I really don't have a good definition of time.
I think you've given a very good definition... but that may just be because you have presented an analysis that directly correlates with what I call the "Integrated Matrix of Massive SpaceTime".
So perhaps you can think of time as an inverse measure of space-time density. The more dense it is, the slower it must move through time. Time = 1 / Density. Density = Mass / Volume. Therefore, Time = Volume / Mass.
FINALLY someone who has a good grip on science, AND has independently come to the same conclusion that I have! /ttiforum/images/graemlins/smile.gif
Your dimensional analysis comes at it from a bit of a different angle (and ends up with the reciprocal of how I would define Time), but it is so close as to be the same. Let me throw my progression at you and see if it makes sense:
1) Is there a single, common precept for how we measure Time?
2) Yes. That principle is (for ALL our instruments that measure Time) TIME is measured by MATTER that is in MOTION.
3) You can think of any timepiece you like, and you will see this:
____a) Sundials = MOTION of the Earth (MASS) about its axis with respect to the Sun.
____b) Solar Calendar = MOTION of the Earth (MASS) around the Sun.
____c) Mechanical Watch/Clock = MOTION of gears (MASS) powered by a coiled spring (MASS).
____d) Atomic Clock = Oscillatory emissions (MOTION) of a specific form of MASS (Cesium).
4) Now we ask: What is MOTION? Technically, it is the TIME-DERIVATIVE of POSITION, and we call it Velocity. And the units of Velocity? SPACE per unit TIME.
5) Now we ask: What is MATTER? (This is where my theory slightly modifies standard theory to distinguish between MASS and MATTER). My body is MATTER, which is MASS that changes with respect to TIME. IOW, the Mass of my body today is NOT THE SAME Mass that my body was 5 years ago. Similarly, on a atomic scale, we know that atoms are by no means "static". The electrons form a "probability cloud" of where they might be at any point in TIME. And furthermore, we also know that subatmomic particles are constantly "changing into each other" which forms the perception that there are "static" protons and neutrons. So back to the question: What is MATTER? I say that MATTER is similar to MOTION, but it is measured as how MASS changes per unit TIME. In engineering we call this "Mass Flow Rate", and it is THE primary concept behind the production of thrust in a jet engine and torque in an internal combustion engine.
6) So now for the punchline... If TIME is measured by MATTER in MOTION, then we say TIME = MATTER/MOTION. Using the definitions of these provided above we end up with:
TIME = Matter/Motion = (Mass/Time)/(Space/Time) = Mass/Space (or Mass/Volume)
Now... this is the reciprocal of what you came up with, and the reciprocal of a measure of Time is a measure of Frequency. But in either case, we must finally realize that:
TIME (and Frequency) are measured by a CHANGE IN MASS with respect to a CHANGE IN SPACE.
Ultimately, what my theory states is that ANY attempt to separate the measure of Momentum or Energy into component "parts" (i.e. Mass, Space, or Time) will result in error. Thus, I deem that the things we call Mass, Space, and Time are CONCEPTS that are APPROXIMATIONS of what we perceive to be true. None of these three things are "real". The only "reality" is Momentum and Energy, and this is completely backed by science via Conservation Laws.
Now.... let me go further. If you accept this premise that Mass, Time, and Space are "concepts" which are actually all tied-together (integrated), we can use "similar triangles" logic to analyze how you change one by a change in the two others. The one we are familiar with is:
To move THROUGH SPACE, we need to expel MASS over periods of TIME. Hmmmm...sounds EXACTLY like how we produce thrust from a jet (see above), and indeed it is! The difference between the Mass Flow Rate input to a jet's inlet and the Mass Flow Rate coming out of the jet's exhaust nozzle is directly proportional to the amount of THRUST we get out of it...and that Thrust is what makes us move through Space.
Using the "similar triangles" approach, we now simply swap-out the parameters we wish to control. IOW, we wish to travel THROUGH TIME (viz. SPACE). Then it must stand to reason that if we wish to do this we will need to modify BOTH Mass AND Space such that we can create a displacement in TIME.
RMT