1 Introduction

One of the least understood aspects of physics is time. It is well known that the fundamental laws of physics do not discriminate between the two orientations of time, i.e. the fundamental laws work equally well towards the future and towards the past. There are a few contemporary physicists who think that the accepted description of the universe is incomplete because there is no passage (or ‘flow’) of time in physics, i.e. the present moment continually ‘advancing towards’ the future. These physicists believe that everyday experience and intuitions about time (such as its passage) ought to be reflected in our physical theories. One notable physicist who has been developing a relativistic model of the universe which explicitly incorporates a passage of time is the leading cosmologist George Ellis. The model is called the Evolving Block Universe in which time emerges, i.e. comes into existence, and the four-dimensional (3-space plus 1-time) spacetime block evolves by enlarging in both space and time (see: Ellis 2007, 2014a, b; Ellis and Goswami 2014). This article aims to offer some clarification in respect to the Evolving Block Universe model and to concisely highlight some of its principal shortcomings.

2 The Evolving Block Universe

The Evolving Block Universe (EBU) must be distinguished from the (standard) Block Universe which does not evolve. There is no objective passage of time in the Block Universe. All events have a fixed position in spacetime independent of whether the event is judged to be past, present or future, i.e. events are ‘laid out’ in spacetime analogous to a spatial landscape (Dainton 2010, Ch. 3; Dyke 2021, Ch. 5). In the Block Universe, the tense relations of past, present and future are the temporal equivalents of the spatial terms of ‘here’ and ‘there’ (Price 1996, 12–13; Dyke 2021, 39).

Ellis takes the starting point of the EBU to be the Friedmann–Lemaître–Robertson–Walker (FLRW) spacetime of relativistic cosmology which is a solution of the field equations of General Relativity that is homogeneous and isotropic (Guidey 2019, 369–370). The primary difference between Ellis’ EBU and evolving models proposed by some other physicists (e.g. Muller 2016) is the role of quantum mechanical indeterminacy in defining the present moment (see Sect. 3). Problems with Muller’s theory are detailed elsewhere (e.g. Riggs 2019). However, it is philosophers who effectively began the development of an evolving universe theory (albeit non-mathematical) about a century ago. Philosophers call this the Growing Block Theory, also known as Possibilism (cf. Thomas 2019; Perović 2021). Extensive discussions of the difficulties with the Growing Block Theory have occurred (e.g. Earman 2008; Smith 2011; Braddon-Mitchell 2013; Lee 2016; Petkov 2017) and will not be dealt with here.

The newest version of the EBU model appears in a 2020 article by Ellis and Barbara Drossel which provides an account of their ideas on the physical structure and processes of the universe (Ellis and Drossel 2020). Their article has the potentially misleading title of ‘Emergence of Time’ which might suggest that its topic focusses on a beginning of the universe with time (or spacetime) emerging from a ‘timeless realm’ as described in some quantum theories of gravity (see: Oriti 2014; Huggett 2022). Such a beginning is not a subject of concern for Ellis and Drossel. In the EBU model, the past exists (as it does in the standard Block Universe) but the future does not. The present moment is that time where events ‘come into being’ (temporal ‘becoming’ in philosophical jargon). This emergence of time is part of an ‘enlargement’ (or ‘growth’) of the spacetime block and, as such, provides the passage of time. The global direction of time’s passage is conferred by the expansion of the universe.

In their 2020 article, Ellis and Drossel attempt to connect the ‘enlargement’ of spacetime with the following:

  • ‘Collapse’ of quantum mechanical wavefunctions of physical systems;

  • The global direction of time;

  • The local arrows of time; and

  • some other phenomena, e.g. the conscious experience of the passage of time.

In doing so, Ellis and Drossel are trying to provide a cosmological model which explains not only global aspects of the universe but also local physical phenomena together with human perceptions of time. These issues will be discussed below. Note that the cosmological constant as appears in General Relativity’s field equations (and which has become an important aspect of relativistic models over the last two decades) plays no significant role in the EBU model. In light of the broad array of issues encompassed, the EBU model is a rather ambitious enterprise. Needless to say, there are going to be a few problems with any such model.

3 Defining the Present Moment, the Emergence of Time and the Passage of Time

Ellis and Drossel state that the passage of time is irrefutable on the macroscopic scale (Ellis and Drossel 2020, 163). What an astonishing claim to make! They maintain that there is a vast amount of evidence that time passes by which they are primarily referring to evidence of the evolution of physical systems. Nonetheless, such evolution may be described and perceived without needing to invoke an objective passage of time (cf. Price 1996; Huggett 2014; Prosser 2016; Riggs 2017). Therefore, the appeal to this sort of empirical evidence fails to support their claim. Indeed, the only credible indication for a literal passage of time is gained through conscious experience (Davies 2002, 43; Prosser 2007, 77). The problem then is that human perceptions of time generally, and in particular of the (supposed) passage of time, are regularly altered/ subject to illusions (and occasionally need correction from physics and/ or neurophysiology). Such happenings are well documented in the psychological and neuroscience literatures (e.g. see: Eagleman 2008, 131; Zakay 2016, 61–63; Gruber et al. 2022). This being so, conscious experience cannot be taken as providing unquestionable evidence of the objectivity of the passage of time and consequently, such passage is not irrefutable as claimed by Ellis and Drossel.

Further, there are strong reasons to reject any notion of a physical passage of time (regardless of its characterisation). Four of the most important reasons are:

  1. (i)

    If there is a (physical) passage of time then there should be a parameter representing time’s passage in the fundamental laws of physics. The time variable in the fundamental laws only specifies the time coordinate just as the spatial variables specify space coordinates. There is no parameter for time’s passage to be found in the fundamental laws (Callender 2006, 498; Al-Khalili 2012, 85).

  2. (ii)

    The rate of the passage of time is not measurable by any instrument, i.e. there are no ‘speedometers’ for time (Olson 2009, 447). Clocks are occasionally (and incorrectly) thought to measure this rate but they only measure intervals of time between events (Nerlich 2004, 24; Franck 2012, 95; Davies 2014, 48). If time’s passage was a real phenomenon then its rate would be measurable by a physical device. In addition, if it was true that the rate of the passage of time was demonstrably measurable by some instrument, the long-standing debate over the issue of whether time physically passes or not would already have been settled empirically and would not be on-going (see Sect. 4 for further discussion).

  3. (iii)

    Time’s passage is not an observable (in the physics sense) as it is not measurable and is only known through human conscious awareness (Davies 2002, 43; Prosser 2007, 77) and not by processes of physical measurement.

  4. (iv)

    There are significant analytical problems with notions of time passing (e.g. with the rate of the passage of time) which signal that such notions just do not stand up logically. The relevant logical conundrums have been documented for decades (see: Williams 1951; Smart 1963; Park 1972; Seddon 1987; Price 1996; Oaklander 2002; Yehezkel 2013; Leininger 2015; Dyke 2021).

In fact, every attempt to define the passage of time and/ or its quantitative description has failed in one respect or another and none have ever gained consensus (see: Prosser 2016; Price 2011; Rickles and Kon 2014; Savitt 2017). In the context of the EBU model, the question which the above reasons (i)–(iv) bring to mind is: Does the EBU model fare any better in characterising time than have previous attempts at its characterisation?

Let’s begin with how the (objective) present moment is defined in the EBU model. This will also lead to the definition of the passage of time. The present moment is when time emerges. This emergence of time is defined as the indefinite and non-existent future becoming actualised (Ellis and Drossel 2020, 184) and is postulated to be attributable to the process of the ‘collapse’ of the quantum mechanical wavefunction. A wavefunction describes the quantum state of a physical system. In the EBU model, the present moment is when events become actualised, as distinct from merely being potential events, by virtue of the ‘collapse’ of the wavefunction. It might be thought that the EBU would require some kind of physical wavefunction which ‘collapses’, as postulated in objective collapse quantum theories (cf. Ghirardi and Bassi 2020), but not so according to Ellis and Drossel. Their definition of the present moment is done using Orthodox Quantum Theory (OQT), also called the Copenhagen Interpretation of Quantum Mechanics (Ellis and Drossel 2020, 183). In OQT, the wavefunction is a mathematical entity which does not represent a physical field (Penrose 2004, 805).

Physical quantities not having definite values until measured and wavefunction ‘collapse’ are basic aspects of OQT (Faye 2019). A wavefunction evolves deterministically (as specified by Schrodinger’s equation) until a measurement of a physical quantity is made. The wavefunction of a physical system prior to measurement assigns various probabilities to possible values of measurable quantities of the system. The outcome of a quantum mechanical measurement can only be predicted probabilistically with the origin of this probabilistic circumstance assumed to be an underlying indeterminacy of the physical world. When a measurement is performed in OQT, the wavefunction undergoes a ‘collapse’ which is inherently non-deterministic in the sense that there is no equation governing the (random) outcomes of physical quantities (Penrose 2004, 528–530). This formal ‘collapse’ is essentially an algorithmic procedure which stipulates that physical quantities will acquire values on measurement with a probability given by the squared amplitude of the wavefunction. Upon ‘collapse’, the quantity being measured gains a particular value (with a probability of one), i.e. the range of probabilities ‘disappear’. Although the wavefunction is only a formal (i.e. not physical) entity in OQT, the act of measurement and measurement outcomes are physically real events.

It should also be acknowledged that the ‘collapse’ of the wavefunction is an assumption and is not independently verified (see: Stoica 2018; Ball 2022). There are several other interpretations of the quantum formalism in which the wavefunction does not ‘collapse’ (cf. Pykacz 2015). These interpretations explain the results of measurements made on quantum mechanical systems just as well as OQT does. The choice of interpretation is made on non-empirical grounds and is a topic of continuing debate in the foundations of quantum mechanics. If a non- ‘collapse’ interpretation is chosen then, of course, the present moment could not be defined as Ellis and Drossel have done. A more satisfactory definition of the present would surely be one that does not depend on an individual interpretation of quantum mechanics.

If we accept OQT (for the sake of argument) then, in the EBU model, the present moment comes into existence when wavefunction ‘collapse’ occurs and the transition from an (undetermined and non-existent) future to the (determined and existent) past constitutes the passage of time. The first issue to notice here is that these ‘collapses’ cannot be restricted to just measurements done on physical systems. Ellis and Drossel deal with this issue by requiring wavefunction ‘collapses’ to be dependent on local physical contexts, especially local ‘heat baths’ (i.e. reservoirs of heat). These are triggers for wavefunction ‘collapses’ in addition to experimentalists performing measurements. In respect to wavefunction ‘collapses’, they summarise their position as follows:

[W]hen we have quantum processes taking place on a classical spacetime background, the passage of time takes place through the [‘collapse’ of the wavefunction] process … where the indefinite future changes to the definite past due to collapse events … this process … takes place all the time everywhere in the real world … is determined in each case by the local physical context …, Heat baths … play a key role in this collapse process … (Ellis and Drossel 2020, 184).

The above quotation brings up a second issue as a complication arises with the ‘collapse’ of wavefunctions taking place “all the time everywhere in the real world” (Ellis and Drossel 2020, 184), i.e. an incredibly large ‘hotchpotch’ of quantum ‘collapses’ occurring throughout space and time. The astronomical number of ‘collapses’ happening all over the universe suggests that the present moment and the passage of time would have to be local, not global.

Other physical considerations also support the suggestion of time’s passage being local, such as the gravitational time dilation effect. This is where the time interval between two events for an object close to a strong source of gravity (e.g. a neutron star) is shorter than for an object further away from the same source, i.e. a local effect on time (Guidey 2019, 115–116). Gravitational time dilation is a genuine phenomenon affecting time intervals which is empirically well-confirmed and not some asymmetrical process taking place over time. If an objective passage of time is assumed to occur then the shorter of the two time intervals would be explained by gravity slowing down the passage of time in the close vicinity of the gravitational source but this too would be a local effect on time (see: Dieks 2006 and Newman 2021 for more on local passage). The inference that wavefunction ‘collapse’ yields only a local present moment, and therefore a local passage of time, has implications for whether the EBU model can have a global passage of time since it is not at all clear how local passage can result in the whole universe possessing a global passage. Indeed, Ellis and Drossel need to provide an intelligible account of how local attributes bring about global ones.

A third issue relates to the actual way of making the definition of the present moment with respect to quantum mechanical indeterminacy. An attempt to do so in terms of wavefunction ‘collapse’ was made in the 1950s by Hans Reichenbach (Reichenbach 1953; 1956, 269). It has successfully been shown that Reichenbach’s definition of an objective present moment does not single out a unique present for a local physical context. Without such a unique present there cannot be a global passage of time. It is surprising then that Ellis and Drossel have chosen to define the present moment in the same way.

The critique runs along the following lines. If a statement such as: ‘The present configuration of the polypeptides’ refers to the phenomenon at a particular present moment then which present is this moment of time supposed to be? If the transition to a state of determinacy has always taken place and will always take place, then the indeterminacy of every year earlier than the current year has been changed into determinacy but the indeterminacy of the year 3320 A.D. (say) has not yet undergone such a transformation. The present moment is supposed to be this threshold of transition to a state of determinacy, but for whom? In other words, the criteria of moving from the undetermined to the determined does not single out the ‘present moments’ of years past from our own (Grunbaum 1971, 220–223; 1973, Ch. 10; Kroes 1984, 432). Hence it is the case that:

[E]very event … at all times constitutes a divide in Reichenbach’s sense between its own recordable past and its unpredictable future, thereby satisfying Reichenbach’s definition of ‘the present’ at any and all times! (Grunbaum 1971, 221-222, italics in original).

In other words, Reichenbach’s criterion is not a sufficient condition for defining the present moment (Denbign 1981, 60). The attempt to define the present moment in the EBU model by reference to the ‘collapse’ of the wavefunction is unsuccessful for the same reason.

The global passage of time is understood in the EBU model in terms of the model’s General Relativistic (i.e. spacetime) description. Each present moment is part of an evolving three-dimensional ‘surface of constant time’ which is parameterised by the physically relevant time called proper (i.e. cosmological) time, denoted τ. The ‘surfaces’ constitute a particular foliation of FLRW spacetime into three-dimensional space at a given proper time (i.e. τ = fixed value). These ‘surfaces’ are specified by preferred world lines in spacetime (i.e. a family of fundamental trajectories) starting at the beginning of the universe, τ = 0 (Ellis and Drossel 2020, 173–175). These trajectories are themselves defined by the average motion of matter in the universe (Ellis 2014a, b, 18). The (postulated) evolution of these ‘surfaces’ provides the ‘growth’ of the spacetime block. However, we have seen that in the EBU model the passage of time is afforded by a progressive ‘coming-into-being’ of events which originates through wavefunction ‘collapses’. Moreover, Ellis and Drossel contend that these ‘collapses’ are based in proper time:

“[C]oming into being takes place according to local physical processes based in proper time defined along preferred timelike world lines” (Ellis and Drossel 2020, 175).

Wavefunction ‘collapse’ determines the emergence of the present moment in the EBU model. Yet, Ellis and Drossel are also claiming in the above quotation that the same ‘collapse’ is based on the existence of a moment of (proper) time. If time is supposed to emerge when such ‘collapses’ occur, how can this be? This account needs elaboration for, as presented, it sounds like circular reasoning.

4 The Rate of Passage

Most philosophers of time would agree that if time passes then there would be a rate of passage (Boccardi 2016, 9). It was stated in Sect. 3 that a substantial reason for rejecting any notion of a physical passage of time is the analytical problem of providing a coherent description of the rate of passage. Care needs to be taken here to distinguish between the use of the word ‘rate’ as applies to the actual mechanism of a clock and the quite different use of the word when referring to how ‘fast’ or ‘slow’ the physical passage of time might happen. The former sense of ‘rate’ only concerns the accuracy of a clock, i.e. if a clock ticks at a correct rate then each repeated cycle of its mechanism occurs over an equal time interval (Tal 2016, 300). Ellis and Drossel are, of course, using the latter sense of ‘rate’. In the 2020 article by Ellis and Drossel, there is no discussion of the rate of the passage of time at all (although there is a massive amount of literature on the topic, see: Newman 2021). However, Ellis previously treated the issue of time’s rate of passage in the EBU model in some of his earlier publications. He wrote, for example:

“How fast does time pass?” … I claim that the answer is given by the [spacetime] metric tensor … which determines proper time τ along any world line … This is the time measured locally along that world line by any perfect clock. This is what fixes physical time … The global rate derives from the combination of these local rates (Ellis 2014a, 38).

Note that, in General Relativity theory, the metric tensor is a mathematical entity which details the geometry of spacetime (Guidey 2019, 53). Although the metric tensor does determine proper time intervals along world lines, this (in itself) reveals nothing about any (supposed) passage of time or its rate.

The statement in the above quotation fails to identify in what manner an interval of proper time between specified events along a world line can give rise to any (hypothetical) rate of time’s passage. In this respect, the following points (which have already been stated) are relevant:

  • Clocks measure time intervals;

  • The description provided of the passage of time suggests that passage is only a local phenomenon; and

  • No clear explanation has been provided of how local attributes bring about global ones in the EBU model.

These points raise difficulties for establishing a coherent account of a global rate of passage as part of the model’s mathematical description. What Ellis and Drossel need to offer is a consistent and rational definition of the global rate of passage. They then need to show how the global rate can be obtained from (local) clock readings. In the absence of this, their discussion is no advance on the long-standing debates over what constitutes the rate of time’s passage and whether it is a real physical quantity. These issues remain unresolved (Dyke 2021, 31–32).

5 The Arrows of Time

The term ‘arrow of time’ was coined by British physicist Sir Arthur Eddington to refer to the direction of the passage of time (Eddington 1947, 76). Since the passage of time is an objective feature of the EBU model, the direction of time must be intrinsic too. Observable physical processes which exhibit temporally asymmetric behaviour are also called arrows of time (Vaas 2012, 9). There is no consensus on what should comprise the list of these arrows but they are taken to be defacto indicators of the direction of time. Ellis and Drossel identify the following phenomena as providing local arrows of time: thermodynamics; electrodynamics; gravitation; biology; quantum dynamics; and other wave phenomena. They write:

“Arrows of time are local physical effects which are determined non-locally by the cosmological context of the EBU and the evolution of the universe as a whole” (Ellis and Drossel 2020, 175).

Obviously, they need the cosmological arrow to be the master arrow on which the others depend. These other arrows of time are explained in the EBU model by Ellis and Drossel in terms of:

  • The expansion of the universe (with the consequence that the temperature of the universe decreases over time);

  • The Past Hypothesis (i.e. the assumption that the entropy of the universe was much lower in the distant past); and

  • The non-existence of the future.

Although the first of these dot points is uncontroversial to most physicists and philosophers of science, the second dot point has been challenged by several commentators (e.g. Earman 2006). The third dot point allows Ellis and Drossel to use the non-existence of the future to explain that all wave propagation (be it electromagnetic, gravitational or whatever) is from present to future. This is because in the EBU model there are no future events to be wave sources nor does there exist a ‘venue’ (i.e. future spacetime) for waves propagating from future to present to exist within. The non-existence of the future in the EBU model entails that all arrows of wave phenomena would have to coincide with the cosmological direction of time. Nevertheless, the majority of accounts of the arrows of time require that sound explanations for the various arrows should be ones which do not depend on the existence or nonexistence of future events (e.g. see: Aiello et al. 2008; Loewer 2012; Vaas 2012, 10–11). The EBU model would be more convincing if it did not appeal to the non-existence of the future as part of its explanation of the arrows of time.

6 Concluding Remarks

It has been shown that there is a significant problem in defining the present moment together with other questionable and/or unresolved issues with the theory of the emergence of time given by Ellis and Drossel. In these respects, the EBU model has been found wanting. One might have thought that, since Ellis is a physicist and that the EBU model is partly based in General Relativity theory, he would have proposed some predictions which might be tested by observations of the universe. If it is claimed that the conscious experience of the passage of time can be explained in terms of a physics model of the universe (as Ellis and Drossel want to do) then there is an obligation to provide testable predictions of the model. Alas, no such predictions have been forthcoming. In summary, we have to conclude that the EBU model does not fare any better in characterising the present moment and a physical passage of time than previous attempts.