I am reading this book why does $E=mc^2$ and I learned that causality is what proves that there is a cozmic speed limit-I'm the only one here who is astonished by the looks of it ;-). Anyway. Would a 100% random machine break the law of causality. To visualise it- Think of the universe as a film. In the middle of the film a random event occurs that changes the future of the film. If you rewind it back to the randomised bit something different may occur or by chance the same thing would happen again.

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    $\begingroup$ Out of curiosity, what is the actual statement that is called "the law of causality"? $\endgroup$ – Mark H Feb 13 '18 at 13:48
  • $\begingroup$ Additionally, how is said law supposed to "prove there is a cozmic[sic] speed limit"? $\endgroup$ – ACuriousMind Feb 14 '18 at 22:59

You seems to be mixing up to different notions of causality.

Consider the two principles:

  1. Every cause must precede it's effect
  2. Every event must have a cause

The rule against superluminal motion in special relativity is intended to insure (1), but doesn't care about (2).

In the rest of your post you seem to be talking about (2). That second statement has a long history in philosophical circles but things like Norton's Dome leave it is a bit of a gray area even in pure classical mechanics.

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    $\begingroup$ I'm not sure it is an essential axiom of causality that a cause must precede its effect. Effects could be instantaneous and still be causal. If I flick a light switch on, it does not really matter (to causality) whether the effect is instantaneous or follows shortly after. Relativity presupposes non-instantaneous transfer because that fact is simply inherent in the nature of the physics it describes, not because it is an iron rule implied by the principle of causality. $\endgroup$ – Steve Feb 10 '18 at 20:46

Yes, real randomness is a concept that breaks causality. It is not agreed upon that any such thing exists.

But note that it suffices for most human purpose that a process has obscure or inaccessible causes, in order to be considered random. Where necessary, this latter concept is referred to as "pseudorandom".

I wouldn't say that causality necessarily proves that a "speed limit" exists, although as attributed (probably apocryphally) to Einstein, "time is what stops everything happening at once" - that is, at least some set of natural processes must be non-instantaneous, in order to prevent immediate universal oblivion.

But there is not, a priori, any requirement for every process to be non-instantaneous.

  • $\begingroup$ This goes back to the question whether single "random" events like those described by quantum mechanics (e.g., radioactive decay) have no cause themselves, or whether we just don't know or will never know them. $\endgroup$ – freecharly Feb 11 '18 at 21:37
  • $\begingroup$ @freecharly, indeed. As I remarked (going back), the rate of decay can be influenced, but so long as human knowledge has a frontier (particularly at extremes of distance and scale), it is essentially undecidable whether the natural world continues to be lawlike beyond that frontier. I would only note that extending that frontier has always been a speculative enterprise predicated upon the notion that the natural world is lawlike, and those who insist it is not usually have an agenda hostile to scientific enquiry (accepting, as they must, progress already attained, but wanting no more). $\endgroup$ – Steve Feb 11 '18 at 22:20

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