# How would a mathematical theory of the universe incorporate time?

In Einstein's theory of relativity, we start with describing events as coordinates in 4D Minkowski space. All events that have occurred in the past and future would then be represented as points in this 4D block structure. But is this not in direct contradiction with our experience of time? Why does anything at all happen then?

Consider a 2D being living in 2D space. For our purposes of visualization of this being's time as a dimension, we take the 3rd dimension. Now any dynamical behavior of this particle would be captured as a series of successive "slides" that grow the height of this box. But if we know the mathematics of the dynamical laws, we can compute and build this box ourselves, and this box will be identical to the first box. When we view this box, we can find no information that tells us that this being is in this slice of time rather than that slice of time. There is no implicated direction, only a static block. So why is it that this 2D being should "feel" the flow of time?

If we ourselves live in a 4D block universe, described by a set of equations that are completely deterministic, shouldn't we too not experience time at all? What then causes the illusion of "flow", that enables us to talk about the "present" rather than the future or the past? Is this indicative of a shortcoming of all mathematical models of the universe?

The way I see it, any mathematical description of the universe, if it exists in principle, should predict all events from the creation to the end of the universe at once. Like a solution to a set of equations exists, whether or not we choose to go through the calculations, spend time with it, and arrive at the solution, it exists regardless. Similarly, if a theory of everything is mathematical, why is it not simultaneously a static unchanging solution? The universe "knows" what its initial conditions are and subsequently the entire future of it is determined, so why does a need for passage arise, as evidenced by our experience? The solution already exists, no need for a computation, implying no evolution of state and no passage of time.

So how do we reconcile the fact that any mathematical theory of the universe will incorporate a dynamical nature to it, that is unknown prior till it actually happens? Does it mean that the laws of the universe themselves change over time, giving rise to a notion of time, a present fundamentally different from the past, circumventing the need for a static solution, providing a direction of time?

• You are confusing time with determinism, and relativity with all of physics. Mathematical description of the universe can be indeterministic, and so may not be able to predict everything from initial conditions. "The solution" will have gaps that can only be filled by observation. This will not preclude describing what it can predict in 4D terms, QFT is indeterministic but set up in 4D spacetime. And 4D solution can be presented dynamically as evolving through a chosen time direction (which may be privileged by our physiology), which is why initial value problems are studied in relativity. Commented Apr 22, 2020 at 17:52
• @Conifold That's not the essence of my question, rather, it is how would any mathematical theory incorporate for a transition from past to future states, and if so, while preserving causality. Bottom line is it can't, because if the future is determined, then there arises no need for a "now" transition. Also QFT is far from a theory of time, rather it takes space and time as given entities, and then proceeds to give us "in-determinism" due to the probabilistic nature of the wavefunction, but for explaining time, the reduction of wavefunction could be a strong candidate. Commented Apr 22, 2020 at 18:06
• Are you asking specifically about the conscious experience or qualia of time, or are you asking a third-person question about why certain bundles of worldlines in a block universe would behave as if they experienced time (saying they have memories and expectations in speech, for example), regardless of whether one believes they experience anything or are more like philosophical zombies? Commented Apr 22, 2020 at 18:20
• @Hypnosifl My question is how should one go about using mathematical theories in general, if they do not provide a sufficient description of transition from past to future and simultaneously give a deterministic solution to the equations of motion. Any theory that can compute perfectly a particle's trajectory doesn't allow for such a transitional "now", and any theory that is the likes of quantum mechanics, doesn't provide a sufficient causal reason. So are mathematical models of universe fundamentally flawed by the existence of our direct experience of such a "now" moment ? Commented Apr 22, 2020 at 18:38
• @CriglCragl - Yes, especially where he says thought in physics 'endeavours in principle to make do with “space-like” concepts alone'. Also see his 1952 comment to Michele Besso quoted on p. 9 of this paper that "You do not take seriously the four dimensions of relativity, but consider however the present as it were the only reality. What you call ‘world’ corresponds, in physical terminology, to ‘space sections’, to which the theory of relativity – even special relativity – denies objective reality" Commented Apr 23, 2020 at 20:56

There are several questions here and dozens of possible answers. I suggest reading up (via SEP) on presentism, eternalism, the problem of change, persistence, moving spotlight theory, dispositions, powers, Cartwright on laws, Hume on laws, and causation w/in epistemology and metaphysics. There are a range of views and summarizing them here is unnecessary given the vast literature

I would advise you not to take the 4D 'block universe' issue too seriously. I believe you (among many) are inferring a property of the world from something which strictly speaking is only a property of the model. General Relativity models time as a fourth real-valued dimension in order to represent the relationships between events, but in doing so it deliberately fails to model motion in any intuitive way (in fact, I think ALL mathematical models have this failure).

This issue calls to mind a joke that president Abraham Lincoln once told to several people at a party: "If you call a tail a leg, then how many legs does a dog have?" Someone replies: "Five." He replies: "No, four. Calling a tail a leg does not make it one."

Calling Time 'a dimension' does not make it one.

[I believe the existence of a perpetually-changing 'now' is in fact consistent with GR - unless closed time-like curves actually physically exist.]

• Another feature of the model (in both special and general relativity) is the relativity of simultaneity--you can use multiple frames of reference which define simultaneity differently, and the laws of physics work the same way in all of them. So if you want to have a unique objectively correct "perpetually-changing 'now'" in relativity, it would have to be a purely metaphysical claim that'd never be empirically distinguishable from other possible definitions of simultaneity. Commented Apr 22, 2020 at 21:43
• It actually does. See Noether's theorem. Dimensions are directly equivalent to symmetries under transformation, that is directly equivalent to conservation laws. That is what dimensions are. Commented Apr 23, 2020 at 7:46
• "inferring a property of the world from ...a property of the model" That's an excellent way to describe what I think when I hear physicists talking about the world by referring to their abstractions, I'll be using those words from now on, if you don't mind the intellectual theft.
– Sam
Commented Apr 23, 2020 at 13:13
• @CriglCragl - Do you have a reference for the idea that physicists think dimensions are in some sense equivalent to symmetries? And are you talking specifically about spacetime dimensions or the more broad use of "dimension" in dimensional analysis? My understanding was that Noether's theorem says continuous spacetime symmetries of the action (the time-integral of the Lagrangian) are associated with conserved quantities (translation invariance impies momentum conservation for example), I don't see how this is equivalent to your statement. Commented Apr 23, 2020 at 23:02

I suggest you take a look at the work of Nicolas Gisin, a physicist who is developing a very interesting view of time using ideas from intuitionistic mathematics. His main thesis goes directly against the idea that "any mathematical description of the universe, if it exists in principle, should predict all events from the creation to the end of the universe at once". He wants to recover the notion of time as something that flows, instead of the static entity it became in modern physics. For a summary, check this article