Is Space-Time Finite or Infinite?

[laurence_white]

*note: I had this reviewed by a moderator before posting, so I hope you consider it appropriate to this forum.

Hypothetical proposition (of the form “if p, then q” – without asserting the truth of p or q):

If space-time S is not infinitely divisible, then space-time S cannot be infinite in extent.

Proof:

If space-time S is not infinitely divisible, then there exists a smallest possible increment of S, s. [The precise size of s does not matter; it only matters that it is finite.]

Since S is built from finite space-time components s, S requires an infinite amount of time (t∞) to become infinite in extent. [note that s is a space-time component, not simply a component of a geometric space.]

At any time t, we can assert that t∞ has not yet been reached (since t∞ is infinite).

Therefore, at any time t we can assert that space-time S is not infinite in extent.

Footnote: the number of dimensions of S (or equivalently, s) does not matter; it only matters that at least one is a time dimension.

 

[setAI]

the smallest unit idea is already firmly established by the concept of quanta and quantum observables- as well by causal set mathematics and computation: a non-discrete system has infinite information and thus infinite entropy and thus infinite instability NO causality- if you observe a causal universe with consistant physical laws your world is discrete

however your conjecture on infinite space is a non-starter- there is no model of cosmology which requires or suggeststhat the universe at the Big Bang was finite- this is often confused- some mistakenly think the BB implies a finite point in which the universe expanded- but the BBonly deals with the finite area we observe today- THAT is the tiny point- but there is no reason to think that the universe wasn't http://www.atlasoftheuniverse.com/bigbang.gif"

 

[laurence_white]

i am familiar with commuting/non-commuting observables, Hermitians, etc. i don't accept your proposed counter-argument. an infinite space-time, by definition, cannot appear at once. remember: this is not a space; it is a space-time.

but i am pleased to see someone thoughtful respond. thank you for challenging my idea. i hope to hear from you again.

regards.

 

[EnumaElish]

Since S is built from finite space-time components s, S requires an infinite amount of time (t∞) to become infinite in extent.

Don't you need to prove that each s takes a positive time to be created/established/transversed? What if each (finite) s is "transversed" in "no time at all"? Then isn't t∞/0 = indeterminate?

Is this problem really different from any of Zeno's Paradoxes?