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Why Does Time Move?


Figure 1. Why do we move through time?

Right now you are time travelling.


You don’t need a TARDIS; just sit on your chair and watch the world go by. A car driving past, a person talking, your breaths going in and out – these are a part of something happening all around you which proves you are moving through time: change.


It is like many replicas of the world have been placed on a conveyer belt moving beside you. The future consists of all the replicas up ahead; as they come within arm’s reach you can interact with them, but they soon move past and become unreachable again. The time travelling power in Doctor Who was to jump to different positions beside the conveyer belt, and the time reversing power in Tenet was to switch the direction the conveyer belt moved in, but in all of these stories one question goes unanswered: what machine is driving the conveyer belt along? Why does time move?


There is a common answer physicists will give you, which is not actually an answer at all. It goes something like this.


The universe began in a Big Bang in a highly ordered state; in physics terms, the universe initially had low entropy (where entropy is a measure of disorder). States of higher entropy are much more likely to occur, giving rise to the Second Law of Thermodynamics: systems always move toward higher entropy. Ever since the Big Bang the universe has been on an unstoppable journey from low entropic order to high entropic heat. An egg will crack but won’t uncrack, because ‘yolk and broken shells splattered around your kitchen floor’ has a much higher entropy than ‘egg teetering on your kitchen bench’. The accomplishment of this argument is in explaining the arrow of time: why change occurs in one direction but not the other. It explains why the conveyer belt of time goes in only one direction, and why reversing time is physically impossible (sorry Christopher Nolan) [1].


However, this argument only tells us how time moves and not why time moves. What causes change to happen in the first place? In order to find the answer, we must delve deep inside the conveyer belt’s machinery to discover the mechanism for change.


Imagine the world as a running movie which rapidly flicks through three-dimensional ‘picture frames’; let’s call these frames microstates [2].


An object’s change in position between two consecutive microstates is called its velocity. Velocity predicts position one microstate into the future, and likewise acceleration allows us to predict position two microstates into the future [3].


The relative positions of all objects create what is called a potential field; think of ‘potential’ as a number value associated with every point in space. Your roof might have a potential of -3 whereas your floor has a potential of -10. Newton’s Law of Motion states that objects are accelerated in the direction of decreasing potential [4]. An object knocked off your roof will be pulled toward the ground because the ground has lower potential; this phenomenon is known as ‘the force of gravity’. Any force that works like this, based on a potential field is called conservative. As the famed physicist Richard Feynman states, “all fundamental forces in nature appear to be conservative” (The Feynman Lectures, Vol. 1 Ch. 14).


Change occurs in a self-propagating three-microstate loop of position, velocity, and acceleration. A potential field creates acceleration, affecting the velocities of objects, which in turn changes their position. Their new positions update the potential field causing new accelerations, and the process continues (see figure 2) [5]. Our conveyer belt of time is like a perfectly oiled machine that once set in motion will continue running indefinitely.



Now the crux of the solution is clear. The cause of time’s motion is the very thing that jumpstarted the conveyer belt of time at the beginning of our universe, setting off this endless process of change. Let’s rewind our clocks back to the Big Bang itself, where the entire universe expanded from a singularity. In the very first microstate (the first picture frame of our universal ‘movie’) we see all objects contained within a single point in space [6]. We know the objects have velocities since they spread out from the initial point in the next microstate as the universe expands, thus initiating the three-microstate loop of change. What caused this first velocity that pushed everything out of a singularity? There are three possible answers.


The first answer feels like a cop-out. Everything simply began in a single point with expanding velocity, and nothing caused this to happen. There was no microstate before the Big Bang, and asking what caused it is as meaningless as asking what is south of the South Pole (see figure 3; in this option the microstate before time 0 doesn’t exist).


The second more satisfying answer employs one of physics most trusted principles: the Law of Inertia. It states that in the absence of a force, objects will continue moving with the same velocity. There existed a microstate before our initial singularity which is an exact mirror image of the microstate following our singularity. The cosmos has been in an endless cycle of universes expanding out from singularities before collapsing back into singularities and re-expanding again, thus forming new universes. The cause of time’s motion extends infinitely backwards.


The third answer requires just one simple extension: there existed at least one microstate before our initial singularity that looks identical to it. In our universal ‘movie’ there were two (or more) picture frames in which everything simply sat in a singularity before suddenly erupting out in a Big Bang. The Law of Inertia tells us that the sudden change from stillness to expansion can only have happened due to a force. Newton’s Law of Motion states that objects sitting in the same point in space cannot create a potential field (which requires relative positions), and hence are unable to create a force. Putting two and two together, there must have existed a force not created by the objects themselves that accelerated them to their initial velocity; the mechanism for change was jumpstarted by a nonconservative force. If we are to believe Richard Feynman’s claim that all known fundamental forces are conservative, then there must have existed an as yet undiscovered force at the beginning of the universe.



How do we know which of the three options is correct? Science can’t answer this due to a severe lack of pre-Big Bang understanding, so just pick your favourite.


We have finally answered the question of time’s motion, down to three possibilities. Time moves due to a perpetual three-microstate loop of change. This mechanism was jumpstarted by whatever caused our universe’s beginning; either it began without cause, it began through an external cause, or it is part of an infinite cycle. The reason why you see change happening in the world all around you is because whatever caused the Big Bang also sparked the universe into constant motion, endlessly driving time onwards.



Notes:


[1] The Second Law more accurately states that ‘closed systems cannot decrease in entropy’. Open systems are able to decrease in entropy and maintain high order by exchanging heat with their environment, as long as there is a net increase in entropy in the total system (the open system plus its environment). Small open systems can theoretically change ‘backwards in time’, but large systems and the universe on the whole cannot.


[2] I am using the term ‘microstate’ to refer to the exact configuration of the universe at a particular instant of time, somewhat different to its statistical definition.


[3] I am defining velocity as

where x is position and ∆t is the time length separating two consecutive microstates. If this interval is the unit of time ∆t=1, velocity is simply the change in position. Discrete acceleration is defined as

when ∆t=1. Knowing the current position x(t) and the next x(t+1) given by velocity, acceleration predicts the following position x(t+2). A more complicated symmetric definition of discrete velocity is used in numerical differentiation since it approximates continuous motion with lower error; however, there is no error involved if motion is truly discrete. The idea of doing mechanics in discrete time was inspired by Leonard Susskind’s Stanford lecture series ‘The Theoretical Minimum’ (Classical Mechanics Lecture 2. 2011).


[4] What I refer to as ‘Newton’s Law of Motion’ is more accurately ‘Newton’s 2nd Law of Motion for conservative forces’.


[5] This self-propagating loop is where classical determinism comes from. Given the positions and velocities of all objects in a single microstate, we can solve for the potential field U, which in turn gives us acceleration using Newton’s Law

(where m is inertial mass which resists acceleration, and U is the potential field – called potential energy – which causes the push/pull). Velocity gives us the next position and we can again solve for the updated potential field, giving us the next acceleration; this process can be forever continued, allowing us to predict arbitrarily far into the future. Since the laws of physics are time-reversible, we can also predict arbitrarily far into the past. In the case where the mass of objects can vary, we are instead required to know the positions and momenta p=mv of objects in our initial microstate.


[6] In the high-energy state of the Big Bang normal objects could not have existed. Here the word ‘object’ instead means ‘particle’, or ‘field excitation’, or really any form of energy in general. It is also not certain if the universe began from a single point, and I am assuming a classical Newtonian space.

References

  • The Feynman Lectures. https://www.feynmanlectures.caltech.edu/

  • The Theoretical Minimum. https://theoreticalminimum.com/courses/classical-mechanics/2011/fall/lecture-2

  • Figure 1: Stein V., Harvey A., ‘Is Time Travel Possible?’, space.com, 2023. https://www.space.com/21675-time-travel.html


By Peter Lavilles

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