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This is probably the stupidest question I have ever asked, but it is bugging me and I am looking for an illuminating answer - not one that simply tells me I have the wrong idea, but one that explains in what way I have the wrong idea.
I can, based upon some knowledge of initial conditions and some equations, predict a future state of some system. For example, I can predict the next eclipse. Now, this prediction is based upon information that I have at the present, and some of that information is the initial conditions (where the sun, moon and Earth are now) and some of that information is the equation (how they move). With this information, I can know information about a future state before it happens.
Here is the troubling bit. I know that information cannot exceed the speed of light, and if it did it would be virtually or practically traveling into the past. But when I have information of the future state of something, that seems like information "from" the future, or at least, virtually indistinguishable from information from the future. That would entail, of course, information traveling faster than the speed of light. Yet I am pretty sure this hasn't happened - no information has been transmitted in the traditional sense from one location to the other.
However, when I think about this example backwards, I feel like information has been transmitted. If I calculate an eclipse that happened in the past, it is by virtue of it happening in the past that I have the information with which I can calculate the previous eclipse. The fact that it happened contributed to my current observations which I use as my initial conditions, though I set time to -1 to calculate the past.
Why doesn't predicting the future violate the speed of light? What is different about the circumstance or the information in this case?
I can, based upon some knowledge of initial conditions and some equations, predict a future state of some system. For example, I can predict the next eclipse. Now, this prediction is based upon information that I have at the present, and some of that information is the initial conditions (where the sun, moon and Earth are now) and some of that information is the equation (how they move). With this information, I can know information about a future state before it happens.
Here is the troubling bit. I know that information cannot exceed the speed of light, and if it did it would be virtually or practically traveling into the past. But when I have information of the future state of something, that seems like information "from" the future, or at least, virtually indistinguishable from information from the future. That would entail, of course, information traveling faster than the speed of light. Yet I am pretty sure this hasn't happened - no information has been transmitted in the traditional sense from one location to the other.
However, when I think about this example backwards, I feel like information has been transmitted. If I calculate an eclipse that happened in the past, it is by virtue of it happening in the past that I have the information with which I can calculate the previous eclipse. The fact that it happened contributed to my current observations which I use as my initial conditions, though I set time to -1 to calculate the past.
Why doesn't predicting the future violate the speed of light? What is different about the circumstance or the information in this case?