McTaggart saves Physics? Abstract This paper proposes an interpretation of time that is an 'A-theory' in that it incorporates both McTaggart's A-series and his B-series. The A-series characteristics are supposed to be 'ontologically private' analogous to qualia in the Inverted Spectrum thought experiment and is given a definition. The main idea is that the experimenter and the cat do not share the same A-series characteristics. So there is no single time at which the cat gets ascribed different states. It is proposed one may define a 'unit of becoming' that coordinatizes the future/present/past spectrum as well as allowing one to calculate the rates of becoming. We give a picture of this interpretation and discuss how it relates to the Schrodinger's Cat 'paradox'. Also a 'paradox' from General Relativity is briefly considered. 2 AB-series time Famously, McTaggart (1908) identified two different series that characterize time. There is the B-series and the A-series. "Positions in time, as time appears to us prima facie, are distinguished in two ways. Each position is Earlier than some, and Later than some, of the other positions. And each position is either Past, Present, or Future. The distinctions of the former class are permanent, while those of the latter are not. If M is ever earlier than N, it is always earlier. But an event, which is now present, was future and will be past." I will not follow McTaggart to the conclusion that time is unreal, but suggest that time is real and has both B-series and A-series characteristics, as most A-theorists posit. The B-series is a series of times ordered by the relation of 'earlier-than' (or 'later-than'). The Bseries is usually thought of as going from earlier times to later times. It could be argued the B-series is the kind of time that's most often used in physics. For example, both coordinate time and proper time are B-series. And the time parameter of the Schrodinger equation is a B-series. The B-series relations do not change. Also, going 'backward in time' in the B-series just means going to earlier times. I would argue, as many A-theorists do, the A-series is also a part of a comprehensive view of time. The A-series consists in the ontologically private (defined below) now and becoming. In contrast to the B-series, the A-series values change. Also in contrast to the B-series, going 'backward in time' is undefined, on this view. It's a Zen observation that "Time constantly goes from past to present and from present to future. This is true, but it is also true that time goes from future to present and from present to past." (Suzuki 1986), p. 17 or 33. The former is the B-series (interpreted as 'earlier-times to latertimes') and the latter is the A-series. As in several theories of time, instead of asserting 'time goes from past to present to future', it'd be more appropriate to assert 'time goes from earlier times to later times as it goes from future to present to past'. As later and later times become present, time to go on. The question is how to incorporate the A-series in physics, while of course retaining the Bseries, into what I will for the purposes of this paper call the AB-series, denoting that a single dimension of time has both A-series and B-series characteristics, in a way that is consistent with relativity. The ideas here are related to at least Tense Realism, Perspectival Realism, and Fragmentalism, (Hare 2010), (Fine 2005) see also e.g. (Markosian 2013), (Roberts 2015), (Carr 2013), (Rovelli 2018), (Miller 2005). The idea will be to add to each system a 'now' and a 'becoming' (of the A-series) that is 'ontologically private' to that system, while retaining the ontologically public B-series interrelations already in wide use in physics. [refs.] These are 'private' now's, so, presumably, the apparent 'universal now' that humans live in on earth results from some kind of averaging function over the more-or-less local or ubiquitous private nows. [refs.] 3 Ontological privacy An ontologically private parameter may be defined as one that takes on a definite value when a system S specifies its own ontic state, but does not take on a definite value when a different system S' specifies S's ontic state. This could be because, for S', 1. S has no such parameter, 2. S has such a parameter but it does not have a definite value, or 3. there is a parameter and it has a definite value but it is not known or knowable, for some reason, as might be appropriate in Qbism, though to be sure it is the ontological questions that concern us here. It is easy to write these definitions in mathematical notation. 4 Panpsychism I am conscious, and this is certain to a degree even greater than the certainty that there are physical laws. But there is, in one sense, nothing special about my composition-I'm made of electrons and quarks etc. Thus there is good reason to think that the basic elements that make up my brain are accompanied by the basic elements of subjective experience-qualia. One is lead to the hypothesis that an electron is accompanied by a quale-a subjective experience-for example, the color green. Perhaps a muon is accompanied by a blue quale. There's been an amount written about this and surrounding ideas but the basic idea is clear enough and is called (dualist) Panpsychism. (Stanford 2017). (Other correlates to qualia such as complexity could be entertained.) 'Ontological privacy' in the sense of the above is basically what happens with the Inverted Spectrum, familiar from the philosophy of mind (Stanford, 2018). Suppose Alice looks at the leaves on a tree and she experiences the color green. She cannot know, in some ontological sense, that if her friend Bob looks at the same leaves he experiences the same (color) quality. Now suppose they look at a color circle. Alice's color spectrum does not determine Bob's color spectrum, for Alice. Bob could have a systematically 'opposite' color experience. Indeed, it may be that Alice has a single definite spectrum, whereas Bob's spectrum can vary over a wide range of spectrums or even other possibilities, for Alice. Alice's (qualitative) experience while looking at the leaves, in some ontological sense, leaves Bob's experience without a definite value (for Alice), and therefore this color-parameter is 'ontologically private'. The theory of time explored in this paper posits that the A-series characteristics of time are similarly ontologically private. A consequence is that Alice's 'now' does not determine when Bob's 'now' is. One desires ontological parsimony. There is no experiment Alice can do to determine Bob's qualia. So those kinds of experiments should not be in the ontology. 5 Definitions and rates Mathematicians were taking square roots of positive numbers, e.g. finding x in the equation x2 = 1. But one wanted to generalize to equations like x2 = -1. There was no real number that did it, so to a real number mathematicians added a non-real parameter i. That is, i is a kind of standardized placeholder for a would-be root, whatever kind of creature that is. One thing to try is start with a parameter t whose unit is change in B-series 'indexical' time, for example seconds. Add a parameter τ whose unit is not an interval in B-series clock time. In AB-theory, τ is part of the A-series, and "e" will be a unit of what temporal becoming is like per second, as a kind of standardized place holder, whatever kind of creature it is. Let τ be the future-present-past spectrum. e coordinatizes τ. Define an indexical clock to be a clock that's not accelerating, has relative velocity 0, and is spatially local, to a centered inertial reference frame, all in terms of a B-series. Define 1 e is what becoming is like for 1 second of indexical clock time If becoming is indeed phenomenal in the way that qualia are, then it must be 'defined' or 'referred to' in this curious 'what it is like' way, on salient views. [refs. ] E.g. a green quale is defined as 'what it is like' to experience green. The necessity of doing this has to do with their ineffability. e can be well-defined across systems. 1 second is well-defined across systems such as Alice and a protozoan, even though the protozoan doesn't have the mental capacities Alice does. It's plausible that it's the same way with 1 e of A-series time. Suppose one just ran marathon, for some reason. Under this condition, it might be that the Bseries seems to go by the A-series faster, or slower, than usual. But this just amounts to a recoordinatization of the relations between B and A. Just the way one can re-define seconds to be longer or shorter than the usual seconds, one can re-define es to be further or closer into the future than the usual es. The physically significant stuff should be invariant under these changes. Define 1 sec./e = d(Alice's B-series)/d(Alice's A-series) is the change in 1 second of indexical clock time per change in e. For example, the position of a particle at 1 sec. later than t = 0 is also 1 e closer to the present from the future (or further into the past). Consider the rate r = 2 sec./e. This can be interpreted as meaning there are 2 seconds of indexical clock time per unit of becoming. Presumably, the 2 seconds are in a series. That would seem to imply that, for 1 e, 2 seconds go by, so earlier-to-later relations would appear to go by faster. Let the rate r be in units of sec./e. The general idea is r > 1 B-series time appears sped up (earlier-times to later-times appear to be going by faster than normal) r = 1 the change in B-series information per change in A-series information is given by 1 second of indexical clock time per unit e of becoming. This unit e is assumed to be invariant across all panpsychist systems, the way 1 second of indexical clock time is invariant across such systems as Alice and a protozoan. 0 < r < 1 B-series time appears slowed down, as in relativistic dilation between Alice's B-series and Bob's B-series, according to either Alice or Bob r = 0 B-series time appears stopped (but the appearance goes on) r < 0 one appears (from future to now to past) to be going backward in B-series time, e.g. timereversal One may define dr/de. e2 would have something to do with the rate of becoming accelerating. e-2 would be something like "per unit of becoming, per unit of becoming". 6 Picture of AB-series time One doesn't need to suppose the present is a single infinitesimally small point centered at, for example, τ = 0. For each τ there could be a degree of 'existence' or 'actuality' or 'presentness' p = p(τ), so the now is spread out in A-series time somewhat. (Smith, 2010). One attractive example is for p some Gaussian function of τ (in a centered world). Also non-symmetric functions. A place on τ is thus assigned a degree of existence/actuality/presentness p(τ), and there's no reason to make the assumption that the present is at τ = 0 only (in the obvious coordinatization). The growing-block theorist supposes the past is real, which might be defined as p(τ) = 1 for τ < 0 and τ = 0, for a particular system. The block theorist would have p(τ) = 1 for all τ. The presentist (like me) has p(τ) > 0 on the support of τ. This is the model t_1 is earlier than t_2 which is earlier than t_3... The earlier-times to later-times timeline stays in one ordering (of one kind or another), but the whole timeline moves from future to present to past, with the present staying put. (The present does not 'move up the B-series' as in some spotlight theories because ipso facto the presents wouldn't be ontologically privileged.) As later and later B-series times become present, time goes on. Time-reversal goes as t_3 and then an earlier time t_2 and then an even earlier time t_1 become from Alice's future to her present and then to her past. As earlier and earlier times become present to her, time appears to be going in reverse. Time-reversal invariance obtains only for a B-series, on this view. Time-reversal for an A-series is undefined. There's no unit of going from past to future defined in the A-series. 7 McTaggart saves Schrodinger's Cat? We ask the question of how McTaggart's insights might apply to Schrodinger's Cat. A. The Schrodinger's Cat paradox is fascinating here. (I will assume the reader is already familiar with the paradox.) Suppose the experimenter is Alice. At some point (time) during the experiment, Alice has it that the cat's state is a superposition (in obvious notation) psi = [meowing> + [purring>. Yet at that time the cat has it that it is definitely in one or the other states 'meowing' or 'purring', and not in the superposition psi. What's going on? The problem from the perspective of the AB-theory is that we assumed the A-series of the cat is the same as the A-series of Alice. Suppose that Alice has a 'now' and at this particular 'now' her clock reads 7:10 pm. This is 7 hrs and 10 min later than noon, which is the B-series information. Yet the 'nows' of Alice and the cat are taken to be ontologically private. Therefore the 'now' of Alice does not determine (fix) the 'now' of the cat (according to Alice). Therefore Alice cannot determine when the 'now' of the cat is. The cat's 'now' need not temporally line up with Alice's 'now' analogous to the case of qualia in the Inverted Spectrum and the ontology ought reflect that. This is so from the beginning of the experiment (when she closes the box) until the end of the experiment (when she opens the box). But if, during the experiment, Alice and the cat never are in a shared present, or 'now', then there is never a single time at which the cat gets ascribed different states. I will explore two more ideas. B. In addition to defining functions f of time and space, (1, 3) = (t, x^3), as in Minkowski spacetime, one is now free to define functions h of the A-series, B-series, and space, (1, 1, 3) = (τ, t, x^3) in a new kind of AB-spacetime. These are functions of how far something is in the future, τ, how much later than clock time t = 0 it is, and the three space dimensions x^3. This is not a theory of two time dimensions, but a theory of one time dimension, for Alice, that is characterized by two different but closely related series. C. It is clear that it might be that relativity can be handled similarly to the Cat paradox but, as merely an example of what might be possible with an AB-theory does not have to be consistent with the Cat paradox example. E.g. suppose Alice is a constant 10 feet above the surface of the earth and Bob is another constant 10 feet straight above Alice. Alice and Bob each hold a clock. Alice's clock runs slower (as I understand it) than Bob's clock because she is in a stronger gravitational field. But these clocks only give us the B-series information. The A-series information of Alice is that (in what might be called 'temporal equilibrium' if the rate is constant) her later times become into her present at a rate r = 1 sec./e. Yet Bob has r' = 1 sec./e'. It is not possible to make a numerical comparison between e and e' because they coordinatize the private A-series τ and τ' and are themselves private. Thus there is no contradiction. Since it is not possible to directly compare them, such as Alice in the case of Bob's qualia, the ability to do so should not be part of the ontology. Yet it is possible to compare Alice's B-series sec. with Bob's B-series sec. One can just read them off the respective clocks. In our case one has a rate s = Alice's sec./Bob's sec., where s is less than 1.