Ben & John,
When it comes to time, I have no particular objective concerning its ontology. I find the idea that one want to can remove time and then say that objects in motion move through space with a velocity which we interpret as time as just another way of defining time. I find there is a sort of epistemological "dog chasing its tail" issue going on here. Space and time may exhibit a quantum uncertainty, where with quantum black holes if you measure a coordinate with arbitrary accuracy you lose all measurement of time and visa versa. I illustrate below how one can show ΔrΔt ~ 2Għ/c^4 = L^2_{Planck}/c with black hole physics. I tend to think that if one is going to "thump on time" then you have to thump on space as well. This is in part of why I think there is this curious duality between shape dynamics that plays with space and causal sets which play on time.
You might want to check out Hestenes, who is emeritus at U Arizona. He has been working a lot on figuring out how we can teach physics better. He cites examples about how students can take first year physics and learn to work the problems in the texts well enough to pass the course. Then when asked various conceptual questions about how something will move or behave under a force etc they completely get things wrong. He also makes a point that attending lectures and focusing in on them is itself a learned talent. We don't normally learn this way, and if you think about indigenous people young people learn by experience with their elders and by imitating them. I know that it was not until I was into college when I could actually focus on most of a lecture. Even still there were down times during lectures.
Of course now compound that with our digital age, which is duplicitous in my opinion. While there is much information available, much of our technology is meant to force us to think in tiny time frames. From 140 Twitter characters to split second video games I suspect the way our brains are being dendrite wired is different from the past, even the very recent past. Here you have a generation of young people moving up who have been acculturated by the digital age to think in split frame/time modes, rather than focusing in on something for long periods of time. We then wonder why young people have trouble in school, particularly boys. In fact my daughter has done very well in school, but my son is struggling horribly. He is not dumb either, but the whole classroom, lecture, book study and homework routine is just outside his personal ken.
The complementarity of space and time and the quantum mechanics of black holes could have had a much earlier start. At the 1930 Solvay conferences Neils Bohr and Albert Einstein debated the nature of quantum mechanics. Einstein was convinced of reality and locality and argued staunchly for an incompleteness of quantum mechanics. Quantum theory could only be made complete if there are some hidden variables that underlay the probabilistic, nonlocal quirky aspects of quantum mechanics. Einstein proposed an interesting thought experiment. Einstein considered a device which consisted of a box with a door in one of its walls controlled by a clock. The box contains radiation, similar to a high-Q cavity in laser optics. The door opens for some brief period of time t, which is known to the experimenter. The loss of one photon with energy E = ħω reduces the mass of the box-clock system by m = E/c^2, which is on a scale. Einstein argued that knowledge of t and the change in weight provides an arbitrarily accurate measurement of both energy and time which may violate the Heisenberg uncertainty principle ΔEΔt~ħ
Bohr realized that the weight of the device is made by the displacement of a scale in spacetime. The clock's new position in the gravity field of the Earth, or any other mass, will change the clock rate by gravitational time dilation as measured from some distant point the experimenter is located. The temporal metric term for a spherical gravity field is 1 - 2GM/rc^2, where a displacement by some δr means the change in the metric term is \simeq~(GM/c^2r^2)δr. Hence the clock's time interval T is measured to change by a factor
T-- >T sqrt{(1 - 2GM/c^2)δr/r^2} ~ T(1 - GMδr/r^2c^2),
so the clock appears to tick slower. This changes the time span the clock keeps the door on the box open to release a photon. Assume that the uncertainty in the momentum is given by the Δ p ~ ħ/Δr \lt TgΔm, where g = GM/r^2. Similarly the uncertainty in time is found as ΔT = (Tg/c^2)δr. From this ΔT > ħ/Δmc^2 is obtained and the Heisenberg uncertainty relation ΔTΔE > ħ. This demands a Fourier transformation between position and momentum, as well as time and energy.
This holds in some part to the quantum level with gravity, even if we do not fully understand quantum gravity. Consider the clock in Einstein's box as a black hole with mass m. The quantum periodicity of this black hole is given by some multiple of Planck masses. For a black hole of integer number n of Planck masses the time it takes a photon to travel across the event horizon is t ~ Gm/c^3 ~ nT_p, which are considered as the time intervals of the clock. The uncertainty in time the door to the box remains open is
ΔT ~ Tg/c(δr - GM/c^2),
as measured by a distant observer. Similarly the change in the energy is given by E_2/E_1 ~= sqrt{(1 - 2M/r_1)(1 - 2M/r_2)}, which gives an energy uncertainty of
ΔE ~ (ħ/T_1)g/c^2(δr - GM/c^2)^{-1}.
Consequently the Heisenberg uncertainty principle still holds Δ EΔT ~ ħ. Thus general relativity beyond the Newtonian limit preserves the Heisenberg uncertainty principle. It is interesting to note in the Newtonian limit this leads to a spread of frequencies Δω ~ sqrt{c^5/Għ}, which is the Planck frequency.
The uncertainty ΔE ~ ħ/Δt larger than the Planck mass gives an event horizon. The horizon has a radius R ~ 2GΔE/c^4, which is the uncertainty in the radial position ΔR associated with the energy fluctuation. Putting this together with the Planckian uncertainty in the Einstein box we then have
ΔrΔt ~ 2Għ/c^4 = L^2_{Planck}/c.
So this argument can be pushed to understand the nature of noncommutative coordinates in quantum gravity.
Cheers LC