htam9876's thread "tramp and electron" in philosophy.)