What on earth is the speed of causality?

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Saw this as an answer to another question and can’t wrap my head around the logic. What? How? Why??

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Anonymous 0 Comments

Let’s say I send you a letter telling you that there’s a new game coming out for the Switch. After I send the letter, but before you get it, you buy a switch.

In analyzing this interaction one may say “I told you about the game before you bought the switch, so that may have caused you to buy the switch.” In response, someone may point out that the letter hadn’t arrived at your house by the time you made your purchase, so there’s no way that my letter could have caused your decision: letters move at some finite speed.

We could repeat this exercise with progressively faster methods of communication, up to the point of boring a hole through the planet, pulling a vacuum on it, and shining a laser through that hole. This information travels as fast as possible–the speed of light–but still at a finite speed. If, between the time when I send the information and the time when you receive it, you make a decision then we *know* that that information didn’t cause the decision. This actually happened with a stock exchange, where information was released in, if I recall correctly, Chicago, then trades executed in New York “in response” to that information being made public, but the time between the information being released and the trades being made was so short that it was proven that there was no way the information had traveled fast enough. It was *impossible* for that information to have caused those trades, which showed they had been carried out for some other reason (insider knowledge, in this case).

The reason we care about this interaction is because we expect–and all physics supports this expectation–that causes cannot come after their effects. If I tell you about the new Switch game tomorrow then that can’t cause you to buy a game today. The speed of causility just takes that one step further and notes that causes have to not just come before their effects, but have to come before their effects by long enough for the information to get from the cause to the effect.

That may seem like a pointless thing to go into all of the trouble of specifying, but it becomes more important when you start looking at scenarios in relativity where time and space are not the rigid constructs that we’re used to in classical physics. One of the outcomes of relativistic physics is that you could have two events, A and B, where A comes before B in one reference frame, but B comes before A in another, and they’re simultaneous in a third. However, if it is possible that A *caused* B then A will precede B in *every* reference frame. For it to be possible that A caused B we could start at the time and place where A occurs and travel towards the time and place where B occurs, moving at the speed of causality (light). If we get to the place where B occurs before B actually occurs then A could have caused B.

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