In contemporary physics, time is generally partnered with three-dimensional physical space, the three-dimensional space of position, to form a four-dimensional geometrical structure, the spacetime continuum. We discuss the mathematics of continua in Chapter 7.

In non-relativistic mechanics, the distinction between time and space is maintained, so in that context we shall refer to the space-time continuum as space-time. In contrast, in special and general relativity, time and space are merged into a single structure that we shall refer to as spacetime, that is, without a hyphen. The model of the spacetime continuum as a four-dimensional manifold (discussed in the Appendix) is referred to by philosophers as manifold time, leading to the Block Universe paradigm, discussed in Chapter 8. Points in the spacetime manifold are referred to as events.

Manifold time is contextually incomplete in two ways. First, it says nothing about any primary observer, about who or what is ‘looking in’. In other words, it does not address the question for whom is the existence of the spacetime manifold relevant or even defined? We should keep in mind Schwinger’s view quoted in Chapter 3 that space and time are abstractions derived from the context of our current apparatus and human modes of perception, a view reinforced by Meschini in his doctoral thesis [Meschini, 2008].

Second, in addition to a lack of reference to any primary observer, manifold time says nothing about how events are related to the processes of information extraction. This question is generally ignored by theorists because of a widespread belief that physics is all about the properties of SUOs. It is our contention that this is wrong: quantum physics is all about how observers interact with SUOs. Therefore we need to focus on the information extraction question (IEQ): how do we actually extract information during an experiment?

The IEQ is resolved empirically in particle physics experiments by the use of three-dimensional arrays of detectors. These come in a number of forms such as the Wilson cloud chamber, the Glaser bubble chamber, the spark chamber, and the streamer chamber. Their common feature is that they attempt to detect signals at a sufficiently large number of points in spacetime to allow an effective picture to be built up of what might be going on in the idealized spacetime manifold.

The IEQ remains a difficult and as yet unresolved problem and theoretically matters could not be in poorer shape. It suffices to see how many different opinions there are about quantum wavefunctions to appreciate this point. The intrinsic approach explicitly avoids the IEQ by discussing quantum wavefunctions as if they had objective identities rather than being contextual theoretical devices. This was the conceptual error, in our opinion, that Schrodinger made in 1926 when he published a remarkable series of papers on wave mechanics [Schrodinger, 1926a,b,c,d,e,f,g]. He originally interpreted the wavefunction of an electron state as the particle. Although better interpretations of QM have been developed over the decades, there remains a core of theorists who assign an objective reality to quantum wavefunctions [Bohm, 1952].

Corresponding to the intrinsic approach in quantum mechanics is the principle of general covariance, which asserts that the laws of physics take the same form in all suitable frames of reference. A corollary to the intrinsic approach is that it does not matter which frame of reference or coordinate patch is used to describe components of tensors (the intrinsic objects of interest in GR), and therefore it is permissible to use any convenient set of coordinates.

As it was classically motivated, the principle of general covariance takes no account of the IEQ. It is our view that the reason quantum gravity (the programme of quantizing gravity) has made no significant progress over several decades is because the IEQ is ignored twice: once on the gravitational side and once on the quantum side. Used carefully, the principle of general covariance has been successful when it is restricted to relative external context. Examples are the laws of black hole thermodynamics as formulated by Bekenstein [Bekenstein, 1973] and

Hawking [Hawking, 1976], and explored by Unruh [Unruh, 1976]. In such cases, quantum information extraction is discussed in relatively localized experimental contexts with laboratories embedded in a classical relativistic background.

The problem with current quantum gravity is that no analysis of the primary observer is made usually. Our view is that physical primary observers have to look in two unrelated directions: they look inwards when describing quantum processes of SUOs and there they can use the rules of quantum mechanics; they also have to look outwards to the idealized spacetime that they believe they occupy and there they use the classical rules of general relativity. The two sets of information are about different things: quantum information coming from experiments is about the observer-apparatus-SUO relationship, whilst classical information about the background spacetime in which these experiments are embedded is more about the observer-environment relationship. Trying to equate the two sorts of information is an example of what is called a category error. It makes no sense physically and has proven mathematically near impossible to apply a quantum description outwards. Attempts to do this ultimately lead to the metaphysics of the Multiverse [Deutsch, 2001].