Time A Very Short Introduction

Book on time by Jenann Ismael

• Two main debates about the nature of what space and time as gauged by their effects on the observable movements of material bodies
  • Newton viewed time as absolute and independent of human perception or physical events, flowing uniformly in the background of the universe. He believed in absolute, mathematical time that existed separately from any measurements or changes in the physical world.
  • Leibniz, in contrast, held a relational view of time. He argued that time had no independent existence but was simply the ordering of events and changes in relation to each other. For Leibniz, time couldn’t exist without events and changes to mark its passage - it was fundamentally about the relationship between things happening, not an absolute container in which they occurred.
• Leibniz’s main objections to Newton’s ideas were on the grounds of the principle of sufficient reason. Newton’s ideas would imply that there are an infinite number of distinct physical situations between which we have no way of distinguishing either by observation or experiment.
  • Say, for example, we have two bodies of equal mass in vacuum orbiting each other. By Newton’s theories, there is some absolute coordinates we can assign each body.
  • Now, translate both bodies by some fixed amount. This produces no distinguishable difference in the observable movement of the material bodies.
• However, Newton devised a counter example. The experiment imagined two globes connected by a rope in empty space, far from any other matter in the universe. If you spin the globes around their common center of mass, the rope would become taut due to the centrifugal force. Newton argued:
  1. Even in the complete absence of other matter to measure motion against, the tension in the rope would reveal whether the globes were truly rotating
  2. You could measure the angular velocity of rotation by measuring the tension in the rope
  3. Therefore, absolute rotation must exist independently of any relative motion to other objects in the universe
• Eventually, this resulted in the assumption is that there is no way to detect whether an object is at rest or what velocity it is moving at so long as that velocity is uniform (in a closed system, motion is undetectable unless there is acceleration).
• Maxwell started developing equations to model electromagnetism which did seem to show sensitivity to differences in velocity. Light, when emitted, travels at a constant speed $c$ regardless of whether the source of the light is moving or not.
  • Newton’s ideas aligned with what was called the “luminiferous aether” - a hypothetical absolute reference frame through which light was thought to propagate, similar to how sound waves propagate through air
  • The Michelson-Morley experiment split a light beam into two perpendicular paths, reflected them back, and recombined them. If Earth was moving through the hypothetical aether, the light speeds should differ based on direction, creating detectable interference patterns.
  • No such patterns were found, proving light speed is constant in all directions, disproving Newton’s ideas.
• There were a bunch of ideas in the meanwhile that attempted to explain these bizarre results:
  • Lorentz suggested that the true speed of light is still $c$. For observers moving at a velocity $v$, the speed of light is $c-v$ but they still get $c$ when measuring because both distances shrink and clocks run slower proportional to $v$. This length contraction and time dilation is a physical effect of motion through aether.
  • Einstein arrived at the same mathematical conclusion but interpreted it differently. Einstein took a more radical approach by rejecting the very concept of absolute space and absolute time as separate entities.
    • Instead of physical contraction/dilation caused by motion through aether, he proposed that length contraction and time dilation are natural consequences of two postulates:
      1. Physics laws are the same in all inertial frames
      2. Speed of light is constant in all frames
    • He created the idea of a combined spacetime as a unified entity where space and time are fundamentally linked via the underlying geometric principles that follow from the two postulates.
      • A worldline is the path of an object through spacetime - it shows all spacetime points (events) that the object exists at during its history. This is static regardless of which inertial frame you view it from.
      • Since light always travels at $c$ in any reference frame, photon worldlines always make a 45-degree angle with the time axis (assuming equal units for space and time).
        • As a result of this cosmic speed limit, it placed an upper bound on how tight the causal ordering is
• Entropy and why we evolved to perceive and remember temporal information
  • In the flux of transition from order to disorder, complex structures arise, at first spontaneously, and then by design: Parts are thrown together by accident and some of them bind together into stable configurations. Among the stable configurations, some prove able to do things that promote their survival and among those that survive, some find ways to make copies of themselves.
    • As it happens, systems that are able to utilize and process information in effective ways tend to survive and reproduce more easily.
    • A deer, for example, can read the signs of a recent lion hunt, or a predator who knows that a beaver dam means a beaver, will do better than one that doesn’t.
  • Once we have systems that reproduce themselves, with some mutation, and a selected mechanism operates on these systems, the process of Darwinian evolution is launched. Evolution over long time scales is an effective search mechanism for complex systems that are able to survive and reproduce.
• Intersubjectivity of time
  • The universe is a network of events. Chains of these events correspond to the histories of objects.
  • There isn’t a well-defined temporal order for the network as a whole, but we can always choose some system in the world — a rock, a lobster, a person — and follow how things unfold from its perspective.
  • Communication among observers (and the creation of time-keeping technologies like clocks and watches) serves to stabilize an intersubjective notion of “what time is” well enough for practical purposes