A Brief Introduction to Time in Physics

In short, we can can say P = (x, y, z, t), and that (x, y, z, t) constitute a reference frame, or a moment in time, if you will.

Given the values of x, y, z and t, as well as the magnitude (length), and direction (the measure of the angle between the particle and the positive side of the x-axis, usually marked by the lowercase Greek letter theta), we can then comfortably analyze the evolution of P as t changes.

  • If we’re treating time as something discrete, we index t to the Natural numbers, which begin at 0, and end at ∞.
  • If we’re treating time as something continuous, and we index t to the Real numbers, then we are forced apply the concept of limits, from Calculus, to the value of time, meaning it will get arbitrarily close to, but never quite reach the lower bound of 0, or the upper bound of ∞.
  • I should also note that the uppercase Greek symbol delta, Δ, is usually what is used here, in that delta denotes a change in some variable, in this case t, written Δt, but it’s technically the difference in the value of t, given two different reference frames.
  • If we take some function of time, f(t), in our case the location of a particle which we know is (x,y,z), the change in location over some interval is given by Δf = f(t + Δt) — f(t), and the changes in the values of the spatial coordinates, by, x(t + Δt), y(t + Δt), z(t + Δt).
  • By deterministic, what we mean is that there are a set of logical rules that allow you to derive the correct state of a system at some point in the future, given its current state.
  • By reversible, we mean that given the state of the system at some point in the future we should be able to derive the state of the system at some point in the past.
  • The collapse of the wave function is an event that sharply distinguishes the future from the past, due to the marked difference in the state of the system on either side of the event.
  • This is not deterministic, because prior to the collapse of the wave function, we can’t say where the particle is, and it’s not reversible, because, given a particle with a definite location, we can’t say where it was prior to the measurement.

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