According to I.B. Pestov (2004), time can be viewed as scalar temporal field. In his paper with title New Concept of Time and Gravity, he wrote: "A new concept of internal time (viewed as a scalar temporal field) is introduced which predicts the existence of matter outside the time and allows one to solve the energy problem in General Relativity. It is demonstrated that introduction of the temporal field as an objective property of physical systems permits one to derive the physical laws of the electromagnetic field (the general covariant four-dimensional Maxwell equations for the electric and magnetic fields) from the geometrical equations of this field. It means that the fundamental physical laws are in full correspondence with the essence of time. On this ground, from the geometrical laws of the gravitational field the physical evolution equations of this field are derived. Two characteristic solutions of these equations are obtained (including the Schwartzschild solution)." See his paper at: http://www1.jinr.ru/Preprints/2004/105%28E2-2004-105%29.pdf. His other paper is: http://arxiv.org/abs/gr-qc/0507131.
While his theory may lack observability so far, I think his new concept of time seems worth to consider further, especially considering some puzzles in cosmology such as dark matter.
Btw, I met Pestov once around 2009 while he was giving a lecture on "Self-organization and gravity" (in Moscow), but at the time I only asked him some questions which are not related to his suggestion that time is scalar temporal field. I think his 2004 paper is more relevant with the question above.
It's an interesting concept, but it probably does not work, because different observers at different locations and different motions within the same universe would unavoidably see a different field - i.e., they would see different values attached to a same field point.
More generally speaking, time is a non observable, and whether you'd be able to build a field from non-observables is rather moot ....
Thank you, Chris, for your answer. Yes, you are right that time is non observable, but the fact that it can be combined into spacetime metric seems to suggest that it is possible to regard time as vector, then the next generalization is to consider time as temporal field. Anyway, i think that Pestov's concept reflects many attempts by some Russian scientists to explore the meaning of time in physical sciences, in particular during 1980s-2000s. Best wishes
Quite frankly, sounds similar to my approach which is rather well documented here on Researchgate...
BTW, there is no real problem with different observers seeing a different field because each observation point would be observing the same field but with different localized effects - no different than observing a large body of water at different points along the shoreline or even out in the middle of it. That's relativity.
Thank you, Marshall, for your answer. I will try to find your paper. Best wishes
Marshall, not sure I understand your comment - every observer would see different values attached to every single point of the field, in other words all of the field point attributes in every point would have different values - so that every point would have an infinity or near infinity (depending on whether the field is a continuum or discrete) of values attached to each point - which defeats the definition of an objective field, really.
In a non-relativistic body of water - your example - every observer sees the same objective field attribute values at every point. What am I missing ?
NOTE: * I am by no means an expert!
Time is an interesting concept; given the fundamental discontinuity of space (As Feynman conjectured) would not time also have to be discontinuous. If so I am under the impression that temporal vector field will more aptly describe time. From my present understanding acquired from proponent Frank A. Wilczek, "Inner-space" is a concept which pops up in QCD and may be closely related to your query on "Inner-time".
Good luck in your endeavors,
Sincerely,
--
Jordan D. Ulmer
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