Misconceptions on Time
At first glance, time seems to be an elementary component of our world. It is one of the seven fundamental physical quantities in the International System of Units and finds application in many social, economic, financial, machine learning and physical models. I find the question of the representation of time interesting for those who particularly care about having an accurate representation of the real world. One would commonly represents the concept of time by an universal arrow directed from the past to the future. On this line, the present is usually represented by a single point denoted by a variable t which continuously and homogeneously passes everywhere in the universe (see Fig.1). However, this standard conception of time is not correct. It leads to major physical and philosophical inconsistencies with tangible repercussions on the objective and phenomenal times. The goal of this article is to dismantle intuitive but wrong conceptions on time. To this end, we will explore philosophical and physical theories and try to synthesize important concepts from previous works [6, 8, 7].
Time is not unique. One might a priori think that time flows at the same pace everywhere in the universe. However, time passes slower for an observer closer to a massive object or for an observer who move at a higher relative speed. This phenomenon — usually called time dilation — is described by the theory of relativity and has been empirically confirmed many times (e.g. Hafele and Keating experiment in 1971). For example, a clock on the International Space Station with a relative speed of 7,700m/s around earth approximately lags 0,01 seconds every year compared to a static clock on Earth (see Fig. 2 for visualization). Hence, the physical time is provably not unique. From a philosophical point of view, the subjective time experienced does not seem to be unique either. Indeed, individuals perceive duration in different ways. One example is the Kappa effect or perceptual time dilation [5] showing that people tend to overestimate or underestimate time duration when experiencing different frequencies of stimuli. For example, speeding up the pace of a melody might give the feeling of a faster time. Further, the time value is also not unique even for a single person. Indeed, the phenomenon of temporal discounting explains that people assigns lower value to time far into the future than close to the present (see Fig. 3).
Time is not directed. One might think that time is directed from the past to the future. However, all fundamental physical equations have a symmetric time (i.e. they do not require time direction). For example, if you ignore frictions in mechanics, a sequence of events and its reverted sequence of events are both equally possible. The only exception is the second thermodynamic law which states that the “disorder” of an isolated system (i.e. its entropy) can only increase. An important precision to this law is that it occurs when averaging the particle behavior at a large enough scale. As an example, Boltzmann argued that successive world states are actually equally unique (or “ordered”) if we observe them at a detailed enough level [8]. Hence, this suggests that time perceived by human eyes is biased by our limited capacity to observe the state of the world in full details. In particular, quantum physics which describes the real world at a very small and detailed scale does not require time direction [3] and might violate the second thermodynamic law [4]. This property is often called T-symmetry or time symmetry. If you are interested, you can also find amusing discussions on this topic on this forum and this forum.
Time is not ordered. Time is commonly seen as defining a universal order between events (e.g. January 1st 2019 < January 1st 2020 < January 1st 2021). However, time as described by special and general relativity only determines a partial order between events. Given a specific event A, other events can be classified in 3 categories: events which could affect A (causal past), events which can be affected by A (causal future) and other events which can neither affected nor being affected by A (see Fig. 4 for visualization). Indeed, as the speed of light is assumed to be the absolute upper limit by relativity theory, all events on Proxima Centauri between 4.2 years ago and 4.2 years in the future do not have a strict order compared to current events on Earth.
Time is not past, present and future. We commonly distinguish between two families of philosophical theories about time. The first family divides time in mutually exclusive regions: the past, the present and the future. Examples are presentism — which considers that only the present exists — , and non-futurism (a.k.a. growing block universe) — which considers that the past and the present exist but not the future. Although intuitive, this distinction leads to numerous philosophical and physical problems. On one hand, the philosopher Mac Taggart [7] explains that past, present and future cannot be mutually exclusive since an event (e.g. January 1st 2020) would belong to past, present and future depending from when we observe it (e.g. January 1st 2019, January 1st 2020, January 1st 2021). Furthermore, defining tenses w.r.t. a given time would lead to circular definitions. On the other hand, as explained in the previous paragraph, modern physic theories are unable to classify all events as past, present or future events. In particular the concept of present time on Proxima Centauri is meaningless from the Earth point of view. They prefer a description of the real world as a four dimensional block of events with coordinates (x, y, z, t). This view called four-dimensionalism, eternalism or block universe theory composes the second family of time philosophical theory and states that all events coexist. Eternalism which does not assume mutual exclusive past, present and future is also easier to defend from a philosophical point of view. Indeed, humans do not experiment the present but rather the specious present [1] or the perceived present [9]. The specious present can be defined as an aggregation of memories from the past, perception from the present and anticipation from the future. This naturally leads to an overlap of the three traditional tenses. An illustrative example is our music experience which combines memorization from the past notes and anticipation from the future ones. Similarly, the perceived present is defined as the earliest perceptual processing stage capable to store information with a duration up to 100ms. Interestingly, our present temporal resolution is inherently limited by our physiological characteristics.
Time is not independent from the world. One might view time as an independent grounding building block of the universe. This theory, sometimes called substantialism, states that time behaves like a substance in which objects flow. However, relativity theory disagree again. Indeed the time flow is not independent from the rest of the world but rather depends on other quantities as the mass distribution or the object speed (or more accurately gravitational potential and velocity). Further, while time is dependent on the rest of the world, accurate physical descriptions of the world often aim at being independent of the space-time coordinates. This condition is known as Background Independence. As mentioned earlier, loop quantum gravity surprisingly does not require a time dimension for example.
Time is not continuous. While time appears to us a continuous flow, it exists a smaller possible time interval between two events at a physical level. This smaller piece of time is called the Planck time and is approximately equal to 5.39e-44 s. This unit described the time required for light to travel one Planck length which is itself the shortest explorable length in physical world. This conclusion suggests an underlying discreetness of time which contradicts the standard representation of time as a real valued variable t (potentially arbitrarily small). Note that this point is still not accepted in conventional physics but supported by recent loop quantum gravity and doubly special relativity.
In conclusion, time appears to be highly counter intuitive. On a large scale, time is non-unique, not directed or not ordered. On a small scale, time appeared to be non-continuous or even barely existing. On a human scale, perceived time is a non-universal mix of memories, feelings and anticipation. These subtleties motivate a careful description of time in scientific models. Nevertheless something remains from the common conception of time: its capacity to measure changes between two related events. Interestingly, Aristotle already supported that time does not exists on its own, it rather describes the relative amount of change between the “before” and the “after” [2].
Acknowledgements
I would like to thank Bengamin Genta for useful discussions and Johannes Klipcera for helpful comments on relativity theory and perceived present.
