Past and Future

Question

I'm new to physics we've had and argument in our class about: we know that present (and/or past) can and will affect future. But how do we know if the future can affect past or present? Is that even possible? What principles are in effect here? for example: if I throw a piece of paper in trash can, how it can affect my grand grand grand grand (...) parent?

Answer 1

When you study special relativity, there's a concept called "causality". It explains how different events can be related with each other. This is, of course, due to the speed of light being constant and only achievable with electromagenitc waves.

Moreover, we have to consider the light cone (see figure below). It arises from the relation between two different events in space. There are time, space and light type of events (or so I've been taught). For example, a type time event can ocurr at the same place but never at the same time. Also it is fascinating that, when talking about space events (let's say we have two events, E1 and E2) , if E1 happens after E2 for some inertial system of reference, then for another SRI could see how E1 happens before E2.

Now, if we take a look at the light cone, you can see that the surface of the cone is the boundary of any event that has happened "inside" the light cone. Notice too that the center should be a given event, let's say E0. Every event inside the light cone will be able to be related with E0 by a cause-effect relationship, but if it is outside the light cone, then, because the surface represents the travel of information at the speed of light, it can't be related with E0 since, to do so, information would have to travel faster that the speed of light, which we assumed that is impossible.

Answer 2

Suppose that you have thrown a piece of paper with a certain initial velocity $\mathbf v$, and after that, only gravity acts on the paper. The horizontal velocities $v_x$ and $v_y$ don't change along the movement, but $v_{zf} = v_{zi} - g\Delta t$, (considering positive the movement upward). If we invert the time direction, considering the paper going back to your hand: $$\Delta x(\Delta t) = v_x\Delta t \implies \Delta x(-\Delta t) = -v_x\Delta t = -\Delta x(\Delta t)$$ $$\Delta y(\Delta t) = v_y\Delta t \implies \Delta y(-\Delta t) = -v_y\Delta t = -\Delta y(\Delta t)$$ $$\Delta z(\Delta t) = v_{zi}\Delta t - \frac{1}{2}g\Delta t^2 \implies \Delta z(-\Delta t) = -v_{zf}\Delta t - \frac{1}{2}g(-\Delta t)^2$$ Using the expression for $v_{zf}$: $$\Delta z(-\Delta t) = -v_{zi}\Delta t + g\Delta t^2 - \frac{1}{2}g\Delta t^2 = -v_{zi}\Delta t + \frac{1}{2}g\Delta t^2 = -\Delta z(\Delta t)$$

The example shows that we can think of a piece of paper in the basket with a known final velocity, go backward in time following the laws of physics, and get the initial configuration. They work both ways: past determines future and future determines past.