n-dimensional time

summary
wherein it was conjectured that a coordinate set containing more than one time component (what was informally called a "time manifold") may lead to a non-constant speed of light

fresh ideas 22.XI.2008

• [Waerden] 's first mention of Lorentz transformations groups , in $10 , with past and future non-interachangeable raised some interest.
  


• [Weinberg] p. 51, section 2.2:




• "continuity demands that any symmetry like a rotation or translation or Lorentz xform that can be made trivial by continuous change of parameters (physical params, eg, angles, distances, velocities) must be represented by a linear unitary group U rather than an antilinear antiunitary group "


• here it comes : "Symmetries representable by antilinear antiunitary operators all involve a reversal in time's flow. see section 2.6"


• Cf. 2.3 Lorentz groups , and 2.6 as per above quote.
  
  





• [Waerden] set of permutations on coordinates
  
  
  
  
  
  • (can this include time?) because that was precisely the idea of seeing time-dependent functions from the perspective of function-dependent time, which is very much a permutation of the coord. of a 4-spacetime.
    
    
  
  
  • from reading notes waerden: … cyclic permutation in parentheses,… xformations e.g.: [Waerden] §10 p. 45 - permutations : __of the coordinates of particles e- and ["h… elements…
    
    
    
  
  
  
  


• In "Gauge Theory: past present and future", Chinese physics journal, 30, 7, David Gross writes that Einstein gen. relativity gives "a dynamical role to geometry" (p. 956).


• in these terms, Our question is then : what dynamical role can be given to time?

n-Dimensional time , 2007 - 2008/II/08

Time is generally a scalar quantity that is part of some input or state vector.

When considering that simultaneity is relative to the respective frames of reference and velocities of the observers, a time-"space" may be conceived in which the axes represent the different observer's timelines, and a coordinate point represents a "simultaneous" event that occurs at different times for different observers.

This however is potentially a simplistic and a superfluous usage.

The other notion is whether time is not merely a scalar but a multidimensioned linear vector space like for instance physical space or a Minkowski real 4-space.

We can thus also finally think of time as a linear vector space or a physical field of force (except it does not seem to have a force at all. does it?) , which could be shown (or not) to have relativistic perturbations the same way a gravitational or an em field - if we could determine time forces, we could have a time field equation.

functional time

Time being a function of what? Well among other things, the most obvious candidate is energy, as well as fields but these must arise out of the energies (labour as it were) of the fundamental particles. As such then there is little we can possibly do as humans to alter the valuation of time as a function of the physical or mass-energetic processes of the universe.

This is also raises the question of why time was not factored in before as a vector?
(lack of time causality, time does not cause anything).

time functional

so long as one is so far gone beyond the pale of proper mathematical physical thought, iow, jamming with the concept, several points arise.

The notion that time could be thought of in the same way as a force "field" or an abstract field can lead to expressing time as an integral, iow, finding a time functional. What with time being a linearly additive function of things like energy.

Different directions could be examined relating time with other concepts in new ways. Relations could be sought with probability as it is another "reality-based" observable, and an integral measure.

Other

Time is a scalar not dissimilar to energy in the numeric properties of being real, positive. It is also a symmetry. We speak of time progressing, but this very progress has a constant rate (at least nonrelativistically?).

Yet this accumulation in the form of progression, where is the accumulation?
We do not see time piling up.
What we do see however, in the framework of a bunch of conserved quantities lik energy, is change.
Change is the additive , signed quantity that increases directly with kin. energy and inversely with potential energy.