'Would you tell me, please, which way I ought to go from here?'
'That depends a good deal on where you want to get to,' said the Cat.
'I do not much care where–' said Alice.
'Then it does not matter which way you go,' said the Cat.
'–so long as I get SOMEWHERE,' Alice added as an explanation.
'Oh, you're sure to do that,' said the Cat, 'if you only walk long enough.'
Like archers, with a mark in view, we shall be more likely to hit upon what is right
Time tricky; need to be explicit in objective in investigation here.
Per the discussion in [Schick-1995] and particularly famous discussion in [Langmuir-1953] we propose as our goal meeting the following set of requirements, that quantum time should be:
Well-defined
Makes well-defined predictions .
While getting started will need to make some guesses about the initial shape of the wave function and the like; will need to consider preparation of the wave function and related issues.
Manifestly symmetric between time and space
Our defining condition
Not simply covariance but the manifest symmetry between and the space dimensions at every point.
Consistent with known experimental results
Further useful to ask if temporal quantization might have been seen by accident at some point.
Testable
Or not science
Further, temporal quantization not completely well defined till defined operationally, in terms of the experiments needed to see it.
Benefits of defining "starter set" of experimental tests:
Completes definition of temporal quantization.
Establishes temporal quantization is testable.
Experiments breed experiments; starter set opens up lines of attack.
Null results may themselves be interesting; for instance, a preferred frame might be defined as one where temporal quantization is maximally falsified.
Reasonably simple
Or not interesting
These requirements present a series of filters: if quantum time fails any of these tests, we should reject it.
On the other hand, if it passes all of them it may be worth exploring further.
Could also require uniqueness: will argue simplest available.
Could also require fruitful: argue this as well, but not a strict requirement.