A keystone of modern science is the view that everything physical exists within time and space. Of course, these notions have themselves gone through radical revision, but they still form the basis for formulations of modern physics, and only recently have some theoretical physicists begun to consider the possibility that time and space might emerge from some more fundamental objective reality.
If we carefully examine the process of measurement, however, we see that time and space actually emerge empirically. To illustrate, let’s first consider just time. When multiple measurements of position are performed, we assign the measurements a linear ordering to form an ordered sequence of measurements. We then correlate these sequential measurements to construct something called time that is a useful parameterization of position (and perhaps other constructed quantities). So, to do all this we need to presuppose some ability to define a linear order of measurements, and to define the position measurements in some systematic way so that they can be correlated with each other in some coherent way. You might say, we need to superimpose some primitive structures of protospace and prototime in order to even start studying the world in a systematic way by relating measurements to each other. And when we do this, various kinds of time and space might emerge, such as Newton’s space and time and Einstein’s space and time.
To elaborate a bit on these ideas of proto-time and proto-space, if we start from a purely empirical basis, then you might say we have a set of measurements, which by nature are discrete. Then proto-time would be the linear order of this set, giving it the structure of a linear sequence of measurements. The continuous time parameter would then emerge as a kind of interpolated continuum constructed as a layer that emerges when we correlate the discrete sequence of measurements.
The proto-space is a kind of presupposed unit of measurement and method for systematic measurement of position using that unit. Its the very least we need to measure something like space or distance or length. Once this is defined, then if it is consistently used in all the measurements, then it provides a coherent way to make the correlations among the measurements at different times in the sequence. Without any such standard for position measurements, there is no basis for making sensible correlations between different measurements in the sequence. Then, just as continuous time emerges as a derivative layer from the discrete sequence of measurements, continuous space emerges as a derivative layer expressing the coherence between position measurements.
Thus, time and space emerge not objectively, but are constructed through the very process of measurement itself. This provides a new conceptual foundation for the formulation of physics that does not presuppose objective time and space.