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Is the assumption that space-time has to be a continuum just a matter of mathematical taste? Isn't there any physical significance associated with it?

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@Qmechanic although Lubos addressed this in those questions, this one is the most direct asking of "is physics continuous". Regardless of one's position on it, I think it suffices to say that there is very significant continued interest in the question. –  Alan Rominger Jul 5 '11 at 3:31
    
(Please correct me if I am wrong) I think if space-time is proven to be discrete, that would mean that calculus would be useless at the very fine levels of calculation, so one could argue that assuming a continuum is very convenient to the math tools to be used. –  Jiminion Aug 10 at 15:12
    
@Jiminion : Totally disagree with it. Calculus will be there as it exists now. Every theory is backward compatible with a old theory. Atleast I am not searching/believe for something that doesn't require calculus. –  Rajesh D Aug 10 at 15:46
    
Calculus still could remain as an important construct in the new theory, but discreteness could just come out as a physical interpretation. Just like wave function in QM is not real but just a construct in the theory. –  Rajesh D Aug 10 at 15:51

2 Answers 2

up vote 11 down vote accepted

Underlying this question is an erroneous assumption about what physics is and what it isn't.

The point is that physics is a description of reality. However, it does not say anything about whether the description equals reality.

In particular, nobody knows whether space-time truly is continuous or not. But continuity sure describes it extremely well. Also note that this description might change in the future when we can do even more precise measurements.

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More precise than this IBIS experiment? Discussion elucidation at : motls.blogspot.com/2011/07/… –  anna v Jul 4 '11 at 15:55
    
anna makes a good point - which is that physics is apparently very concerned with testing for things that indicate whether or not a continuous model of spacetime holds in all extremities. Regarding this answer, it's hard to say if a GUT would or could potentially equal reality. Arguing either way seems toxic to me. I'm generally skeptical that the motivation of physics stops short of a comprehensive description of reality, but better definitions must be made for this discussion to be of merit. –  Alan Rominger Jul 5 '11 at 3:38
    
I completely disagree with this answer. The problem is that continuous space might describe reality extremely well...until doesn't. Then we might find ourselves in a box canyon of theory that might take us some time to find our way out of. –  Jiminion Aug 10 at 15:14

Space and time are inclusive notions. Many do not know it but it is so.

When you tend the number of information bits (measurement points, pixels, if you like) to infinity, then certainty emerges. Space and time are those certainties.

As inclusive entities, they are not fundamental, primary but secondary. In other words, they are illusions. Elementary, fundamental are those bits of information which constitute the whole picture.

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