The speed of light is usually thought of as a speed limit for how fast an object can travel, but you’re right to also think of it as a speed limit on the transfer of information. If you want an object to influence another object, you first have to transfer some information around. In the case of light, this influence can come in the form of light arriving on a detector, or perhaps a burst of radio waves, and this light unsurprisingly traverses the cosmos at precisely the speed of light.
The definition of causality from a physics perspective goes beyond a simple cause & effect link. It’s more than just tying an event to the thing that caused it, though this is a critical component. If I knock a glass over onto the floor, we can reasonably blame me for being the cause of that glass tipping over – that’s the cause and effect part.
However, say I was in the other room, and I just heard the glass fall, and don’t know what caused it. The physical principle of causality imposes limits on the number of things which could have caused the glass to fall. The first rule of causality is that the order of time must be kept. Nothing you can do now will influence events that have already happened, earlier in time. The second rule is that to influence anything in the universe later in time, the first event or object must transfer information across space and time. Bu we already know that we have a maximal speed of information transfer – a maximum speed that can link two things causally; the speed of light.
The speed of light seems quick, and on human frames of reference, it is. But a lot of information travels much slower than the speed of light. Sound, for instance, travels significantly slower than the speed of light. You’ll catch the flash of light from a lightning flash, but it’s the rolling thunder that will rattle the windows. The causal link between lightning strike and rattled windows travels slower than the speed of light, and so you have to wait for the sound wave to arrive for it to influence your windows.
You can draw out the regions of space which can possibly affect anything around you, and the regions of space which you can affect in the future, and it looks a bit like an hourglass. This hourglass is called a light cone, with the point at the very centre as the present. In your domino example, you start the dominos tumbling at “now”, at this central point. Your cone of influence extends out through time, as information about your push of the first domino extends outwards in space and time. Someone watching you pushing over the domino sits along the edge of the light cone, as the information they need to see (light) travels at the speed of light. Of course, as time progresses, the “now” point progresses, and the light cones travel with it. In your example, the domino hits the next domino at some point in the future, which in turn hits the domino after that, all of which must be contained within this cone-space.
So yes – your dominos are bound to fall one after another within this light cone, which limits us to communicating at the fastest, at the speed of light. So assuming that the dominos fell exactly instantaneously (unlikely to impossible), and no time was taken in transferring the energy from domino to domino (also unlikely to impossible), the fastest the furthest one could fall, while having the first domino be the cause, is one year after the first. By the same token, if you see the last dominos fall before a year has gone by, it guarantees that something other than the domino stack is responsible for its fall.
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