Undergrad Dimensionless Time: Rindler & Minkowski Spacetime

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Dimensionless time in Rindler spacetime serves as a scaling method for the time coordinate, allowing it to be expressed in relation to the mass of a black hole. This concept is complemented by a dimensionless radial coordinate, which similarly normalizes the radial coordinate against a constant multiplied by the black hole's mass. The purpose of using dimensionless quantities is to isolate universal physical aspects that remain consistent across different mass scales. This approach aids in simplifying the analysis of spacetime dynamics in both Rindler and Minkowski frameworks. Overall, dimensionless time and coordinates facilitate a clearer understanding of gravitational effects independent of specific mass values.
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What does the dimensionless time in Rindler spacetime signifies? And how something dimensionless can be regarded as time and coupled up with proper distance in Minkowski spacetime?

(Page 7: https://www.perimeterinstitute.ca/images/files/black_holes_and_holography_course_notes.pdf )
 
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The "dimensionless time" is just a way of scaling the time coordinate in relation to the mass of the hole. Some sources also use a dimensionless radial coordinate which is constructed basically the same way, as a ratio of the usual radial coordinate to a constant times the hole's mass. The idea is to separate out aspects of the physics that are the same regardless of the mass of the hole.
 

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In an inertial frame of reference (IFR), there are two fixed points, A and B, which share an entangled state $$ \frac{1}{\sqrt{2}}(|0>_A|1>_B+|1>_A|0>_B) $$ At point A, a measurement is made. The state then collapses to $$ |a>_A|b>_B, \{a,b\}=\{0,1\} $$ We assume that A has the state ##|a>_A## and B has ##|b>_B## simultaneously, i.e., when their synchronized clocks both read time T However, in other inertial frames, due to the relativity of simultaneity, the moment when B has ##|b>_B##...
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