In special relativity (Einstein, 1905), one is faced with the difficulty of reconciling the reality of one’s present experience with that of the four-dimensional continuum. What does really exist, the entities moving along their worldlines, or the worldlines themselves? These seemingly irreconcilable questions, which reflect the dichotomy between the views of ‘presentism’ and ‘eternalism’, outline the debate about the nature of time and change, in the background of which lies the fundamental question about what can truly be considered to exist in our reality.

This question was also central to the research on the foundations of quantum mechanics, which began in the 1970s, building on the EPR article (Einstein et al., 1935), then leading to Bell’s inequalities (Bell, 1964) and the experimental confirmation of quantum entanglement and nonlocality (Freedman and Clauser, 1972; Weish et al., 1998). One of us actively participated in these developments, particularly in the construction of an axiomatic operational-realistic quantum formalism, which allowed for a general representation of physical systems, containing as special cases the quantum and classical descriptions (Aerts, 1982, 1983). What is important for the matter at hand, is that similarly to what Einstein did with the measurement of distances and durations, ‘what exists’ was also obtained in this formalism from an analysis of the measurement procedures and their relation to ‘prediction’, also allowing ‘potentiality’ to have its proper place in reality. And when in the 1990s this general approach was applied to relativity, an important addition to Einstein’s operational analysis resulted (Aerts, 1996).

Note that from an ontological perspective, ‘what exists’ should not be operationally defined, being independent of any measurement; but an ‘operational reality’ must be part of reality in a more general metaphysical sense, as experiments always have the last word (consider the emblematic case of entanglement). Let us dwell for a moment on how in pre-relativistic physics ‘what exists’ was conceived. The ‘present reality’ was considered to be everything that could be seen, touched, felt, and more generally experienced, in a given moment of time. The conditional is important here, as reality does not reduce to the content of our actual present experience, but encompasses all our ‘possible’ experiences, those we could have had in our present moment, should we have made other decisions in our past. And this highlights the importance of ‘free choice’ in our reality’s construction, the robustness of which is grounded in the consistency of all our experiences, and those of other human beings. And of course, our operational reality construction can continue beyond the limited reach of our senses, thanks to the much broader reach of our knowledge, particularly the scientific one.

That being said, for the ‘personal present realities’ of the different observers to be coherently integrated into a ‘global present reality’ construction, one needs a Newtonian absolute and invariable time that advances unhindered by anything. Special relativity, on the other hand, shows us that every present is strictly personal, so there is no global present. More so, time itself becomes strictly personal: there is not ‘one time’, but ‘multiple times.’ Hence, when operationally constructing reality, there is not ‘one global present reality’, but ‘multiple present personal realities.’ And there is a surprise when considering these multiple operational constructions, which we will now try to highlight (Aerts, 1996; Aerts and Sassoli de Bianchi, 2023).

In Newtonian physics, when the wristwatch of a person — let us call her Alice — indicates 5 pm, of a given day, it is 5 pm of that day across the universe. In relativity, Alice can still consider 5 pm as her personal present moment, and she can also extend her present towards everything that does not move with respect to her, for example, a wall clock in her office, also indicating 5 pm. But suppose that a week earlier Alice chose to take a space round trip, so that when she returns to the office, that same day, with her wristwatch indicating 5 pm, the wall clock now indicates a different time: a time in the future when compared to that of her wristwatch, the difference being determined by the speed and duration of her trip. Considering an operational construction of reality, based on possible experiences, where the conditional is fundamental, hence ‘what Alice could have decided differently in her past’ counts as ‘potential’, we must then conclude that Alice’s personal present reality contains both states of the wall clock, one of which is in the future with respect to the other. And since Alice can make trips of arbitrary duration and speed, it is the entire worldline of the wall clock that is part of her personal reality at 5 pm, and of course this equally applies to all entities not travelling with her.

We can observe that the collection of all these worldlines, in Alice’s present reality, forms a block universe which is strictly personal to Alice, and which does not contain Alice’s body, since Alice cannot jointly travel and remain in her office. It is only the entities external to Alice, which are available in taking part in her present experience, in different age versions, that form a genuinely four-dimensional construction in her present reality. Also, this appearance of a personal block universe does not imply that change would be impossible. Alice’s reality is dynamic, the four-dimensionality of the entities different from her body being a consequence of the fact that, through her free choice, she can select her own possible experiences, enabling her, via the time dilation effect, to possibly travel into the future of other entities, and experience them there. Note that from a quantum perspective, if Alice’s reading of the wall clock is viewed as a ‘measurement’, then her possible round trips correspond to different possible ‘preparations’ of the state of the measured system. And the fact that in relativity time and reality become personal, this is also a typical quantum-mechanical state of affairs, called ‘contextuality’, albeit we have here a spatiotemporal kind of contextuality, proper to relativity.

Our recent work builds on this approach of identifying in a rigorous way ‘what operationally exists’ in the specific situation of relativity (Aerts and Sassoli de Bianchi, 2023). In fact, some of this work has been done long before us, for instance when in textbooks one introduces quantities like the ‘proper time’ and ‘proper length’, which are personal to a given observer. But remnants of Newtonian thinking still live on in relativity treatises, especially when it comes to correctly interpreting what the formalism reveals to us, if taken seriously. Consider the ‘proper velocity’, which was also given a special name, ‘celerity’, whose magnitude ranges from zero to infinity. It is rarely used for interpretive purposes, or even in formulas; for example, Lorentz transformations are written using coordinate velocities, whose magnitude ranges from zero to c. But if one thinks of velocity as proper velocity, light then has an infinite proper speed, which explains why it can be the same in any reference system (light’s coordinate speed c becoming then a calibrated infinite contraction of its infinite proper speed).

The proper velocity is also the spatial component of a ‘four-velocity’, and the magnitude of the latter, for any entity, in any reference system, is always equal to c. This is a result that can be found in any textbook, although it is usually regarded as a mathematical property having no particular physical meaning. But considering that Lorentz transformations can be derived without using Einstein’s second postulate (Ignatowsky, 1910, 1911; Lévy-Leblond, 1976), the structural parameter can be given a more general interpretation, as the ‘absolute speed of all material entities’, whose motions occur in the entire spacetime, since they are always characterized by a nonzero time component.

Here we have to conceive the temporal t-dimension as the equivalent of a spatial ct-dimension, i.e., measuring time in units of lengths, for instance in light years. Note also that the time component of the spatiotemporal movement can explain the origin of ‘mass energy’ in Einstein’s E = m₀c², since when an entity is spatially at rest, it still moves in time at proper speed c, with proper momentum m₀c, with m₀ the rest mass. Hence, the latter can be interpreted as a form of ‘temporal kinetic energy’, i.e., energy associated with a movement in time.

Coming back to Newtonian thinking, we can see its presence in our continued use of the notion of ‘coordinate velocity’ (expression of our prejudice that space would be a container of everything that exists) instead of studying motion from a four-velocity perspective, as we do consistently with relativity in Aerts and Sassoli de Bianchi (2023). When we limit ourselves to the description of the centre of mass of macroscopic entities, the illusion of a spatial reality can be partly maintained, but fundamental problems are rapidly encountered when considering spatially extended entities and nonlocal quantum entities.

Speaking of quantum mechanics, we believe it has a distinguished role to play in further revealing the deeper nature of our spatiotemporal construction, and we refer to Aerts et al. (2020) for a possible line of investigation. Here we simply say that spacetime can be seen as an emergent structure, with classical entities manifesting a permanent dynamical presence in it, whereas quantum nonlocality, both in space and time, tells us that our personal reality is essentially of a nonspatiotemporal nature. Note that the notion of ‘nonspatiality’ was introduced by one of us in the late eighties (Aerts, 1990) and discussed since then in several works (Aerts, 1998, 1999). In the run, others have realized its importance, like Ruth Kastner in her ‘possibilist transactional interpretation’ (Kastner, 2012, 2023; Aerts and Sassoli de Bianchi, 2017; Sassoli de Bianchi, 2021).

Coming now to the article by Gruber, Block and Montemayor (2022), we observe that it builds on the earlier work by Hartle (2005), where the position was taken that past, present and future are notions that arise from the cognitive information-processing capacities of humans, within a reality otherwise described by a spacetime continuum in which no change takes place. This is clearly different from our view, where change is considered to be intrinsically part of the very operational construction of our personal spatiotemporal reality. Hartle (2005) introduces what he calls an ‘information-gathering and utilizing system’ (IGUS), a simplified model for a human whose operation is compatible with his interpretation of relativity theory, and Gruber, Block and Montemayor (2022) realize elements of such an IGUS to concretely test some aspects of the ontology of time. Reading these interesting works, one can wonder if similar investigations can be pursued for aspects of the operational reality we discussed above. We will certainly reflect on the issue in the future.

Coming to Buonomano and Rovelli (2022), they argue that spacetime is not frozen, but a complex network of processes of change. Their view is closer to ours, although they do not specify the dynamic nature of this complex network. Both in Hartle (2005) and Buonomano and Rovelli (2022), the second law of thermodynamics is indicated as the cause of the asymmetry between past and future, which could also explain why it is also present in our human experience of time. Our suspect, however, is that there could be a more direct nonstatistical cause for it. We explored so far two hypotheses, still speculative: a possible role played by natural selection, which could be operating already at the level of matter (Aerts and Sassoli de Bianchi, 2018), and, not incompatible with it, the splitting of matter and anti-matter, giving rise to two different time directions (Aerts and Sassoli de Bianchi, 2022).