[talanum1 (OP)]

            Defining time.
            Willem F. Esterhuyse

            Abstract
  We define Time, not by stating it is what a clock measure, and then describing a clock.

1. Defining time.

  We start with the required axioms:

A1: Complex numbers exist.
A2: x = x
A3: x + y = y + x
A4: A is a subset of B if B contains A and B - A not = Empty set

  We have to define a particle, from 4-dimensional space. So define first a complex space: two superimposed copies of the complex plane call this C <-> C (from A1). From C and a copy of C for both C's construct two superimposed
Riemann Spheres (RS <-> RS). Identify a circle in RS <-> RS going through the north and south poles of RS <-> RS call this Pp.

  We prove RS <-> RS is a particle: RS <-> RS can have spin and has finite size and can have momentum. Therefore RS <-> RS is a particle.

  Construct physical space as: RxRxR (R is the Real numbers) set this = S_p. Where x = Cartesian Product.

  Define "advance by one of Pp" by "Pp rotates by one unit as measured along the circumference of the circle, let this rotation be a quantum rotation: a rotation from state A to state B without visiting the in between states". The advancement does not move the infinity at the RS <-> RS north poles since: infinity - constant = infinity.

  Let the particle part "Pp" advance by one if it encounters a physical space point. Call this "freq" = T_s. Space expands and fluctuates so this does not give a static Pp.

  Now construct changes in freq by: T_sf - T_si. Construct {for all n = 1 toN: n(T_sf -T_si)_n}. Call this changes in freq.

  Define "basic time interval" = Delta t_B = 1/[(1/N) \sum \limits_{n=1}^N n(T_sf - T_si)_n]

  Couple Delta t­_B to every point of S­_p and call the result "basic spacetime"= B_st.

  Having defined B_ST we can now define time. We need another particle, so define like above a RS <-> RS. Isolate a circle in RS <-> RS going through the north and sout poles and call it Pq. Let Pq advance by one when encounntering a B_st point. Call this "freq3" = T_bst.

  Construct KxT_bst with K element of Natural numbers. Now we can define tim1 as: "Tim1" = t_1 = 1/[(1/K)(\sum \limits_{n=1}^K n#T_bstn)].

  If we require Pq is in every particle of the clock, we can prove tim1 = time. This is done by listing the properties of tim1 and comparing these with the properties of time:
tim1 advances like a clock, it depends on Pq in the clock and on the route in B_st. This is exactly the properties of time therefore:

tim1 = time, and we are done.

  In practice we only require that the clock contains particles with circles not containing any left out or added points.

Bibliography

[2] Nagashima Y, Elementary Particle Physics. Volume 1: Quantum Field Theory and Particles. Wiley-VCH Verlag GmbH & Co. KGaA. 2010.

[puppypower]

The main conceptual problem with the contemporary conceptual framework of time, is we measure time with clocks. The problem is, clocks do not behave like time. Clocks cycle like waves; noon and midnight. Whereas, all observations show that time does not cycle, but rather time propagates in one direction. We cannot relive our youth by waking at 1AM. Using clocks to measure time is like measuring length with a barometer. The barometer, like the clock, does not behave in the same way as the phenomena it measures. It requires a chart to translate.

A better conceptual model for measuring time, that is consistent with the nature of time, is entropy. According to the second law, entropy has to increase and therefore, like time, it moves in one direction. The traditional clock says I will return to midnight each day as though time cycles. In my own experience, what II did yesterday at midnight was not the same as the day before. In terms of an entropy clock, because the entropy of the universe has to increase, each midnight cannot to be the same, no matter how hard we try to pretend. This clock is closer to the reality of time. It can clear the head of fantasy in time.

The wave clock appears to have been invented by civilization so it could structure human time usage. You will punch into the factory at 7 am each day, like a wave of punctuality. This is not how time works, in the more general sense. Each day should be unique and not an assembly line with no deviation from management dictates. Wave locks are a time manipulator. That sounds like self serving science cynicism, that will resist any change to the established cycle. It does not recognize the second law and how time changes things.

An example of an entropy clock would be the  "dead fish clock". We buy a dead fish, bring it home and place in on the counter. When it begins to stink, that will be a unit of time. Unlike a wave clock where the clock measures the same unit of time, all the time, the entropy clock allows time to fluctuate, in real time, based on the absorption of energy into the local entropy. If we place the fish in the refrigerator time will slow and if we heat the room time will speed up, analogous to relativity. Each fish may weigh differently, and therefore like evolving planets and stars each moment in time, has it own time flow.

In spite of this obvious conceptual flaw, and my having pointed it out, on many occasions, established science is ignoring the truth and perpetuating a conceptual flaw. Science is not about  truth time,  but about perpetuating a cyclic bureaucracy in time, like its own clock. In terms of having some empathy, so much theory is based on this faulty time measuring cornerstone, that the needed system wide change is frightening. It is better to repress the truth and hope it goes away. 

I would suggest redoing the math, from the POV of an entropy clock, since this will be the future It is more truthful and consistent than a wave clock. Eventually science will be held to its own philosophy. Maybe if a math bridge is built, not everyone will be afraid of the change. Don't get sucked into try into evolve the existing the bad time theory, since that approach has to deal with mystical wave dogma that assumes time does not have to change anything.