First I open the floodgates of imagination; then I employ a sharp file.
Problem: physical laws symmetric with respect to direction of time at lowest level, asymmetric at ours.
Note the exception of CP / T violations in the weak interactions. Since these do not seem to have anything to do with time in the causal or directed sense and since: "The discrete symmetries C (charge inversion), P (parity, or space reflection), and T (time reversal) are preserved by strong and electromagnetic processes, but violated by weak decays. For a brief period of several years, it was thought that the products CP and T were preserved by all processes, but that belief was shattered with the discovery of CP violation in neutral kaon decays in 1964 (Christenson, Cronin et al. 1964). The product CPT seems to be preserved, as is expected in local Lorentz-invariant quantum field theories." per [Rosner-2000], we will ignore them.
Possibilities: arrow of time not present at base, present.
Whence the arrow?
Quite a few arrows actually, thermodynamic, decay, electromagnetic, cosmologic, psychologic, and so on.
All can, arguably, be accounted for by entropy and ultimately by the presence of low-entropy conditions at the start of the universe (of course in this view the low-entropy conditions are what make that end the start). See for instance [Price-1996] [Stenger-2000] [Barbour-2008] [Schulman-2008].
While we will assume that any directionality in time is due to entropy, it is only fair to note this is not proven.
It has been suggested that the collapse of the wave function in the Copenhagen interpretation could provide an arrow of time, i.e. [Vinson-2008]. Continuous spontaneous localization (CSL) [Ghirardi-1986], and related theories attach reality to the collapse, but the collapse has not been detected. See [Dickson-1998].
There has been some effort to locate an arrow of time "below" the usual laws of physics, as in causal loop theory. See for instance [Smolin-2000], [Barcelo-2009].
"I suggest that the significance of quantum states is neither purely ontological nor purely epistemological. It is rather a synthesis of these two interpretations, namely: A quantum state of a system at time represents the knowledge that is available about the system at time t, regardless of whether anyone actually knows it."
”Existential quantum mechanics
I would go further and suggest that the collapse is simply the name for the place in the analysis where we shift from using quantum mechanics to using classical approaches; the collapse marks the boundary between where the quantum mechanics theory required for "sufficiently accurate" results and where the classical approximation adequate to question at hand. Not seen because is "behind the eyeballs".
Decoherence part of explanation of this; coherence also part of explanation!
See also Marchewka and Schuss's [Marchewka-1999]: they interpret absorption of Feynman paths as measurement: the absorption serves as a boundary between quantum paths and classical counts.
See in particular [Polkinghorne-2002]for a short summary of alternatives.
Time so thoroughly wired into our thought processes, hard to see the unexpected. Melges ( [Melges-1982]) notes that a number of psychiatric conditions are most naturally interpreted as failures of the time sense. He quotes as one example among many a paranoid physicist:
“`Time has stopped, there is no time… The past and the future have collapsed in to the present, and I cannot tell them apart'
”Given that the penalty for losing our normal sense of time may be madness, one is pleasantly surprised by the number of alternatives to "normal" time one can find. We list only a few.
The approach we are taking here is most similar to some work by Feynman: [Feynman-1950] [Feynman-1951]. He uses the proper time of the particle to provide a reference time for paths. This creates problems in muliple particle problems, however, one of the main reasons we prefer to use laboratory time, which is shared by as many particles as we are experimenting on.
We see resemblance at Schrödinger equation to Stuckelberg propagator used by [Land-1996] [Horwitz-1998]. They treat the fifth parameter dynamically, so takes it takes part in gauge transformations and the like. Another fifth parameter formalism in [Seidewitz-2005]. The principle difference between fifth parameter formalisms and quantum time as developed here is here we really only four parameters: laboratory time and quantum time have to share a dimension, they are really only different perspectives into one single dimension.
Stochastic time proposed [Bonifacio-1999], random time [Chung-2003], complex time [Asaro-1996], discrete times [Bender-1985] [Jaroszkiewicz-1998] [Qi-2000] [Date-2002], multiple time dimensions [Weinstein-2008], and so on.
There is no end to times; see Alan Lightman's thirty or more kinds of time, in his novel Einstein's Dreams, [Lightman-1993].
There is an excellent summary of possible times in a Scientific American article by Max Tegmark [Tegmark-2003], including massively parallel time, forking time, distant times, and more times than we have time to explore here.
Suarez is an important source for this work: his analysis helped clarify the problem (at least for us); the failure of Multisimultaneity (along with the failure of every other alternative/addition to quantum mechanics) suggests it will be more productive to look for a resolution of the problem within quantum mechanics.
Very impressed by "continuous spontaneous localization" analysis, [Ghirardi-1986]. Effectively posits a physical collapse and asks what it might look like and how to find. Very disciplined in statement and development of assumptions. Not seen inspite of some effort, [Dickson-1998], but a necessary line of attack, In some sense, CSL opposite in spirt to temporal quantization, but in some sense both are necessary lines of attack on the problem.
Temporal quantization plays nicely with many of these: If we have two times or discrete/chunked time can still quantize using the rules here.
But we argue, of course, that the chief merit of temporal quantization is its lack of originality. Rather than doing anything particularly new here we are taking two well-established ideas – relativity and quantum mechanics – and pushing them as far as they go.