The Speed of Time, Part 1
Let’s start with a more basic question. What is speed? In physics, the speed of an object is the magnitude of its velocity. Speed is measured, like velocity, in units of meters per second (m/s). Meters are easy to visualize in three dimensional space (3-space, or R3). Each tick on the XYZ axes is one meter, or negative one meter for objects traveling “backwards.” We can measure position by simply observing where the object is in 3-space. Time however is a bit trickier.
Classically, time (or Newtonian time) was thought of as a fourth dimension, independent from the three spacial dimensions, which defined a platform for the sequencing of events. According to the Newtonian notion time, seconds are universally measurable with a clock; and all correctly synchronized clocks progress equivocally. However, Einstein shook this understanding with his Theory of Special Relativity (TSR).
According to TSR, the 3 axes of 3-space and time unite to form the 4 axes of spacetime (4-space). Consequently, temporal measurements of an object or event are intrinsically related to the observer’s velocity through spacetime. In other words, two clocks moving relative to one another will (correctly) produce different measurements of time and simultaneity. Events that occur simultaneously in one reference frame may happen in sequence according to another. Furthermore, velocity through spacetime is governed by a universal speed limit, the speed of light (c), or 300,000,000 m/s. These measurement differences are not observable in our day-to-day lives, since they only become substantial at very high velocities (significant fractions of the speed of light). As a clock approaches the speed of light, it’s tick-rate approaches zero, according to a synchronized, stationary clock.
This is where science and philosophy begin to blur together. It’s possible, maybe even probable, that the speed of light is not just a limit, but is in fact the only possible speed. That is to say that everything moves at the speed of light through spacetime; and our notion of time is derivative of the fact that we are traveling at a very slow rate through 3-space (and consequently a very high rate through the 4th axis, time). This brings us to our initial conclusion:
Speed of (perceived) time (in m/s) = c - |v|
Where c is the speed of light, and |v| is the speed of the observer.
An astute reader will notice a plethora of unanswered problems with this formulation however. Firstly, the units of meters per second when measuring the speed of time are nonsensical. It might make more sense to define the speed of time in seconds/meter, as spacial speed is defined in meters/second. In a second attempt:
Speed of (perceived) time (in s/m) = (c - |v|) * X
Where X is in (seconds squared / meters squared)
Another question is whether the entropy of a system traveling at the speed of light increases or remains static, according to an observer traveling with the system. An outside observer would likely observe the system to be completely “frozen in time.” But could consciousness be possible for a sentient being traveling at the speed of light, or do all particles traveling at light speed simply become light, immortal and unchanging until they slow down? If forward entropy does exist at light speed, we might have to entertain the notion of recursive spacetime coordinate systems. Further exploration of these questions and many more to come.